AN EXPLORATORY APPROACH TO THE INTEGRATION OF A CONJOINT ANALYSIS WITH A FISHBEIN ATTITUDE ANALYSIS Dissertation 'for the Degree of Ph. D. f MICHIGAN STATE UNIVERSITY TERRY C. WILSON 1976 "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIII L 517 5792 This is to certify that the "f thesis entitled AN EXPLORATdRY APPROACH TO THE ENTEGRATLON OF A CONJGLNT*ANALYSIS WITH A FISHBEIN ATTITUDE ANALYSIS presented by Terry C. Wilson has been accepted towards fulfillment of the requirements for Ph D Marketing and degree in Transportation Admin. flit/x” (a? Major professor Date 10/29116 0-7 639 PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or More data duo. DATE DUE DATE DUE DATE DUE I I I I ‘ MAGIC 2 3 W199 I; _____LI__J fiI—‘T—T MSU I: An Affirmative Action/Equal Oppommuy ImthIon . g LIBRARY iwdfigfll State ‘3 University , ABSTRACT AN EXPLORATORY APPROACH TO THE INTEGRATION OF A CONJOINT ANALYSIS WITH A FISHBEIN ATTITUDE ANALYSIS By Terry C. Wilson The Fishbein attitude models, included in the group of models frequently referred to as compensatory multiattribute models, are specified as multiplicative functions of belief about an outcome (Bi) and desirability of the outcome (a1). The desirability component has alluded precise measurement and has been referred to many times as a suppressor variable in spite of the fact that the models are believed to be misspecified without it. The purpose of the present study was to explore whether the inte- gration of a conjoint analysis estimate of the desirability component with the traditional Fishbein model would improve the predictive validity of the Fishbein model. Three subcompact automobiles and the relevant attributes for their purchase were chosen as they provide a setting conducive to use of both conjoint analysis and the regression methodology usually associated with the Fishbein model. Data for both the conjoint analysis and the Fishbein model were collected from an undergraduate marketing class during Spring quarter 1976 at Michigan State University. This provided a final sample size of 218 which is considered an adequate base for analysis with both of the methodologies utilized. The limitations of the study were: 1) it was essentially explora- tory, 2) sample is not generalizable, 3) the Fishbein model is considered Terry C. Wilson representative of the class of attitude models referred to as compensatory multiattribute attitude models, and 4) conjoint is a relatively unexplored technique with only meager evidence as to its proper and efficient use. The conclusions of the present study were: 1) no statistically significant difference between the predictive validity of the traditional measurement techniques associated with the Fishbein model and the Fishbein model with the conjoint analysis integration, 2) the desirability component has very different distributional characteristics with the different esti- mates of that component, yet the predictive validity is unchanged which points to the danger of multiplying non-ratio component measures, and 3) the continued use of the traditional measurement methods of desirability is preferred on the grounds of simplicity with the reservation that a construct validity study of the desirability component should be conducted and replication of the present study made for final judgment to be valid. AN EXPLORATORY APPROACH TO THE INTEGRATION OF A CONJOINT ANALYSIS WITH A FISHBEIN ATTITUDE ANALYSIS By Terry C. Wilson A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for.the degree of DOCTOR OF PHILOSOPHY Department of Marketing and Transportation Administration 1976 © Copyright by TERRY C . WILSON 19 76 1%» M 0'? Uv‘lsfi‘oke’ \9 519‘, 09¢ ’S/ 134‘ ACKNOWLEDGMENTS First and foremost, thanks must go to Pamela Ann, who has provided the much needed understanding, patience, and love needed for the comple- tion of such an encompassing project. She has also provided much of the technical assistance required in understanding the technical material associated with this project. The dissertation committee, acting as a committee of the whole, has provided better turn around time than could be expected of any committee. All have provided consistent comments from the beginning and have somehow managed to maintain a sense of humor to create a positive working atmos- phere. Professor Frank R. Bacon, Jr. has provided immeasurable assistance in technical and editorial detail, and, probably most importantly, the encouragement and support necessary to complete the project. He has also assumed many of the responsibilities of a chairman. Professor Gilbert D. Harrell provided direction and the assistance so necessary in the behavioral aspects of this dissertation. Professor Donald S. Henley has contributed in terms of concept and direction of the research. Diane Scribner typed the preliminary and final drafts, both accurately and quickly, which was so necessary for a timely completion. ii Chapter TABLE OF CONTENTS I 0 INTRODUCTION 0 O O O O O O O O O .0 O O O O O I O O O O 0 II. THE III. THE Research Objectives Model Merits and Limitations Research MOdel Applicability Research Areas Medel Conceptualization Methodology and Measurement Design Outline FISHBEIN ATTITUDE MODELS . . . . . . . . . . . . . . Research Background Compositional Compensatory Multiattribute Models The Compositional and Decompositional Approaches The Compensatory and Multiple Criteria Approaches The Multiattribute Approach The Mbdels The A0 Model The Aact Model . The Disaggregated Attitude Model Recent Research Advancements Mbdel Conceptualization and Description Model Methodology and Measurement CONJOINT APPROACH . . . . . . . . . . . . . . . . . Research Background Conjoint Measurement and Conjoint Analysis: A Clarification The Model Assumptions Desirable Dimensions of a Market Situation Computer Algorithms Data Collection The Trade-Off Method The Full Profile Method Differences Between the Two Methods Applications in the Literature Limitations and Advantages of Conjoint Analysis IV. SCOPE AND GENERAL METHODOLOGY . . . . . . . . . . . . . Estimated Models Attribute Determination Research Sample Model Considerations The Fishbein Models Conjoint Analysis: Implications Conjoint Analysis: Assumptions Conjoint Analysis: Consideration of Desirable Characteristics Limitations of the Present Study 111 10 v. ANuYSIS MD RESULTS C O O O O O O O O O O O O 0 Respondent Consistency Results from Fishbein Analysis Conjoint Analysis Results from Integrating the Models VI. CONCLUSIONS AND RECOMMENDATIONS . . . . . . . . APPENDICES A. B. Conclusions from Synthesis of the Two Models Recommendations for Further Research Questionnaire and Instructions . . . . . . . Conjoint Procedure and Algorithm . . . . . . BIBLIWWIIY O O O O O I O O O O O O O O O O O O O O 0 iv 72 77 82 96 LIST OF TABLES Table 1A Selected Results From Tests of Collinearity . . . . . . . 1B Correlation Matrix For Ao Model . . . . . . . . . . . . . 1 Correlation Matrix . . . . . . . . . . . . . . . . . . . 2 A0 Madel Estimates 0 O O O O O O O O O O C O I O O O O O 3 A Madel Es timtes O O O O O I O I O O O I I O O O O 0 act 4 Disaggregated Fishbein Models of Behavioral Intent . . . 5 Beta Weights For Each Product Attribute By Brand For Disaggregated Models of Behavioral Intent . . . . . . . . 6 A.o Mbdel With Utility Substituted For Desirability . . . 7 Aact Model With Utility Substituted For Desirability . . 8 Disaggregated Medal With Utility substituted For DQSirability O O O O O O O O O O O O O O O O O I O O O O 9 Distributional Characteristics 0f Utility And Desirability CHAPTER I INTRODUCTION Research Objectives The past two decades have witnessed a vast expansion of research literature on the topic of consumer behavior as applied to marketing situations. Within this arena of study much research, discussion, and controversy have focused on the various aspects of attitudes. The pre- ponderance of this research on attitudes has been published since 1970. Within the attitude research sector two general topics have been of the greatest interest to researchers (Wilkie and Pessemier, 1973). These are 1) model conceptualization and 2) methodology and component measure- ment. Component measurement is the primary concern in the present re- search, the purpose of which is to explore whether the integration of a conjoint analysis model with the traditional Fishbein analysis would imr prove the predictive validity of the latter. Specifically, this research will attempt to integrate the utility weights from the conjoint analysis with the Fishbein model as objective weights for the predictor variables. Although the use of both conjoint analysis and the Fishbein model has been advocated for predicting brand preference (Wilkie and Pessemier, 1973), there has been no previously known attempt to integrate the two models. When confronted with more than one model for possible use, a researcher or decision maker must weigh the situational specific advan- tages and disadvantages of each as well as reviewing their unique as- sumptions and implications. The model, or combination of models, to be chosen is the one which offers the best prediction or explanation depen- ding on the research purpose. The results of this research do not obviate the necessity for such careful observation and judgment, but rather facilitate a more objective decision as to the appropriateness of the models. Model Merits and Limitations In order to promote an effective discussion of the two models under consideration here, it is necessary to briefly discuss why these models have provided fruitful ground for research. As models evolve to the stage of algebraic specification, a number of advantages are avail- able to the researcher. First, algebraic models provide for explicit variable definition of the essential components. For example, the com- ponents of the Fishbein expectancy/value model can be specifically de- fined as opposed to a simple verbal description of diagrammatic repre- sentation. Second, the algebraic model allows a specific statement of assumptions. This includes assumptions inherent in the theory plus the assumptions inherent in the methodology used in representing a theoretical model. Third, these models allow the researcher to simplify complex arrangements of variables that otherwise elude precise measurement and sometimes even approximation. And finally, because the models abstractly measure a "real" situation, they provide a potentially useful method for the evaluation of explanatory and predictive power. In fact, attitude models have been justified and evaluated on both explanatory and predic- tive criteria. While the benefits are substantial, however, there is a major shortcoming in algebraic models that is especially noticeable in the behavioral sciences. This drawback is the lack of normative measures. Such a lack of a clear-cut standardization point or benchmark makes it difficult to evaluate the meaningfulness of the results, a problem which has forced the behavioral scientist to rely on less explicit methods of evaluation. For example, a model of attitude structure has no norm referencing point. Whereas in the physical sciences the total absence of heat is a reference point for temperature, there is no sudh counter- part in the behavioral sciences that would establish a reference point for something like the degree of desirability of carbonation in soft drinks. A model must then be chosen that is as consistent as possible with available theory and provides a relative measure. The problem of defining such a model is not so much that it fails by omitting some vital detail, but rather that it proves useful in consideration of its purpose, either explanation or prediction or both. Only after this step will the validity and reliability of a particular model warrant further research. By definition, then, a model is an abstract representation and not the exact duplication of some system or process. Indeed, models do not attempt to incorporate all restrictions and complexities of a process. Both the merits and limits of the model lie in its ability to isolate some essential factors with rigorous logical underpinnings. By focusing attention on a few aspects at a time, a model can bring into perspective the implications of the underlying assumptions and relationships. It is, however, all too easy to lose the implications in the enthusiasm of a research project, and it is always good procedure to outline them in advance. Research Model Applicability There are two models under scrutiny here, the Fishbein attitude model and a conjoint analysis model of utility. Of the two, a consider- able amount of attention has been devoted to the Fishbein model which is also referred to as the expectancy/value attitude model in the marketing literature (Wilkie and Pessemier, 1973). Chapter II is devoted to the historical evolution and the advantages and disadvantages of using this model. By way of contrast, the conjoint analysis model, a recent addition to research methodology, has had little exposure in the marketing liter- ature. Chapter III discusses the technique, its assumptions, and the advantages and disadvantages inherent in its use. These models have been chosen for examination for several reasons. First, conjoint analysis is a relatively new methodology and needs clari- fication and explication as it relates to marketing if it is to be utilized properly. Second, although there are several alternative atti- tude models reported in the marketing literature, the Fishbein model is one of the most widely utilized. Many of the models contain similar, if not identical, advantages and limitations. Third, the Fishbein and con- joint models have been advocated for comparison notwithstanding the different advantages, limitations, conceptualization, and results of each (Day, 1972; Wilkie and Pessemier, 1973; Schmidt and Wilson, 1975). Fourth, the present project is within a framework that enables marketing to advance as a scientific discipline. For instance, the methodology yields results that are readily replicated, while, at the same time, it specifies the degree to which the two models under consideration can be integrated. Such specification provides greater reliability in future research efforts since it sensitizes researchers to the advantages and limitations of the models and thus facilitates more valid interpretation of the results. It will be helpful to specify the advantages and limita- tions of each of