THE IDENTIFICATION AND COMPARISON OF PREFERENCES FOR RECREATION LOCATIONS: THE EXAMPLE OF ONTARIO PROVINCIAL PARK CAMPERS Thesis for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY DONALD EMERSON HALLMAN 1973 WIN Immunmmmmmmm I _ r, 3 1293 00848 1859 A- MICIIIJL University This is to certify that the thesis entitled THE IDENTIFICATION AND COMPARISON OF PREFERENCES FOR RECREATIONAL LOCATIONS: THE EXAMPLE OF ONTARIO PROVINCIAL PARK CAMPERS presented by Donald Emerson Hallman A has been accepted towards fulfillment of the requirements for JILLdegree in M 7" Major professor Date May 9. 1973 0-7639 BE: n 1' m; MW r ”If“. T TENTIFACAI‘" I“ 1 me E) In a numB ofdezand for recre; adapt direct measurc TECI cation resource - k. stuiv rs based on t.. IGCI‘QE 1 A *' “rnt' LIOII COIISLAAI and recreational des It ' ...a d. ereatron den n movements of recreat' cnaices among availaI preferences independe approach appears cap: locational pref erencc 0rigin~destination s. In the rev: pavements to recreatr Pairwise choices betk . "N «H a1 ternat ive are I “”10““ tInes base we“ . I ABSTRACT THE IDENTIFICATION AND COMPARISON OF PREFERENCES FOR RECREATION LOCATIONS: THE EXAMPLE OF ONTARIO PROVINCIAL PARK CAMPERS By Donald Emerson Hallman In a number of studies examining the spatial characteristics of demand for recreation opportunities, there has been a tendency to adopt direct measures of spatial origin—destination movements of recreation resource users as indicators of recreation demand. This study is based on the assertion that such measures indicate only recreation consumption under the particular spatial pattern of origins and recreational destinations in which the movements occur, not recreation demand. A model is discussed and applied in which spatial movements of recreation resource users are regarded as the outcome of choices among available alternative destinations based on locational preferences independent of particular patterns of destinations. This approach appears capable of revealing a number of characteristics of locational preferences from knowledge of spatial flows within known origin—destination systems. In the revealed preference approach adOpted in this study, movements to recreation destinations were conceptualized as revealing pairwise choices between the destination alternative chosen and each other alternative available for choice. Destinations were grouped into locational types based on their distance-from-origin and site attract- iveness attributes, and these locational types constituted the alternatives gang which choiC misible to achie‘ preferences, and I tire extent to 5513‘ :xeness of destina aless desirable a the other attrihut differences in loc. crierted populatior betseen pairs of 1c The anal) :oz'ezents of camper fails. The data er. sazpie of campers LIi 0f1968 campers. I: SLEFle was utilized f0? preference diffs for this purpose in: at Park, and type Of Results of 3‘: sSESI that this a“, l I 35%! a\‘y ““695 Underlvin Gen sprk destinatr is: ence of Similarr I?! ch - Donald E. Hallman among which choices were recorded. From this information, it was possible to achieve a scaling of locational types according to revealed preferences, and ultimately, to formulate a preference surface indicating the extent to which trade-offs exist between distance and site attract— iveness of destinations (that is, the willingness of users to substitute a less desirable amount of one attribute for a more desirable amount of the other attribute). The analysis was further extended to examine differences in locational preferences of subgroupings of the recreation- oriented population through comparison of the choices by these subgroups between pairs of locational types. The analysis described above was applied to information on the movements of campers from 54 Ontario origins to 81 Ontario provincial parks. The data employed consisted of a one percent (approximately) sample of campers during the 1966 camping season and a 100 percent sample of 1968 campers. Information on characteristics of campers for the 1966 sample was utilized to formulate camper subgroups which were analyzed for preference differences. The three camper characteristics selected for this purpose included extent of camping experience, length of stay at park, and type of occupation. Results of the application of the revealed preference model suggest that this approach has considerable utility in indicating preferences underlying patterns of recreation travel. A considerable degree of order was discerned in the preferences of Ontario campers among park destinations, a significant finding since it points to the existence of similarities in preferences, despite obvious variations in choice situations and observed destination choices. The seal indicated that the m Unolve shorter 3;;eared to be nor site attractivenes iistance-to-destin substitution betwe locational types h tejural aspects, the 1906 and 1968 I Ej~pothesis that pr< The anal; indicated little 2'1 preference and the with r“Elect to ler SiSr-ificantly great to further define a IOCational PTGferer Finally, Donald E. Hallman The scaling of locational preferences of Ontario campers indicated that the more preferred locational types definitely tended to involve shorter distances than less preferred types. Distance appeared to be more strongly related to locational preference than the site attractiveness measures employed. Despite the prominence of the distance-to-destination variable, there was evidence of some degree of substitution between distance and attractiveness, largely involving locational types having short to moderate distances. With respect to temporal aspects, few major differences in preference structure between the 1966 and 1968 camper data were found. This result supports the hypothesis that preferences have considerable stability over time. The analysis of preference differences among camper subgroups indicated little relationship between observable differences in preference and the camper characteristics under consideration. Only with respect to length of stay did subgroup differences appear to be significantly greater than expected. These results point to the need to further define and measure user attributes having relevance to locational preferences held. Finally, it was shown that potential exists for applying the revealed preference approach in a predictive campacity as an aid to planning for future development of recreation opportunities. The need for developing improved methods for measuring attractiveness of recreation destinations and for defining locational types was underlined. Once such problems are resolved, future research might well refine and extend the results of this study to other temporal and spatial situations as well as to other forms of recreation pursuits. TH PR5 THE EXAI 1“ Partiai THE IDENTIFICATION AND COMPARISON OF PREFERENCES FOR RECREATION LOCATIONS: THE EXAMPLE OF ONTARIO PROVINCIAL PARK CAMPERS By Donald Emerson Hallman: ” A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Geography 1973 I wi individuals an blile it is it: particularly t': Dr. ( Cotittee whose dissertation, f greatly to the Dr. M for his much ap .re draft stage The C; renewal which 51 M ' “epic. Mr. J, and ForeSts (I‘m. at“ the data on D l :h ‘ e dissertatmn The. Cor ‘u .r \ LP ACKNOWLEDGMENTS I wish to acknowledge the assistance of a number of individuals and organizations in the preparation of this dissertation. While it is impossible to identify here all who assisted, I thank particularly the following who made significant contributions: Dr. Gerard Rushton, former chairman of my Doctoral Guidance Committee whose research constituted the point of departure for this dissertation, for his advice and constructive criticism which contributed greatly to the progress and ultimate completion of the dissertation. Dr. Michael Chubb, current chairman of my Guidance Committee, for his much appreciated comments and encouragement particularly during the draft stages of the dissertation. The Canada Council, for the award of a Doctoral Fellowship and renewal which supported me in undertaking research on the dissertation topic. Mr. J. Keenan of the Parks Branch, Ontario Department of Lands and Forests (now Ministry of Natural Resources), for making available to me the data on provincial parks and park users which was essential for the dissertation. The Computer Centers of Lakehead University and Brock University for provision of computer time and programming assistance in the analysis of data for the dissertation. Colleagues in the Department of Geography, Lakehead University, for various forms of assistance provided me. ii Miss E in typing the ma: illustrations. My wife st riding and sup; dissertation. Miss Elizabeth Taylor and Miss Sandra Klukie for their help in typing the manuscript, and Mrs. Robin Spenceley for drafting the illustrations. My wife Cindy, who helped immeasurably through her under- standing and support throughout the period of preparation of the dissertation. iii l”RChLEDGMENTS . HSTOF TABLES . . HSIOF ILLUSTRATI Decision ' Locatio: Revealec of Loca! The Scalir Further Ar Comparin Random C liL APPLYING TIE: RECREATION Informatio; Measuring I or Camp: II. LOCATIONAL PF CAMPERS . . The Nature OriyatiOn TABLE OF CONTENTS Page ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . ii LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . .. vi LIST OF ILLUSTRATIONS . . . . . . . . . . . . . . . . . . . . . . viii Chapter I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . .. 1 The Problem Structure of the Dissertation Reasons for Selecting Provincial Park Campers Spatial Interaction of Recreation Resource Users - Review of Studies II. A REVEALED PREFERENCE APPROACH TO MODELLING LOCATIONAL CHOICE . . . . . . . . . . . . . . . . . . . 20 Decision Theory: Relevance to Modelling Locational Choice A Revealed Preference Approach to Analysis of Locational Choice Data The Scaling of Pairwise Locational Preferences Further Analysis of Locational Preferences: Comparing Population Subgroups and Identifying Random Choice III. APPLYING THE MODEL TO LOCATIONAL CHOICE IN RECREATION: DATA CONSIDERATIONS . . . . . . . . . . .. 52 Information on Choice of Location Measuring the Attractiveness of Parks for Campers IV. LOCATIONAL PREFERENCES OF ONTARIO PROVINCIAL PARK CAMPERS . . . . . . . . . . . . . . . . . . . . . . . . 86 The Nature of Locational Preference of Campers-Hypotheses Derivation and Analysis of Locational Preferences iv Loca FutL r A C135 in. 01133“ Enpl n; Park C V. 1966 O Ques r1. Computl and I III. Samplil Camps SELECTED B I BL IC Chapter V. COMPARATIVE ANALYSIS OF LOCATIONAL PREFERENCES OF ONTARIO CAMPERS SUBGROUPS . Definition of Camper Subgroups and Formulation of Hypotheses Analysis of Camper Subgroups for Preference Differences VI. CONCLUSIONS . Locational Preferences of Ontario Campers Future Research Possibilities APPENDIX 1. A Classification of Decision Theories . 11. Some Characteristics of Ontario Provincial Parks . III. Ontario Provincial Parks - Attraction Variables Employed in the Factor Analysis . IV. Park Capacity and Locational Preferences . V. 1966 Ontario Provincial Park User Survey - Camper Questionnaire . VI. Computer Program for Revealed Preference Analysis and Comparison of Subgroup Preferences . . VII. Sampling Information: Ontario Provincial Park Campers, 1966 . SELECTED BIBLIOGRAPHY . 156 167 168 I70 179 184 186 ‘ t 13319 L . Ranking of LC . Revised Trans. . Attraction Int Revealed pref Probability t to Row TIPC Preferred I Probability t to ROW TYPE Perceived Sir“ Matrix . Transitivit,v Road MileageS Southern 0h Thpothetical of Campers Contingency T Chi-Square Te Ontario Provi:l| Names and (f. Origin Center rovinvical lndices Measu: rovincial F Table 10. 11. 12. 13. 14. 15. LIST OF TABLES Revealed Preference Data Matrix . Probability that Column Locational Type is Preferred to Row Type . Ranking of Locational Types by Percentage of Times Preferred to Other Types . . . Probability that Column Locational Type is Preferred to Row Type . ' Perceived Similarity between Locational Types - Proximity Matrix . . . . . . . . . . . . Transitivity Test for Consistency of Preference Surface . Revised Transitivity Matrix . Road Mileages between Pairs of Selected Centers in Southern Ontario . . . . . . . . . . . . . Hypothetical Camper Subgroups Based on Characteristics of Campers . . . . . . . . Contingency Tables for Hypothetical Camper Subgroups . Chi-Square Test Results: Hypothetical Camper Subgroups Ontario Provincial Park Destinations, 1966: Names and Code Numbers . Origin Centers Used in the Analysis of Ontario Provinvical Park Camper Data, 1966 . Indices Measuring Attractiveness of Site: Ontario Provincial Parks . . . . . . . . . . . Attraction Index Extremes: Ontario Provincial Parks . vi Page 32 32 34 34 34 34 41 46 47 48 59 60 7O 76 Table 16. Preference Mai Expected Pre IT. Results of Te. ll. Ratrix Repres: 19. locational Ty; Preferred O‘ 20. Transitivity .\ .r. Locational Ty; Preferred O: . 19% Ontario A Related to «; .3. Ontario Provii Analysis of . Chi-Square TOT Subgroup Si; Casper Subgro; Significant [1, F. and Rand: . Significant [r Significant [h i and R51an PredICI ion 0 (1968) fro”; ampers (19, Table 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. Preference Matrix Indicating Consistency with Expected Preference Ranking . Results of Tests of the Attraction Indices . Matrix Representation of Locational Types . Locational Types Ranked by Percentage of Times Preferred Over Other Types - Case I Transitivity Matrix - Case I Locational Types Ranked by Percentage of Times Preferred Over Other Types - Case III 1966 Ontario Provincial Park User Survey: Questions Related to Characteristics of Campers and Visits . Ontario Provincial Park Campers: Subgroups for Analysis of Preference Differences . Chi-Square Tests for Significant Differences in Subgroup Sizes . Camper Subgroups Compared for Preference Differences . Significant Difference Proportions: Subgroups B and F, and Random Groups . Significant Difference Proportions: Subgroups A and B, and Random Groups . . . Significant Difference Proportions: Subgroups C and D, and Random Groups . Prediction of Locational Choices of Hamilton Campers (1968) from Preference Structure of Ontario Campers (1966) vii Page 85 92 99 101 117 124 127 131 132 139 146 151 163 riane L LI. 'J‘ 0 IO p.‘ (x) a 14, Provincial Park Destir Park Destir Distance Locational TWO-Dimensj Major Origf Provinci; Preference Hl'Pothetica PTEferem H)‘pothetiCE IS P0551! DBfinitiOn Sample P] of Trip 1 Unidimensic Park Cam; Locational erg, Figure 1. Provincial Park Destinations Available to Kingston Campers .. 2. Park Destinations Classified by Distance from Kingston . 3. Park Destinations Classified by Attractiveness and Distance from Kingston . . . . . . . 4. Locational Types Available to Kingston Campers . S. Two-Dimensional Scaling of Ontario Cities . 6. Major Origin Centers and Park Destinations: Ontario Provincial Park Campers, 1966 . 7. Preference Matrices, Consistency and Discrepancy Indices . 8. Hypothetical Preference Surfaces Showing Increases in Preference . . . . . . . . . . 9. Hypothetical Preference Surfaces Where Little Substitution is Possible . . . . . . . . . . 10. Definition of Locational Types: Equal Mileage Intervals . 11. Definition of Locational Types: Equal 1966 Camper Sample Proportions . . . . . . . . . . . 12. Distance Classes Defined by Cumulative Frequencies of Trip Lengths . . 13. Unidimensional Preference Scale: Ontario Provincial Park Campers, 1966 (Case I) . . . . 14. Locational Preference Surface: Ontario Provincial Park Campers, 1966 (Case I) 15. Locational Preference Surface Fitted to Case I Preference Scores . . . . . 16. Test for Randomness of Choice: Ontario Provincial Park LIST OF ILLUSTRATIONS Campers, 1966 (Case 1) viii Page 27 30 30 42 58 81 89 89 94 94 95 104 106 106 11() fipxe H ER 3L Q! In.) D lhidimensic Park Can; Locational Park Cam; Locational Preferenc Unidimensic Campers, Locational Campers, Locational Preferent Groups A a: “1th Sig: Gr0up5 B at with Sig‘ CTOUpS B 3 Where B 3 GTOUPS B 8 Where 3 Groups C a with S Gmups o a h‘lth Sig with Si; Groups A a Where A Groups A a "here A Groups Figure 17. Unidimensional Preference Scale: Ontario Provincial Park Campers, 1966 (Case II) 18. Locational Preference Surface: Ontario Provincial Park Campers, 1966 (Case 11) 19. Locational Preference Surface Fitted to Case 11 Preference Scores . 20. Unidimensional Preference Scale: Ontario Provincial Park Campers, 1968 (Case III) 21. Locational Preference Surface: Ontario Provincial Park Campers, 1968 (Case III) 22. Locational Preference Surface Fitted to Case III Preference Scores . ' 23. Groups A and E - Proportion of Pairwise Comparisons with Significant Differences . . . 24. Groups 8 and F - Proportion of Pairwise Comparisons with Significant Differences . . . . 25. Groups 8 and F - Fraportion of Significant Differences where B Reveals Lower Preferences than F . 26. Groups B and F - Proportion of Significant Differences where B Revals Greater Indifference than F . 27. Groups C and G - Proportion of Pairwise Comparisons with Significant Differences . 28. Groups D and H - Proportion of Pairwise Comparisons with Significant Differences . 29. Groups A and B - Proportion of Pairwise Comparisons with Significant Differences . 30. Groups A and B - Proportion of Significant Differences where A Reveals Lower Preferences than B . 31. Groups A and B - Proportion of Significant Differences where A Reveals Greater Indifference than B . 32. Groups C and D - Proportion of Pairwise Comparisons with Significant Differences . ix Page 112 114 114 118 120 120 137 138 140 140 143 144 145 147 147 150 FQpre 33. Groups C a where C 34. Groups C a where C i 35. Groups A a with Sig 36. Choice Pro? Figure Page 33. Groups C and D - Proportion of Significant Differences where C Reveals Lower Preference than D . . . . . . . . . . 152 34. Groups C and D - Proportion of Significant Differences where C Reveals Greater Indifference than D . . . . . . . . 152 35. Groups A and C - Proportion of Pairwise Comparisons with Significant Differences . . . . . . . . . . . . . . .. 154 36. Choice Probabilities for Hamilton Campers . . . . . . . . . . 162 Pttng and 051931 The rece tnmalopportuniti . . . 1 an statistics. change in attitude m On following 5 The trac of recre status 2 Indeed t that sur in impor centered $3561)? because of of recreational ac ~‘i'fisnstrate this c CHAPTER 1 INTRODUCTION The Problem Settipg and Objectives The recent rapid growth in participation in various recrea- tional opportunities has been amply documented by a variety of studies and statistics.1 Accompanying such growth in participation has been a change in attitude toward recreation as a focus of research, reflected in the following statement: The traditional view that human activities in the pursuit of recreation are a form of indulgence having marginal status among the concerns of society is no longer tenable. Indeed the institution of recreation and the action systems that support it (should be) treated . . . as comparable in importance and priority with the social structures centered on production and consumption. Largely because of the obvious spatial and environmental components of recreational activities, geographers were among the first to demonstrate this change in attitude by embarking on research in recreation.3 1Perhaps the best known evidence of such growth is found in reports of the U.S. Outdoor Recreation Resources Review Commission in the early 1960's and subsequent surveys by the Bureau of Outdoor Recreation. 2National Academy of Sciences, A Program for Outdoor Recreation Research (Washington: National Academy of Sciences, 1969), p. l. 3Initial research by North American geographers is discussed in a review of recreational geography by McMurry and Davis (K.C. McMurry and C.M. Davis, "Recreational Geography", American Geography: Inventory and Prospect, eds. P.E. James and C.F. Jones (Syracuse: Association of American Geographers, 1954), pp. 251-5. l One evident focus which has developed in recreation research is that of recreational demand. As Knetsch has suggested, merely to know that demand is increasing is not enough. "What is needed is not a collection of miscellaneous facts, but an understanding of the relation— ships inherent in recreation behavior and the ability to forecast the effects of proposed alternative actions."1 He goes on to identify a significant problem apparent in many demand studies: The trouble arises from a confusion over the difference between demand and consumption. Use or attendance figures are incorrectly called demand, instead of being interpreted as consumption or the interaction of both demand, which certainly exists, and the supply of Opportunities, which also exists. The single most serious and most fundamental deficiency in most demand surveys and studies is that they do not provide any means of determining how recreational use will respond to changes in supply -- and that, after all, is the portion on which guidance is needed. The problem is thus seen as one of determining demand charac- teristics which exist independent of the present supply of Opportunities: Demand is one element of a system. Analysis of the preference of individuals and groups can indicate the directions and amount of total demand. These, together with the other elements of the system -- the location of recreation places and the way resources are used -- produce a pattern. lJ.L. Knetsch, A Design for Assessing Outdoor Recreation Demands in Canada, A Report to National and Historic Parks Branch, Canada Depart- ment of Indian Affairs and Northern Development (Ottawa: 1967), p. 5. 2Ibid. 3Ibid., p. 7. 4Outdoor Recreation Resources Review Commission, Outdoor Recreation for America (Washington: U.S. Government Printing Office, 1962), p.10. It is rea recreation have 111'; activities cannot b residence, some deg resource users (de: {supply centers) u recreation opportu seasurement of the centers and the fl This d1: tions of the prob providing much of interaction Patte if“ from (High W2 nOt PattErns are C10 and recreat 1011 O to better Unders It is readily apparent that both demand and supply in recreation have important spatial components. Since many recreation activities cannot be pursued in the immediate vicinity of places of residence, some degree of spatial separation between origins Of recreation resource users (demand centers) and locations of recreation opportunities (supply centers) usually exists. Attempts to assess the adequacy of recreation opportunities in meeting demand, then, inevitably include measurement of the extent of spatial separation of demand and supply centers and the flows of the users from origins to recreation destinations. This dissertation is concerned with certain spatial implica- tions of the problem identified above by Knetsch. A fundamental tenet, providing much of the motivation behind this study, is that the spatial interaction patterns established by recreation resource users (i.e. flows from origins to destinations) are indicative Of recreation consumption, not recreation demand. Accordingly, such interaction patterns are closely linked to the specific spatial pattern of origins and recreation Opportunities within which they are observed. In order to better understand demand, an attempt must be made to view existing recreation use characteristics outside of the distorting influences of specific configurations of origin and opportunity locations. Knetsch has suggested that the significance of demand state- ments lies in their function as "guides to what people actually want"1 (as Opposed to what people are observed to select). This dissertation, then, contributes to recreation demand research by vitue Of its concern g 1Knetsch, A Design for ASsessing Outdoor Recreation Demands in Canada, p. 5. with the preferences of recreation resource users underlying their choice of recreation destination. The methodology adopted involves the analysis of observed origin-destination interaction patterns viewing these as the outcome of choices among the alternative locations available.1 Most important to the approach, choices are conceptualized as the result of evaluating available destinations in the light of preferences which are independent of the actual pattern of destinations available to the chooser. The identification of preferences among destination locations (termed "locational preferences")2 indicating some attributes Of under- lying demand, comprises the major contribution of the dissertation. Specific objectives Of the dissertation may be stated as follows: (1) the description and discussion of an approach which appears to be capable of modelling preferences for recreation destin- ations from data on the spatial movement of recreation resource users. (3) the application of this preference model to a specific example of recreation interaction emplOying available empirical data, and the evaluation of the results of this application. (3) the examination of the contributions and potential uses of the preference model in recreation research. * l . . . . . . "Interaction" here refers to movement of 1nd1V1duals from origins to destinations for recreational purposes. 