the models so that it is possible to gain a perspective of the project's scope. Research Areas A discussion of the respective advantages and limitations of each model under consideration can be clearly focused by utilizing the three areas of research outlined earlier. Recall that these were 1) model conceptualization, 2) methodology, and 3) component measurement. Recent research in these areas is discussed in Chapter II, while the aim of this section is clarification of the framework of the models. Model Conceptualization In terms of model conceptualization, a substantial difference between the models is that the attitude models are compositional while the conjoint approach is essentially a decompositional approach. Basi- cally, the compositional approach attempts to build up the component parts to produce an attitude toward an act or object, while the decom— position approach attempts to break down an attitude into its component parts. This difference is further discussed in Chapter IV. An advantage enjoyed by the attitude models is the compiled evi- dence from many research endeavors as to predictive and construct vali- dity. This research addresses the issue of the comparative predictive validity as there is yet no evidence of superiority for either model. In terms of construct validity, at this time the Fishbein model is more highly rated. It has been shown to include the relevant variables as well as representing the actual cognitive map of individual respondents. On the other hand, conjoint analysis is a kind of 'black box' approach. There is very little evidence at this time to support the contentions of decomposition (Sheth, 1976). Conjoint analysis enjoys only the intui— tively appealing prospects of face validity. The conjoint analysis model does, however, have advantages inherent in its use. For instance, it does not require interindividual utility comparisons whereas the empirical use of the attitude models has such a requirement. A method of analyzing data intraindividually has been intro- duced to the attitude literature and is frequently used to avoid this problem (Bass and Wilkie, 1973). The attitude models are for the most part compensatory. This means that a low rating on one attribute can be counterbalanced by a high rating on another attribute. The interpretation of conjoint analysis in published studies has also implicitly assumed a compensatory framework, although such a framework is not inherent to the technique. The disadvantage of assuming a compensatory model is, of course, that the object or act toward which the attitude is directed may fall below a consumer's qualifying level. That is to say, a brand may not rate high enough on some criteria to be included in the consumer's evoked set. The evoked set is that collection of brands which is considered for purchase. Several other considerations are shared by both models. Both assume that the attributes under Consideration are relevant and non- redundant. Both admit to the theoretical realization of the possible effects of intervening variables which poses a problem in that the models may evaluate the attributes quite precisely but other factors may intervene before actual behavior occurs. Both models assume a rational, i.e., consistent, consumer and both are essentially cross- sectional. Methodology and Measurement The second area for consideration is the methodology of each of the techniques. Any separation of methodology from component measure- ment becomes arbitrary at some point. The following discussions classify each of the advantages and limitations under one area or the other, but the classifications are not irrevocable, although it would hardly be a crucial distinction. Again, under methodological considerations the Fishbein model requires only a short interview period compared to one that is typically quite long for conjoint. The reason the Fishbein model enjoys this advantage is that attitude questions are much more easily comprehended by respondents than the conjoint questions. Another advantage of the Fishbein model in this area is that it requires a minimum sample of about fifty while the conjoint model requires at least 200. This advantage, in part, stems from the fact that regression analysis is utilized in most of the attitude model procedures, while conjoint analysis typically estimates through use of a distance function. Regression is a thoroughly investi- gated technique through its constant use and is subject to the rigorous underpinnings of probability theory. On the other hand, conjoint analysis enjoys no such advantage of possessing an error theory and is subject to many rules of thumb. It essentially involves a heuristically derived solution with little assurance that the results are statistically signi- ficant. Conjoint analysis, however, is not restricted by the scale assumption of the regression technique. For example, it can be used with only nominal data, whereas regression requires at least intervally scaled input. Both models rely on data from survey techniques and neither purports proof of causality. Extrapolation of utility weights to combinations other than those under study appears more valid with conjoint analysis since the regression technique used in the Fishbein analysis is constrained to only those combinations of attributes which are specifically outlined in the study. In fact, mixes of attributes other than those used for original input are beyond the relevant range of consideration for regression analysis. Both models can be adjusted to both consumer and industrial settings and both have the potential to consider curvilinearity. The third and final area of consideration is that of component measurement. Conjoint analysis enjoys the advantage of not being sub- ject to some of the possible bias and constraints of attitude scales, but at the same time suffers from a complex questionnaire format. This leads to the subject of measurement constraint. As noted above, any scale level is acceptable for conjoint analysis whereas regression generally requires at least interval data. This latter constraint has surfaced as an area of concern with several researchers in that the attitude models, such as Fishbein, are assumed to be subject to a multi- plicative combination rule. Legitimate multiplication requires that all variables being multiplied have attained a ratio level of measure. Typi- cally, however, attitude models measure their components with bipolar or Likert type scales which attain interval level of measure at best. The multiplication of two variables measured only on an interval scale can easily produce spurious results, a problem which presents a potentially significant limitation in use of the attitude models. Design Outline The differences between the two models being considered provide the thrust of this research project. Any evaluation must be based on the purpose for which a model is employed. Moreover, the situation chosen in which the models can be evaluated must be consistent with the assumptions and purposes of both. In order to approximate an acceptable setting for both models, then, American subcompact cars are used. A consumer durable is appropriate for both the conjoint and Fishbein models. Since the purpose of this research is examination of alternative models, it is not necessary to select a random sample. The empirical . results are being used for evaluation purposes and not for generalization. As previously indicated, Chapters II and III will discuss the Fishbein attitude model and conjoint analysis, respectively, while the scope and methodology are further detailed in Chapter IV, the results of the models are presented in Chapter V, and the final chapter is a discussion of those results. CHAPTER II THE FISHBEIN ATTITUDE MODELS Research Background Attitude theory and measurement, the topic of a great deal of marketing research in recent years, has proven useful for both under- standing and prediction. The various theories of attitudes generally have their roots in psychology and social psychology and have been refined and adapted to marketing situations. Much of the work in marketing has taken place since 1970 with more than forty studies being reported between 1970 and 1973 (Wilkie and Pessemier, 1973). An equal number have been published since then. Research in the area has be- come quite sophisticated and refined as a result of such a vast amount of study. And this high degree of sophistication has spawned consider- able debate as to the superiority of the many alternative models. Compositional Compensatory Multiattribute Models Much of the debate on attitude models concerns a class of models that have become known as compositional compensatory multiattribute models. As this class of models is rather specialized, it requires some further explication. The three words describing this class of models, compositional, compensatory, multiattribute, are important in understanding the general framework of recent research. 10 11 The Compositional and Decompositional Approaches The compositional approach in essence specifies the model components and functional form of a cognitive map. Further, such an approach assumes that the components are separately specified a priori, according to theoretical considerations, and that consumers consider the components separately. A technique utilized for compositional models is regression analysis. The Fishbein attitude models are ex- amples of compositional models. The counterpart to the compositional approach is the decompo- sitional approach which attempts to dissolve a cognitive map into its component parts. It assumes that the consumer thinks of a process or system in wholistic terms and does not weigh each component explicitly. Multidimensional scaling and conjoint analysis are essentially decom- positional techniques. Proposals advocating both compositional and decompositional approaches, separately and in combination, can be found but neither approach has been shown to be superior in all situations (Day, 1972; Wilkie and Pessemier, 1973). The Compensatory and Multiple Criteria Approaches The term compensatory, as used in the phrase compositional com- pensatory multiattribute models, refers to the manner in which the attributes are combined. Specifically, it infers that a low rating on one attribute can be balanced out by a high rating on another attribute. For example, a brand of automobile may rate low on comfort and high on economy. The high rating on economy compensates for the low comfort rating. This compensatory approach assumes that the consumer gives an overall rating to an object or action because such a rating is required 12 to compare and decide about that object or action. All attribute scores are collapsed to one dimension for decision making. The alternative to the compensatory model is the multiple cri- teria or multiple cutoff model, a model, similar to the disaggregated model to be discussed later, which contends that the measures of different variables should not be combined. Combining positive and negative elements, say advocates of this model, renders a composite score uninterpretable and, hence, such elements require separate measurement. The superiority of compensatory vs. multiple criteria models has a long, involved evolution which is peripheral to this study but has been well documented (Schmidt and Kaplan, 1971). It is sufficient here to point out that the disaggregated attitude models are generally, but not always, preferred in consumer attitude studies (Wilkie and Pessemier, 1973). The Multiattribute Approach The final term under scrutiny, multiattribute, simply refers to the consideration of more than one attribute. Indeed, there is general consensus that attitudes are formed by reflection on more than one attribute. The object or act is viewed as a bundle of attributes leading to costs and benefits which are differentially desirable to individuals or total market segments. A significant advantage to the multiattribute approach is that it incorporates both understanding and prediction. Again, if the automobile is used as an illustration, attitudes are not formed by one attribute such as economy, but by several attributes such as economy, comfort, warranty, etc. Given that attitudes are formed through consideration of several attributes, 13 it is of paramount importance that a methodology be employed that pro- duces a relevant but nonredundant attribute list. The usual procedure for generating such attribute lists relies on methods for attribute generation. Exhaustive lists of attributes are gained from expert judgment, group depth interviews, or previous research. A technique such as factor analysis is then appropriate for the selection of the relevant and nonredundant list for inclusion in the attitude model (Wilkie and Pessemier, 1973). The Models Fishbein has suggested two separate models of attitude structure and from.these a third model has been developed in the marketing literature. The A0 Model The A0 model involves an attitude toward an object and is algebraically formulated as (Fishbein, 1963): n A0 = 1318131 where: Ao ‘ attitude toward an object Bi - the individual's belief about the probability that the object is related to an outcome, 1 a1 8 the individual's evaluation of outcome 1 n . number of beliefs Note that this model has two components. The first is the cog- nitive component of belief that the object under consideration possesses 14 some attribute (B1); for example, belief that a Pinto is economical. Typically, consumers have been asked to respond to a bipolar scale such as the following: Very . very Improbable Probable -3 _ -2 -l 0 +1 +2 +3 The second component is the affective component (a1) measuring the desirability of the outcome. For example, the desirability of economy in a subcompact automobile would require a consumer response to a scale such as: Very Very undesirable Desirable -3 —2 -1 0 +1 +2 +3 These two components, Bi and a1, are the reason the Fishbein model is often referred to as an expectancy/value model. The cognitive compon- ent is a measure of expectancy and the affective component is a measure of value. The scales of measurement noted above have been used for all models mentioned in this chapter (Bettman, Capon, Lutz, 1975; Wilkie and Pessemier, 1973). The Aact Medel A second model, which was later developed by Fishbein and focused more directly on behavior, was intended to have greater validity because of such a focus. For example, an individual's attitude could very well be different for an object that is purchased as a gift as opposed to one purchased for personal use. This second model, sometimes referred to as the individual's attitude toward an act, requires a highly specific situation. In other words, the act of purchasing a specific brand is necessary if the model is not to be 15 confounded by situational specific intervening variables. The model is referred to as the Aact model and is specified in algebraic form as follows (Fishbein, 1967): n B 2 Bl z Aact - 2 (Biai)wo + (NB-Mc)w1 i=1 where: B - behavior regarding a specific brand BI - behavioral intention regarding a specific brand in a specific situation A - attitude toward an action B - beliefs about the outcome of performing the behavior a - the evaluative aspects of the consequences NB = normative (peer group) beliefs M = motivation to comply with the norms c w1 - regression derived beta weights n - number of relevant consequences of the behavioral act The Aact is based on Dulaney's theory of propositional control (Dulaney, 1967), a theory which states that behavioral intent is a function of the attitude toward performing a specific behavior and the norms relevant in that situation together with the motivation to comply with the norms. The first application in a marketing setting of Fishbein's A.ac model and its theoretical underpinnings appeared in t a study of physicians prescribing behavior (Harrell and Bennett, 1974). The physician's attitude toward drug prescription for antidiabetic drugs was investigated, and specific brands of drugs were matched with specific Patient descriptions. Normative beliefs and motivation to 16 comply were also measured. This additional construct has since been suggested as a measure of social compliance rather than a part of attitude (Ryan and Bonfield, 1975). It is therefore believed that it is unnecessary for attitude measurement. The Disaggregated Attitude Model A third attitude model has evolved in the marketing literature based on empirical considerations of the two models already noted. The model, usually referred to as the disaggregated attitude model, is algebraically noted as: A - f(Bi, a1) The A can represent the attitude toward an object or an act, depending on the researcher's objective, while B1 and a1 are the same as pre- viously defined. Note that the difference between this model and the previous models is that the summation sign (2) has been replaced by a function sign (f). The function sign is meant to imply that each attribute, rather than being summed, now acquires a beta weight of its own.1 The model might also be expressed more explicitly as: A - (B1a1)wb + (B2a2)w1 . . . . . (B1a1)w1 where w is the beta weight value corresponding to each attribute. 1 Recent Research Advancement Given this discussion of the formulation of the attitude models relevant to this research, it is appropriate to note recent advancements 1Note that the term beta weight is used in its technical sense. That is, beta weight is a standardized coefficient rather than a simple regression coefficient (Kerlinger and Pedhazur, 1973). 17 within this class of multiattribute attitude models. Two areas have been of general interest to researchers: 1) model conceptualization and description, and 2) methodological and measurement issues within the models. Both of these are discussed in an excellent review article by Wilkie and Pessemier (1973). Model Conceptualization and Description In the area of conceptualization and description there have been relatively few studies since that review article. The attitude toward an act model was thoroughly examined by Harrell and Bennett (1974) who are believed to have conducted the first test of this model in a marketing environment. A cross-validated sample held up well with an attribute list generated through factor analysis. Another model, noted as the vector model which is very similar to the Fishbein models, has been proposed and briefly tested (Ahtola, 1975). This model may be expressed as: n Ak ' 1:1 Bikai where: Ak = an individual's attitude toward alternative k Bik - vector of probabilities of k's association with categories of i a - vector of evaluations of categories of i n - number of salient dimensions Although obviously very similar to the Fishbein models, the vector model has an objective which leans more toward predictive than construct validity. It purports to possess the advantages of more clearly l8 measuring B1 as only probabilities, and thereby gains more discrimina- tory power and more precisely measures the cognitive mapping dimensions of an individual. A brief test was conducted using a sample of fifty- two students' attitudes toward soft drinks. The results confirm that the vector model predicts preferences substantially better than Fishbein (Ahtola, 1975). Recall, however, that it also trades off some construct validity for this increase in predictive power. The most highly prized model should yield understanding and suggest feasible procedures for favorable control. various formulations of Fishbein's models and Dulaney's theory of propositional control have also been tested (Bonfield, 1974). Al- though the action model as well as the empirical evidence indicate that intention explains more variation in behavior than do attitudes, the model does not view behavior as essentially stochastic. Some people are of the opinion that social psychological influences, which vary according to the situation, outweigh the importance of the deterministic components of the attitude models. This would account for the typically low coefficients of determination, usually between .2 and .5, found in attitude studies. It does appear, however, that brand choice is less random, i.e., more deterministic, for segments of high income, education, and medium brand experience as well as low brand loyalty and high product importance. The more predictable results in situations with these characteristics are most likely the result of a more cognitive buying approach relative to other situations. And the more cognitive a purchase decision, the less likely it will be influenced by environmental factors, a conclusion also supported by 19 research in the predominantly cognitive purchase of industrial capital equipment (Wildt and Bruno, 1975). The relationships among the components of beliefs, knowledge, intentions, and behavior have also been investigated (Olshavsky and Summers, 1974). Beliefs appear to be consistent with intentions, behavior, and knowledge, although intentions were not consistent with behavior or knowledge, nor was behavior consistent with knowledge. The obvious intransitivity of these findings is attributed to factual and reasoning distortions on the part of the respondents. These findings are difficult to generalize, however, because of the situ— ational specifics involved in the psychology of cigarette smoking which was the topic of investigation. Experiments have also been conducted for purposes of model comparison (Mazis, Ahtola, Klippel, 1975). These comparisons, in spite of several multivariate statistical problems, conclude that pre- dictive superiority is much clearer than the understanding of cognitive structure when alternative attitude models are dealt with. Again, the results indicate that the importance of the cognitive components is greatly affected by the situation specifics. Other research indicates parallel findings (Beckwith and Lehmann, 1975). For instance, the greater the ambiguity of a belief statement the less importance will be attached to that belief. Model Methodology and Measurement The second area of inquiry, methodology and measurement, has received considerable attention from researchers. One problem in this area is a direct descendant of utility theory in economics, that being 20 interindividual utility comparisons. Such comparisons cannot be given rigorous meaning since utility measures vary from individual to indi- vidual (Nicholson, 1972; Scott, 1973; Wilkie and Pessemier, 1973). This problem of interindividual utility measurement is circumvented by using within individual estimates as Opposed to across individual analysis utilized by some early studies. Another issue here is the tOpic of scaling which in turn poses certain other problems. First, Fishbein advocates bipolar scales with plus and minus poles as exemplified earlier in this chapter. This position is important when the form of each individual's cognitive map is considered (Bettman, Capon, Lutz, 1975). Scale coding makes no difference, however, in the use of regression techniques (Kerlinger and Pedhazur, 1973). The fact that such bipolar scales yield no better than intervally scaled data does make a difference. Note that the Fishbein models propose the multiplication of the B1 and a1 components. Given only interval data, such an operation is illegitimate since all components entering into a multiplicative function must be of ratio scale. With non-ratio data it can be shown that any resultant corre- lations are often times spurious (Schmidt and Wilson, 1975). The complication of non-ratio data can be avoided by use of an analysis of variance paradigm. And the first legitimate attempt at specifying a correct combinatorial rule for the Fishbein model utilized such a paradigm. The specification of functional form on the basis of construct validity is much more difficult and less common than Specifi- cation on the grounds of predictive validity (Bettman, Capon, Lutz, 1975). Studies of functional form have reached several important conclusions. 21 First, lack of involvement in the task by the respondent may lead to simple additive combination rules. Second, respondents may use dif- ferent combinatorial rules for different subsets of attributes. Finally, there is ample evidence that the multiplicative rule proposed by Fishbein reflects the true cognitive algebra of a majority of con- sumers. The second conclusion proposing different combination rules for different sets of attributes poses some interesting possibilities. Attribute list generation, as previously noted, is an important task if the results of the attitude models are to be interpreted as reliable. The number of attributes employed is situation specific and generally depends on diagnosis of attitude structure, predictive efficiency, saliency assessment, and parsimony (Wilkie and Pessemier, 1973). As with many situation specific problems, a great deal of judgment is obviously required on the part of the researcher. One consideration omitted from the above list is the requirement of determinance. Dif- ferent choice criteria play different roles in the behavioral process (Myers and Alpert, 1968). Those criteria which are equal for all brands or are relatively unimportant could be termed qualifying attri- butes without which a brand would not be considered part of the evoke set. Once the evoke set is established, however, the choice criteria related to intention or actual purchase could be termed determining attributes. For example, subcompacts could easily be viewed as equi- valent when judged on safety factors, while electric cars may not qualify for inclusion within the evoke set because they do not meet a minimum safety requirement. However, given that a car has qualified 22 on the relevant criteria, price may determine which product will actually be purchased. It is quite probable that many product purchase decisions would involve trade-offs of several determining attributes. It would be necessary to use only determinant attributes when behavioral intention is predicted. Qualifying attributes may confound results by violating the assumption of relevance and nonredundance. This discussion of attribute types also has implications for the methodology. Regression analysis is many times utilized as the analytical technique for the Fishbein model. Given that regression will be used, one consideration is the variable selection procedure. Two possibilities are logically valid: 1) forward stepwise, or 2) multiple regression. Forward stepwise is a procedure developed for cost efficiency which adds one regressor at a time according to which regressor explains the most variance in the dependent variable. The alternative, multiple regression, estimates all coefficients simul- taneously. According to Wennacott and Wonnacott (1970), "...if there are clear prior guidelines indicating that a few specific regressors are appropriate, then they should all be used right away in a multiple regression, rather than tested one at a time with any sort of stepwise approach." The reason, of course, is that the regressors are very likely to be biased with a stepwise approach. The multiple regression approach is therefore the appropriate alternative and, although no specific discussion has appeared in the literature, it has been correctly applied in marketing studies (Bass and Wilkie, 1973; Wilkie and Pesse- mier, 1973). There are situations with many variables, however, in which forward stepwise is the appropriate choice (Harrell and Bennett, 1974). 