2 . . The term "space preferences" 15 also used to describe such preferences. I Note on the Resen The disse basis of spatial a: points in geographi By virtue of its cc associated with suc spatial analysis.1 phenomena and Spat of "behavioral geo Some wri an"illrtic and behav ations sought. 0‘, aPPToaches might t aFQ pTOCeS S: A Note on the Research Approach The dissertation concerns the analysis of the behavioral basis of spatial activity. This approach appears to embrace two view— points in geographic research, the spatial analytic and the behavioral. By virtue of its concern with spatial patterns and the processes associated with such patterns, the approach may be defined as that of spatial analysis.1 In emphasizing the relationship between behavioral phenomena and Spatial patterns, the approach falls under the heading of "behavioral geography."2 Some writers, however, distinguish between the spatial analytic and behavioral approaches on the basis of the types of explan— ations sought. Olsson, for example, has suggested that the two approaches might be differentiated by their inferences regarding form and process: 1Spatial analysis frequently is defined to include study of the regularities of spatial patterns, identification and analysis of processes influencing and influenced by such patterns, and prediction of future spatial processes and patterns. 2As Gould has noted (P.R. Gould, "Methodological Developments Since the Fifties," Progress in Geography, Volume 1, eds. C. Board et al. [Londonz Edward Arnold, 1969]) the behavioral approach in geography appears to have two emphases -- one, the analysis of the behavioral bases of spatial patterns, and two, the impact of perception of environment on decision making. The first of these foci is exemplified by the papers edited by Cox and Golledge (K.R. Cox and R.G. Golledge, eds., Behavioral Problems in Geography: A Symposium [Evanston: Northwestern University, Department of Geography, Studies in Geography, XVII, 1969]). Research included in the second of these emphases is reviewed in articles by Brookfield (H.C. Brookfield, "On the Environment as Perceived," Progress in Geography, Volume 1, eds., C. Board et a1.) and by Wood (L.J. Wood, "Perception Studies in Geography," Transactions, Institute of British Geographers, L (1970), pp. 129-42.) is oriente; individual as mutuallj 3n the 0th SPr‘itial st] . while the spatial analyst attempts to infer individual behavior from knowledge of a given spatial pattern, the behaviorist argues for reasoning the other way around. If, from the above, it is concluded that spatial analysts attempt to infer behavior solely from spatial pattern while behaviorists attempt inference of spatial pattern solely from behavior, then the dissertation is oriented toward some sort of middle ground between these two extremes. Individual behavior and the spatial patterns relevant to it are viewed as mutually dependent phenomena rather than one considered as dependent on the other. As Rushton has stated concerning the study of urban spatial structure: Although the spatial structure of activities in an urban area will reflect both current and past patterns of behavior, explanations of spatial structure based on such patterns of behavior often seem to be tautological since it would appear to be just as reasonable to explain behavior as a function of spatial structure as to explain structure as a function of behavior. The relationship is clearly one of mutual dependence. The dissertation focuses on what might be termed "spatial behavior", i.e. decision making by individuals about their use of and action in space. The movement of an individual from point A to point B is evidence that a spatial choice has been made, but the decision process, not the movement is spatial behavior.3 1G. Olsson, "Inference Problems in Locational Analysis," Behavioral Problems in Geography, eds. Cox and Golledge, p. 14. 2G. Rushton, "Behavioral Correlauxscfi?Urban Spatial Structure,” Economic Geography, XLVII (1971), p. 49. 3Rushton (G. Rushton, "Analysis of Spatial Behavior by Revealed Space Preference," Annals of the Association of American Geographers, LIX (1969), pp. 391-402.) suggests making a distinction between "spatial behavior" (procedure by which alternative locations are evaluated and choices made) and ”behavior in space" (description of spatial choices made). The st objectives alrea chapter reviews :ethodological c‘ :oiel is based a concerned with 1 these requireme: the movements 0‘ le. t' he fourth cf caper data and The 0 be ur ‘ lovement Structure of the Dissertation The structure of this study follows the general order of objectives already described. The remainder of the introductory chapter reviews relevant recreation research. Chapter II discusses the methodological developments and assumptions on which the preference model is based and outlines the form of the model. The third chapter is concerned with the data requirements of the approach and discusses how these requirements can be met in applying it to a specific case study, the movements of campers utilizing provincial parks in Ontario, Canada. In the fourth chapter, the model is applied to Ontario provincial park camper data and the resulting information on locational preferences is presented and discussed. The fifth chapter discusses the application of the approach to examine differences among groups with respect to locational preferences. Finally, Chapter VI draws conclusions about the preference model and its application, and discusses the implications and logical extensions of the approach. Reasons for Selecting Provincial Park Campers for the Study; The previous section indicated that the spatial interaction data to be utilized in the application of the preference model concerns the movements of campers to Ontario provincial parks. In view of the many different types of spatial interaction which might have been ;..551ectin8 th Ax-a‘l 13‘ “7'79? data in t] of stay etc. haw iterated camng‘01 :32: ing part 1e 5 1 912113" ‘ wit charact< information is f: :a:;ir.g parks is reguires informa‘. For On1 zerpiled on camp: :arried out perig ;":.-\ ‘, “what 101'] for l i, \. seedless to 9.6;. H considered, all under the general heading of recreation,1 the reasons for selecting this type of interaction are discussed briefly. Availability of Data. -- The primary reason for employing camper data in the study is that considerably more information has been compiled for this group than for other types of recreational groups. Reasonably detailed data on total numbers of campers, camper days, length of stay etc. have been gathered for a number of years for most publicly- operated campground facilities. Also, for many areas, sample surveys of camping parties provide information about origins of campers, their socio- economic characteristics, purpose of visit and so on. The fact that information is frequently available about the site characteristics of camping parks is also important, since the technique to be employed requires information on destination site characteristics. For Ontario, a substantial amount of information has been compiled on camping in Ontario provincial parks. User surveys have been carried out periodically since 1964, providing origin-destination information for a sample of campers. While the reliability of some of the survey data has been questioned as will be discussed later, it appears suitable for the purposes of the preference approach. Information 1Needless to say, considerable space could be devoted to defining the term "recreation” since it has been defined in a variety of ways. For the purposes of this study, recreation is identified through a group of recognizable outdoor activities under the assumption that individuals participating in such activities are experiencing recreation. The activity groups commonly included are: driving for pleasure, playing sports, swimming, sight-seeing, picnicking, walking and riding, fishing, boating, hunting, camping, winter sports, and spectator events. (after O.R.R.R.C., Study Report No. 19, National Recreation Survey (Washington: U.S. Government Printing Office, 1962), pp. 108-9. concerning 1 available a: later). C9: in the prov: ietailed an. concerning the characteristics of Ontario provincial parks is readily available and has been compiled and analyzed to some extent (as noted later). Certain information is available on other recreation pursuits in the province (see Wolfe1 for example), however it is much less detailed and there are major problems in obtaining data on destination site characteristics. Neglect of Commercial and Other Public Camping Facilities. -- In discussing the availability of interaction data for Michigan recreation resource users, Chubb has suggested that the lack of information on camping in areas other than state or federal areas constitutes an important restriction on the analysis of camping on a statewide basis.2 Such a criticism applies equally well to Ontario, where it is estimated that slightly over one-half of all campers in Ontario in 1966 used commercial or other campground facilities as Opposed to provincial parks. However, there are several reasons which can be advanced for proceeding without the inclusion of non-provincial park users and opportunities. It has been argued, for example, that in Ontario, camping facilities other than provincial parks offer a different type of camping opportunity not directly comparable to provincial park camping (e.g. more commercialized in the case of privately-operated facilities, or more 1R.I. Wolfe, Parameters of Recreational Travel in Ontario: A Progress Report (Downsview, Ontario: Ontario Department of Highways Report No. RBlll, 1966). 2M. Chubb, Outdoor Recreation Planning in Michigan by a Systems Analysis Approach: Part III - The Practical Application of "Program RECSYS" and "SYMAP" (Michigan State University, Department of Resource Development, Recreation Research and Planning Unit, Technical Report No. 2, 1968) p. 10. primitive in th is that Cam?"erS aasng alternati gari' opportunit verified it HOU separately from The n inaodelling th and interaction ofirportance 0‘ have significan uricanpers (i results conside' assertion. Eve “39 for keepin SiJPl)’ because . ifti'een them. Aside q. .1 collecting t' ar‘ ‘ ' .n. oestination no“ _ h. .‘\ , L“ have to b 10 primitive in the case of non-developed wilderness areas).1 The suggestion is that campers do not lump together all camping opportunities in deciding among alternatives, but rather make a distinction between provincial park opportunities and other facilities. If this hypothesis were verified it would lend support to analyzing provincial park opportunities separately from other opportunities. The main problem in ignoring other camping Opportunities is that in modelling the locational choice process, not all available alternatives and interactions are being considered. However, this would seem to be of importance only if campers frequenting non-provincial park destinations have significantly different locational preferences than do provincial park campers (i.e. that including these campers would affect the overall results considerably). There is little basis for making such an assertion. Even if such a situation was suspected, a good case might be made for keeping these two types of campers separate in the analysis simply because combining them would obscure the significant differences between them. Aside from the above arguments, the magnitude of the problem of collecting the required information on origin-destination movements and destination site characteristics for the many and frequently smaller non-provincial park opportunities is such that the benefits to the analysis would have to be substantial to justify the additional effort involved. 1R.G.R. Rogers, "An Analysis of Some Elements of Demand for Ontario Provincial Parks" (unpublished Master's thesis, Faculty of Graduate Studies, University of Guelph, 1966), p. 10. ll Thus whii include in the ana appears that emplo; providing this lit: Spatial Int' A number of recreation reso: destinations. It cf such research t1 attempted to model of user ' s incorpora behavior. Thev di facto ‘ r. The first 11 Thus while from certain standpoints it might be desirable to include in the analysis all camping opportunities in the province, it appears that employing provincial park data alone is justifiable, providing this limitation is recognized in interpreting the results. Spatial Interaction of Recreation Resource Users - Review of Studies A number of studies has focused on the interaction patterns of recreation resource users and the basis of choice of recreation destinations. It is pertinent at this point to assess the contribution of such research to the dissertation tepic. Each study reviewed has attempted to model certain characteristics of the spatial interaction of users incorporating assumption (often implicit) about their choice behavior. They differ somewhat in their treatment of the locational factor. The first group examined devotes little attention to the influence of destination location on choice behavior of users. The second group refers much more explicitly to location of destination and includes this information in modelling procedures. Modellingof Destination Selection -- Site Emphasis Research efforts by Lucas, Lime, Shafer and Thompson, and Hodgson are representative of the first group of studies identified above} All four ground facilities activity). Each 1 attributes througl those variables mr has examined dest: resource quality : and their relatior rational forests similar studies f. MZSOD examined 1 ‘63 Bill Of stay 0+" 12 above.1 All four concern camper utilization of publicly-operated camp- ground facilities (probably the best-documented type of recreation activity). Each has striven to relate use to various campground attributes through the development of mathematical models identifying those variables most closely associated with variations in use. Lucas has examined destination attributes including physical resources, resource quality indices, extent of deve10pment and relative location, and their relationship to percentage occupancy of campgrounds in two national forests in Michigan.2 Lime3 and Shafer4 undertook essentially similar studies for campgrounds in Minnesota and New York respectively. Hodgson examined relationships of campground characteristics to average length of stay of camping parties.S While these studies will not be discussed in detail here, several observations are in order. 1R.G. Lucas, User Evaluation of Campgrounds on Two Michigan National Forests (St. Paul, Minn.: North Central Forest Experiment Station, U.S.D.A. Forest Service Research Paper, NC—44, 1970). D.W. Lime, "A Spatial Analysis of Auto-Camping in the Superior National Forest of Minnesota: Models of Campground Selection Behavior" (unpub- lished Ph.D. dissertation, Department of Geography, University of Pittsburgh, 1969). E.L. Shafer and R.G. Thompson, "Models that Describe Use of Adirondack Campgrounds" Forest Science, XIV (1968), pp. 383-391. R.W. Hodgson, "Campground Features Attractive to Michigan State Park Campers" (unpublished Master's thesis, Department of Resource Deve10pment, Michigan State University, 1971). 2Lucas, User Evaluation of Campggounds. 3Lime, "A Spatial Analysis of Auto-Camping." 4Shafer and Thompson, "Models that Describe Use." SHodgson, "Campground Features." Differf either dismissed superficial gener So att apt 5'35 ma campgrounds. Rat example the dista the implicit assc ibility for campe Each oi carpground attrii Sore explanatory amual total visj Viewed in the cor "explaining" cam; all of the campe] n 9 k ic c - 5 (‘Or inst: :nl . l3 Differences in accessibility of camping destinations were either dismissed (as in Shafer's study) or considered only in terms of superficial generalizations (for example the studies by Lucas and Lime). No attempt was made to look at origins of campers frequenting particular campgrounds. Rather, accessibility was measured in general terms, for example the distance from one or two nearby urban concentrations, with the implicit assumption that this measure is representative of access- ibility for campers. The validity of such an assumption is questionable. Each of the studies mentioned above found that only a few campground attributes were useful in accounting for campground use. Some explanatory variables appear self-evident, (for example, that average annual total visitor days is affected markedly by size of campground). Viewed in the context of choice behavior, some variables contributing to "explaining" campground use are puzzling. They appear to suggest that all of the campers had knowledge of rather obscure campground character- istics (for instance, number of islands accessible by motorboat), and employed this knowledge in choosing a destination. From the above, it is apparent that these studies are not related to the individual decision maker. Rather they have considered aggregates of decisions and have attempted to explain, not by looking at choice procedures, but by establishing associations between these aggregates and environmental characteristics with little regard to how such characteristics enter the decision process. Shafer offers a clue to a major difficulty in such an approach in his observation about the mutual interdependence between campground size and use: or ar va ac‘ cc Thus to atte ttributes i many destina It independent independence interdepende l dnfortunatel: between the : SO‘Called Hi] In CEF‘El‘mlnd a1 \ 14 . . . campground size has an organic quality and grows over time in response to inherent physical opportunities and demand. Campground size is not an independent variable in the main, but a summation of many administrative judgements and responses over the course of years. Thus to attempt to account for use in terms of existing facilities and attributes is to miss the fundamental interdependence between use and many destination characteristics. It seems illogical to consider destination attributes as being independent of use characteristics, when it is apparent that such independence frequently does not exist. Great care in dealing with interdependence among destination attributes is evident in some studies. Unfortunately similar attention is not given to the interrelationships between the so-called "dependent" variable (i.e. campground use) and the so-called "independent" variables.2 In summary, three main points have been made; first, that locational characteristics have been inadequately treated, second, that campground attributes identified as influencing use have not been linked to choice behavior, and third, that use is considered to be dependent on 1Shafer and Thompson, "Models that Describe Use," p. 389. 2It might be argued that to clarify the nature of such a relationship is the purpose of such a study. However, the technique commonly employed, regression analysis, does not provide answers to the question of causality of association. Rather, it ascertains the degree of explanation achieved if one variable is assumed to be dependent on one or more variables in- dependent to it. Thus (as in Shafer's study) a correlation coefficient of 0.97 between campground use and campground size can be obtained without considering the possibility of interdependence. Predictions of the use of new or expanded campgrounds on the basis of this size variable might then be made without an adequate understanding of the inter- relationship between the two variables. campground attril of mutual int erde Modelling of Des The Gr. a gravity functit ., 1 . users. In this represented in t ”sir Population general fem of lS campground attributes and consequently the existence of a certain amount of mutual interdependence is ignored. Modelling of Destination Selections -- Site and Situation Emphasis The Gravity Model. -- A number of researchers have employed a gravity function to model the spatial interaction of recreation resource users.1 In this model, interaction (V1,2) between two places is represented in terms of some characteristics of the places, frequently their population (P1 and P2), and the distance (d1,2) between them. The general form of the gravity equation is: k (Pllx (P2)x V1,2 = z d1,2 where k is a constant, and x, y and z are exponents derived through fitting of the equation to available interaction data. 1Cf., E. Ullman and D.J. Volk, "An Operational Model for Predicting Reservoir Attendance and Benefits," Papers, Michigan Academy of Science, Arts and Letters, XLVII (1961), pp. 473-84. C.C. Crevo, "Characteristics of Summer Weekend Recreational Travel" Highway Research Record, XLIV (1963), pp. 51-60. Wolfe, Parameters of Recreational Travel. C.S. Van Doren, "An Interaction Travel Model for Projecting Attendance of Campers at Michigan State Parks: A Study in Recreational Geography" (unpublished Ph.D. dissertation, Department of Geography, Michigan State University, 1967). H.K. Cheung, A Day;Use Park Visitation Model. Canadian Outdoor Recreation Demand Study, Technical Note No. 1, (Ottawa: National Parks Branch, undated). by letting destinatil such a ca; represent agart fro Btploying was able for sever provincia in these is that 1 Will not 16 Wolfe, has modified the general form of the gravity function by letting P1 represent origin p0pu1ation, P2, the capacity of recreation 1 Introduction of destination, and d, the origin-destination distances. such a capacity measure, varying with type of recreation pursuit, represents an attempt to measure some characteristic of destinations, apart from distance, which might be exPected to influence interaction. Employing interaction data for Ontario origins and destinations, Wolfe was able to derive values for the exponents and k-in the gravity fUnction for several recreation pursuits including patronage of cottages, provincial parks and commercial resorts. He found substantial variation in these values for the different recreation pursuits examined. One of the most important restrictions of the gravity model is that it assumes spatial interaction among origins and destinations will not vary with differences in availability of alternative destinations.‘ That is, interaction between a specified type of origin and destination for a given distance will be represented as invariant regardless of the pattern of alternatives which might exist. As Ellis and Van Doren have suggested,2 interaction more logically might be expected to vary with different spatial systems. In terms of choice behavior, it seems more realistic to conceptualize interaction as a choice among available alternatives, rather than as a choice among the entire range of destination types included in the system, whether available or not (as in the gravity model). 1Wolfe, Parameters of Recreational Travel. 2J.B. Ellis and C.S. Van Doren, "A Comparative Evaluation of Gravity and System Theory Models for Statewide Recreational Travel Flows," Journal of Regional Science, VI (1966), pp. 57-70. As noted locational prefere functions to inter aodel existing 10¢ "trial and error" The Svs the modelling of method involves c describe all par1 their linkages. flow of water th' at origins), pip Capacities. 17 As noted by Rushton,1 gravity models imply the existence of locational preferences, and the fitting of increasingly complex gravity functions to interaction data represents attempts to more accurately model existing locational preferences.2 The inefficienCies of such a "trial and error" approach are apparent. The Systems Model: -- Ellis has applied a systems approach to the modelling of spatial interaction of recreation resource users.3 The method involves derivation of a set of simultaneous equations which describe all parts of the system including origins, destinations and their linkages. The movement of users in the system is analogous to the flow of water through a distribution network consisting of pumps (demand at origins), pipes (linkages), and cisterns (destinations) of various capacities. One significant advantage of the systems approach over the gravity model, according to Ellis, is its consideration of the inter- dependence of alternative destinations.4 A change in attractiveness of a destination for example, will be reflected in changes throughout the system not identifiable in the gravity model. 1Rushton, "Analysis of Spatial Behavior," p. 396. 2R. Malm, G. Olsson and O. Warneryd, "Approaches to Simulations of Urban Growth," Geografiska Annaler, XLVIII B (1966), pp. 9-22. 3Michigan State University, Department of Resource Development, Michi an. Outdoor Recreation Demand Study (Lansing, Michigan: State Resource Planning Program, Michigan Department of Commerce, Technical Report No. 6, Vol. 1, 1966). 4Ellis and Van Doren, "A Comparative Evaluation of Gravity and Systems Theory Models." While ‘ the systems mode computes the res derived through to increase the The systems mode interactions to pattern of dest alternatives av Of these patter accuracy in mod accomplishes t} a e" vasisfactory ac Anot ‘hat lstZinc 18 While the gravity model assumes the form of spatial interaction, the systems model assumes only the forms of the system components and computes the resulting interaction. The forms of these components are derived through initial estimates subsequently modified by "tuning" to increase the accuracy of the model's prediction of known interactions. The systems model, unlike the gravity approach, does not employ actual interactions to derive a fUnction to predict interaction under any pattern of destination alternatives. Rather, the systems model considers alternatives available for each origin and derives interaction for each of these patterns. The result is a technique which achieves greater accuracy in modelling spatial interaction than the gravity model, but accomplishes this largely by adjusting the parameters of the model until satisfactory accuracy in representing known flows is achieved. As Ellis has noted subsequently, the ultimate result of adjusting parameters to obtain exact representation of interactions is a model "with absolutely no validity for prediction"1 since the basis for measuring component influence has been destroyed in the tuning process. Another characteristic of the systems model is its assumption that distance between origin and destination (measured in terms of time and cost) always has a deterring (frictional) effect. While this assumption appears to be useful in modelling many types of interaction patterns, there is some question as to its utility in modelling the interaction patterns of recreation participants (i.e. travelling to a 1J.B. Ellis, A Systems Model for Recreational Travel in Ontario: Further Results (Downsview: Ontario Department of Highways, Report No. RR148, _"5—1969 , p. 15. recreation destinat recreational experi The systr pattern of origins representing locat destination patter contribution. No patterns are achi. The lit relatively littls hhile several stl resource users, are simply descr structures in wh chapter, this st 0‘ \ 19 recreation destination may be considered an important part of the recreational experience). The systems model, then, is tied to the specific spatial pattern of origins and destinations that exist. Relevant to the goal of representing locational preferences independent of particular origin- destination patterns, this model does not appear to make a significant contribution. No generalizations of preferences from interaction patterns are achieved. Summary The literature reviewed above, by and large, contributes relatively little to the type of approach adopted for this dissertation. While several studies have examined interaction patterns of recreation resource users, frequently they are subject to the criticism that they are simply describing interaction patterns in terms of the spatial structures in which the interactions occur.1 As seen in the following chapter, this study adopts a more fundamental approach to the analysis of observed locational choices. 1Rushton, "Analysis of Spatial Behavior," p. 392. A REVEALE purpose of adopted in the chapte DE“1<:C Q CHAPTER II A REVEALED PREFERENCE APPROACH TO MODELLING LOCATIONAL CHOICE The first part of this chapter reviews theory relevant to the purpose of modelling locational preferences. The methodological approach adopted in this dissertation is developed in detail in the remainder of the chapter. Decision Theory: Relevance to Modelligg Locational Choice Decision theory may be viewed as primarily an analysis of the environment; that is, an orderly summary Of those features of the environment that control behaviour. Such a description of the environment, combined with simple assumptions about behaviour tendencies that the organism brings to that environment, may yield an effective description of behaviour. 2,3 This comment on the focus of decision theory reveals its relevance to this study. Locational decisions may be conceptualized as 1W. Edwards and A. Tversky (eds.), Decision Making (Harmondsworth: Penguin Books Ltd., 1967), p. 8. 2This body Of theory has been designated variously as utility, preference, decision-making, choice or consumer's choice theogy, Basically these terms re er to the same theoretical concepts, although some are more restrictive than others (for example the theory of consumer's choice limits analysis to the choice of commodity bundles by consumers). The distinction between utility and preference appears to lie in the designation of utility as a measure of strength Of preference (although measurement methods are subject to debate). For the most part the general term "decision theory" shall be adopted in this discussion. 3The term "theory" is widely employed in the literature and is thus retained in this discussion. However, in the writer's Opinion, the term "model" would be a more apprOpriate designation (indicating a simplification or idealization of reality). 20 21 choices among alternative locations. Interest lies in summarizing certain factors hypothesized to influence locational choice and in using such a summary together with simple behavioral assumptions to describe spatial interaction. Drawing from the literature in economics and psychology (the disciplines responsible for virtually all of the existing developments in decision theory), this section reviews characteristics of decision theory pertinent to the dissertation tOpic. Pertinent Characteristics of Decision Theorx Typically, theory about decision making has been formulated by making assumptions about choice behavior and then deducing theorems from these assumptions. The nature of such assumptions provides a convenient basis for distinguishing among different types of decision theories.1 It is sufficient to note here that the more realistic the .assumptions made, the more complex is the theory formulation and the more demanding are its data requirements. Employment Of Decision Theogy. -- Atkinson 35 El: differentiate among alternative approaches to the employment of decision theories.2 One method uses choice theory as a measuring technique. Given a pattern of choice probabilities among alternatives, the theory provides a measure 1Appendix I provides a classification scheme for theories on the basis of their major assumptions. zR.G. Atkinson, G.H. Bower, E.J. Crothers, An Introduction to Mathematical Learning Theory (New York: J. Wiley, 1965), pp. 135-137. of the strengths led to the obser‘ decision theor.V ‘ of alternatives, choice probabili values. Decisi of smnarizing 6 constraints on 1 "transitivity" , probabilities a Decis ieihnique in th 5““? ' - u“Marlee Choi C 22 of the strengths of responses to the alternatives which are said to have led to the Observed patterns of probabilities. The chief value of decision theory then is as a method of identifying the "attractiveness" of alternatives, and the degree to which these values can recreate the 'choice probabilities is an estimate of the accuracy of the attractiveness values. Decision theory might also be employed to derive laws capable of summarizing data on choice behavior. The laws take the form of constraints on the pattern of choice probabilities. The term ”transitivity", for example, summarizes a particular pattern of choice probabilities as will be discussed later. Decision theory will be utilized chiefly as a measuring technique in this study, although certain laws shall be employed to summarize choice data. Accordingly, decision theory is designated as "the set of postulates relating the response strength variable to 1 response probabilities." Revealed Preference Theogy. -- This term is employed to designate one type of decision theory which relates preferences underlying decision behavior to observable choices among alternatives.2 1Ibid., p. 136. 2P.A. Samuelson, "Consumption Theory in Terms of Revealed Preference," Economica, XV (1948), pp. 243-53. 23 A fundamental axiom of this theory is that choice reveals preference. Accordingly, if an individual has a choice among alternatives, by selecting one of these, he reveals a preference for it over others, and by observing these choices it is possible to draw conclusions about preferences among alternatives. Graphical representation of preferences can be achieved through the use of indifference curves, with each line (curve) linking combinations of alternatives to which the chooser is indifferent. A series of such curves constitutes an indifference (preference) surface.1 To assist in the application of revealed preference theory, it appears useful to simplify the analysis of the choice situation by considering choices among pairs of alternatives and consequently employing the method of paired comparisons.2 Each response (choice) is viewed as a comparative judgment between the alternatives, indicating whether one of the pair is greater than the other in some respect. From such responses, 3 matrix can be derived, indicating the number and proportion of times each alternative is judged higher on the scale than every other alternative. From this information, attempts are made to scale the alternatives on the basis of the attribute being judged. Luce's Choice Axiom. -- The paired comparisons approach applies 1Further references to revealed preference theory include W. Edwards, "The Theory of Decision Making," Psychological Bulletin, LI (1954), pp. 380-417, and H.S. Houthakker, "The Present State of Consumption Theory: A Survey Article," Econometrica, XXIX (1961), pp. 704-40. 2J.P. Guilford, Psychometric Methods (2nd ed. New York: McGraw-Hill Book Co.,_l954), Chapter 71 to presentations or provides the means . 1 ; alternatives. Th , probability of choc another alternative other alternatives This cor For one thing, it alternatives) can 0i alternatives , sets as choices 1 can be Scaled on The 24 to presentations of two alternatives. A choice axiom formulated by Luce provides the means of expanding consideration to more than two alternatives.1 This constant ratio rule states that the ratio of the probability of choosing one alternative to the probability of choosing another alternative is constant regardless of the number and type Of other alternatives in the choice set. This constant ratio assumption has a number of consequences. For one thing, it means that choices from larger sets (three or more alternatives) can be accounted for by Observing choices between pairs of alternatives. Also by conceptualizing observed choices from larger sets as choices between pairs of alternatives, the set of alternatives can be scaled on a preference scale. The Modelling of Locational Choice Rushton, drawing on the methodology briefly referred to above, has developed a model of revealed space preference for analyzing choices involving alternative locations.2 It is recognized that the preference structure so defined must provide a description of locational choice which is independent of the specific pattern of locational alternatives within which choices are made. A number of principles are applied toward achieving such an objective, as outlined below. 1R.D. Luce,Individual Choice Behavior (New York: John Wiley 6 Sons, 1959). Atkinson, Bower and Crothers, An Introduction to Mathematical Learning Theory, pp. 146-50. 2Rushton, "The Scaling of Locational Preferences." The firs made We Segment by the 5 preferer and Site the OPPC experimfi situatic relative be iden‘ by pref< this di the mos be the In the as revealing pail other alternativ' cuthmtions whi m Hmir locatic parisons approa. enables the rev. Pairs of locati 0f 3 preferenc 0 falocationz fgum‘ing sec 25 The first principle is that whenever a choice is made we regard this choice as revealing a small segment of a total preference structure possessed by the subject. That segment is a statement of preference between the combinations of location and site attributes of the choice selected and of the Opportunities rejected. Since in any experimental situation the total set of conceivable situations will not be complete, an ordering of the relative frequency of choice combinations will not be identical with the ordering of the same combinations by preference. In other words, one consequence of this distinction between preference and choice is that the most commonly chosen locations will not necessarily be the most preferred.1 In the model, movements to destinations are conceptualized as revealing pairwise choices between the alternative chosen, and each other alternative available for choice (the alternatives here are destinations which have been generalized into locational types based on their location and site attributes). Employment of the paired com- parisons approach in conjuction with the constant ratio assumption, enables the revealing of degree of similarity in preference between pairs of locational types. From such information, the establishment of a preference scaling of locational types and ultimately formulation of a locational preference surface are possible (as discussed in the . . 2 following section). The model is a static one, considering preferences at one point in time. Individuals are assumed to act in a rational manner, achieving the maximizing of utility (satisfaction) through their choices. Hence the model is a riskless one and does not provide for errors in choice which might be expected to occur. In addition, this model is 1G. Rushton, "Behavioral Correlates of Urban Spatial Structure," Economic Geogrgphy, XLVII (1971), p. 51. 2Rushton, "The Scaling Of Locational Preferences." probabilistic in t': are unrestricted (. local, then, embed; to be essential in arplication. A Reveal This Sec tneory in deriy in data. The Proced Assume origins and numbt C-EStinar‘1Qns 26 probabilistic in the sense that the probabilities which govern choices are unrestricted (i.e., they can range between 0 and 1). While the model, then, embodies certain unrealistic assumptions, these appear to be essential in order to use simple spatial interaction data in its application. A Revealed Preference Approach to Analysis of Locational Choice Data This section discusses the utilization of revealed preference theory in deriving information about locational preferences from empirical data. The procedure employed follows that described by Rushton.1 Assume that information is available concerning the home origins and numbers of individuals frequenting various recreation destinations. In effect then, there is knowledge of a system consisting of the origin points of recreation resource users, the destinations which they patronize and the flows between origins and destinations (Figure 1).2 If each origin and destination as well as the flow between them is considered to be unique, little can be done toward establishing rules whereby movement occurs. Each individual presumably would act in a unique, unpredictable manner and no summarizing of such spatial behavior would be attainable. 1Rushton, "The Scaling of Locational Preferences." 2The origins here are the cities from which the major recreation flows originate and the destinations (opportunities) are existing facilities for a type of recreation pursuit (in this case, camping in provincial parks). —>2 ,KINGSTON + Provincial Park l—J..._l—| 0 75 150 225 (opportunity set) Fig. 1.-—Provincia1 park destinations available to Kingston campers. + Provincial Park numbers refer to distance classes (75 mile interval) Fig. 2. -- Park destinations classified by distance from Kingston. g? 0L1: shew ill an Var} ,2) 0‘ I]; 28 It is obvious, however, that destinations frequently have certain characteristics in common, and it seems likely that individuals have some awareness of the similarities of various destinations. For example, in Figure 1, it is apparent that a number of destinations are located at similar distances from the origin center of Kingston. Thus, when examining movements of Kingston campers, it would seem useful to group destinations on the basis of the distance attribute. Figure 2 shows how such a grouping might be accomplished.1 Obviously when more than one origin is considered, a destination often will be situated at varying distances from each of these origins. _Some degree of generalization of destinations in this system has now been achieved, based on one attribute of the destinations (distance from origins) which is hypothesized to have some influence on flows in the system. Site characteristics logically might be hypothesized as an additional attribute(s) of destinations relevant to flows in the system. It is evident, though, that the measurement and grouping of destinations on the basis of such an attribute is a much more difficult task than for the distance-from-origin attribute. Not only is there a wide variety of types and combinations of characteristics which might be included in such a category, but frequently there are problems in measuring and obtaining such information. The problem is compounded by the fact that it is not simply a classification of destinations by site character- istics that is desired, but rather a classification based on site characteristics considered relevant to the users' choice of destination. 1Straight-line distances are used in this example, but it would be relatively easy to substitute actual road mileages in the calculations. 29 Thus, the fact that one camping destination may provide 400 campsites while another may provide only 33 campsites may have no bearing on choice between the two destinations, and accordingly would have little usefulness in the classification.1 While the problems, then, are considerable, the knowledge that such classifications indeed have been attempted is an encouragement to efforts to consider relevant site characteristics.2 It would appear then, that recreational destinations can be generalized into "locational types" on the basis of common distance-from- origin and "attractiveness" characteristics. Figures 3 and 4 illustrate such a classification scheme. Left until later is the explicit definition and derivation of locational types used in this study. For each individual movement in the system, information is now held about locational type selected and locational types (opportunites) available from that origin. For example, in Figure 3, campers cannot choose a destination with attractiveness of 1 in the closest distance zone, 1The possibility exists, of course, that number Of campsites may be closely related to other variables which are relevant to choice, and thus may serve as a useful index in such a classification. 2Rushton (Rushton, "Analysis of Spatial Behavior by Revealed Space Preference," p. 395.) has made use of a surrogate (town size) to represent those attributes presumed to be of importance in decisions about grocery purchases. Similarly, Wolfe (Wolfe, Parameters of Recreational Travel.) has employed capacity of a destination for a particular recreational pursuit as a surrogate for attractiveness of site. Ellis (J.B. Ellis,"Svstems Analysis of Provincial Park Camping: 1966 Park Users Survey,"report prepared for Parks Branch, Ontario Department of Lands and Forests [Toronto: 1968]) has utilized factor analysis of many site characteristics to achieve measures of overall attractiveness for parks. 75 P81 Va: 9 :18. .3." fro [ All I In 56‘ n. «x.m_h W>sh mmwz ‘ LOca Attractiveness Index ° A ’ B O c 6 D g E (most attractive) Fig. 3.—-Park destinations classified by attractiveness and distance from Kingston. DISTANCE ATTRA CTIVENESS (figures indicate no. of parks) Fig. 4.—- Locational types available to Kingston campers, PM. dwell! 'r1 3’ 31 consequently this locational type does not constitute an alternative here.1 Revealed preference theory states that given data on choices among pairs of alternatives, a unique preference scaling of such alternatives can be derived. Each movement to a particular locational type is regarded as indicative that a series of pairwise choices between that alternative and other alternatives has been made.2 Figure 4 provides an illustration. There is a total of nineteen locational types available to Kingston campers. Therefore, if a camper chooses locational type 15, he is regarded as having made pairwise choices between this type and each of the other eighteen available types. Once information is possessed about locational choices and available locational types, a revealed preference data matrix can be formed. Table 1 represents a portion of such a matrix in which only two of the forty locational types are not available from any of the origin centers considered. This matrix of choice data is employed to achieve a representation of locational preferences (as described below). Revealed preference data can be presented in terms of probabilities. For example, if 400 individuals choose locational type A over type B, while only 100 select B over A, then the probability tha: 1Figure 4 shows that, in a number of cases, more than one destination is assigned to a locational type. Note that in the analysis, the choice alternatives are locational types, not specific destinations. Accordingly, choices among destinations represented by the same locational type are not dealt with. 2The question of whether this conceptualization of the decision process is a useful and/or realistic model has been discussed earlier. .ueqmu floccuuuoo~ uzemouqou euogauz A .ouo: veoamouaou an manna onu.uo.cowuuoa.ngm~co .Aumuma aweuov cw vommaomavv oooa cu exham unwoc«>ouo owuauco ua uuoaaao mo oHQEeu a scam one ounce wm.o x_.sm . o a mug in} 1.. m no.o ~n.~o o a mm.o se.ca mw n em.o ea.sa s. m cc.o oo.cc¢ nn . . eerie—m2 bmmmp .004 {It ommmwh «make 08 ammMMmmmm mNZHB mo Hzmommm Mm mmmwfi Ak IO! 0... wn.>h J¢ZO~kmm H uqm¢a. val» no a ‘4“ 6.» A: vi ¢ ‘IA ‘flh . Q Q Did uVL 0 33 A will be chosen over B is 0.80 while the probability for B over A is 0.20. Table 2 indicates the probabilities obtained from the revealed preference matrix in Table 1. The two locational types that are not available are then eliminated from the matrix (since no choices are present on which to assess preferences). Locational types may then be ordered on the basis of percentage of time they are revealed as preferred to other types (i.e. percentage of the pairwise choices in which they have a probability of choice greater than 0.5). Table 3 shows such a ranking, while Table 4 illustrates a portion of the re-ordered matrix. When the probability of choosing locational type A over type B is 0.5, it follows that the probability of choosing B over A is also 0.5 (since the probabilities must sum to 1.0). In this situation, indifference is apparent between the two alternatives; both are equally preferred. Hence the absolute difference from 0.5 of the probability of choice between any pair of locational types may be regarded as an indicator of the similarity of preferences for the two types. If the difference is 0.0, preferences are similar, while a difference of 0.5 indicates maximum dissimilarity. Table 5 represents a portion of a matrix of differences from 0.5, referred to as a proximity matrix. Note that the upper half of the matrix is the same as the lower half, hence only half of the matrix is required. The degree of transitivity (consistency) of the pairwise choices of the population is also of interest. For example, if A is preferred to B (A-oB) and B-eC, then A must be preferred to C in order for trans- -(-(n. ._ . s9. :\ a....—emaa.tt wiuz .l v-.->..n. Invi- 0' us- ! Uri. .49. F. .v. .n....o.(. :- A.u.. to corn... V- Q... 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Kendall, Rank Correlation Methods (Third Ed. London: Charles Griffin and Co. Ltd., 1962), pp. 144-148. 36 section has produced a proximity matrix whose cell values are considered to express similarities between preferences for pairs of locational types. While such a matrix is of considerable value, much of its meaning is hidden and requires translation into a more easily understood form. A solution to this problem would appear to be the construction of a scale which would summarize and clarify preferences for locational types. Such a scaling of locational preferences involves the derivation of a preference function representing rules of choice among alternative destinations. The simplest scale to construct and to comprehend is one which scales objects (locational types here) along one dimension according to preferences. However, frequently the benefits of simplicity of the unidimensional scale are accompanied by disadvantages stemming from the greater assumptions which must be made about the data. For instance, a unidimensional scale can be constructed by assuming that pairwise similarity measures from the proximity matrix should be additive. That is, if A is preferred to B and B is preferred to C, then the distance on the scale between A and C should equal AB plus BC. By averaging a number of estimates for such distances, we arrive at a scaling of preferences along one dimension.1 There is little basis for assuming that preferences can be adequately scaled along one dimension.2 Thus, the situation appears 1Rushton, "The Scaling of Locational Preferences." 