23 Several studies have appeared examining different types of atti- tude scales. Statement polarity, for example, has been shown to be misleading in some instances (Falthzik and Jolson, 1974). Most marketing studies have used positively posed statements, and the intensity of agreement for positive statements is higher than the intensity of disagreement for negative statements. Also, respondents with relatively lower levels of education are most likely to be affected by statement direction, while those with very strong convictions are least likely to be affected. In another project the similarities and differences of the stapel and semantic differential were examined (Hawkins, Albaum, and Best, 1974). Both scales produced similar results and both were shown to be quite reliable. Constant sum and semantic differentials have also infrequently been employed for situationally specific problems (Wilkie and Pessemier, 1973). Another measurement problem that has been encountered with the attitude models is presence of a halo effect. The halo effect which is the extent to which belief ratings vary across attributes for a given brand, poses the threat of potentially suppressing important variation (Wilkie and Pessemier, 1973). However, it has been shown to be less confounding for major consumer durables and industrial goods than for other goods categories which can be substantially affected (Beckwith and Lehmann, 1975). A variation of the Fishbein models, the single attribute model, has been shown to be misspecified due to halo effects, misspecification referring to the fact that the ai element is eliminated from.the attitude model and, hence, the 24 estimate of B becomes biased (Wonnacott and Wonnacott, 1970). i The weighting of predictor variables by both subjective and objective schemes has also been a topic of research interest (Harrell and Anderson, 1976). The independent (predictor) variables in models being considered here have the two components of belief and desirability. The desirability component, which has been intensively investigated and reported in the literature (Mazis, Klippel, Ahtola, 1975), has been de- fined as performance vector, force, behavioral potential, aroused motivation, subjective expected utility, attitude, affect, importance, reinforcement value, and valence by various researchers. Given the large number of descriptions of this component, it becomes obvious that opinions abound with respect to exactly what the component is and how it should be measured. In several projects the operationalized version of the desirability component has been shown to cause negative beta weights (Bass and Wilkie, 1973; Sheth and Talarzyk, 1972; Wilkie and Pessemier, 1973). There appears to be substantial agreement that this is a result of unreliable measurement of the desirability compon- ent. The specific goal of the present research project is to employ the utility weights derived from a conjoint analysis in lieu of the desirability component based on the contention that this component ‘will provide greater predictive validity through more reliable measure- ment. Due to the measurement problems explained above, several researchers have proposed alternative methodologies (Wilkie and Pessemier, 1973). One possibility that is frequently alluded to is conjoint analysis, a technique explained in the following chapter. CHAPTER III THE CONJOINT APPROACH Research Background The first published composition on conjoint measurement is attributed to Luce and Tukey (1964), although bits and pieces of the background were developed by Fisher in the 19308. After the initial conceptualization of the technique, the literature in the field of mathematical psychology was then extended by Tversky (1967), Lingoes (1967), Krantz and Tversky (1971), Young (1972), Krantz (1972), and Johnson (1973, 1975). These references provide the theoretical under- pinnings of the technique. Conjoint Measurement and Conjoint Analysis: A Clarification Before a discussion of the literature and the technique in detail, it will be useful at this point to definitionally clarify some of the terminology. There is much interchanging in the literature of certain terms which provides an ideal setting for confusion and ambig- uity. The definition of conjoint measurement in its originally used context applies to the measurement models of conjoint variables (Luce and Tukey, 1964). The terms conjoint analysis and conjoint scaling also appear in the literature. In this paper conjoint analysis refers 25 26 to the measurement of the values of jointly occurring variables through quantification of respondent value systems. An example of jointly occurring variables can be taken from the expectancy/value type models, one of which is the Fishbein model of attitudes explained in the pre- vious chapter. The jointly occurring variables are ai (desirability) and B1 (belief), the measurement of which has traditionally been separ- ated in the marketing literature. In other words, they are measured separately with different scales. Conjoint measurement is a method of measuring a B as one unit and then searching for a combination rule 1 i that best fits aiB1 when they are decomposed into separate entities; that is to say, conjoint measurement provides a systematic search pro- cedure to test whether a1 and B1 are best predicted by a multiplicative, additive, or quadratic function. Berner (1976) has performed such an analysis for the expectancy theory in work motivation which is a closely analogous case. Conjoint analysis, in contrast to conjoint measurement, heuris- tically searches for an intervally scaled utility function that best fits the rank ordered responses on a specified list of attributes. The utility function can thus be examined for rank order of attribute levels for each respondent. Alternative methods of obtaining the rank ordered responses are presented in the section entitled Data Collection. Con- joint scaling is an anomaly referring to the similarity between conjoint and non-metric multidimensional scaling algorithms. Two major similari- ties exist between the two methods. First, both require non-metric, i.e., nominal or ordinal, input yet produce output that is metric, i.e., interval or ratio. Second, there is no error theory for either method. 27 Neither can test the significance of the solutions, a limitation suffered by all of the multivariate interdependence algorithms (Kinnear and Taylor, 1971). Other examples of these methods are cluster and factor analysis. The first reference to conjoint measurement in the consumer. research literature was made by Green and Rao (1971) whose article noted that the original work of Luce and Tukey was the foundation for the type of analysis employed. Conjoint analysis is also refer- red to in some literature as trade-off analysis (Johnson, 1974). The reason for the latter designation is that both methods were being developed simultaneously but independent of each other. The trade- off terminology simply refers to a specific method of obtaining re- spondent data. There is, however, no other difference between the two terms. More explication of this method is found later in this chapter under Data Collection. There is no evidence that any method of data collection is more valid than any other or gives rise to different results (Johnson, 1973). With the above definitional clarifications, then, the remainder of this chapter deals with specifying the important aspects of conjoint analysis required to gain a working perspective of the technique. The general conjoint analysis model, including the inherent assumptions, is explained. Following that explanation is a general discussion of the computer algorithms, alternative data collection procedures, and finally a review of the published literature which utilizes this methodology. 28 The Model Assumptions The assumptions of conjoint analysis have been previously specified in bits and pieces in the theoretical literature, although they have not been outlined specifically for application of the tech- nique. Nevertheless, it is important that they be so outlined as the technique has undergone relatively minor investigations thus far with respect to its robustness. First, in order to delimit a workable scope, the basic model of interest in this paper is assumed to be additive. The major use of the additive model is the measurement of the joint effects of a set of independent variables on the ordering of a dependent variable, analogous to the main effects model in analysis of variance. The general model can be expressed as: U(X) - lel + sz2 + . . . . . Unxn where: U(X) - the overall worth (utility) of a set of attributes le1 thru U'nxn - the part worths (utilities) for each level Second, the reapondent is assumed to have completely ordered all of the orthogonal combinations of attribute levels. Orthogonal (nonre- dundant) combinations imply that the efficient use of fractional fac- torials can be apprOpriate. Fractional factorials are especially important when there are many attributes with many levels which would induce respondent fatigue and non-involvement (Green, 1974). The assump- tion of complete ordering is a more restrictive assumption than need be made for conjoint measurement, but it is applicable to this study. In their original conceptualization Luce and Tukey assumed only nominally 29 measured data, but the more restrictive case of ordered data is much easier to handle as a measurement model than the nominal case (Coombs, et. al., 1970). In the event of obtaining ordered data, there is a third assump- tion called cancellation axiom which must be satisfied (Luce and Tukey, 1964; Coombs, et. al., 1970). This axiom, coming from.mathematical psychology, has a simple counterpart in the economics literature which is more familiar to marketers. This assumption states that indifference curves do not cross unless a consumer has inconsistent tastes, which is an inadmissable contradiction (Scott, 1973). Researchers have developed methods of dealing with this predicament. One method of evaluating respondent consistency, i.e., the can- cellation axiom, in a conjoint analysis context is by Kendall's tau statistic (Conover, 1971). This statistic, proposed by Kendall in 1938, is of the form: _ Nc - Nd T n(n-l)/2 where: T - tau coefficient from sample data Nc - number of concordant pairs Nd number of discordant pairs n = total number of rankings Pairs are concordant if the rank order by the respondent agrees with the rank order of the utilities produced by the conjoint algorithm. A pair is discordant if the rank orders disagree. The above formula is sometimes referred to as indicating "badness of fit" or "stress." A value of 1.0 would indicate perfect agreement of the rank order of the 30 algorithm with the rank order of the respondent, a ~l.0, a perfect negative rank order, and a value of zero, an unrelated ordering. As a rule of thumb, a tau value of less than .70 would denote too great an inconsistency on the part of the respondent to be included in the analysis (AT & T, 1974). Admittedly, this is not a scientifically derived number, but it does indicate a reasonably close fit and therefore will be utilized in this study. A fourth implicit assumption is noted in mathematical psychology as solvability which is analogous to the assumption in economics which states that indifference curves are everywhere dense. In other words, an indifference curve passes through each point in a commodity space, an assumption which is, of course, not technically true, especially in the case of indivisible goods (Nicholson, 1972). However, given that a consumer develops a relevant range of utilities for a commodity space, and that the commodity space is a function of product attributes rather than separate and individual products, this assumption will be met to such a sufficiently high degree of approximation that it will be unlikely to develop as an empirical problem. A fifth and final assumption is that the product attributes are independent; that is to say, the model precludes any interaction effects among attributes being present. Implicitly included in this assumption is an underlying measurement model which reflects the utility of each attribute to the respondent. From the literature on attitudes the elements of the model are combined multiplicatively. Multiplicative here means that a utility value can be derived for each attribute level so that, when multiplied, the pairwise products have the same rank order 31 as the original data. It is interesting to note at this point that the multiplicative model is a trivial derivation of the additive model. The reason for this derivation is that numbers have the same rank order as their logarithms and logarithms (antilogs) are taken of multipli- cative (additive) utilities they become additive (multiplicative) (John- son, 1974). Desirable Dimensions of a Market Situation Given the above assumptions, it is useful to outline the desir- able characteristics of a market situation whereby conjoint analysis becomes an appropriate technique. Following is a list of such desir- able dimensions. 1. Product (or service) is realistically decomposable into a set of basic attributes leading to the decision pro- cess. This is primarily a reductionist viewpoint. For example, the purchase of a durable good such as an auto- mobile would be decomposable. People use explicit criteria to purchase such an item such as price, seating capacity, and warranty. 0n the other hand, an impulse or fad purchase would most likely not be required to meet such explicit criteria. A chunk of bubble gum is probably bought without consideration of attribute levels. 2. Product (or service) choice tends to be an economically rational, high stake decision process. It generally follows that the choice tends to be high cost and high individual involvement, and that there is substantial time devoted to making the decision. Again, the above example of a durable good would fit these criteria. 3. There is one decision maker. Although this statement needs no explanation, it can pose difficulties. In an industrial setting it can usually be determined whether the decision is made by an individual or a committee. But it also is possible, as it is with consumer purchase decisions, that one person may make the decision but only after considerable external influence. A case in point is the purchase of a consumer durable. The family unit may not make the decision, but it is reasonable to con- clude that the decision maker was influenced by family 32 members. Specifically, then, the problem is that a respondent may be able to provide attribute rank orders, but these rank orders may not be the ones actually used in the final decision process. One possibility is for husband and wife to respond to the measurement instrument together. Another possi- bility is that each individual may revise the rank order after input by other family members. Rank order revision, however, has no empirical evidence presently and would be a fertile topic for further investigation. 4. Product (or service) is chosen according to highly spe- cific, non-subjective attributes. In other words, attribute level specification is perceptively homo- geneous across consumers. Specificity and objectivity are factors to be considered in the choice of attribute levels, but it is flexible almost to the point of being arbitrary. For example, attribute levels that mean totally different things to different people are un- acceptable. Seating capacity in an automobile might be denoted as four. To some people, this may mean four adults; to others it may mean two adults and two children. The solution is to state the levels more specifically, such as adult seating capacity. In many instances it is possible to argue either way concerning the homogeneous meaning of words. The solution is an a priori consideration, but not to the point of labor- ious proof. 