2Employment of the previously mentioned test of weak transitivity can help ascertain the validity of unidimensional scaling of the preference data. It is suggested that the lesser the prOportion of intransitivities (i.e. A~B, B*C, CeA) the more likely it is that individuals rank locational types along only one dimension in deciding among alternatives. ...Q. 37 amenable to a multidimensional scaling procedure, with a unidimensional scale considered simply a special case of the general approach. The underlying purposes of multidimensional scaling "of somehow getting hold of whatever pattern or structure may otherwise lie hidden in a matrix of empirical data and of representing that structure in a form that is "1 indicate its relevance to the much more accessible to the human eye, problem. Attention is focused on those multidimensional scaling procedures generally designated as "nonmetric", that is, they make use of only the ordinal properties of the empirical data. As noted by Shepard,2 these nonmetric procedures have several advantages over the earlier metric approach.3 For one thing, in observation of choices or judgments, researchers may be reluctant to attribute much importance to exact numerical measures because of the possibility of errors in judgment or measurement. Employing only the ordinal attributes of the data would seem to be one way of reducing the possible error. Nonmetric procedures also improve over earlier methods by the adoption of goodness-of-fit criteria enabling evaluation of the resulting scale in terms of how accurately it represents the original data. In addition, the newer approaches are more flexible than metric scaling, capable of 1R.N. Shepard, "Introduction to Volume I," Multidimensional Scaling; Volume I, eds. R.N. Shepard, A.K. Romney and 8.3. Nerlove (New York: Seminar Press, 1972), p. 1. 21bid., pp. 6-7. 3Much of the development of metric multidimensional scaling is associated with Torgerson (W.S. Torgerson, Theory and Methods of Scaling [New York: Wiley, 1958]). 38 treating a wide variety of scaling problems -- for instance, situations where data are missing or are to be weighted. Pioneering contributions to nonmetric multidimensional scaling 1’2’3 The essential features of these were made by Shepard and Kruskal. developments are briefly considered. Given some measure of similarity (proximity) between pairs of objects, the objective is to find the scaling configuration of these objects such that the resulting distances between object pairs correspond to the proximity measures. Correspondence here means obtaining a relationship between proximity measures and the distances of the scaling configuration which is monotonic (i.e. if AB represents the largest proximity measure, then the resulting distance AB should represent the smallest distance). The degree to which mono- tonicity is achieved serves as a measure of the adequacy of the scaling configuration. Since a trivial solution could be attained by adding one dimension for each object scaled, a further requirement is that the final configuration be of the smallest possible dimensionality. The multidimensional scaling algorithm developed by Kruskal was adopted in the scaling of the locational preference data of the study. More recently, several additional multidimensional scaling algorithms 1R.N. Shepard, "The Analysis of Proximities: Multidimensional Scaling with an Unknown Distance Function," Psychometrika, XXVII, (1962), pp. 125-39. 2J.B. Kruskal, "Multidimensional Scaling by Optimizing Goodness of Fit to an Nonmetric Hypothesis," Psychometrika, XXIX, (1964), pp. 1-27. 3J.B. Kruskal, "Nonmetric Multidimensional Scaling: A Numerical Method," Psychometrika, XXIX, (1964), pp. 115-29. V! vhu all an be? ite .Ix e r. uis 35.6. 3hr. 39 have been developed.1 However, as noted by Shepard, these approaches all undertake basically the same kind of analysis.2 Important attributes held in common include assumption of a monotonic relationship between scaling distances and the proximity data, adoption of an iterative procedure adjusting scale points to approach the monotonic relation, and attainment of results which frequently are indisting- uishable when the approaches are applied to the same data. Differences among the procedures relate to less significant aspects including speed, adaptability, data capacity, type of metric and susceptibility to local minima (degenerate) solutions. Since commencement of this dissertation research employing the KIUSkal algorithm, a recent analysis by Roskam has concluded that the Kruskal approach has some tendency to favor degenerate solutions, particularly when ties occur in the data to be scaled.4 Roskam suggests a new procedure incorporating what he considers to be the strong points 1For example, the smallest space analysis of Guttman and Lingoes reviewed in J.C. Lingoes, "A General Survey of the Guttman-Lingoes Nonmetric Program Series," Multidimensional Scaling: Volume I, eds. R.N. Shepard. A.K. Romney and S.B. Nerlove (New York: Seminar Press, 1972), pp. 49-68, or the work of Young and Torgerson (F.w. Young and W.S. Torgerson, "TORSCA: A FORTRAN IV Program for Shepard-Kruskal Multidimensional Scaling Analysis," Behavioral Science, XII (1967), p. 498). 2R.N. Shepard, "A Taxonomy of Some Principal Types of Data and of Multidimensional Methods for their Analysis," Multidimensional Scaling: Volume I, eds. Shepard, Romney and Nerlove, pp. 21-47. 3Problems with local minima occur when the iterative approach finds a solution which, relative to other solutions attempted, minimizes departure from monotonicity but which does not comprise an absolute minimum for the scaling problem. 4E.E. Roskam, A Comparison of Principles for Algorithm Construction in Nonmetric Scaling, Michigan Mathematical Psychology Program Technical Report MMPP 69-2 (Ann Arbor, Michigan: 1969), p. 6. w ...... Q.» £8.11 23.“. an' \- in be A 40 of both Kruskal and Guttman-Lingoes approaches.1 Certainly future scaling efforts should be based on full consideration of these recent developments. The multidimensional scaling technique adopted in this study can be better understood through an example in which it is possible to compare actual versus optimal scaling configurations. The proximity matrix here consisted of road mileages between pairs of urban centers in Southwestern Ontario (Table 8). The objective was to scale in two dimensions this half matrix of distances producing a two-dimensional "map" of these centers. Through comparison with the map of actual locations of these centers, the effectiveness of the scaling techniques can be ascertained. Successive analyses dealt with five, ten, fifteen and twenty urban centers and Figure 5 illustrates results of three of these. Where five centers were scaled (Figure 5, part A), stress (a measure of the degree of attainment of a monotone relationship) was 0.0, indicating that the ranking of inter-city distances in the data input was maintained in the scaling results. Note that the correspondence between derived location and true location is not particularly good, primarily because of the relatively few restrictions the stress minimiz» ation requirement places on locating such a small number of points. Analysis of the ten centers produced a stress of .030 (3%). The fit between real and derived locations again was not particularly good (Figure 5, part B). 15.5. Roskam and J.C. Lingoes, "MINISSA-l: A FORTRAN-IV Program for Smallest Space Analysis of Square Symmetric Matrices," Behavioral Science, XIV, (1969), p. 41 IOSPUEM oz T. .l .0 .8 l S O 3 l I O B u 14 m. .... 1 D. 0mm mmH mm QIHJBS LI NOH hum mm \D :3 sauuwnea '13 91 me am 05H auioq103 310d 51 Hmm ow n- and NN punos “3M0 VI VIIIIJO SI no~ oma omN ova an cm .wooH .uueno 0 00a“: 000m .mxmxsmw: m0 ueoauuoooa owuepco aIIIMWO ZI oHN 0N Hm nma me mad om 5118a BIBBBIN II wmm 4H0 and NH MN moo 0m“ 0m uopuoq OI wan v- mm No nag mNH mNH 55H om emu louaqoutx 5 mug mm HNH am am mNH ~m mm m0 «000(920 zxmzeaom 20 uontIavH s and Ne. 00 um" om NHH AHA AN 50 an on thano L me me «mm 00 an em oo~ we mm mm 0H mm JI39 9 meunvua 5 mm owm cod Nm 55H nwa mad new flog omH mNH Nvu wn~ cud uoifluttang y wad en neg pxogluexg g mmmhzmo nmhomamw mo mmwxmo mmamm mummmwz 000000 nocozuuwx coughed: rafioso Home emsumzu coumcwfiusm whomacmum coumamum awaken ANMVMVDNQO’D {A} 42 N (A) 5 CFHES stress 9- 0.000 x\ ‘. BRAMPTON 0 BURLINGTON BRANT FORD /'I .‘~ I’ \x I O 25 50 I_ o cum»: I I 0 25 so L‘ 1 A w B . summon o oueum ' measures . o ‘ I \ I. \\ . (a) 10 cmss \ (I. ’ 0 LONDON x. \ HAmuou (3.07” ~ IRANTFORD \\ \ ‘ s \‘ a \\ chmAu \ 0 Actual location ‘~§ \\ . . -.-.“ \ x Domed lac-non ‘. 0 Actual C Derived ‘ locafion w owew souwo a 0‘ omLuA name grit l Cl 20 CITIES stress - .034 at ‘3‘1’ BRAMPTON . smnroao g I 810!qu Q“ OGALT . °”“"“-‘ “0 auaLmo'rou mmuow LONDON ox IWMHKHO sncMMAmuaI x" If NIAGAIIA nus Own: n 080 08 PORT cowonwc g, chmAu - \ ‘x L 2.5 2° ‘\ I Fig. 5 . --Two-dimensiona1 scaling of Ontario cities. I an uk. 83 63- 43 In the fifteen and twenty center analyses, stress remained around 2-3%, however the fit of the derived locations to the actual locations improved substantially (Figure 5, part C) illustrates the 20 center cases. Obviously, the greater the number of pairwise comparisons, the more accurate will be the derived locations. It can be seen that in this example, the scaling technique does a reasonably good job of reconstructing the original scale (map) from which the similarities data were obtained. It is quite likely that the fit would have been improved by using airline distances between the urban centers instead of road mileages, particularly where road routes are circuitous (for example, St. Catharines - Toronto).1 There are obvious differences between the data used in this example and the data to be employed in a typical analysis. In the example, the original configuration, from which the inter-city distances were obtained, was known (a two-dimensional surface). Thus a rationale was provided for selecting the two-dimensional scaling configuration. It is evident that such a basis for selecting dimensionality will not normally exist. Kruskal has suggested that stress values be employed to determine dimensionality.2 Stress values and associated dimensions are plotted along the two axes of a graph and these points are connected. 1It is also possible that adoption of a scaling procedure which reduced the possibility of a degenerate scaling solution (as discussed earlier) might have led to a closer correspondence between observed and derived distances. 2Ibid. 44 Existence of a significant change in lepe provides a rationale for selection of that dimensionality for the scale. This multidimensional scaling technique thus appears to be a useful tool for determining the optimal dimensionality of the pre- ference space which locational types appear to occupy, as well as the relative positions of locational types within this space. The method also provides an indication of the loss of accuracy which results from collapsing this space into fewer dimensions. To the extent that locational preferences can be represented by a unidimensional scaling of locational types, a preference (in- T difference) surface can be derived using the one-dimensional scale values from the Kruskal technique. Equal-preference lines representing this surface may be interpolated from the values assigned to each locational type. The fact that preferences are consistent does not preclude the existence of anomalies in the preference surface, since consistency in preferences need not involve consistency over distance and/or attractiveness attributes. Thus consistency is no guarantee that the preference surface can be easily represented and interpreted in terms of these criteria. Obviously, interpretation of the preference surface, in terms of preference variation over distance-attractiveness combinations, is facilitated when few or no anomalies are present. Further Analysis of Locational Preferences: Comparing Population Subgroups and Identifying Random Choice Comparing Preferences of Population Subgroups A further aspect of the methodology concerns the investigation 45 of the relationship between locational preferences and various characteristics of the population members. One method of commencing such an examination is to group population members on the basis of one or more characteristics and to derive preference surfaces and scales for each group by the method already described. The detailed comparison of preferences derived for the groups, however, involves techniques not previously discussed. The following example outlines an approach to this problem. Assume that locational choice data can be compiled for groups 3;! formulated on the basis of three characteristics of the camper population: for example, income, camping experience and type of camping party. If each characteristic is differentiated into two categories, eight different subgroups are possible. TableS) indicates hypothetical choices between two locational types (A and B) for these eight groups.1 Each of the 450 population members has been assigned to one of the 16 groups on the basis of income, camping experience and camping party attributes, as well as his choice between locational types A and B. 1The example used here is after Blalock (H.M. Blalock, Social Statistics [New York: McGraw-Hill Book Co. Inc., 1960] pp. 234-239). 46 TABLE 9 A HYPOTHETICAL CAMPER SUBGROUPS BASED ON CHARACTERISTICS OF CAMPERS Camping Loc. type A chosen Loc. type B chosen Totals Income experience over B over A Family Non-family Family Non-family 4;group group group group Less than Less than $10,000. 5 yrs. 60 40 20 16 136 5 yrs. or more 40 18 24 38 120 $10,000. Less than or more 5 yrs. 40 6 24 32 102 5 yrs. or more 24 2 12 S4 92 - Totals 164 66 80 140 450 Among these attributes, what comparisons would appear to be most meaningful? A logical criterion would be that the groups compared be mutually exclusive, that is, there is no chance of individuals be- longing to more than one of the groups being compared.1 If, for example, two mutually-exclusive income groups are compared, it is not clear that observed differences in preferences can be attributed to income differences, since individuals in the groups vary in other respects 1For example, if a particular income group is compared with a group having a certain amount of camping experience, it is apparent that a number of individuals could belong to both groups, since possession of the one attribute does not preclude possession of the other. 47 than just income. Thus, to show impact of income differences, it is desirable, where possible, to control for variation in other known attributes. In the example below, the relationship between locational preference and income class is examined, while controlling for variations in experience and type of camping group. From the previous table, the following series of contingency tables can be derived (Table 10). TABLE 10 CONTINGENCY TABLES FOR HYPOTHETICAL CAMPER SUBGROUPS Income Less than 5 yrs. eXperience 5 yrs. experience or more Loc. type A Loc. type B Loc. type A Lee. type B chosen over B chosen over A over B over A Family group Less than $10,000. 60 20 4O 24 $10,000. or more 40 24 24 12 Non-family group Less than $10,000. 40 16 18 38 $10,000. or more 6 32 2 54 The chi-square test is appropriate to test these contingency tables for significant differences in preference. The results of this 48 test are indicated below (Table 11). TABLE 11 CHI-SQUARE TEST RESULTS: HYPOTHETICAL CAMPER SUBGROUPS Type of Camping Chi-square Significance camping experience x2 level 02 party Family 0-5 yrs. 2.565 not signif. .017 S + yrs. .188 not signif. .002 Non-family 0-5 yrs. 28.064 p < .001 .298 5 + yrs. 15.582 p <.001 .139 For the non-family group there is a moderatley strong relationship between preference for locational type A over B and income less than $10,000. This relationship is somewhat stronger for campers with 0-5 yrs. experience. While only two locational types are considered here, this analysis could be expanded to consider the entire revealed preference matrix of locational types. A matrix of chi-square values could then be formulated which could be used to indicate, for each pair of locational types, whether or not significant differences in preference exist for the two population subgroups. Two problems are evident in the above application of chi- square analysis. One is that the chi-square test is inappr0priate when expected cell values are small (i.e. when the smallest expected frequency is less than five) or when the population is small (i.e. less 49 than 20). The other problem relates to the fact that chi-square values are directly proportional to the size of the population trested.1 Since varying population sizes are anticipated for different locational types, some method of compensating for these differences is desirable. The problem of dealing with small expected frequencies and/ or small populations may be resolved by employing the Fisher exact probability test.2 This test can determine significance of differences in preferences among pairs of locational types, where only a few choices are observed. Thus the matrix resulting from the analysis of choice data would consist of both chi-square and Fisher exact probability values and significant differences could be identified. The second problem of varying population sizes is more difficult to resolve because of the existence of both chi-square and Fisher exact probability values. Where the chi-square test has been employed, the chi-square value can be divided by the total population (XZ/N) to give a coefficient (02) which, for a 2 X 2 contingency table, varies from 0 (no difference) to 1 (maximum difference). However, no equivalent coefficient can be calculated for the Fisher exact probabilities. The only feasible solution appears to be the setting up 1For example, in the case of the following two contingency tables, the chi-square statistic for the second table is double that of the first, despite the similarity of the proportions (after Blalock, Social Statistics, p. 226). so 20 so 60 40 100 go go so 40 60 100 so so I 100 100 100 | 200 2S. Siegel, Nonparametric Statistics for the Behavioral Sciences (New York: McGraw-Hill Book Co. Inc., 1956), pp. 96-104. 50 of arbitrary dividing points for both the 02 coefficient and the Fisher exact probability values which differentiate between "significant" (for the purposes of our analysis) and "non-significant" differences in preference. Various summary statistics for the matrix of test results are discussed in conjunction with test results in Chapter V. It is apparent that, in determining the number of variables to be included in the comparison technique, and the number of categories in each variable to be considered, one major influence is that of number of individuals included. It may not be possible to subdivide the population as much as desired, simply because the number of cases in each cell becomes too small. It is essential to achieve a balance such that significant variables are included yet frequencies of the cells remain large enough to permit the analysis. IdentifyingRandomness of Choice Among_Locationa1 Types It is also feasible, using the technique discussed in the previous section, to identify instances where choices appear to be random in nature. As indicated earlier, the probability matrix derived in the revealed preference approach serves as an indicator of preference between pairs of locational types. If the probabilities for type A being preferred over B, and B being preferred over A are both 0.5, then indifference between the locational types is defined (that is, they are equally preferred). In situations where pairwise probabilities are close to 0.5, it might be suspected that these simply represent random fluctuations 51 from an indifference relationship. In other words, if individuals do not care which of two locational types they select, their random choices would be expected to yield pairwise probabilities which are not significantly different from 0.5 (the indifference situation). By testing observed frequencies against frequencies expected if the in- difference relationship applied, those cases with insignificant differences can be identified. The chi-square and Fisher's exact tests are appropriate for this purpose and are each applied under conditions noted in the previous section. Where differences from 0.5 probabilities are not significant, it might be concluded that the pairwise choices here simply mask a relationship of indifference. Again, various summary statistics can be employed to indicate the general pattern of apparent random choice. These are described later in conjunction with the application of the test. (*9 [U '1 0 ..., 21’ p.- CHAPTER III APPLYING THE MODEL TO LOCATIONAL CHOICE IN RECREATION: DATA CONSIDERATIONS A revealed preference approach to the modelling of preferences for location has been outlined in the previous chapter. Discussion of the means of applying this model to specific data on the location choices of recreation resource users comprises the topic of this chapter. Information on Choice of Location Data Requirements As previously noted, the basic information required in the revealed preference approach concerns the interaction of individuals with locations, in this case, the movement of individuals from origins to destination locations for recreation purposes. Also essential are measures of site attributes of the destinations and their situation with respect to origins of users frequenting them. There are a number of desirable attributes regarding origin- destination flow data utilized in the revealed preference approach. It is important that the interactions included should involve a common purpose as much as possible and be measured in a conSistent manner.1 1For example, it would be useful to be able to indicate not only origins and destinations of trips, but also particular routes chosen, stapovers along the way and so on. 52 53 Since each interaction provides information about a limited number of pairwise locational choices, it is necessary to include a sufficient number of interactions so that data is available for most if not all of the possible pairwise choices. Attempted control of extraneous variables which might adversely affect the analysis is another desirable feature of the data. For example, since locational preferences and the characteristics of destination alternatives can undergo change over time, the time period over which the interaction data is collected should be as short as possible.1 Where sampling of interactions is undertaken, steps should be taken to ensure an adequate and representative sample of the population in order that conclusions may be drawn about the entire population, not simply the sample. To facilitate the compiling and analysis of interaction data, frequently it is necessary to limit the number of origins and destinations included. In many cases this may be accomplished simply by grouping nearby origins or destinations and determining a represent- ative point location for each group. The validity of such generalizations depends on a number of criteria such as: size of total area involved, size of the areas encompassing the grouped locations, the degree to which clustering of origins and destinations occurs, and the extent to which distance and site attributes are generalized in the revealed 1For instance, it could be hypothesized that the locational preference of campers differ depending on the particular season of the year. Information compiled over several seasons would mask such differences. Ir. S4 preference analysis.1 Distance between origin and destination locations can be indicated in a variety of ways. The simplest approach involves the use of straight-line mileages between origins and destinations. For greater accuracy, however, actual mileages of the shortest routes might be employed. r A number of models utilizing origin—destination distances i have employed travel time and/or travel cost estimates to represent these distances.2 The value of employing such estimates depends on whether or not they are more realistic than simple mileage measures. 1'. ...4m The assumption in these studies is that travel time - cost measures are more relevant criteria to recreation resource users than simple mileage measures. As is apparent in recent writings, such an assumption 1Ellis, (J.B. Ellis, "Systems Analysis of Provincial Park Camping: 1966 Park User Survey," A Report prepared for Parks Branch, Ontario Department of Lands and Forests [Torontoz Mimeographed, 1968], pp. 33-36.) and Chubb, (M. Chubb, Outdoor Recreation Planningfin Michigan by a Systems Analysis Approach, pp. 91-99.) discuss problems in generalizing origin-destination information concerning recreation resource users. N For example, Ellis (J.B. Ellis, A Systems Model for Recreational Travel in Ontario: Further Results. [Downsview, Ontario: Ontario Department of Highways Report NO. RR148, 1969] p. 13) has employed the following formula to determine "resistance" of highway links between origins and destinations. Rh = (Lh/Sh + 0.67 x 0.031h)1.25 where Lh is length of link h in miles S is average speed over link h (m.p.h.) 0.67 and 1.25 are constants 0.03 is average cost of vehicle Operation ($ per mile) Note that resistance increases disprOportionately with increasing time-distance in this function. 55 , may not be realistic. Certain systematic inaccuracies in the predictions of interaction models (particularly the gravity model) has been attributed to inadequate representation of the distance variable.3 It has been suggested that perceived distance rather than actual distance is the important measure to be incorporated into the model. However, little information about distance perception of recreation resource users is available, and hypotheses are few.4 Given this situation, it would seem desirable, for the purposes of this study, to determine locational preferences in terms of "objective" characteristics of spatial structure (i.e. distances expressed by mileage) rather than in terms of subjectively-derived measures of uncertain representativeness. HOpe- fully, the results will point out certain characteristics of perceived distances. Origin-Destination Data for Ontario Provincial Park Campers As already intimated, the interaction pattern to be analyzed in this study concerns the movement of Ontario provincial park campers from hometown origins to provincial park destinations. Much of the origin-destination data to be employed in the analysis was obtained 1J. Beaman, Distangg and the "Reaction" to Distance as a Function of Distance, CORDS. Technical Note No. 14 (Ottawa: National Parks Branch, 1972). 2R.I. Wolfe, "Communications," Journal of Leisure Research, 11 (1970), pp. 84-87. 3R.I. Wolfe, "The Inertia Model," Journal of Leisure Research, IV (1972), pp. 73-76. 4Ibid. ~. I.- ‘ 56 from a 1966 survey of a sample of provincial park users.1 This survey, carried out during July and August 1966, attempted to obtain a minimum sample of fifty camping parties frequenting each of the provincial parks.2 The representativeness of the sample data has been questioned. Eleven of the 81 parks, for example, have sample sizes significantly lower than the specified minimum of fifty. Also, Ellis has noted discrepancies between certain sample characteristics and known population characteristics.3 While these conditions would be important if conclusions were to be drawn about all campers in each park (as Ellis and Wolfe sought to do), they are less significant when interest is in the entire Ontario provincial park camping population (as in this study). There is, however, one aspect of the sample affecting its representativeness for this study. This is the apparent variation in sampling fractions from one park to another, as a result of specifying a sample size of one percent gr_fifty camping parties (whichever is larger). The effect of this requirement is to raise above one percent the sampling fractions of the less-patronized destinations, and thus 1This park user survey was jointly undertaken by the Ontario Department of Lands and Forests and the Ontario Department of Highways. The relevant questionnaire (long form) and its accompanying instructions are included as Appendix V. Wolfe, (R.I. Wolfe, A Use Classification of Parks by Analysis of Extremes: Final Report of a Recreational Travel StudyIIDownsview, Ontario: Ontario Department of HIghways Report No. RR134, 1969]) and Ellis (Ellis, A Systems Model, Further Results) have discussed various aspects of the survey. 2A "camping party" consisted of individuals entering the park in one vehicle. The sample to be obtained was specified as one percent of the camping parties or fifty parties, whichever figure was larger. 3Ellis, A Systems Model, Further Results, p. 11. "'— 57 over-represent these users in the sample.1 The impact of this variation in sampling fractions is examined in the following chapter. The destinations included in the survey consisted of the 81 provincial parks having campground facilities.2 There was little difficulty in representing these destinations in terms of point locations since parks were not grouped in the analysis. Each sampled camping party originating in Ontario was assigned to one of 89 origin centers in the province which most closely approximated its hometown location. Campers originating outside the province were designated only by region or state of origin. These parties from non-Ontario origins were eliminated from consideration, not only because of insufficient information about origin locations, but also because it is unrealistic to conceptualize them as choosing primarily among Ontario provincial park alternatives.4 It was decided to reduce the origin-destination matrix to a more manageable size by combining origin centers situated reasonably close to each other, resulting in 54 instead of 89 origin points.S 1Appendix VII provides information about these sampling fractions. These destinations are listed in Table 12 and their locations are indicated in Figure 6. 3Thereby reducing the sample size by about 35 percent to approximately 3300 camping parties. 4Correspondingly, the failure to include non-Ontario destinations as alternatives for Ontario campers must be recognized as a weakness of this study which was unavoidable because of the lack of data. 5These origins are indicated in Table 13 and Figure 6. II' -. .wwm. .BonEuo ...—on. 335.600. 3.2200 2.5222280 {on Ea c2230 22.20 8.82-10 232... Ar.— .35 ~— 003-... v” on. acct-3:303 .2 M 0903:: 0‘00 .20.: .I I c. I E: u. .3? I .2 sé ... . 2 M; “ 000303.300 asun— O ’ nun-loo Eur—O 0 g 2 .2. 2. 2. 2. 2 59 TABLE 12 ONTARIO PROVINCIAL PARK DESTINATIONS, 1966: NAMES AND CODE NUMBERSa b Clay Creek 011 Devil's Glen 122 Holiday Beach 012 Earl Rowe 123 Ipperwash 013 Mara 124 Long Point 014 Sibbald Point 125 Pinery 015 Six Mile Lake 126 Rock Point 016 Antoine 131 Rondeau 017 Finlayson Point 132 Turkey Point 018 Marten River 133 Wheatley 019 Samuel de Champlain 134 Five Mile Lake 021 Arrowhead Lake 141 Greenwater 031 Grundy Lake 142 Kettle Lakes 032 Killbear Point 143 Caliper Lake 041 Mikisew 144 Lake of the Woods 042 Oastler Lake 145 Quetico 043 Restoule 146 Blacksand 051 Sturgeon Bay 147 Klotz Lake 052 Algonquin 151 MacLeod Lake 053 Carson Lake 152 Neys 054 Driftwood 153 Rainbow Falls 055 Inwood 161 Ivanhoe Lake 061 Kakabeka Falls 162 Craigleith 071 Middle Falls 163 Inverhuron 072 Sibley 164 Point Farms 073 Lake Superior 172 Sauble Falls 074 Mississagi 173 Nagagamisis 081 Pancake Bay 174 Remi Lake 082 Ojibway 181 Fitzroy 091 Pakwash 182 Rideau River 092 Chutes 191 Silver Lake 093 Fairbank 192 South Nation 094 Killarney 193 Aaron 101 Windy Lake 194 Blue Lake 102 Esker Lakes 201 Rushing River 103 Kap-Kig-Iwan 202 Sioux Narrows 104 Black Lake 211 Balsam Lake 111 Bon Echo 212 Darlington 112 Lake St. Peter 214 Emily 113 Outlet Beach 215 Presqu'ile 116 Obatanga 221 Serpent Mounds 117 White Lake 222 Bass Lake 121 8Except for the deletion of Clay Creek and the addition of two parks (Selkirk and Bonnechere), the 1968 list of destinations is unchanged. bPark code assigned by Ontario Department of Lands and Forests. n'.'l‘ri' A'W'v-‘r‘, OWVO‘U‘IAMNl—i 14 15 16 17 18 19 20 21 22 23 24 25 26 27 60 TABLE 13 ORIGIN CENTERS USED IN THE ANALYSIS OF ONTARIO PROVINCIAL PARK CAMPER DATA, 1966 Windsor Chatham, Wallaceburg Sarnia St. Thomas London Woodstock Simcoe Stratford Niagara Falls, Welland, Port Colborne St. Catharines Dunnville Brantford Kitchener, Waterloo, Galt, Preston, Guelph Hamilton, Dundas Burlington Oakville, Georgetown Brampton, Mississauga Metropolitan Toronto Aurora, Newmarket, Richmond Hill Oshawa, Whitby Lindsay Goderich Walkerton Owen Sound Orangeville Barrie Orillia Cobourg 28 29 3O 31 32 33 34 35 36 37 38 39 4o 41 42 43 44 4s 46 47 48 49 so 51 52 S3 S4 Peterborough Belleville, Picton Trenton Gravenhurst, Haliburton Kingston, Napanee Brockville Smith Falls Ottawa, Rockland Prescott, Cornwall, Morrisburg Hawkesbury, Alexandria Parry Sound Pembroke North Bay, Sturgeon Falls Sudbury Espanola, Little Current Sault Ste. Marie, Thessalon Chapleau, White River New Liskeard Kirkland Lake Timmins, Cochrane Kapuskasing Geraldton Thunder Bay (Port Arthur, Fort William), Nipigon Atikokan Dryden, Sioux Lookout Fort Frances Kenora )l" 1"."- 61 While some loss in accuracy occurred, this was judged to be small.1 As noted, the "camping party" was designated as the unit for which information was to be compiled. A number of writers have suggested that "camper days" (number of campers times length of stay in days) is a much more precise measure of park usage than party visits.2 For this study, however, the camping party was considered to closely 9 approximate the decision-making unit and hence was a more appropriate measure of locational choice than camper days. Length of stay (measured in camper days) can be treated later as one variable differentiating camping parties. One of the benefits anticipated from the user survey concerned the question of importance of use of parks as stopovers by campers on extended trips. Lack of such information forced previous modelling efforts to assume that each camping party travelled directly from hometown to park and back again to hometown. Such an assumption is obviously unrealistic in a number of cases. A "carbon—tracer" procedure, whereby visits of camping parties sampled were to be recorded for each park visited following the initial interview, proved to be largely unsuccessfhl in revealing patterns of subsequent visits.3 In fact, 1In fact, an estimated 85 percent of Ontario residents camping in provincial parks originated in or near 13 major Ontario centers in 1966. 251115, A Systems Model, Further Results, p. 14. 3Wolfe, (Wolfe, A Use Classification of Parks, pp. 2-3.) discusses this failure and the reasons for it. 62 because of faults in the questionnaire,1 it is difficult to identify those parties in the sample utilizing parks as stopover points only. It would appear to be desirable in the analysis to separate "stop-over" visits from other camping party visits because of the substantial differences in locational preferences that might be expected between these two types of visitors. It appears logical that the range of alternative destinations is considerably more restricted for stop-over visits than for other types of visits. Since the questionnaire data does not permit a distinction between stOp-over campers and other types for the sample, an attempt was made to separate out those park destinations having high proportions of stop-over campers. While information on these proportions is lacking for 1966, estimates are available for the 1970 camping season.2 The 1970 proportions were employed since they were considered unlikely to differ significantly from the 1966 situation. If the criterion is adopted that parks having proportions of stop-over campers greater than fifty percent should be separated from those having proportions of fifty percent or less, several facts emerge. For one thing, with only three exceptions, all parks north of a line through Algonquin Park are designated as stop—over parks (each lNotably a previous stopover or planned subsequent stOpover was recorded only if it involved a period of two or more nights (Ibid., p. 19). Thus one-night stopovers were ignored. 2Ontario Department of Lands and Forests, "Park Use Statistical Report, 1970,” (Mimeographed). Information concerning length of stay of campers was used to distinguish between stop-over and destination campers. 63 having more than fifty percent stop-over campers). In fact by this criterion, over one-half of all parks are defined as stop-over parks (46 out of 81 parks). Clearly, such a division of the park system into two parts -- one, consisting of distant "stop-over" parks, and the other consisting of nearby "destination" type parks -- is un- satisfactory for analysis of locational preferences. It would be impossible to ascertain preferences of campers other than the stOp- over type for the more distant locations, or of stOp-over campers for closer locations. The separation of park destinations thus is not considered to be a satisfactory solution to the problem of separating stop-over campers from other types. A more fundamental problem in separating stop-over campers from other campers relates to the definition of "stop-over camper". It seems likely that there is a continuum of types of stay ranging from "one night stop-over" to "park as sole destination" along which individual camping parties might be placed. Accordingly, it would be difficult to draw a line between stopovers and other stays. It would also be misleading, since the type of visit may not be distinguished correctly by such a procedure. In a situation where purposes of park stays were well- defined it would seem desirable to distinguish among different types of stays and deal separately with locational preferences related to them. In the absence of such information it would appear pointless to attempt to separate out imperfectly only one such group. Rather, it was concluded that each destination choice, regardless of the characteristics of the chooser or the situation under which it was made, should be 64 regarded as contributing to the overall preference structure of Ontario campers. Measuring the Attractiveness of Parks for Campers General Considerations The derivation of attractiveness measures for destination sites has proved to be difficult, largely due to problems in defining "attractiveness" as well as problems in quantifying and measuring those characteristics it is considered to encompass. What are some of the desirable features of a technique adOpted for rating site attractiveness? Certainly one important aspect should be the minimizing of subjectivity both in the rating scheme and in its application (i.e. results should be replicable by different evaluators using similar criteria). The evaluation process, then, should be well- defined and the attributes to be examined should be specified in detail and operationally defined. The criteria should also be consistent with information about the basis on which individuals choose among destination sites. For the purposes of this study, one of the most important characteristics of an attraction index is that it be derived independ- ently of the specific destination choice patterns exhibited by the individuals of concern. Since the revealed preference approach has 1Later in the study, attempts are made to relate such variables to differences in locational preference. 6S hypothesized the combining of distance and site attractiveness attributes in choices made among alternative destinations, the use of raw choice data to define site attractiveness alone obviously would be contrary to this hypothesis and hence unacceptable. Relative to problems of measuring attractiveness of destinations for most other types of recreational pursuits, measuring attractivity of parks for camping has certain advantages.1 In contrast to other pursuits, number of destinations to be treated is limited, and these sites are well-defined by park boundaries. Also, many of the attributes of park sites frequently can be ascertained from available information.2 In addition, since campers have been scrutinized more closely than other recreational groups, more is known about their preferences for destination facilities than about those of other groups. Prior to the consideration of specific attraction indices, several questions should be briefly dealt with. For one thing, since the destinations of interest include only provincial parks, are there significant differences among the site characteristics of these parks which influence their attractiveness to users? Cursory examination of parks quickly points to the affirmative. In fact, the term "provincial park" includes areas having widely varying natural environments and 1Chubb, Outdoor Recreation Planning in Michigan, pp. 155-56. 2 . . 'This situation contrasts to that of cottaging or boating, for example, where much more extensive, more diverse, and less well- known destinations frequently must be dealt with. 66 facilities for recreational activities.1 Recognition of diversity within the parks system is evident in the provincial park classification scheme used in Ontario to identify park areas having different management and use objectives.2 Given that variation in site characteristics of Ontario provincial parks does exist, to what extent are campers aware of such variation and consider it in choosing among destinations? The results of the 1966 survey of Ontario provincial park users provide some information on this question, suggesting that there is a link between recreation activity preferences of campers and the facilities available for such activities in the parks they patronize.3 It appears that campers have at least some awareness of differences in park character- istics and consequently choose their park destinations accordingly. For all parks, an average of 4.2% of the camping sample expressed an intention to go boating.4 However, in parks where boat launching facilities were not available (and therefore boating would be difficult or impossible), the average percentage preferring boating dropped to 1Appendix 11 gives some indication of the lack of uniformity of Ontario provincial parks. 2Ontario Department of Lands and Forests, Classification of Provincial Parks in Ontario (Toronto: 1967). Park classes include: Primitive Parks, Wild River Parks, Natural Environment Parks, Recreation Parks, and Nature Reserves. 3Question 26 of the camper questionnaire asked which two activities were considered most important to the enjoyment of this park visit. Note the possibility for discrepancies between intention and participation. 4These figures were derived by averaging together the number of first and second choices for each activity (expressed as a percentage) for each park and then averaging for all parks in the group. 67 half of the overall average (2.1%). Similarly, for the entire park system, an average of 29.3% of the campers in each park intended to go swimming. For the parks where swimming facilities were negligible, this average dropped to 12.7%.1 Evidence that campers do not seek the same things in a camping experience suggests that different attraction ratings might be devised to serve different types of campers. For example, a number of studies have distinguished between the "wilderness camper" and the "social camper" having markedly different purposes and preferences.2 However, in most cases, campers have been so classified not by ascertaining their motives or desires, but rather by defining destinations as wilderness or social destinations on the basis of their attributes. The characteristics of the users of such parks then become the attributes of wilderness or social campers. Thus these types of campers are designated in terms of the specific pattern of opportunities which exists. For instance the fact that most campers must travel con- siderable distances to reach wilderness parks results in wilderness campers being defined as campers willing to travel long distances to destinations. Is it not possible that there are "wilderness" campers who make the best of closer, less desirable parks simply because of the poorer accessibility of the more ideal parks, in essence trading 1The possibility exists that in some cases, the park may simply serve as a base for a recreation activity pursued outside the park boundaries. 2The following reference is an example of this type of study. J.B. Ellis, A Systems Model for Recreational Travel in Ontario: A Progress Re ort (Downsview, Ontario: Ontario Department of Highways, Report No. RR126, 1967), pp. 16-30. 68 off quality for accessibility? Therefore, to the extent that different camper groups are defined by their locational preferences (as above), separate analysis of locational preferences of these groups is not very meaningful since the results would largely "reveal" the preferences whereby the groups were defined. Given the inadequate information available on true motives and preferences of the camper sample utilized in this analysis, there is little point in devising separate park attractiveness indices for different camping groups. Techniques for Measuring Park Attractiveness Simple Attraction Functions. -- One of the simplest and most easily applied measures of park attraction is the type discussed by Ellis1 utilizing a simple function to determine attraction (as indicated below). = (W +K ) Ad cdsd d 1Qd K2 where Ad is the attraction value for park d Cd is the index of relative camping capacity of the park (0.2, 0.6, 1.0, 2.0, or 3.0) Sd is a value denoting the presence of any special factor (0, 0.75, or 1.25) W is an index of relative quality of water-related resources (0.2, 0.6, 1.0, 1.5, 2.0) Qd is an index of relative quality of outdoor setting (0.5, 1.0, or 2.0) K1 and K2 are constants 1Ellis, A Systems Model, Progress Report, p. 8. 69 As is apparent in the definitions of the variables, the chief dis- advantage is the amount of subjective judgment involved both in the designation of possible values as well as in assignment of such values to particular parks. Such a technique, however, appears to have some use as a "stop-gap” device, serving in the absence of a more satisfactory scheme. This technique has been applied to Ontario provincial parks1 and the results are listed in the first column of Table 14. Comparison of highly rated parks against those with low ratings suggests that relative capacity is perhaps the most important factor in this rating (the final attractiveness ratings correlate quite highly with capacity ratings). A technique employed by Cheung is another example of a relatively easily applied function measuring park attractiveness which requires little detailed information on park characteristics.2 The attraction function attempts to incorporate measures of both the general popularity of specific activities and the facilities available for such activities at particular parks.3 Again the arbitrary definition of values assigned to park characteristics and the degree of subjectivity are major problems. 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Departures from the expected ranking are indicated by 0's (underlined) in the lower half of each matrix. The three lowest distance classes each have only one departure from the expected ranking, in all cases involving slightly greater preference for the third most attractive type over the second highest type. The higher distance classes exhibit a greater number of departures from the expected ranking, however, only in the case of the sixth class do these departures constitute more than one-half of the maximum number possible. Two other measures of attraction were also examined in order to compare the above results with those of other indices.1 One such 1These attraction values are indicated in Columns 7 and 8 of Table 14. COP. The the at CC 84 measure uses average length of stay of campers at a park as a measure of site attractiveness, with the assumption that the longer the average length of stay, the more attractive is the park.1 The other measure employs the results of a question of the 1966 Ontario Park User Survey concerning attractiveness of the area in which the park is situated. The assumption is made that the higher the proportion of campers viewing FIT the area as attractive, the more attractive is the park destination located in that area.2 Locational types were derived using each of F these measures of attraction and employing similar distance-from-origin vl.._’ "V:.."l’ 1“ categories as in the preceding analysis. If. x\ The results of analysis of the choice data using the two attraction indices discussed above are indicated in Table 17. The coefficients of consistency among choices are quite high for most of the distance categories of both attraction indices. It thus appears that locational choices can be found to be equally consistent even when several different attractiveness measures are used. Hence, consistency measures do not seem to be of great assistance in assessing the validity of one measure of attractiveness compared to another one. Values for the discrepancy index indicating proportion of pairwise choices which differ from the expected direction of preference reveal significantly greater discrepancies for the latter two attract- 1This assumption has been employed in other studies (e.g. Hodgson, "Campground Features," pp. 31-35) and appears to be supported by some evidence (c.f. W.F. LaPage, The Role of Customer Satisfaction in Managing Commercial Campgrounds TUpper Darby, Penn.: North East Forest Experiment Station, U.S.D.A. Forest Service Research Paper, NE-lOS, 1968].). 