5. In the event of many attribute level combinations the factorial combinations of the basic attribute levels must be believable. The alternatives must be realistic or non-involvement by the respondents confounds any research results. For instance, an automobile with a seating capacity of six adults that gets forty mpg, and costs $2,000 is ludicrous in today's marketplace. The attribute levels must be within a range considered relevant for present consumers. As is true with most methodologies, it is difficult to imagine a product that would fit exactly all of the model assumptions detailed above. Recall, that conjoint analysis is still highly experimental, and the above market characteristics are based on the statistical assumptions and meager empirical work now available. It is desirable to satisfy as many of the above dimensions as possible and note the 33 limitations of the research with respect to the others. Just as with the assumptions, a definitive list of publicly available computer algorithms is not to be found. The following sec- tion outlines such algorithms. Computer Algorithms It is not within the scope of this paper to delineate all of the technical aspects of the available algorithms, but rather to describe their general characteristics and origin. All algorithms noted here are non-metric decomposition methods similar to the techniques of non- metric scaling (Green, Carmone, and.Wind, 1972). They all attempt to do the same thing in slightly different ways; that is, they convert respondent rank orders into utility estimates. This conversion is usually accomplished by an heuristic iteration procedure which searches for a set of utility values for each respondent that will minimize a badness of fit or stress measure. or equivalently maximize a phi or tau value such as the one explained earlier. Arithmetically, a phi or tau value could be visualized as an attempt to minimize the difference between the original rank orders (Y) and the computed utility values (T). Thus, with the difference (Y — §) - d, the algorithm is in search of a configuration of utilities to minimize the d value or badness of fit. It becomes obvious at this point that the procedure thus far is very analogous to the least squares method of regression analysis, the major difference between the two being that least squares is a metric proce- dure while conjoint is a non-metric procedure. The conjoint programs seek a unique configuration in that the configuration is subject only 34 to similarity transforms. A similarity transform is invariant only with respect to operations that will not change the observed rank orders, which is the constraint under which all of the non-metric programs operate. Permissable operations are addition or subtraction of a constant and rotation of a configuration about the origin (Green and Tull, 1975). Through operation with similarity transform constraint, the iterations of the algorithm continue in an attempt to find perfect monotonicity, that is to say, perfect agreement between observed rank orders and computed utilities. As is the case with many statistical multivariate algorithms, each of the programs listed below has its own special technical pecu- liarities. These unique properties may be important for mathematical purposes, but tend not to be revealed in empirical work (Green and Tull, 1975). l. MDNANOVA - J. B. Kruskal 2. CCM - Frank Carmone 3. POLYCON ADDALS - Forest Young MDRALS 4. CM-I - James Lingoes S. LINMAP - Allan Shocker and V. Srinivasan 6. NMRG - Richard Johnson 7. 0RDMET - Gary McClelland and Clyde Coombs 8. PREFMAP, Phase IV - Douglas Carroll and J. J. Chang As with other statistical algorithms, there is presently no evi- dence regarding the choice of one of the above algorithms rather than another for empirical work. The program utilized for this study is 35 Richard Johnson's NMRG program, which was selected simply on the basis of its availability and the opportunity for technical advice on its use and which has been employed in many other instances, as is noted in a later section entitled Applications in the literature. Appendix B contains Johnson's program and the method of deriving the solution. Given this background on the computer algorithms, the next step is a delineation of alternative data collection procedures. These pro- cedures are outlined in the following section. Data Collection Thus far, the data collection procedures for conjoint analysis in market settings have generally involved one of two methods. The first is referred to as the trade-off method and the second as the full profile or concept evaluation method. Under similar conditions similar results will be obtained using either method (Johnson, 1973). The Trade-Off Method The trade-off method requires rank ordering by a respondent of preferences in all levels of two attributes. An example will clarify exactly what a trade-off matrix attempts to do. A respondent might be shown a matrix like the following pertaining to automobiles Purchase Price $3,000 4§3,500 $41990 U.S. Manufacturer Foreign.Manufacturer 36 and be asked to fill in the respective alternatives by rank ordering each. Note that one axis is a ratio scale (price) and the other is a nominal (origin). These axes could be any combination of levels of measure because the respondent is able to rank order any combination of levels. The attributes can be determined from a comprehensive list by use of a technique such as factor analysis, or from previous re- search (Harrell and Bennett, 1974). With respect to attribute levels, there is a need for believa- bility, i.e., levels within a relevant range for consumers, as noted in the previous section. Each combination of levels must be realistic, but there is no other specific criterion for establishing the levels. They must not, as also was previously noted, be ambiguous, but this is hardly a strict criterion. Now, let us suppose that given the above matrix the respondent has hypothetically rank ordered the alternatives as follows: Purchase Price $3,000 $3,500 $4,000 U.S. Manufacturer 1 2 4 Foreign.Manufacturer 3 5 6 By simple inspection, it can be ascertained that this respondent pre- fers an auto that is manufactured in the U.S. as Opposed to a foreign manufacturer and lower prices to higher prices, other things being equal. By a joint examination of the attributes in the above matrix, more information can be obtained. For instance, while this consumer's second choice is a $3,500 auto manufactured in the U.S., it would be 37 more desirable to switch to a foreign manufacturer than pay another increment in price. This conclusion assumes that the consumer trade- off is with only these two attributes with the ceteris paribus assump- tion holding. Thus, the relative influence of the factor level can be ascertained, and, through investigation of other attributes such as warranty, seating capacity, etc., the respondent's value system for an automobile purchase can be reconstructed. Such reconstruction would be done by allowing an algorithm such as NMRG to restructure as closely as possible all combinations of rank ordered factor levels and by assigning appropriate utility values to each level. Through knowledge of the utilities of each level, the rank order of preference of a given combination of levels for that respondent could be made. The Full Profile Method The above data collection procedure is quite different from.the procedure described initially by Green and Rao (1971) whose approach has been referred to as the full profile or concept evaluation method which is closer to the functional form investigations in psychology (Berner, 1976). With this procedure respondents are asked to rank order product concepts which differ simultaneously with respect to several attributes. An example might be: An automobile manufactured in the U.S., for a price of $3,500, with a 2 year warranty, and a dealer that is a 20-minute drive from your home. The above statement would be in an array of statements that varied with respect to the relevant attributes, i.e., country of origin, price, length of warranty, and dealer location. The assortment of choices can be written, verbal, or pictorial. In the event of a totally new product 38 concept, such a concept could even take the form of the actual experi- mental product. When the number of options requiring rank order is large a sort board can be efficiently utilized. Differences Between The Two Methods An examination of the two methods described above reveals differences which would concern researchers under varying circumr stances. The trade-off method is laborious for the respondent and requires the respondent to abstract each comparison due to the ceteris paribus assumption. 0n the other hand, the full profile method specifies a concept fully and thus promotes a higher proba- bility of commonality of perception. Still, the greater inherent realism in the full profile method is limited by the fact that re- spondents cannot easily interpret profiles including more than five to seven attributes (Johnson, 1974). A drawback in this method is the cost, especially for the more reliable pictorial method where scale drawings are a necessity and where mock models are often needed. Both methods call for a great deal of respondent training with each requiring an interview of approximately 1% hours. The problem of too many factor level combinations for rank ordering by respondents is solved through various orthogonal designs, e.g., Latin square, fractional factorials (Green, 1974). Applications in the Literature A limited number of examples of conjoint analysis have made their way into the literature. Although such diverse applications as consumer non-durables, financial services, industrial goods, automobiles, 39 and transportation have been noted they are generally unavailable for academic perusal (Green and Rao, 1971). Major attempts at the use of the technique which have been published are noted below. From the beginning the published marketing research applications have contained the detail to make the technique plausible under varying circumstances. The original marketing publication specifically out- lined possible applications in media planning, discount pricing, and Opinion research (Green and Rao, 1971). Much of the groundwork was also developed in terms of general use of the technique including the model, the assumptions, and the available algorithms. Also outlined were possible applications of the model in physical distribution, new product evaluation, packaging and branding, attitude measurement, and cost benefit analysis. Implementing some of these ideas was the initial step taken in the literature. Applications in consumer menu preference and condominium design and pricing appeared first (Green, Wind, and Jain, 1972; Fiedler, 1972). Both were applications of the additive conjoint model, although one difference was that the MONANOVA algorithm was utilized in the menu preference study while NMRG was used for the condominium study. Another published study investigated worth of discount cards to housewives (Green, Carmone, and Wind, 1972). This study introduced the possibility of combining the use of multidimensional scaling and conjoint analysis. The complementarity of the two techniques is natural as the criteria (axis) must be subjectively evaluated for the scaling procedures while conjoint prespecifies the axes. The ideal, of course, is a matching of the subjective and prespecified criteria, 40 a matching which depends largely on the care taken to prespecify the correct attributes. MONANOVA.was the algorithm utilized for the conjoint analysis. The first publication in the area of physical distribution was conducted for Air Canada (J. D. Davidson, 1973). After a random tele- phone survey of 20,000 households for the relevant geographical area, 1055 respondents were selected for personal interviews. It was deter- mined from initial group depth interviews that people could describe their preferences for mode of travel, i.e., car, bus, train, conven- tional air, and STOL (short take off and landing), in terms of thirteen independent attributes. The objective of the study was to build a model that would forecast and evaluate the different modes of trans- portation and the effect of different marketing strategies on the STOL market share. Respondents were asked to complete twenty-one trade-off matrices to determine their utility function for each of the transpor- tation modes. The NMRG program was utilized in the analysis. Trade-offs in automobile brand choice was the tOpic of yet another investigation (Johnson, 1974), the bulk of which was devoted to the explication of the practical considerations when conjoint analysis is implemented. For instance, the assumptions, the computa- tions, and the validity of the technique were addressed. It was also noted that to date there were not enough data available to validate the procedure through a comparison of the results with actual variables in the marketplace, another point which emphasized the pioneering nature of the technique. The NMRG algorithm was used for the analysis. Still another applied example of conjoint analysis is in the area of consumer non-durables (Green and Wind, 1975). Together with 41 many other examples is a detailed one examining the market for a new spot remover for carpets and upholstery. As the article was exemplary in content, many of the technical details were omitted, but five attri- butes were used in a 3 x 3 x 3 x 2 x 2 design (indicating the number of levels for each attribute). This design would involve 108 alternatives to be tested in a full factorial design. Due to considerations such as cost and respondent endurance, however, an orthogonal array of combina- tions was utilized and the number of combinations was thus limited to 18. Further consideration in the use of orthogonal designs is given by Green (1974). In the above analysis of non-durables, MDNANOVA.was used for the analysis. A final example of conjoint analysis, in the context of a location problem (Parker and Srinivasan, 1976), involved the location of rural health care facilities according to consumer preferences combined with community considerations and in terms of cost/benefit constraints. Several elements of reliability and validity factors were noted as being favorable to the conjoint procedure. A subprogram of the LINMAP procedure was utilized to analyze the data base (Shocker and Srinivasan, 1974). Limitations and Advantages of Conjgint Analysis Clearly, the above examples indicate the initial spectrum of possibilities using conjoint analysis, although, admittedly, there are limitations. For instance, it is difficult to obtain an interview of 1% hours with industry personnel. Because the technique is cross sectional in nature, it would be desirable to repeat such interviews 42 at selected intervals and this would again be difficult to do. It is also obvious that utilities change over time and at different rates for different situations. In general, it is believed that a sufficient sample size would be from 200 to 500 and this too could present pro- blems.1 It is also possible that in industrial settings, where the product specifications are explicit but numerous (greater than ten or twelve), the technique would not be efficient. And it is worthy to note that no error theory is available for conjoint analysis; that is to say, there are no significance tests as such for the utilities or the general models. Another problem that is difficult to overcome is that of non-involvement by respondents. The mental task of explicitly comparing multidimensional statements is quite rigorous. Many respon- dents find the task involves too much thinking and they therefore require a substantial incentive to participate.2 The distinct and unique advantage of the technique is, of course, its potential ability to construct consumers' value systems given the satisfaction of the assumptions. People are generally unable to expli- cate utility values either because they do nOt know them or they feel they must adhere to socially acceptable norms. Conjoint analysis imr plicitly constructs the utilities within each respondent's system. 