2Such an interpretation is largely untested, however it is employed here to provide a simply derived measure against which other indices might be compared. Dis C31 85 TABLE 17 RESULTS OF TESTS OF THE ATTRACTION INDICES Length of Stay Index Attractiveness of Area Index Distance Coefficient Discrepancy Distance Coefficient Discrepancy Category of Consistency Index Category of Consistency Index 1 1.0 .10 l 0.8 .40 2 1.0 .10 2 1.0 .30 nr‘ 3 1.0 .50 3 1.0 .30 4 0.6 .60 4 1.0 .20 S 1.0 .20 5 1.0 .30 6 0.8 .60 6 1.0 .30 7 1.0 .50 7 0.5 .50 8 1.0 .50 8 1.0 .17 iveness indices than for the index initially examined. This result suggests that of those indices examined, the factor analysis measure is the most meaningful index of site attractiveness. The tests of attraction measures have not included the simple attractivity function derived by Ellis and discussed initially in this section. In fact, the attractivity scores derived from this function are quite highly correlated with the factor analysis attractivity scores (correlation coefficient of 0.81), suggesting that the two techniques are measuring much the same types of site attributes, and hence that results of the test would be quite similar. In conclusion then, it appears that of those measures of attraction whose application is currently feasible, the factor analysis approach represents the most appropriate index of site attractiveness. Good possibilities exist for improving attractiveness measures through employment of other techniques (notably that of Ross) however additional research is required. pre par 15: CHAPTER IV LOCATIONAL PREFERENCES OF ONTARIO PROVINCIAL PARK CAMPERS This chapter is concerned with applying the revealed preference approach to the interaction system for Ontario provincial park campers, identified in the previous chapter. Initially an effort is made to formulate hypotheses regarding the nature of such preferences. This is followed by derivation and discussion of locational preferences under several slightly different model formulations. The Nature of Locational Preferences of Campers - Hypotheses It should be reiterated that the term "locational preferences" as employed in this study refers to preferences among different com- binations of distance and site attributes of destinations. Locational preferences, in essence, define the trade-off between distance and site attributes which is established by the individuals concerned. The preferences of interest, then, are not simply those for site character- istices or distance characteristics alone, but rather, for combinations of these characteristics. Relatively little information is available on preferences of recreationists for combinations of site and distance characteristics. Most studies have dealt with either the site characteristics or the 86 diste Thus over such dimer dimer that of On relat SUPPC studj pref. prob type ail 87 distance characteristics, assuming the variable not examined is constant.1 Thus if a graph is envisaged illustrating variations in preferences over distance (horizontal axis) and site attributes (vertical axis), such studies might provide information about variation along one dimension but rarely along both dimensions. Such predominantly one- dimensional studies are of some use in suggesting hypotheses, provided that their restriction to one dimension is noted. An initial hypothesis is that individual preference structures of Ontario campers will be quite similar -- i.e. that campers have relatively similar locational preferences. A variety of evidence lends support to such a hypothesis, including the results of a number of studies already discussed in the dissertation.2 Similarity of individual preferences would be indicated by values approaching 1.0 or 0.0 in the probability matrix (expressing the probability of choice of locational type A over B when both are available). Another hypothesis which appears plausible is that the aggregated pairwise locational choices of Ontario campers will have a 1For example, Aldskogius, (H. Aldskogius, "Vacation House Settlement in the Siljan Region," Geografiska Annaler, XLIX B (1967), pp. 67-95.) concentrates on the site dimension while disregarding the position dimension. Also in Shafer and Thompson, "Models that Describe Use of Adirondack Campgrounds," parks located at roughly similar distances from population centers were chosen to minimize the effects of unequal distances on park patronage. 2See, for example, the studies by Wolfe (Wolfe, Parameters of Recreational Travel in Ontario, and Wolfe, A Use Classification of Parks). 88 fairly high degree of consistency. In other words, aggregating such choices leads to the formulation of an aggregate preference structure which has considerable consistency. This attribute will be measured by the coefficient of consistency referred to earlier, with values approaching 1.0 indicating a high degree of consistency. Focusing on those site attributes that contribute to "attractiveness", hypotheses can be advanced concerning the combining of attractiveness and distance attributes. If rational choice behavior is assumed, it might by hypothesized that, given a choice between two destinations at similar distances, preference will be shown for the one having the more attractive site characteristics. We might also expect that, given two destinations of approximately equal attractiveness, the one closer to the origin center will be preferred. Thus preferences might be expected to be greater with increasing attractiVeness or decreasing distance (other things being equal). The possibility exists that the 'trip' aspects may be an important contributor to the recreation experience and thus that increased distance may not always be regarded as a liability. Despite this possibility, it is hypothesized that in a majority of cases, distance is regarded as a liability. According to the above hypotheses then, a preference surface of the form illustrated in Figure 8 is envisioned (the lines join equally-preferred alternatives). At distance d (or any distance), the greater the attractiveness of the destination the higher the percentage of individuals choosing that destination over other alternatives. Similarily, at attractiveness a (or any attractiveness) the shorter the distance of the destination, the higher will be the percentage choosing it. 89 Decree-In. Decreasing Preierence o Preference a a i o a c / o o > .Z ..__ .. 0 Eu 2 ~ .- .- O- .- < <2 0 o f: f; (n U) a d Dietonce Distance Figure 8.--Hypothetical preference surfaces showing increases in preference for destinations with higher attractiveness and/or shorter distances. . . erPreference . I . o c r: . O .2 Decree-inc .Z .5 Pre'erence E 0 b 5 :::::::———“’ z < < Dietence Dietance Figure 9.--Hypothetical preference surfaces where little substitution between distance and attractiveness of destinations is possible. 90 The hypotheses advanced above have not dealt with site attractiveness and distance characteristics simultaneously. That is, no rationale for choice has been suggested when both attractiveness and distance characteristics differ between two alternatives. Thus, aside from broad limits, the slope and alignment of the lines of preference have not been specified. In general, the greater the extent to which substitution between distance and attractiveness is possible, the more the preference lines will depart from a vertical or horizontal position. Maximum tradeoffs between the two variables are indicated by slopes approaching that of the diagonal. The two illustrations in Figure 9 show situations where relatively little substitution is possible. One might expect that it is easier to determine and evaluate distance as opposed to attractiveness of destinations. Attractiveness tends to be evaluated more subjectively than distance. Thus it might be anticipated that distance variations would have a greater impact on locational choices than changes in attractiveness. Accordingly a preference surface similar to the one on the right of Figure 9 might be hypothesized. While there appears to be little point in further hypothesizing about locational preferences, because of the lack of information on which to base such hypotheses, one further aspect might be mentioned -- the alignment of the preference lines. A parallel alignment of such lines suggests, for instance, that a given change in distance always can be traded for a given change in attractiveness (i.e., a 50 mile difference has the same effect, whether talking about the difference between 50 and 100 miles or the difference between 500 and 550 miles). On the other 91 hand, lack of parallel alignment indicates that a given distance interval is substituted for varying attractiveness intervals depending on location on the preference surface. Wolfe has suggested the existence of an inertia factor which tends to increase one's resistance to short trips (i.e. the effort required to get going on any trip is constant) and decreases one's resistance to long trips (little effort is required in extending distance travelled).1 This hypothesis would suggest for short distances, substitution of a greater than average attractiveness interval per distance interval, (i.e. steeper slope) while for long distances, substitution of a lesser than average attractiveness interval per distance interval (i.e. lesser lepe). Derivation and Analysis of Locational Preferences Distance and Attractiveness Classes The attractiveness and distance measures to be utilized in the revealed preference model have already been discussed. It remains to define the classes into which these data are grouped for analysis. It is apparent that there are limits to the number of attractiveness and distance classes that can be handled readily because of the necessity of analyzing pairwise choices among all attractiveness- distance combinations (locational types). For example, with only three attractiveness categories and three distance categories, nine different 1R.I. Wolfe, "The Inertia Model," Journal of Leisure Research, IV (1972), pp. 73-76. 92 combinations of these are possible creating a total of 72 pairwise choices to be examined -- excluding the diagonal cells pairing similar locational types (TTable 18). There are also limits beyond which it is not useful to subdivide the attractiveness and distance measures. If little additional information is derived from using a greater number of classes, there is little point in undertaking the extra effort required. TABLE 18 MATRIX REPRESENTATION OF LOCATIONAL TYPES Distance - Locational types 1 2 3 Al A2 A3 Bl etc. 3 a) A A1 c: G) 0.3 B A2 UH 2533 #1 C A3 .1.) :3 Bl Without a considerable amount of experimentation, it is difficult to determine the number of combinations which is most desirable in terms of both economy of effort and sufficiency of detail. While such experimentation would have been useful, it represented a tangential aspect of the study and therefore was not undertaken. Consequently, in the interests of economizing on computer time and capacity, it was decided that a maximum of forty locational types would be handled. The attractivity indices derived from factor analysis of Ontario provincial park attributes were employed following slight modifications to some park attraction scores to take into account degree 93 of usage of park camping capacity (Column 5 and 6 of Table 14).1 In fact, these adjustments had a negligible impact on the attractivity ranking of parks. Each of these attraction scores was assigned to one of five attraction classes (Figure.H)). The primary concern in estab— lishing the class limits was to achieve roughly similar numbers of parks in each category and to position class divisions where natural breaks in values seemed to occur. Origin-destination distances (in miles) were calculated for all possible combinations of the 54 Ontario origins and 81 Ontario provincial park destinations designated earlier.2 There is a wide range in origin-destination distances, from less than 20 miles to well over 1,000 miles.3 From the graph in Figure 12 however, it is apparent that approximately three-quarters of the 1966 sample of camping parties travelled less than 500 miles to park destinations. Two distance classifications were established for use in the revealed preference analysis. One classification scheme defined eight equal distance classes of 75 miles, thus excluding origin-destination 1The adjustments were made in recognition that while, theoretically, a camper may choose any park as a destination, in peak periods, use of a given park to capacity or near capacity may well deter a substantial number of campers from utilizing such a park. Appendix IV discusses this aspect and the method of refining the index which was adopted. 2Where sufficiently accurate, straight-line distances, calculated from locational co-ordinates of origins and destinations, were used. However due to the shape of the province, a number of destinations can be reached only by circuitous routes (Figure 6). In these cases, mileages for the shortest possible highway routes were substituted. 3Highway 17 for example, traverses a distance of approximately 1350 miles across Ontario from Quebec to Manitoba, and even this distance does not represent the longest possible origin-destination trip within the province. ' ATTRACTION INDEXa Fig. 1600 190 'ik u: 90 £2 H 1% 30 H E3 i§ :3 12 < o 1600 190 90 30 12 94 51b 52 53 54 55 56 57 58 41 42 43 44 45 46 47 48 31 32 33 34 35 36 37 38 21 22 23 - 24 25 26 27 28 11 12 13 14 15 16 17 18 75 150 300 450 600 miles DISTANCE ‘ lO.-Definition of locational types: equal mileage intervals used in classes defining distance I 5 31115st 54 55 56 57 '58 41 424344 45 46 47 48 31 333334 35 36 37 38 21'22 23 24 25 26 27 28 111121314 15 16 17 18 40 160 270 390 700 DISTANCE Fig. ll.--Definition of locational types: e'qual 1966 camper sample proportions used as acriterion for the distance classes miles aIndex va1ues refer to the modified factor analysis indices, multiplied by 100 to simplify presentation. bLocational type identification number 9S 7...___._._______._._______..___ II'UlU'I'lllUl 'lll 'll'l'||'|l"l --—---.--_ ~ - -— — _ - —— - D- -_ — — - — - - ”~-———— 404....— z”_ - — — - — - - — — — - - u - - 3”. apozud ..ch Within 3‘69 #31? CUMULATIVE FREQUENCY Fig.12. Distance clsssss defined by cumulative frequencies of trip liflgth! ( 10" camper sample ). 96 distances of more than 600 miles. Since less than twenty percent Of sampled camping parties travelled more than 600 miles to a park destination, this limit appears justifiable. The other distance classification method divided the range of origin—destination distances into eight categories, each including approximately the same proportion of the 1966 sample of campers. That is, the lowest distance class included the lowest one-eighth of the origin—destination trips of the sample, ordered in terms of distance. The class boundaries are indicated by the dashed lines in Figure 12 dividing the sample into octiles, each constituting 12.5 percent Of the total sample size. Each distance classification has certain advantages. Establishment of distance classes using similar mileage intervals permits the examination of preferences over uniformly changing distance cat- egories, however -- as Observed from Figure 12 -- the lowest two classes contain more than half of the camping parties included in the sample. Adoption of the distance classification based on equal sample proportions ensures that roughly similar numbers of trips will be included in each distance category. This method also includes the entire range of origin-destination distances in the categories established. The locational types, formed by combining each attraction class with each distance class, are illustrated in Figures 10 and 11 for the two distance categorizations adopted. These locational types are identified by a two-digit number, the first digit referring to rank of attraction class (lowest attraction class = 1), and the second digit indicating rank of distance class (shortest distance class = l). 97 Identifying_Locational Preferences: Case I- 1966 Camper Sample, Equal Mileage Classes The 1966 camper data, consisting of 3,426 camping parties listing Ontario hometowns interviewed at Ontario provincial parks (long form questionnaire) is analyzed initially using equal distance classes in defining locational types.1 The headings adOpted below indicate the major steps in the analysis. Because of space limitations only selected portions of the results have been reproduced. The Problem Of Variability in Sampling Fractions. -- As noted in the previous chapter, because Of the sampling technique employed in the 1966 survey of Ontario provincial park campers, there is considerable variability from park to park in the proportions of park users sampled in this survey. The effect has been over-representation in the sample of parks with low numbers of users, frequently those of lesser attract- iveness (Appendix VII). Obviously, such variability could have a significant effect on locational preferences derived for the sample, perhaps chiefly by indicating that parks of lesser attractiveness were chosen more frequently than they actually were. 1The 1966 Park User Survey data was obtained from the Ontario Department of Lands and Forests in the form of punched cards (one card per interview). A listing of the computer program utilized to perform the revealed preference analysis is included as a part of Appendix VI. This program is a modification of that developed by Kern and Rushton (R. Kern and G. Rushton, "REVPREF: Paired Comparisons Analysis from Revealed Spatial Preference Data" Technical Report No. 95 [Computer Institute for Social Science Research, Michigan State University, 1969, Mimeographed]). Several other programs were developed to compile the data and calculate origin-destination distances but are not listed here. 98 It was thus considered desirable to attempt to eliminate this variability in sampling fraction. The solution adopted was to expand each park sample tO a 100 percent sample by multiplying the original sample by the reciprocal of the sampling fraction for that park. This involves multiplying each origin—destination linkage identified in the sample by the reciprocal of the park's sampling fraction. Such an expansion assumes that the original sample is representative Of the entire p0pu1ation. However, the advantage gained by reducing variability of the sampling fractions appear to justify such an assumption in this C356 . Initial Ranking Of Locational Types. -- Following the assigning of interaction data to the revealed preference data matrix indicating choices between each pair of available locational types, a probability matrix is created representing, for pairs of locational types, probabilities of choosing one over the other. The ranking of locational types by percentage of pairwise comparisons in which they were preferred over other types (i.e., having a probability Of selection of greater than 0.5). is derived from the probability matrix and is shown in Table 19. This ranking is one indication of preference for locational types —- those locational types near the top of the ranks are preferred to most, while those at the bottom largely are by-passed for others. The notable feature of this preference ranking is the sub- stantial correlation between rank on the preference scale and distance rank of locational types. Those locational types with the shortest distances are highly ranked on the preference scale, while those with 99 longer distances achieve progressively lower preference ranks. There is evidence Of little correlation between preference rank and degree of attractiveness Of locational types, however. TABLE 19 LOCATIONAL TYPES RANKED BY PERCENTAGE OF TIMES PREFERRED OVER OTHER TYPES IN PAIRWISE COMPARISONS - CASE I Rank Locational type Rank Locational type Rank Locational type 1 51 14 34 27 36 2 52 15 54 28 18 3 31 16 23 29 26 4 41 17 13 3O 56 5 21 18 24 31 17 6 32 19 55 32 37 7 53 20 44 33 48 8 42 21 35 34 4S 9 33 22 16 35 14 10 11 23 15 36 57 ll 22 24 47 37 27 12 12 25 25 38 46 13 43 26 38 The locational preferences of Ontario campers, then, appear to be closely related to the distance attributes of the locational types, but much less closely related to attractiveness characteristics. Degree of Consistengy of the Data. -- The extent to which the above preference ordering of locational types is shown to be consistent has an important bearing on the further scaling of locational preferences. Without a high degree of consistency, choice probabilities do not permit scaling of preferences on a one-dimensional scale and the construction of the commonly employed preference surface becomes impossible. 100 The test for weak stochastic transitivity of the choice probabilities for Ontario campers results in a coefficient of con- sistency of 0.989 (where a coefficient of 1.0 indicates complete consistency).1 Thus, by this criterion, the aggregated choicesiof Ontario campers among the locational types are quite highly consistent. Table 20 provides a graphic illustration of the extent of this consiStency. Were the choice probabilities fully transitive, the lower left half of the matrix would consist entirely of 1's (indicating probabilities greater or equal to 0.5) and the upper right half would consist of 0's (probabilities less than 0.5). Intransitivities are identified by the discrepancies from this pattern (circled in Table 20). This high degree of consistency of the aggregated choices is important in several respects. For one thing, it suggests that the locational choices Of Ontario campers can be conceptualized as the application of a unidimensional preference ranking of locational types to the set of destination alternatives. In addition, such consistency indicates that while the choice probabilities represent accumulations of choices by many individuals, these aggregated results are to a considerable extent, in harmony with each other (with respect to contributing to a consistent scaling of preferences). 1The test, discussed in Chapter II, measures the proportion of intransitive triplets occurring in the ordered probability matrix (an intransive triplet occurs when, for example, A is preferred to B, and B to C, but C is preferred to A). 101 .o G; .u .u .— oo .o .u so .0 so so so .u .o o— .u .o .o .0 00 0H 00 0d 00 0° 0° 0° 00 0° 00 Cu .0 0U 00 0° 0° 0° 0° 0° 0° 0° .0 CU 0° 0o 00 0° 0° 0° 0° 0U 0U 00 0° DU 00 0° OJ 0° 09 0° 0° 00 0° 0° 0U 00 00 0° 00 0° 0° 0U 0° 0° 00 0° 0° 0° 0° 0° CU 0° 00 Cu .6 .O .6 0° 0° 09 .o .u .u so so .u .o so .u so so .u so .u .u .o .u .o .o .o .u so so cu mu 0! an .~ .~ .~ .~ .~ .~ .— ._ .u .~ .~ .~ .. .~ .a .d .— .— .— .~ .— 6.. .. o. .0 Any .~ .0 .o .— .o .o .o .— .o .o .c .0 .o .o .o .o .o .o .o .o .o .u .o .o .o .c .o .o .o .c .o .o .o .o .o .c .o .o so .o .c .0 .o .o .c .o .o .o oo .o e cm on e— e— cu e— on ed on on en en ea e~ on e— cu ea .— on e— .— ou cu .— eu on on e— en en AMVeu ed e en en e— AU e— e~ eu en 6.. 6 0o 0” .- 00 0° ed so e— en 0" .o .0 0° 0— 00 so so so 0— 0° .0 e0 e0 e0 e0 e. e0 e0 e0 e0 e6 e0 e0 06 so e0 e0 e0 e0 s. so so e0 e0 so so so so so so e0 e0 so 00 0° 0° 0° e0 e0 e0 e0 e0 e0 so e0 e0 so e0 e0 ~n a ”N mma>b 4PH>HFHmz6 >~_>_b_ut¢¢b .— o— .— .— .— .— .— .— .— .— 0 O I I O 0 ~-——-————--—— 0 O 0 O O 0 O O o 0 _~——--—--~-~ 0 so... 000.... Uu—~-—---e—-C—~-_-—~e——e—u———--‘s———-—- OOOOOOOOOOOOOOOOOOOOOOO “U'J--~—~---—-—-~-_———~_—— “\ _ _ ~ _ _ _ — _ _ .— o— o— .— .— 2 c; mm X o. L4 K R . .4. w s v9 5? an 102 Perceived Similarity between Locational Types. -- It is readily seen that considerable information from the revealed preference analysis has not yet been utilized. The pairwise choice probabilities thus far have been used only to the extent of determining whether they are less than, equaltoi, or greater than 0.5. As noted by Rushton, these probabilities may be interpreted as independent measures of perceived dissimilarity between locational types.1 That is, the closer to 0.5 are the probabilities expressing preference for A over B, and for B over A, the greater the revealed similarity between the two locational types is considered to be. Note that it is the similarity between locational types as revealed by pairwise choices that is being considered here. It should be apparent that this measure of degree Of similarity between pairs of locational types is directly related to the degree of dissimilarity of choices between the locational types. For example, if the choice probabilities for locational type A over B and B over A are both 0.5, similarity is indicated between these two locational types. However probabilities of 0.5 also indicate that disagreement occurred among individuals choosing between the two types, with half choosing A over B and the other half choosing B over A. This topic of agreement among choosers is discussed later. By representing choice probabilities in terms of absolute difference from 0.5, measures of locational type dissimilarity are obtained in which 0.0 indicates completely similar types (proximity 1Rushton, "The Scaling of Locational Preferences." 