1This has not been scientifically validated but it has been proven empirically true according to a discussion by David K. Hardin at a University of Chicago sponsored seminar, March 16, 1976. Seminar entitled, "Marketing Trade~0ffs Using Conjoint Analysis." 2Discussion by Joe Murphy, Research Director at General Foods at seminar entitled, "Marketing Trade—Offs Using Conjoint Analysis," March 16, 1976. 43 Given the above discussion of conjoint analysis and the pre- viously outlined discussion of relevant attitude literature, the next section details the methodology of this research project. CHAPTER IV SCOPE AND GENERAL METHODOLOGY Estimated Models The background and underpinnings of this study were given in Chapters I, II, and III, while this chapter explicates the specific methodology for integrating a conjoint analysis model and the Fishbein attitude models. Theoretical considerations were listed in Chapter I. There are no criteria that points to one model as superior to the other but instead each yields a rather different interpretation. Given the purpose of integrating two models, then, there are three estimation procedures involved. The first estimation procedure involves the Fishbein models of attitude. The more recent model of attitude toward an action, A is act' estimated here. Recall from Chapter II that this model takes the validated algebraic form: n BI = OZ Biai i=1 The model in its disaggregated form is also estimated in the form: BI a f(Biai Second, a utility based estimate of each respondent's value system is obtained from a conjoint analysis which produces an intervally scaled utility weight for each attribute level. 44 45 The third and final estimate is for a combined model which sub- stitutes the utility estimates of the conjoint analysis for the desir- ability component of the Fishbein models. This is a legitimate sub- stitution based on previous research discussed in Chapter II. The combined models would be expressed algebraically as: A0 - ZBiUi B1 = ZBiUi B1 = f(B1Ui) where the U1 is the utility estimate from the conjoint analysis. Chap- ter V also contains an analysis of the distributional characteristics of the desirability and utility components. The assumptions of the Fishbein and conjoint models are discussed below. Attribute Determination Subcompact automobiles were chosen as the consumer non-durable category to be investigated. Three major American brands were selected for evaluation since consumers are likely to be more familiar with these than with non-American cars. The relevant determinant attributes used for this study, attributes obtained from previous research (Nazis, Ahtola, Klippel, 1975) and confirmed as currently relevant for subcom- pact cars,1 were: 1) Brand, 2) Price, 3) Style, and 4) Dependability. Although it is interesting to note that only these four attributes rate as highly important to consumers, it is generally believed that consumers use no more than three criteria for any purchase. This has been found to be the case in multidimensional scaling and factor analytic studies 1From communication with.Robert Bierley, Research Department at General Motors. of determinant attributes. 46 If other than determinant attributes were specified for inclusion in the models used here, the results could well be spurious. For instance, it is a well known fact that if a non-determinant attribute is included in a regression equation it is likely to increase explained variance and have a biased beta weight. This is especially likely to occur if the non-determinant variable is collinear with a determinant attribute. For this reason, then, only important determining attributes should be included in the model. It is, of course, quite possible that consumers would like to have other attributes determinant but they are without a variation in choice. For example, automobile warranty may be very important to some consumers, but it is relegated to the status of a qualifying factor if it is equal for all brands, which is, in fact, the present state of affairs. For use in both the Fishbein and the conjoint models the levels of each attribute were specified as follows: 1. Brand 2. a. Chevette b. Pinto c. Vega Dependability 4. a. Sturdy, Quality Workmanship b. Average Workmanship c. Minimum Workmanship Style ‘ a. Modern Style and Lines b. Average Styling c. Constant Style that is Functional Price a. $3,000 b. $3,500 c. $4,000 The definitions and implications of these levels for both models are discussed below. 47 Research Sample The sample consisted of 238 undergraduate business students en- rolled in MTA 317 at Michigan State University for Spring quarter, 1976. Before this number was arrived at, six questionnaires were determined not usable because they were incomplete. This sampling procedure, of course, does not constitute a random sample. Randomness, however, is only an issue in the discussion of external validity, and the issues under examination in this study involve only internal validity. Since generalization to the sampled population is not a concern, a random selection of respondents is unnecessarily cumbersome and time consuming. Another concern relevant only to external validity is the elimination of order bias within the questionnaire which can be achieved by switching the order of the questions. But there was no attempt to generalize to a sampled population and, therefore, order bias became irrelevant. The sample size was sufficient to reliably employ both techniques used in this study. Each individual in the sample was requested to complete the questionnaire that appears in Appendix A. Note that the questionnaire obtains data for both the Fishbein and conjoint models. Model Considerations Given this research scenario, it is necessary to explain the implications for each of the models under consideration. The Fishbein Models The Fishbein model has received considerable attention by researchers, and, hence, the implications specific to this setting 48 can easily be established. Empirical considerations for the Fishbein model are 1) attribute determinance, 2) a brand specific setting, and 3) attribute independence. Attribute determinance is discussed above and requires no further explanation. The setting is brand specific, i.e., Pinto, Vega, and Chevette; hence, this criterion is satisfied. The independence of the attributes, which is a requirement common to both Fishbein and conjoint, is established by examining the correlation matrix of all attributes included in Chapter V. As noted in Chapter II, the usual method of determining attribute independence is through a technique such as factor analysis which is most appropriate when the attributes cannot be specified a priori. Factor analysis also assists the researcher in establishing factors that are independent and avoids subsequent attribute redundancy. Although the attributes for this study were suggested from previous research, as was noted above. For the present study it is necessary to check factor independence. Factor analysis then becomes an unnecessarily arduous procedure. A totally valid alternative to factor analysis in this situation is borrowed from econometrics (Farrar and Glauber, 1967). The procedure is quite simple and straight-forward. The criterion for attribute collinearity is established from the comparison of the first order correlations with the multiple correlations for each set of attributes used in a regression equation. If the first order correlation, i.e., the simple correlation between two attributes, is less than the multiple correlation from the total regression equation, then the factors are considered sufficiently uncorrelated so as not to bias the regression 49 weights. This procedure is carried out in Chapter V in order to insure that the attributes are indeed independent for this study. As a cross- check on the stability of the beta weights, a cross-validation is per- formed. The sample is cross-validated by estimating the beta weights for a 50-50 sample split. With this procedure, the confidence levels of the beta weights should overlap if the sample is stable, i.e., collinearity is not present (Kane, 1968). This completes the empirical considerations for the Fishbein models. Conjoint Analysis: Implications With only a meager amount of empirical evidence available on conjoint analysis, it is necessary to consider the implications in more detail. First, a choice must be made between the full profile and trade-off data collection methods as explained in Chapter III. The full implications of each of these methods are of current interest to researchers, but the choice must be made on a, subjective basis. The trade-off method was used in this study as it has several inherent advantages not available with the full profile method. First, given four factors with three levels each, there is a total of 12 factor levels. When these are taken two at a time, there are only six possible unique combinations of factor levels. In the alternative full profile method, however, the number of possible factor level combinations would be 34 - 81. In order that reapondent fatigue and non—involvement be avoided, the full profile method would require a fractional factorial design. Hence, the trade-off method is more efficient. It is also worthwhile to note that there is no research indicating superior accuracy in the use of either technique. 50 The major problems encountered with the trade-off approach are the ceteris paribus condition and lack of reSpondent task comprehension. using the trade-off method requires the respondent to vary levels of two factors while giving no consideration to variant conditions of other factors. With little experience or training in this task, it is to be expected that the average consumer will find it difficult to abstract a problem into a ceteris paribus setting. This first problem is mostly avoided by using a student sample since students understand the assumption from their economics courses and, because of their academic experience, are more likely to be able to abstract a situation than other randomly selected respondents. As for the second problem of lack of respondent task comprehension, it has been noted that an average inter- view length for a conjoint questionnaire has historically been 1% hours. Much of this time is spent explaining to respondents the task at hand. The administration time for students was substantially less, however, approximately 25 minutes or one-third the usual requirement, again because of their greater ability to abstract and follow directions with only minimal instructional effort. Conjoint Analysis: Assumptions The previous chapter stated the applied assumptions of the type of conjoint analysis used here. First, it is assumed that the general model is additive. It seems reasonable, although again there are no strict criteria, that no interaction exists in the choice of subcompact cars. For instance, it is assumed that a respondent is equally as likely to require a given level of dependability regardless of the style of the car; that is to say, dependability does not vary across levels of style. If, in fact, the model for subcompacts is non-additive, polynomial 51 (non linear) conjoint would be appropriate. Unfortunately, there are presently no studies which apply polynomial conjoint analysis. Of course, the attitude models suffer a like disadvantage in their lin- earity assumption. Second, the respondent is assumed to have ordered all relevant combinations of factor levels. This criterion has been met which leads to the assumption of the cancellation axiom. In order that this assump- tion be met, any respondent with a tau value of less than 0.70 is re- moved before the analysis is completed. Recall that tau reflects the consistency of each respondent's answers with the computed utility values. A cut-off of 0.70 seems to reasonably exclude any inconsistent respondent, although, again, no specific cut-off point has been estab— lished as being best. A fourth assumption, that of solvability, appears well grounded as the levels of each factor provide a total range from high to low. By virtue of using this total range, it is likely that a re- spondent is sufficiently free to locate the position of his indifference curve for that attribute. The final assumption of attribute independence is examined with the same procedure discussed under the Fishbein model. Conjoint Analysis: Consideration of Desirable Characteristics Given the above assumptions, it is now desirable to examine whether this study meets the practical characteristics outlined for con- joint analysis. First, there is no reason to believe that subcompact automobiles are not decomposable into a set of basic attributes which lead to a decision process. In fact, it seems reasonable that such a decision is decomposable given that such a substantial expenditure will 52 not be taken lightly by the buyer. Decomposable attributes then lead to the second characteristic, that the decision process tends to be rational in an economic sense. Since subcompacts fit into the con- sumer durables category, the decision is most likely to have a high involvement as it is a high stake, high cost decision. It is also quite likely that such an important decision would involve more than one decision maker. For example, the purchase of consumer durables is usually influenced by family members or at least reference groups. In most instances the perceptions of a single individual decision maker are necessary or the computed utility values will not reflect the total decision process. If others' attitudes are a significant influr ence in a purchase, they may or may not be incorporated into the respondent's utilities. In any event, this again becomes an external validity issue. The sample results are not generalizeable if the criteria of a single decision maker are not met. However, the inten- tion here is not generalization but rather model comparison. And model comparison, in which internal validity becomes the important issue, is not affected. The final assumptions of believability and perceptive homogeneity of factor levels are much more difficult to validate than the preceding assumptions. They are subjective formulations at best and are difficult to evaluate except in a logical framework. Because the brands chosen hold substantial market shares in the United States, they should be among the most familiar alternatives. Students, especially business majors, are more aware of alternative auto purchases than would be consumers who are more isolated and less educated. 53 The attribute of dependability is probably composed of several components including workmanship, maintenance, and reputation. Work- manship seems to be a core issue here. If quality workmanship goes into a car, it is quite probable that it will require less maintenance and over a period of time establish a reputation as being dependable. Workmanship, then, seems a logical proxy for that attribute referred to by consumers as dependability. Style is another attribute that is only justifiable with logic. Style has been specified from constant (low) to modern (high). It would seem that the phrase "modern style and lines" would provoke the respondent to think about how the car looks. The other end of the spectrum permits the respondent a choice opposite of modern. A constant style, such as Volkswagen uses, repre- sents a full range of choice. It is also noteworthy that both models suffer from an ambiguity in attribute level specification, but probably the Fishbein model is less disadvantaged as it provides a zero point on the bipolar scale which, in essence, permits the respondent to ignore the attribute. The attribute must be ranked, however, in the conjoint model. The specification of price levels, $3,000 to $4,000, is within the current price range of the subcompact brands. But, again, the intervals are $500 between levels, whereas the interval could have been virtually any amount. The $500 seemed to represent an interval that would require the respondent to consider it rather than ignore it before going up or down one level. This concludes the discussion of the methodology. The following section addresses the limitations of the present study. 54 Limitations of the Present Study This research must be viewed as essentially of an exploratory nature. The objective of integrating the models has been accomplished but not without limitations. First, the Fishbein model is considered representative of the group of compensatory multiattribute models in that it shares with them many of the same advantages and disadvantages. Other models in this group could conceivably perform differently under the conditions outlined in this study, however. This study does not attempt to speak for those models. Second, the sample for this research was not generalizeable in that it does not represent a random selection of respondents. The random selection process was not necessary to accomplish the objective of this study, but the possibility exists that it could affect the results. As discussed previously, such an effect is intuitively unlikely but it still should not be overlooked. The technique of conjoint analysis is relatively new and future research will most likely uncover theoretical limits presently unknown to researchers. With any such new technique, it is, of course, advis- able to view the results cautiously. Other than simple logic, there is relatively little evidence as to the best data collection methods. The trade-off method was used for this study but the implications of it, or the full profile method, are, for purposes of reliability and validity, virtually unknown. Conjoint analysis faces the additional limitation of a complex respondent task. It requires an arduous mental exercise on the part of the reapondent which, of course, defrays parti- cipation by many respondents. There is also the serious limitation of 55 no error theory. Again, this problem is inherent to heuristic solutions and must be considered as an a priori limitation. Preclusion of the use of common tests of statistical significance severely limits the substantive conclusions that can be drawn from an analysis. Conjoint is, like any methodological technique, prone to misuse by abuse. It presently has only been published in the marketing liter- ature as an additive model, though it is very possible that some utility functions or decision rules do not adhere to this assumption of addi- tivity. It is likely that future efforts will attempt to deal with interactive models. Again, there is little indication of the presence of a particular model in a particular situation or how well the simpler models estimate the more complex ones. These limitations are not im- material but neither are they formidable. This completes the examination of the assumptions underlying each of the models under consideration and the inherent limitations in the present research. The following chapter presents the analysis of both models. CHAPTER V ANALYSIS AND RESULTS Respondent Consistency This chapter includes the results of both the Fishbein model and the conjoint model, along with an attempt to integrate the models. The underpinnings of the models and the general methodology have been discussed in the previous chapters. The questionnaire used to obtain the data and the instructions for the questionnaire are included in Appendix A. Recall that the time required for completion of the entire instrument, i.e., the questions pertaining to both the conjoint and Fishbein models, was approximately twenty five minutes. As this time span is substantially less than the time usually required for completion, it was especially crucial that the respondents understand and complete the task according to instruc- tions. As noted in the previous chapter, an a priori decision was made to eliminate respondents with a tau value of less than 0.70. By use of this criterion, twenty respondents were eliminated from the analysis, a number which constituted 8.4 percent of the usable responses. Since previous research with conjoint analysis is so scarce, it is difficult to say whether this is an inordinate deletion rate. Discus- sions with industry sources, however, have revealed that discards 56 57 varies from six to fifteen percent.1 If this range is in fact correct, then the 8.4 percent is quite acceptable. After consideration of these discards, 218 usable and valid reaponses remain for analysis which is also an acceptable number for the two techniques being utilized. Results from Fishbein Analysis The analysis in this section is consistent with previously pub- lished analysis of the Fishbein models. As discussed earlier, it is important to determine attribute independence. Again, the criterion is relevant to assure stabilization of the beta weights. And the criteria for stabilization in any given regression equation is that the simple correlations between the independent variables be less than the multiple correlation coefficient. Table 1 presents the correlation and disaggregated models. Table matrix for all variables in the Aact IB is the correlation matrix for the Ao model. Of course, the summated models of A0 and Aac are not hindered by collinearity as there is only t one independent variable. The disaggregated model for each brand, how- ever, has three independent variables which could present the problems inherent to collinearity. The problem does not arise in this study as can be seen in Table 1A. 1From a discussion with David K. Hardin of Market Facts, Inc., Joe Murphy of General Foods, and Paul E. Green of University of Penn- sylvania at a seminar, "Marketing Trade-Offs Using Conjoint Analysis," March 16 and 17, 1976 at University of Chicago. 58 8. 3. .¢ 6 »%v %v Mu ..mw .%.%7 .d .d e a. s e e D. J rs m. a a no a... :40 % 03 PD. 03 PD- 9 .fiJ. a 9 oo o o. o O. 4 a s; .q 4 at h. a. a I Ida I a d 9409 I e I I made. a nae. a sue a. ,3 4 a s a [My 9.». ,4 Au. 903. (Q. mhumo O)» \wJOWu ”he 0 9 09). O I J 00¢. mom. mnm. mmo. moo.l wNo. «mo. mmo. own. mmm. mmm. cum. moo. coo. haocoum mom. who. and. «No. ONN. Hem. omo. mom. HNH. omH. «mm. oeo. oNo. hufifififimodommn ooo. hHo. «mm. HoH. coo. moo. ooh. NmH. «NH. Non. NqH. moo. mamum w as m> qu. oom. who. mmH. mmo. wow. owe. mmm. mmo. HmN. Ono. mEOdoom «no. wHH. «an. 500. HHH. mNm. HON. mmo. me. mmo. huHHfinmvcmme wmo. HoH. hma. wNH. mun. NmH. omo. mac. omo. meuw “ouswm saw. coo. one. Nmm. How. “so. see. «so. saocoom “Hm. mam. mwm. mes. Nae. soc. cos. Assassmsaoamo mmo.l «OH. 5mm. mmo.t omo. Omw. mHmum "muuo>oso HNN. mom. Hem. moo. mNo. mmm> «mm. Hmo. mNm. omo. ouafim NHo. wHo. «we. muum>mso ”mom mounofiuuu< omumaasm mom. mNN. mwm> New. Oucfim "vumzoa acousH Hou0H>mnom NHdez onH Pinto §_Vega 4. Chevette > Pinto > Vega 5. Chevette - Pinto < Vega 6. Chevette - Pinto 3_Vega All other possible combinations are redundant with one of the above com- binations. Each respondent will fulfill the criterion for only one of the six possibilities listed above. For respondent 001, the category would be number 6 as that individual has rated all brands equal. By use of the same procedure, ranges for all four attributes can be com- puted for each respondent. Again, in reference to respondent 001, the ranges for each attri- bute would be as follows: Brand 0.0000 Style 0.0750 Dependability 1.2534 Price 0.0496 In order that the importance of each attribute be expressed in relation to the other attributes, it is possible to sum the above utility ranges and compute the percent of total utility attributable to each attribute. 66 For example, the sum of the utility ranges listed above is 1.3780. When each range is divided by this sum, the following percentages are Obtained: Brand 0.0 Style 5.4 Dependability 89.6 Price 3.6 These percentages will, of course, sum to 100, except for rounding errors. It can easily be seen from these figures, then, that dependability is by far the most important attribute to this respondent. Style and price combined account for less than ten percent of the total utility, and there is no differentiation with respect to brand. It must be noted, however, that a factor's relative importance is dependent on the factor levels included in the design. For instance, had the price range been $2,000 to $6,000, that range's relative impor- tance could have easily exceeded style and dependability. The range of $3,000 to $4,000 used in this study is quite likely to include those values of the relevant range which are close to the extreme. In other words, it is difficult to buy even a subcompact car for less than $3,000, and those small cars above $4,000 are usually not direct competitors with the less expensive models because of the price factor. Although this discussion is rather peripheral to this study, since the Objective was the integration Of two models and not generalization of the results, it is quite easy to conceive of studies in a commercial setting which would require generalizability and the issue would become critical. 