103 matrix). Such measures constitute the input for the multidimensional scaling technique discussed earlier. Interval Scalingof Locational Types. -- Figure 13 indicates the computed scale positions on the first dimension for the 38 locational types for which choice data were available. The stress value for this first dimension is 0.295.1 The highest negative value represents the most preferred locational type while the highest positive value on the scale represents the least preferred type. Several features of this preference scale (Figure 13) are readily apparent. With minor exceptions, the ranking of locational types in this scale is similar to the initial preference ranking discussed previously -- i.e., high correlation between preference rank and distance class -— with the lowest distance locational types being most preferred. Those pairs of locational types most closely situated together on the scale have the same distance attributes, or at most, differ by only one distance category. This provides further evidence of the importance of distance attributes in influencing preferences for location. Considering the entire scale, the greatest clustering of locational types occurs in the middle of the scale and involves types with intermediate attractiveness and distance characteristics. The suggestion is that preferences differ little among these intermediate 1The stress value indicates only a fair correspondence between the dissimilarity values and the derived scale values. However stress values for the two and three—dimensional scalings were not deemed sufficiently lower to justify the adoption of multidimension scale in this situation. 104 .AH ommuv ooafi .muomemo Mama HmflOCM>Oum Ownmuco "camom oocohomonm HmcofimCOvaficsuu.mH ousmfim Ashomeuno oocmumwp ecu meueoflpcw mafia ecu mo usage: can .omxu HmcofiumOOH esp mowmwucopw mafia ecu o>onm Honsscv owmxumumm Pmopm Owhmuco ”camom OOCOHOMOHQ chowmcoswvwcaul.nfi Opnwfim ommmwmwma Hmme Axuomoumo ooceumwv can moumOMOCM mafia DAV ecu mo ucmfioc use .Omxu Hmcoflumoofi ecu moflmfiucocw mafia on» o>onm Homescv ommcuuwmm Ema! 0;: owl 9E .2 91 £3 £9 0’ l£_l 9|_ fl— 9|— 9* 3 99 Zl-- 99—— ,ZEI zz—-l - m lZ-I itc- £9 39—- '9 113 (gether destinations which appear similar to the choosers. ~Again as in Case I, differentiation among types is less pronounced in the center of the preference scale than at the extremes of greatest or least preference. The locational preference surface has a somewhat different configuration than that of Case I (Figure 18). Similarities are evident run though in the preference lines representing the portion of the surface including distances up to 300 miles or so. As in Case I, the preference lines here are predominantly diagonal and parallel to each other, indicating existence of substitutions between distance and attractiveness. For the longer distance portions of the surface, there is some tendency toward a reverse preference for site attractiveness (i.e. locational types with higher attractiveness classes are less preferred to those at similar distances with lower attractiveness). This trend, however, is not well-defined. An attempt was made to fit a surface to the preference scores for Case II employing distance and attractiveness variables in a multiple regression analysis. The following regression equation was obtained, accounting for 80.32 percent of the variation in the preference scores (R2 of .8032): y=0.0035x1 - 0.0007x2 — 0.7427 (y represents the preference variable x1 represents the distance variable x2 represents the attractiveness variable) Thus much of the variation in preferences for destinations is accounted for by variation in distance and attractiveness of the destinations. 114 1600 , -I.e -l.O -o.e 0.0 0.6 1.0 1.5 s 8 fl - '2' T 190 a V - s s' 2. g 90 I ' H g 3 E7 \\ ‘3 .- _: \ e- | Q 5 so :- .\ z 3 a e < r - _ §/‘i' \ l2 ' s 3 3. I. a .- c . 0 40 160 270 390 700 LS Distance (miles) Figure 18.-- Locational preference surface: Ontario provincial park campers, 1966 (Case 11). -l.O -O.5 0.0 0.6 IBOO V I 1” .1 A///// J/llllirLo .1 ISO, /r / / 8‘ LD 20 g 90 s 1 1 1 / / s so i a I O O 40 l60 270 390 700 Distance (miles) Figure 19.-- Locational preference surface fitted to Case 11 preference scores by multiple regression analysis. 115 As in the Case I situation, virtually all of the "explanation" of preference variation is achieved by the distance variable (75.58 percent out of the total of 80.32 percent). Figure 19 portrays the preference surface derived from the above regression equation. The configuration of the preference lines resembles that of CaSe I, apart from a somewhat more pronounced trend here toward distance-attractiveness tradeoffs. Identifying Locational Preferences: Case III - 1968 Camper Survey, Distance Classes with Equal Sample Proportions The results of a 1968 survey of Ontario provincial park campers were also analyzed to determine locational preference characteristics. It was felt that a comparison between the 1966 and 1968 situations with respect to locational preferences would be of considerable interest because it might indicate something about the stability of preference structures over time. It has been asserted that preference structures have greater stability than the spatial system within which such preferences have been observed.1 The possession of information on locational choice of campers for both 1966 and 1968 allows limited examination of such as assertion. Also, the 1968 survey involved a 100 percent sample of campers regarding origins and destinations and hence provides the opportunity to compare 1 . Rushton, "Analysis of Spatial Behavior," p. 400. G. Rushton, "Temporal Changes in SpaceuPreference Structures," Proceedings, Associatign 9f American Geoggaphers, (1969), pp. 129-132. 116 locational preferences obtained from a sample (1966) with those of the 1 entire p0pu1ation (1968). Comparison of Preferences, 1966 and 1968 Campers.-«The definition of locational types for the analysis of the 1968 data is similar to that used in Case 11, so comparisons are made chiefly between Cases II and III. Eh— The ranking of locational types by percentage of times they are preferred over other types is shown in Table 21. The similarities between the Case I and II rankings are striking. It is apparent that there is very little difference between 1966 and 1968 data in the a . prOportion of times that particular locational types were preferred over other types. The above preference ranking of 1968 data attained a coefficient of consistency of 0.991, virtually identical to that of the Case 11 analysis. It is interesting that the difference in size of the population included in the analysis (771,306 individuals for Case III versus the sample of 3,426 individuals serving as a base for Case II) has no apparent influence on degree of consistency. This result supports the assertion that meaningful conclusions can be drawn about collective preferences through the aggregation of data on individual choices. It also suggests that little information is lost There are two potential sources of variation between the preference structures derived from the 1966 and 1968 data sets--sampling variability and changes in preference over time. Thus it would appear that only if preferences are found to be similar can conclusions be drawn about stability of preferences and utility of sampling (since any variation in preferences could not be apportioned between the two potential sources). 117 TABLE 21 LOCATIONAL TYPES RANKED BY PERCENTAGE OF TIMES PREFERRED OVER OTHER TYPES - CASE III Rank Locational type Rank Locational type Rank Locational type 1 31 14 35 27 15 ,__ 2 51 15 43 28 25 h 3 52 16 . 44 29 37 i 4 11 17 46 30 36 ‘ 5 41 18 13 31 16 6 54 19 12 32 58 7 53 20 24 33 17 8 21 21 45 34 38 9 32 22 14 35 _ 26 10 42 23 22 36 27 11 55 24 56 37 48 12 34 25 23 38 57 13 33 26 47 39 28 40 18 in sampling locational choices of a pOpulation, desPite the large number of origin-destination combinations contained in the initial data. Interval scaling of locational types along one dimension for the Class III data is shown in Figure 20. The stress measure for this derived scale is 0.269, somewhat higher than the figure for the Class 11 scale. With minor exceptions, the ranking of locational types here coincides with the initial preference ranking. Also a comparison of the 1968 and 1966 (Case II) rankings indicates considerable agreement between the two preference rankings. Thereare definite similarities between the Case 11 and III interval scales. There is a tendency in the 1968 scale toward a progression from highly preferred types with high site attractiveness to least preferred types with low site attractiveness, a trend also noted in ....H ommuv mom. .mpoaemo Jena .mflocfi>opm Ofinmuco “OHmom oocopowonm .mcoflmcoefipflcsun.om onnmwm fixhowoumo commumwv ecu moumowvcw on“. ecu mo ucmfio: can .Omxu .mcofiumoo. esp moflmfiuceuw on“. can o>onm access. 8 H owmmmummm ...m m ens» mm:.m:Ohm sopcmm m .m> m oa5u meocouomm.0 pceo.m.=m.m mo cowunomoua .m:o.ueoo. Emooaenommwp uceo.w.:m.m mo no.0uomona .aco.ueOO. manomo zcaz<¢ az< m oz< m mm=omum=w "1:000 mmuzmmmmmmo muzmmmmmmm HZH .< .26 .29 .25 .14 .33 .12 .16 .29 a so ____ +1 12 +3 +1 +5 +0 11 111 2: _' .20 : .26 .25 .22 .15 .07 .03 .03 :3 30 3%, 31 3g¥ 3+ 35 so 5! 38 E i g .11 ‘ .26 .25 .24 .17 .06 -- -- .1: 12 21 22 23 2+ 25 2.6 2.7 as «4 1 .17 .20 .57 .60 .17 .42 .03 .12 o L 11 12 13 I 1 to IT to 75 15o zoo oso' ooo nnles DISTANCE Fig. 27.--Groups C and G - Proportion of pairwise comparisons of locational types where significant differences in preference are observed. Subgroups D and H (Camping Experience). -- The final com- parison on the basis of camping experience involves campers from occupations other than professional-managerial staying three or more nights at the park destination. Sizes of the two groups analyzed were 372 for D (the inexperienced group) and 896 for H (the experienced group). As in the previous case, significant difference proportions (Figure 28) are generally not large. The overall percentage of significant differences for the matrix is 19.9. A comparison involving randomonly-composed groups yielded significant difference prOportions which equalled or exceeded the above proportions in most cases. It appears then, that no major differences in locational preferences occur between these two subgroups. 144 1600 ’ .oo .15 .24 I .26 .05 4- .11 -- ‘go 11 52 53 5“! ‘6 ‘0 5‘! ‘11 .00 .21 .29 .29 .52 .13 .03 -- X 5 6 L5 90 +1 +2 N 1'1 5' 1- 41 “1L 2 _- .10 1 .13 .18 .26 .38 .19 .25 .11 25 30 3H. 3; éike 3+ 35 so 5! so = z ‘a’ .06 .10 .12 .48 .10 .35 .06 -- E ,2 2.1 2 13 2+ as 2.6 2.1 as p.— < 1 1 .12 .38 .19 .14 .22 .54 .13 -- o L_i 11 12 13 I 1 lo 11 13 7s 15o aoo oso' , ooo nnles DIST71N13E Fig. 28.--Groups D and H - Proportion of pairwise comparisons of locational types where significant differences in preference are observed. Subgroups A and B (Length of Stay). -- Characteristics common to these two groups include 0-2 years' camping experience and pro- fessional-managerial occupation types. The groups are differentiated by length of stay, with Group A staying 1-2 nights and Group B staying three or more nights.1 Significant difference proportions derived for the comparison are substantial for a number of locational types (Figure 29). There is a tendency for the larger proportions to be associated with the lower distance categories, suggesting that preference differences are strongest with respect to these locational types. The overall percentage of sig- nificant differences for the matrix of locational types is 30.8. 1Groups sizes for the analysis were 212 and 168 for A and B respectively. 145 1ooo .40 .38 .37 .07 -- -- -- -- 190 5‘ 52 51L. 5* ‘6 s. :1 5 x .33 .47 .48 .52 .20 -- -- .05 1:13.: 90 +1 42 N +1 +5 1-6 z “1111 Z “ .43 .32 .35 .25 .39 .35 .57 .04 g; 30 3' 4.1 3 3+ 35 so 3: 53 z: 2 .25 .10 .41 .27 .05 .oo -- -- E «'2 2.1 23 21* 25 26 2.7 28 2 .37 .42 .26 .17 .10 .29 .54 .30 o 11 12 c_j§L If 1%. lo 1? 18 75 150 aoo 450' 000 "files DISTANCE Fig. 29.--Groups A and B - Proportion of pairwise comparisons of locational types where significant differences in preference are observed. ‘Table 27 compares the above proportions of significant differences with those derived for two pairs of randomly-composed sub- groups. Although the evidence is not conclusive (as noted earlier), it appears that the A versus B difference proportions for some locational types are greater than might be expected by chance. Most of these locational types are associated with shorter distance categories.1 Further information on preference differences between Groups A and B is provided in Figure 30. There appears to be a tendency for A to exhibit greater preferences than B for locations in the lower attraction categories and lower preferences than B for the higher attraction categories. A possible explanation for such differences 1These locational types are identified by asterisks in Table 27. 146 oocmco 50 wouoomxo zany H0090. on on smegma :o.:3 mco.uuomoam omocu moumo.0:. xm.uoum < 095» 00:.msouw aoucwm 0 .m> < max» mooconomm.0 u:mo.m.=0.m mo :o.uuomoum .mco.umoo. moocouomm.0 u:mu.m.:0.m mo no.unoaou0 .m:o.umoo. [I ll‘ mmboao zoaz9 4< 1.00 .79 .47 .00 .00 - - .00 g u * ALT +1 +6 «1 a s; a: ; .75 1.00 .45 .25 1.00 1.00 .00 .00 2 3o 3‘ J 3? 43. p. is .00 .67 .08 1.00 1.00 - - — u 2 2. 2. 1 28 E ii .00 .00 .75 .40 .67 .00 .00 .00 o 11 131 1 111 11 If. 1? is 75 m on 450 «0 miles DISTANCE Figure 30. -- Groups A and B - Proportion of the number of pairwise comparisons with significant differences, where A reveals lower preference than B. "If .81 1.00 - - - - ‘.. 1 ‘ 3‘ ‘6 __.1_—n ,‘ .87 1.00 1.00 - - 1.00 g .. { +1 +5 +6 1? 11 a: ;; .83 1.00 .81 .50 .50 .00 1.00 1.00 53.1. ....11____si ____££____11____2fl____1i .— 3; .43 .67 .92 .38 1.00 - - - t: 12 ...—J! 2 ____££____3L____21____££ ‘ . .82 .92 .88 .80 .33 1.00 1.00 1.00 . I1 1 1 J 12L 15. 17 is 15 on too «so ooo miles DISTANCE Figure 31. -7 Groups A and B - Proportion of the number of pairwise comparisons with Significant differences, where A reveals greater indifference than B. 148 is that short-stay campers (A) attach less importance to attractiveness of destination than longer-stay campers (B), and hence exhibit less variation in preference among attractiveness categories.1 Figure 31 tends to support the above observation on preference differences. For the large majority of locational types, Group A shows greater disagreement than Group B, particularly in the three highest attraction cateogories. Again it is suggested that longer-stay campers exhibit more agreement in their preferences than short-stay campers particularly with respect to the more highly attractive destinations. The short-stay campers show greater disagreement, perhaps because they do not differentiate among types of location to the extent of the longer-stay campers, or perhaps because their locational decisions are based on a variety of criteria (for example, the weekend camper versus the stopover camper). The major hypothesis advanced earlier is thus confirmed by the analysis, i.e. longer-stay campers do appear to prefer more attractive destinations over less attractive ones more consistently than short-stay campers. Subgroups C and D (Length of Stay). -- These two groups include campers with 0-2 years' camping experience, from occupations other than professional or managerial types. They are differentiated on the basis of length of stay.2 1Unlike this relation with attraction classes, there appears to be little noticeable relationship between distance categories and direction of preference differences. 2Group C had 381 camping parties while Group D had 372. 149 As in the previous comparison, sizeable proportions of sig- nificant differences are apparent for many locational types (Figure 32). For all pairwise comparisons of available locational types, the per- centage of significant preference differences between the two groups is 40.8. The comparison of these significant difference proportions with those from randomly-composed subgroups is presented in Table 28. The results suggest that many of the proportions for the C versus D comparison are larger than those which might have arisen through chance. These significant proportions (identified by asterisks) are well-distributed through the matrix of locational types, with a slight tendency toward concentration in the shorter distance categories. Figure 33 indicates the proportion of significant differences in preference in which C's preferences are lower than D's. In the lowest attraction category and the longer distance categories, Group C generally has higher preferences than D, which in the higher attraction categories and lower distance categories, Group C's preferences are chiefly lower than D's preferences. Similar to the preceding comparison, short-stay campers appear to have greater preference for destinations of lower attractiveness and lesser preference for the more highly attractive destinations than the longer-stay campers. In addition, short-stay campers seem to have greater preference for the more distant destinations. This situation may be the result of st0pover camping by short-stay campers. From the data presented in Figure 34, it appears that, on the whole, Group C members disagree more regarding locational preference than do Group D campers. This observation follows that made concerning 1600 .41 .69 .46 .72 .47 .00 .33 -- ‘90 51 52 53+_ 5‘11 ‘6 $1. 5? A“ x .39 .41 .29 .35 .23 .18 .31 -- 31 90 +1 jzl 1o 11 15 1° 11 ---fl 2 . - .32 ‘ .45 .43 .45 .66 .88 .33 .32 g 30 31% 51 415 31 35 so 3! .53 1:: , 2 .30 .39 .50 .33 .22 .38 -- -- SE ,2 21 2 23 2+ 25 26 27 28 ’3: . .47 .52 .51 .52 .08 .27 .67 .41 o L__. I 12 13 I1» Is Io It 18 75 150 300 450' 800 nhles 150 DISTANCE Fig. 32.--Groups C and D - Proportion of pairwise comparisons of locational types where significant differences in preference are observed. the previous comparison, providing further evidence that short-stay campers do not differentiate among locational types to the same extent as longer-stay campers. This comparison of subgroup preferences thus draws much the same conclusions as the previous comparison about the relationship between length of stay and locational preferences. The two additional comparisons possible involving length of stay variation have not been It would be of interest to investigate these undertaken in this study. to ascertain whether similar conclusions are reached. Subgroups A and C (Occupation). -- The final comparison of subgroups undertaken here involves camping parties with little experience (0—2 years)-and staying only 1-2 nights at their destination. This group is divided on the basis of occupation, professional-managerial 000050 50 wouooaxo cmcu woman. on ou Hammad £0.03 0:0.pu00090 omonu moumo.0c. xm.noum u odxu m0=.a:oam Eovcua 0 .m> o 095» moocohomm.0 ucmu.m.:0.m mo co.paonoum .mco.uaoo. neocouomm.0 acmo.m.:0.m mo co.puomohm .mco.meO0 mmbomo ZoozH q< .36 .52 .15 .12 .28 .08 .52 .21 u: 90 +1 12 16 +1 +5 16 +1 18 C3 :2 - .51 ; .30 .24 .26 .32 .54 .29 .14 g 30 311 3 an .11 §5 ,16 3t .53 1: f “<9 .26 ' .24 .48 .09 .22 .03 -- -- E «‘2 21 22 13 if 25 26 2.? £8 14 .30 .33 .38 .37 .24 .03 .13 .23 o L_i 11 I2 13 I1 I 16 It 18 75 150 soo 450’ ooo nHIes DISTANCE Fig. 35.--Groups A and C - Proportion of pairwise comparisons of locational types where significant differences in preference are observed. 0f the hypotheses advanced earlier concerning the nature of preference differences with respect to the three variables, only those relating to length of stay largely were substantiated. It was found that the longer-stay camping parties did tend to prefer the more attractive destination types to a greater degree than the short-stay parties. The suggestion that no clear relationship would exist between distance to destination and existence of preference differences between the short-stay and longer-stay groups were also supported. With respect to degree of camping experience, only in the case of professional- managerial occupations staying three or more nights is the hypothesis supported that the inexperience group will show less rationality in preference than the experienced group. The little evidence available for the occupation variable_does not substantiate the hypotheses advanced earlier. 155 There are several considerations which restrict the conclusions which can be drawn from these comparisons of subgroup locational preferences. For one thing, a number of rather arbitrary decisions were made during the analysis which may have influenced the results to some degree. For example, different critical values separating individuals into groups for comparison purposes might have been selected. Also, the comparison might have been restricted to individuals with extreme values for certain of the variables (e.g. extent of camping experience). Altering the method of indicating significant differences in preferences or the critical values chosen to separate significant from non-significant results might also have had an impact on the results obtained. Ewing in his analysis found that grouping of individuals on the basis of common spatial behavior and then linking these groups to socio-economic attributes was a more powerful method of identifying preference differences.1 This would appear to be a useful additional approach to apply to the camper data.2 Finally, it would have been desirable to carry out all twelve of the possible comparisons of subgroups. This would have allowed more extensive conclusions to be drawn, particularly regarding the occupations variable. leing, "An Analysis of Consumer Space Preferences." 2It would seem essential that the spatial behavior attributes chosen be distinct from the data used to define locational preferences. Otherwise one would seem to be saying only that grouping by preference differences is associated with significant differences in preference. CHAPTER VI CONCLUSIONS This study has had as its purpose the outlining and application of a model for revealing locational preferences of a population frequenting recreation destinations -- in this case, campers in Ontario provincial parks. The first part of this modelling effort involved the derivation of preference structures representative of the entire camper population under examination, while the second part investigated the extent to which subgroups within the camper population possessed differing preference structures. This concluding section is concerned with two questions —- firstly, "Of what use has the analysis been in revealing the locational preferences of Ontario campers?" and secondly, "Of what potential use might the approach be in the analysis and prediction of choices of individuals among recreation destination alternatives?" Locational Preferences of Ontario Campers The analysis has revealed that a considerable degree of order is discernible in the preferences of Ontario campers for various provincial park destinations. Despite the fact that it was necessary to generalize park destinations into "locational types" based on somewhat arbitrary distance and site-attractiveness criteria, it was possible to derive a preference ordering of such locational types with which the choices of Ontario campers are quite highly consistent. The implications of such a finding are significant since it suggests that, 156 157 while choice situations and choices obviously differ among members of this group, there is some degree of similarity in the preferences under- lying the choices made. The preference scales obtained for Ontario campers also appear to have some relationship to the criteria used to define locational typos -—particularly the distance-from-origin criterion. There is a definite tendency for the more preferred locational types to involve shorter distances than less preferred types. Again, this finding is important, suggesting that preferences for location have definite associations with distance of the destination, while having somewhat weaker ties with the measure of site attractiveness employed. The modelling through regression analysis of the derived preference scales in terms of distance and attractiveness attributes of destinations provided definite evidence of the weak relationship of the attractiveness variable to preference ratings and the relatively strong relationship of distance to preferences. This result could signify that little importance is attached to variation in site attractiveness-- i.e., that park destinations are perceived as more or less uniformly attractive. More plausibly, perhaps, the result could indicate that the measure of site attractiveness employed, does not adequately measure "attraction" of park destinations relative to the individuals engaged in choosing among the destinations. Despite the fact that site attractiveness as defined in this study appeared to be less significant than distance-from-origin in influencing preferences, there is evidence of "trade-offs" made by campers between distance and site attractiveness--largely in the case of 158 alternatives 300 miles or less from origin centers. That is, campers show some willingness to substitute lower site attractiveness for a decrease in distance or higher attractiveness for an increase in distance (or vice-verse). Thus some measure of support is provided for the view that campers base preferences on both site and situation characteristics. The comparison between the preference structures of 1966 and 1968 Ontario campers, while identifying certain differences-~for example, the fact that 1968 preferences are less strongly related to distance and attractiveness attributes--suggests that in general the structures are similar. This result thus provides a measure of support for the assertion that preferences have considerable stability over time. Limited evidence was presented indicating that Ontario campers exhibit greater agreement in their preferences for shorter-distance locational types than for longer-distance types. One implication here is that campers have greater and more uniform knowledge of closer des- tinations and hence show more agreement in choices of these types. The analysis of preference differences among a number of subgroupings of the Ontario camper sample indicated that in the majority of cases, significant differences in locational preferences could not be linked to differences in the camper characteristics under examination. That is, while certain preference differences were identified, these were no greater fer the subgroups of interest than for other randomly- composed groups. Only in the case of variation in length of stay did subgroup differences appear to be greater than expected. These conclusions suggest that other variables should be examined for significance, perhaps, as suggested earlier, those tied to spatial 159 behavior. In conclusion then, it is evident that a substantial amount of information about camper locational preferences has been revealed by the analysis, thus demonstrating the usefulness of this approach. Future Research Possibilities The following is concerned with a few of the possibilities for future application of the revealed preference model in recreation research. Prediction of Spatial Movement The gravity and systems models discussed earlier are both concerned with the prediction of Spatial flows of people between origins and destinations. The utility of such models has been evaluated largely by examining the degree of accuracy of their predictions. While a concern with prediction has not been evident in the dissertation, this aspect does appear to offer promise for future research. The following demonstrates some of the possibilities for using the locational preference model of this study in a predictive capacity. The rationale behind the use of the preference model for predicting spatial interaction lies in the hypothesis that locational preferences are relatively stable over time, unlike spatial behavior 1 which may change frequently. As noted above, this dissertation has 1 Rushton, "The Scaling of Locational Preferences," and Rushton, "Behavioral Correlates of Urban Spatial Structure." 160 provided limited evidence supporting such a hypothesis (Chapter IV). This hypothesized stability of preferences then provides a basis for predicting future interactions. Method of Prediction.——Using the pairwise preference ‘w— probabilities obtained from choices between locational types, it is possible to derive the expected flow pattern from origins to destinations, provided the total numbers from each origin are known or can be estimated.1 Given that locational types A, B, and C are available for choice, the probability of A being selected from these three is defined by the following: 2 P(A) = P LA) - = 1 p(A)+p(B)+p(C) 1+ 2(3) + (C) P(A) p(A) An estimate of p(B)/p(A) can be derived from the pairwise preference probabilities (i.e. p(B chosen over A)/p(A chosen over B). A similar estimate for p(C)/p(A) can be obtained using the pairwise probabilities for A and C. Similarly, to derive the probability of B being chosen from the three locational types, the following is used: p(B) p(B) _ P(B) = p(A) if? p(B) p(C) p(A)+p(B)+p(C) 1+p(Aj+ P(A) 1The method applied here is after deTemple (D. deTemple, "A Space Preference Approach to the Determination of Individual Contact Fields in the Spatial Diffusion of Harvestore Systems in N.B. Iowa" (unpublished Ph.D. dissertation, Dept. of Geography, Michigan State University), pp. 32-35). 2Where P(A) is the probability of A being chosen from the three locational types, and p(A) is the probability of A being chosen from all available locational types. ‘ 161 The method may be expanded to include more than three available locational types simply by adding pairwise probabilities representing the additional locational types to the denominator. It is apparent that the choice probabilities derived for the available locational types will sum to 1.0. Thus, for a given originlocation, available locational types can be ascertained, their choice probabilities derived, and these are then multiplied by the total number of campers estimated for that origin to obtain the predicted number of campers for each locational type. Application to Hamilton Campers.--The technique discussed above has been applied to the system of provincial park alternatives available to Hamilton campers. The objective is to predict flows of Hamilton campers to each of the locational types available from this origin. In this instance data are available whereby these predicted flows may be compared with actual patronage of locational types. In fact, the application employs the preference structure of the 1966 sample of Ontario campers (Case I) to predict locational choices of Hamilton campers in 1968 (which can be checked against known patronage in 1968). With reference to Ontario provincial parks, 26 locational types are available to Hamilton campers. The choice probabilities derived for each of these locational types by the method outlined above are indicated in Figure 36. These probabilities were muliplied by the total number of Hamilton campers in 1968 (38,382) to obtain the initial predictions for patronage of locational types (Column 3 of Table 29). 1 Locational types are those employed in Case I. 162 1600 100 ‘ 200%1° 115252 '047151 1; 56 s1. 5'; j >< .0734 .0275 .0348 .0166 .0176 .0288 1.1.1 90 __ +1 +2 +3 + +5 16 +1 +8 D 2: " :.0451 .0578 .0125 .0096 .0317 .0105 :5 so 3%. l __3 35 Ass 3! 38 5 3 <1 10317' .0096 .0248 .0070 .0096 .0166 E ‘2 )J 23 2f 25 26 2.? 28 ’0' ,0706 .0317 .0134 .0078 .0115 o L 11 12 13 11 15 I6 I! I8 75 15o zoo 450' 600 nnles DISTd\NI3E Fig. 36.-~Choice probabilities for Hamilton campers. It is obvious that in many cases, the initial prediction differs considerably from the actual attendance recorded for that locational type. Column 4 of Table 29 indicates error in prediction as a percentage of the recorded attendance. It was hypothesized that a major cause of these errors is the fact that the locational types in— clude varying numbers and sizes of park alternatives.1 Thus two adjustments were made, the first to compensate for varying numbers of parks (Columns 5 and 6, Table 29), and the second to allow for variation in park size, in terms of total numbers of users (Columns 7 and 8, Table 2 29). Number of parks, for example, varies between one and six. 2 These adjustments consisted of multiplying the initial prediction by the result of dividing the relevant park number or size figure for that locational type by the average number or size figure for all locational types. 163 00 0.- 000 00 000 00. 500 050 00 0- 50 5.0 .0- 000 55 00... 000 50 .. .0- 00 00 00. 000 000 05 50 0 .0- 000 00- .00 5- 050 005 00 0. 0.- 500 .0. 5.0.. .0. 5.0.. 000 00 00 00- 00 00. 00. 000 000 50 00 00 00- 00. 5.- .00 5.- .00 000 0. 0- .51 50 00- 00. 00. 000 .0. 00 5. 00- 0. .0 00 050 000 50 00 00- 0.- 000 0. .00 05 500.. 000 00 5.1 00- 00. 00- 0.0 00. 500 5.0 00 00 001 00 00 00. 500 000 00. 00 05 50- 00. 5.- 5.0 .0. 000 000 00 00 00- 00 0.. 00. 000 000 00 0. 5- 0- 000.0 05- 0.0.0 05- 000.. 005.0 00 50- 00- 0.0 0. .00 50 000.. 005 00 0. 0 000.0 0.- 500.0 00- 0.0.0 500.0 00 .0 00- 00. 00- 000 00- 000 .000 00 00 05- 00. 00- 000 50- 0.0 .00 0. 5.- .00 000.0. 00 050.5 00- 000.0 50..0 00 0. 00- 0.0.0 00- 0...0 00- 000.. 000.0 00 00 00- .05.0 00- 500.0 00- .05.. 0.0.0 00 00.1 .0 000.. 05 000.0 000 ..5.5 0.0.. .0 0 ..- 050.0 00- 050.. 5- 5.0.0 000.0 .0 50 05- 0.. 0.1 000 00. 5.0.. .00 .0 00 00. 000.. .0. 500.. 000 0.5.0 .00 .. .HOHHO 00 HOHHO 00 mucwvcmuum .HOHHQ 00 0050900990 H0900 00 00cmvcmuum mwomav 000.00.0090 0000500 mo 0x900 mo 0000020000 0050 .0...m .o: How 000500300< .00 How u:oEumsnw< 00.00.0000 .0...:. .m:uo< .mco.umoo. .000.0 0000200 0.00020 00 000000000 0020000000 2000 .000.0 0000200 2000.20: 00 000.000 0020.00000 00 20.00.0000 0N mqm .0w00050000 H0000080500z mo x0000cm: :.000H00000n0 0>0000nn=m cam 000H00= .00000000000: .000000 .0 000 0004 .0.mv 000000 000 0000 n000<0 00008 000 wcaxcmn no 000050 0H0800 nmnufio 00 :00 005008 Amxmanv 0800000 050 nm>o 00.000.00000 000.0000000 0 0Hco 000800000 0000000n 000 8000000000n0 00008000.I mmmao0wmn wcfidnm>ow 00000H0nmnon0 0800 nw>o «mango n00 mmuamaoaam 0000 0>onm 00 maamo mammv 00800N0 wcaxcmn no 000050 0H0800 00:000 00 000 00:008 I Ammmaxmfinv 00000000 000 000000000000 msasafium 00 vmcwanmumv 0800000 I 000:0000n wcficnm>om 00000H0000000 co 00000000000 00 I 00 000000n000n o: I oHHmHAHm 000050 0008000 Awawxcmn no 00800000 00 w003000 no 0000L0 000800 00 000 00:008 I 00800000 wco8m 000000000 Ahxmfinv 00800000 000 nm>o 000000 00 000 005008 I 800050000000 0ufiawamnon0 Ammmaxmfinv 0000000n 0 haao 000800000 00:0000n 000 000000000000 00H98000 000 000000000000 00H=8000 I 00 00:08n0000 0800000 I A no .x .o mnm 00000000n A no .x .o mnm 00000000n A0800 n0>o wwamzo wcaanm>ow 00000H0000000 I w800n0>ow 00000H00000n0 I Aoamnnmwaon0 onv UHHmHszmmamo 000000 0000000 200000020 0000.00.00 2000000 0800000 no 0009 00000000 00 0009 mmmHmommH ZOHmHumo mo onHm momaonowcmao on mu. ¢.~m gamma mmauhuc mumuaaum om ¢.nm mvmaucqa ma Aommm mm H.@ Ho>aum can vcmm mu nomom bu w.Hw ccmm ma nommm cm ,1] h.o~ .um oooq um>o gummafi gamma n~ ~.qm .um ooo¢-ooo~ aumcmfi gamma «N o.~n .uw coo“ - H“: sumaufi pagan mN h.m o>onm mo coaumcfineoo ou 05v acowumuwaaa auw>auom yuan: «N o.¢ abuuon uooa ou 05v muowumufiawa huw>wuom Houmz aw . w.o «Monmouw macaw ou mac «cowumquJH huw>uuum Houmz on n.» unflfimsa umums Room ou mav macaumuflaafi >ua>auom noun: ma H.5a mcowuofiuuumu mcweaazm _ no waaumon ou 09v mcowumufiaaa hua>uuom Roam: ma h.m mm>w3 no mucmuuso ou 05v mcouumu«e«a huu>auom noun: NH ¢.~ avoms ou msv mcowuauwaafl huw>wuum “wan: 0H h.o~ um>au a co coaumuoa mH‘L ,om o6.” mmuom coon uo>o 0x3 95.— m :0 cowumooq 3 1. m.wH mmuuw ooomuoooH wxma wand a co sowumooq ma o.¢H mmuuw oooauoo~ «Jag vcua a co cowumoog NH p.¢m uxma umouw a co aowuwooq HH N¢. 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Individuals may not be able to choose among all exisiting alternatives simply because these locations have limits as to the number of persons who can be accomodated. Consequently, preferences may be obscured in the analysis. Methods of dealing with this problem are discussed briefly below. Degree of Confidence in Revealed Preference Results While there appears to be no method of determining to what extent capacities of parks have obscured true locational preferences, it does appear possible to use extent to which capacities are filled as one measure of confidence in the validity of the revealed preferences. That is, the closer capacities of parks are to being completely filled, the greater the possibility that locational preferences are being obscured by capacity limits. Consider a hypothetical example. A population of 1000 camping parties from one origin center can choose among five locational alternatives. Type A - capacity of 400 camping parties Type B - capacity of 100 camping parties Type C - capacity of 300 camping parties Type D - capacity of 700 camping parties Type E - capacity of 300 camping parties Assume that the true preferences of this population are: most pref. least pref. B____sE____,A_____sc ;-D no. of campsites 350 225 200 150 75 desired 171 172 Assuming that if the most preferred type is not open to a party the next most preferred type will be selected, the following situation prevails: 350 want B but only 100 can choose it, therefore 250 will choose E. 225 want E but only 50 can choose it, therefore 175 will choose A. 200 want A and choose it. 150 want C and choose it. 75 want D and choose it. Therefore, preferences change to the following: A—flE ——>C———+B——.’D 375 300 150 100 75 These are the "revealed" preferences. Therefore, probabilities of a camping party visiting these locations according to apparent (revealed) versus true preferences are: Locational Apparent True type (revealed) A .375 (most pref.) .200 E .300 .225 C .150 .150 B .100 .350 D .075 (least pref.) .075 The goal is to be able to predict, when true preferences are unknown, where discrepancies between apparent and true probabilities will be the greatest. Locational Discrepancy between Percentage of capacity type apparent and true probabilities filled B .250 100 A .175 94 E .075 100 C 0 50 D 0 11 These discrepancies occur either where capacity restrictions lead to under-estimations of true preferences (B), or where overflow from a higher preference location leads to over-estimation of true preferences (A and B). As seen in the above table, knowledge of 173 percentage of capacity filled enables prediction of where discrepancies might be expected but notithe extent of these differences nor their direction (over- versus under-estimation of true preferences for a locational type). Since the true preference ordering is not known, the locational types to which overflow might be diverted cannot be ascertained. Although in this case A and B were identified as types where discrepancies might be found, many situations can be envisaged where overflows would not lead to high percentages of capacity filled. Therefore, assuming only the revealed preferences of the individuals in the above example are known, these would be expressed as A-—--—-+E -—->C —-——?B -—>D but indicating that confidence in preferences for B, A, and E is not high because of the extent to which their capacities are filled. The example treated above is a simple situation where campers are from one origin center and choose among five parks having different characteristics. Complications arise where campers are from.more than one origin center and choose among parks which may have considerable similarity (reflected by their grouping into locational types). In this case, one locational type may include one (or several) park(s) for campers from one origin center, but a different park(s) for campers from another origin center. Thus assigning a particular figure for extent to which capacity is filled would be a difficult task. Averaging of these percentage figures within each locational type with perhaps some weighting on basis of patronage would appear to be one feasible solution. An‘Alternative‘Approach The above approach to the capacity problem recognizes that at times, because of capacity limitations, campers cannot choose the location 174 they prefer. A second approach might be to view capacity limitations as part of the group of park characteristics considered by campers in formulating their preferences. Thus the assumption is made that to all potential visitors to a park, the risk that capacity might be filled constitutes a detrimental feature of that park. The degree of risk is reflected in the percentage of total capacity which is utilized. The evaluation of the importance of capacity limitations as a detrimental characteristic is a difficult matter. Obviously to campers who have been turned away from filled parks, this characteristic is the one dominating their behavior. Others, however, may simply rate a park as less attractive because of the possibility they may be turned away. The problem is to arrive at some sort of average rating of this character- istic relative to other characteristics evaluated. As already noted, Ellis1 in adding camping capacity (but not percentage filled) to his rating system for parks, assigned an index multiplier of l to a park having "average" capacity. The extent to which parks deviate from this average determines changes in this multiplier. For example, a park with twice as much capacity as average would have a multiplier of 2. In this case, the parks of interest are those which are considerably above "average" regarding percentage of capacity filled. It was decided arbitrarily to set the value of 65% as an index multiplier of 1. Then, any park with values above this figure would be devalued accordingly. For example, a park with 85% of capacity filled would receive a multiplier of 0.76. For a park with 100% of capacity filled, the multiplier would be 0.65. 1J.B. Ellisf'Systems Analysis of Provincial Park Camping: 1966 Park Users Survey,"report prepared for Parks Branch, Ont. Dept. of Lands and Forests (Toronto: January 1968). 175 This procedure was applied to the park attraction indices derived by Ellis} using data eXpressing percentage of park camping capacity utilized during the peak use months of July and August.2 Of the total 81 parks, 21 had percentages filled of 65 or more. However, the adjustment of these attraction scores made little difference in the ranking of parks by their attractiveness. Also of interest is the fact that little correlation was found between park attraction values and percentage of capacity filled. If the validity of the attraction scores is accepted, then the attractiveness of a park does not appear to be significantly related to the degree of use of camping facilities.3 This approach to the capacity problem appeared to be a more practical one than the one discussed initially, and was adopted in modifying park attraction scores for the study. Obviously, though, it would be desirable to establish a sounder basis for determining the effects of park capacity limits on locational choices of campers. IIbid. 2Ontario Department of Lands and Forests, "Park Use Statistical Report, 1967" (Toronto, 1968, Mimeographed). 3As noted in Chapter I, percentage of capacity utilized is really a product of two types of decisions; decisions by campers to utilize particular parks and decisions by park administration to alter or maintain camping capacity. Therefore these percentages may simply reflect abilities of administrators to estimate demand for camping facilities. APPENDIX V 1966 ONTARIO PROVINCIAL PARK USER SURVEY: CAMPER QUESTIONNAIREa (Long Form Questionnaire) IO. 12. l3. 14. 15. Park Number - see park code sheet. Sticker Number - from special survey sticker affixed to vehicle. Date- -day (use 2 digit code i. e. 01 to 31) and month (use 1 digit code 1. e. ., May l, June 2. -July3, Aug. 4, Sept. 5, Oct. 6) e. g., July 9th would appear as 093; Sept. llth - 115. Where is your home? (Use hometown code sheet). If U.S. resident - what was your point of entry into Canada? Do you live in an apartment, single family detached dwelling, or ................. ?- (a) ' In the area where you live, are there outdoor recreation facilities within a ten minute walk, or not? - If ‘no' mark ‘none’ on form. - if ‘yes’ go to 6 (b). (b) How would you rate these facilities? Number of persons in car including infants - direct count. We would like to know the approximate age of each person in your party. Into which of these age groups do the members of your party fall? Please provide the information separately for males and females - use card Are there any persons in your party who do not live' in the same household as you do? If yes’, how many? (a) What kind ot work do you do? (write in} (b) -What type of organization or company are you employed by? (write in) DO NOT CODE OCCUPATION UNDER ITEM NO. 10. Would you indicate the category on this card which fits the last year in which you went to school? - use card Is this trip part of your annual vacation? How long is your vacation in the average year? Approximately how many nights do you expect to stay in the park on this visit? (a) How long is it since you left your home on this trip? - If ‘one’ night’ record hometown code as ‘origin' and go the question 16. - If ‘two nights’ or more, ask 15 (b). aOntario Dept. of Lands and Forests and Ontario Dept. of Highways 176 16. I7. 18. I9. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 177 APPENDIX V--C ont inued (b) Have you spent two nights or more at the same location between here and your home? - If ‘no’ record hometown code as ‘origin’ and go to question 1 6. - If ‘yes’ ask question 15 (c) (c) What was the last place where you spent two nights? Record location as ‘origin’. . How would you classify your stop-over accommodation in ......... . ...... (origin)? - If ‘home’, this can be entered directly from Question 15 without asking question. How many miles have you travelled since you left ............. (origin)? Excluding stops, how many hours have you travelled since you left, ........ '.(origin)? (a) When you leave the park, do you plan on staying two nights or longer at any location before you return home? - If ‘no’ record hometown as ‘destination’. . - If ‘yes’ ask 19 (b). (b) At which location do you plan to stop-over? (Record as destination) _ How would you classify your stop-over accommodation in ............. (destination)? During the ten year period from 1956 to 1965, about how many years did you camp in Provincial Parks? (a) Have you visited this park previously this year? - lf‘ycs’ - How many camping visits have you made to this park this year? How many day visits have you made to this park this year? (b). Have you visited any other Provincial Parks this year? - lf‘ycs’ - llow many camping visitshave you made to other parks this year? How many day visits have you made to other parks this year? Would you have come to this area on this trip if there were no Provincial Park here? If ‘yes’ to 23 - l f this park did not exist, what alternative accommodation would you use? ~ CamMng equipment - enter directly - no question required. - mark only one category. If camper-back, or bus type of camping vehicle (e.g., V.W. camping bus) - mark under ‘lS’. What activities do you intend to participate in during this visit? Which two would you consider most important to the enjoyment of your visit? (Include activities such as . fishing and sightseeing which are not necessarily pursued within park boundaries) Mark) only two. ' What do you estimate the total amount-of money will be, not including park fees, which you will spend in the immediate area during this camping visit? (Ten dollar range). (a) Have you found the park facilities and services to be generally satisfactory? - If ‘no’ (b) What have you found unsatisfactory? In an average summer. how many visits (for recreational purposes) would you usually make to each of the following:- cottage, private park, commercial resort, other? 178 APPENDIX V-—Continued DEPAIIMEN! 0! WW": ‘ . . . DEPAIWENI OF LANDS AND routs». nu men ' e I a a 4 s o r o 0 l2. . - a... _ — - ..u um n- I-8 II- ’ a." ANWM VACMION Vt: an no .1. l m 0— an: - .- - — — m 3:: “NOW 0! VACAHOQI (Mun) I3. - - :- - I.- .. CI. a: Is- . ' . -- .- -.. ... ..- ‘—. ... ... -- -. . o t 2 3 e “"5: r s e 1 a 3 1:. A. .3. a3. ...:- I In,- A. .3,- rga 3:. u. "'" I... .N' on "l- 5.: O '“I 3“ '3. 3“ 3-3 : 2:: 2:. an as: 3::(NIGNVSI =2: 2: :==. ::: ::: Is- "a m .I at: s In: at. at: an: 3.1 O ' 1 3 ‘ O S . p . . ..- _ ..- CI. ." . -.. ‘3' a ‘3. =3 m ”a n In :31 i n 8:: It! as: :3: 7.2.: 3 z . 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I" n- 33. :2: 3:: :3: 2:: .z- T. .é- '7. .7. .‘ V- '8 ‘8' :3: 3:: lg. n;- .3.- .2- cés‘O'lAG. =2; :2: :32; _-—.-__: e!_: I Q A I 2 3 9 2 can at. ‘ an as: 0:. PIOV Pl 8:: 3:: u: a u: 'l 2 I: ‘ IS :I ‘ 29. no a I I COOIIIIC "" 9 g o I a I. I I II. IISOC' It. 3:: 8:: a: .-. —‘ ... "' m "‘ :2: 3:: 3:: :23 8:: O"!!! :::= 2:: n: =:: :-_= IlllllllllllllllllIllllllllllllllllllllllllllllllllllllllllllllllllllllIlllllllllllllllllllllllIllllll nfififififififlfi 63‘ II II 9 V. d J Pl II?) III) [09 IIO I?" APPENDIX.VI COMPUTER PROGRAM FOR REVEALED PREFERENCE ANALYSIS AND COMPARISON OF SUBGROUP PREFERENCES ponavnn 1r rnnn z vtvvwEF navntcsx awn utter-[NE SlnlLARIYIES OlMt~SION AIOG¢%HI. 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