67 Results from Integrating the Models Now that the conjoint analysis and the Fishbein models have been estimated, it is appropriate to examine how they might be integrated. There is no direct comparison of the two because one is a construct model Of attitudes, while the other is an analytical technique. Both conjoint analysis and the Fishbein model do, however, ultimately attach weights to the attributes under consideration, although these weights are not directly comparable, primarily because the Fishbein model esti- mates are anchored to an Object (automobile) while the conjoint weights are not so attached. In other words, the weights estimated in the Fishbein analysis are for the attributes of style, dependability, and economy as they are related to a specific brand, while, the conjoint analysis assigns weights to each attribute including brand. iMoreover, the conjoint weights are separate estimates which are not anchored to a specific brand, but rather are independent estimates. One possibility exists for integrating the two models and that is the substitution of the utility weights from the conjoint analysis for the desirability ratings in the Fishbein model. This substitution would produce a model, analogous to the original Fishbein model, speci- fied as: n .2311 A0 1.1 i i where: Ao - attitude toward an object Bi - the individual's belief about the probability that an object is related to an outcome, 1 U - the individual's utility for outcome i i 68 Another estimation, also possible for the model of behavioral intent, would be expressed as: 1"]. BI - X B U 1‘1 1 i where the components are the same as above, except for the dependent variable which would be behavioral intent (BI) rather than attitude toward an object (A0). This disaggregated model Of attitudes would then be estimated as: BI - f(B1Ui) The variables are again defined the same as above, with the exception that the summation sign (2) is replaced by a function notation (f) to indicate that the attributes will not be summed but rather will each be associated with a separate beta weight. Tables 6 through 8 present the respective regression estimations Of the above models. When Table 6 and Table 2 are compared, the use of U1 in place of a1 produces slightly different multiple R's. The use of U1 in the attitude models produces a slightly lower multiple R for two brands (Chevette and Pinto), while the third brand (Vega) has a slightly higher multiple R. The same results occur for the summated model of behavioral intent (comparisons of Tables 3 and 7). Estimation of a1 with the traditional bipolar scales again appears to contribute to a slightly higher multiple R for two of the three brands. In all compari- sons an r to 8 transformation shows no statistically significant differ- ence between the multiple R's. The disaggregated model of behavioral intent produces some in? teresting results also. An examination of Table 4 versus Table 8 shows 69 TABLE 6 A MODEL WITH UTILITY SUBSTITUTED FOR DESIRABILITY Multiple R R2 F p Chevette .557 .310 95.7 .001 Pinto .619 .383 132.5 .001 Vega .661 .437 165.4 .001 TABLE 7 A MODEL WITH UTILITY SUBSTITUTED FOR DESIRABILITY Multiple R R2 F p Chevette .452 .205 54.8 .001 Pinto .484 .234 65.1 .001 Vega .567 .321 100.9 .001 TABLE 8 DISAGGREGATED MODEL WITH UTILITY SUBSTITUTED FOR DESIRABILITY 2 Multiple R R F p Chevette .479 .229 20.9 .001 Pinto .500 .250 23.5 .001 Vega .578 .331 34.9 .001 70 the multiple R's to be consistently higher for the model employing a1 as the measure of desirability versus the model using 01' To illustrate an indication of the differences in the distribu- tions of a1 and U1, Table 9 is presented. In terms of kurtosis, the distributions have like signs but different magnitudes, the most sub- stantial difference being for the attribute style. Skewness differs less drastically with respect to magnitude but changes from negative to positive for style, with the other attributes again being consistent. The range and median are presented for more completeness in examining the distributions but are meaningless for comparative purposes as they are not in standardized units. In summary, then, the integrated model has not produced signifi- cantly different results than the Fishbein as the latter has tradition- ally been used in marketing. There are, however, considerations which would indicate continued use of the traditional Fishbein model and these are presented in the following chapter. 71 TABLE 9 DISTRIBUTIONAL CHARACTERISTICS OF UTILITY* AND DESIRABILITY** Style Dependability Economy ai** "1* a1 ”1 31 U1 Kurtosisl 3.538 .344 4.024 1.075 -.191 -.443 Skewnessz -.931 .849 -.348 -.906 .349 .611 Range o-21 o-1.552 0—18 .111-1.720 7-18 .006-1.43 Median 14.32 .347 11.709 1.262 12.293 .457 *Utility estimates from the conjoint analysis. **Desirability estimates from a seven point bipolar scale. 1Kurtosis is a measure of the peakedness or flatness of a distri- bution relative to the normal distribution. A normal (mesokurtic) dis- tribution has a kurtosis coefficient of zero, a peaked (leptokurtic) distribution has a positive coefficient, and a flat (platykurtic) dis- tribution has a negative coefficient. 2Skewness is a measure of the deviation from symmetry in a dis- tribution. A positive coefficient indicates that the cases cluster more to the left Of the mean while a negative coefficient indicates a cluster of cases to the right of the mean. As the skewness (and the kurtosis) is a standardized coefficient, the mean of any distribution is located at zero. (Nie, et. al., 1975). CHAPTER VI CONCLUSIONS AND RECOMMENDATIONS The purpose of this chapter is to discuss the conclusions from this project and outline the implications of those conclusions for future research efforts. In the first section the analysis is inte- grated to reach conclusions on the basis of the combined Fishbein and conjoint models, while the second section offers ideas for future research. Conclusions from Synthesis of the Two MOdels The purpose of this study was the integration of a conjoint analysis model with the Fishbein attitude model, an integration which was accomplished by substituting the conjoint utility weights for the desirability component of the Fishbein model.- As discussed in Chapter V, this integrating procedure produced a model with a multiple R that was not significantly different than the estimate obtained when the original desirability component was used. This result is interesting in view of the quite different distributional characteristics of the utility and desirability components found in this study, a difference which again points to the danger of multiplying non-ratio scales. This research presents clear empirical evidence that quite different distri— butions can lead to statistically equal correlation analysis. The theoretical implications of the multiplication of non-ratio scales have 72 73 previously been outlined by Schmidt and Wilson (1975) who also point out the theoretical possibility of Obtaining spurious correlation analysis. With both empirical and theoretical evidence of Spurious corre- lations, then, the verdict as to which weight has greater construct validity is uncertain. Either or both measures could be valid or invalid, and further study of construct validity would be required to be certain. The results of this study, however, do give several indications as to which measure should be used until such time as the validity Of one or the other is shown to be superior. First, the original Fishbein desirability component is to be preferred on the grounds Of simplicity. The tedious mental task involved in Obtaining conjoint data is definitely a drawback compared to the simpler bipolar scales required for measure- ment of the desirability component. In fact, substantial incentive is required for most respondents to complete a conjoint questionnaire as the task is quite a rigorous mental exercise in multidimensional come parison. The bipolar scale, on the other hand, is familiar to most respondents and requires relatively little thought. A second issue where the continued use of the desirability come ponent is the more prudent course evolves from the mathematical deriva- tion of the conjoint utility weights. Although the marketing literature refers to these weights as utilities, they can be interpreted quite differently. Mathematically, they are a non-metric counterpart of least squares beta weights (Appendix B). Both regression and conjoint analysis can be expressed as: 74 X b = Y where: X is a matrix b is a vector of weights Y is the dependent variable The primary difference between conjoint and regression, when both are expressed in terms of the above model, is that the regression model specifies a metric scale for the X matrix, while conjoint specifies a matrix of dummy variables, i.e., zeroes and ones, for the X matrix. The b term is estimated by a least squares solution for regression, while conjoint solutions are produced by a gradient vector. Although the vector of b weights for conjoint analysis has been loosely termed utilities, this vector mdght or might not in fact be utilities by the accepted economic definition. Heuristically derived solutions, such as conjoint, are useful for generation of weights, but they are not to be relied on to produce dimensions which are interpreted as constructs (Sheth, 1976). The solution to this interpretation problem for the conjoint weights is the use Of simple non-metric regression. Thus, rather than specify the X matrix as a dummy matrix of zeroes and ones, the matrix could be specified exactly as it is for least squares. Then, by the use of a non-metric procedure rather than least squares, the stringent assumptions of the normal regression procedure could be avoided. This procedure, however, again suffers from.the lack of probabilistic underpinnings that provide an error theory. In any event, it should be recognized that the weights produced by conjoint 75 analysis are not necessarily utility weights. It must also be acknow- ledged that the use Of non-metric regression does not avoid the multi- plication of non-ratio scales. In summary, then, the use of the Fishbein model for the predic- tion of brand preference, except for the possibility of spurious corre- lations, is more desirable than the integrated model tested in this study. Moreover, the primary limitations of component measurement for the Fishbein model are not overcome by the integrated model. Neverthe- less, the measurement of the desirability component should continue as a research topic with the aim of overcoming the measurement limitations. The following section points out other areas that would provide fertile grounds for future study. Recommendations for Future Research In the context of the present research it would be useful to test alternative composition rules rather than seek scale values that are in best agreement with a prespecified, e.g., additive, composition rule. For instance, the functional form, i.e., combinatorial rule, Of the Fishbein model is generally thought to be multiplicative. Conjoint measurement would be the appropriate technique for investigating this issue (Berner, 1976). It is also interesting to note that the better performance of the Ao model compared to the Aact model differs from the results of other research projects (Harrell and Bennett, 1974). This discrepancy could be due to the fact that this project used a student sample, but it could also be due to the consumer durable being investigated. Thus, a future project might investigate the hypothesis that brand preference 76 for consumer durables is better predicted with the A0 model than with the Aac model and just the reverse for consumer non-durables. Better t prediction with A0 would assume that durables, with the higher risk and greater economic investment, may well be the target of an attitude rather than the attitude being formed toward the act of purchase. The Aact model could, with the same logic, be more appropriate for predic— ting brand preference for consumer non-durables. A research project to investigate these possibilities could enhance the usefulness of the models by indicating the proper setting for their use. Again, the limitations noted in Chapter IV are relatively unde- veloped areas which provide grounds for methodological research. One aspect that would be especially applicable for marketers in their frequent sample survey analyses would be the investigation of the differences and similarities between the trade-off and full profile methods of data collection. An explicit delineation of these differ— ences and similarities would eventually lead to more accurate and efficient analysis. In such an investigation the possibility of differing combinations of the two methods could also be considered. In other words, it is possible that there are uses for alternative schemes between the specification of factors two at a time versus the specification of single levels of each factor in a single combination. As noted earlier, the effects of qualifying versus determining factors is also a topic for study. Such study could then lead to evidence of second choice theories and other, more complex types of interaction models. In any event, it is clear that there are many uses, both managerial and theoretical, for both conjoint analysis and the Fishbein attitude models. APPENDICES 3'" V kl APPENDIX.A QUESTIONNAIRE AND INSTRUCTIONS 77 INSTRUCTIONS FOR CONJOINT QUESTIONNAIRE As you will note, the first two pages of the questionnaire you have just received are composed of six 3 x 3 matrices° The task at hand is to rank order each of the alternatives in each matrix from (1) most desirable to (9) least desirable, An example will help clarify the procedure. Suppose we are concerned with two attributes (1) top Speed of a car, and (2) price of the car° Our matrix would then appear as follows (on overhead tranSparency): 130 mph 100 mph 70 mph (1) (2) (5) $2,500 5 3 l (3) (4) (6) $4,000 6 4 2 (7) (8) (9) $6,000 7 8 9 The average response of consumers in an actual study (Johnson, 1974) appear in parenthesis above° Your conception may differ from the average respondent, however° For example, you might feel that 70 mph is fast enough (for safety reasons) and your ranking might appear like that of the second numbers in each cell. This would be a perfectly legitimate response as long as it reflects how you would trade oflfthese factors. Of course, trading off only two factors assumes that all other factors remain constant. For instance, in the example matrix attributes such as warranty, seating capacity, miles per gallon, etc. would be assumed constant with only mph and price varying. Now, please begin filling in each of the matrices on your questionnaire° 78 T. WiISHn MTA 3'7 May 20, I974 QUESTIONNAIRE ON SUBCOMPACT AUTOS PLEASE WAIT FOR INSTRUCTIONS; Chevette Pinto Vega Modern Style and Lines Average Styling Constant Style that is functional Chevette Pinto Vega $3,000 $3,500 $4,000 Chevette Pinto Vega Sturdy, Quality Workmanship Average Workmanship Minimum Quality Workmanship Modern Style and Lines Average Styling Constant Style that is Functional Sturdy, Quality Workmanship Average Workmanship Minimum Quality Workmanship Sturdy, Quality Workmanship Average Workmanship Minimum Quality Workmanship 79 $3,000 $3,500 $4,000 Modern Style Average Constant Style and Lines Styling that is Functional $3,000 $3,500 $4,000 80 In general, we would like to know your opinion about several characteristics of small cars, Please tell me thv rallng you would give to each of the churnctcrlstlcs uslng the following Stale, Very Very Undesirable Neutral Desirable -3 -2 -l 0 +1 +2 +3 Brand: Dependability: Chevette Sturdy, quality workmanship Pinto Average workmanship Vega Minimum quality workmanship Style: Price: Modern style and lines Low Average styling Medium Constant style that High is functional Please rank the following automobiles as your first choice, second choice, and third choice, Chevette Pinto Vega Please use the following scale to indicate the probability of your pur- chasing each of the three brands listed below: Very Improbable ' Very Probable -3 -2 -l 0 +1 +2 +3 Chevette Pinto Vega Now indicate the probability that you would buy any compact or subcompact car. ‘ It is also important to know your evaluation of the characteristics of different brands. Please use the following scale in rating each sentence below. Strongly Strongly Disagree Neutral Agree -3 -2 -1 0 +1 +2 +3' 81 The Chevette would be: The Pinto would be: The Vega would be: Dependable Dependable Dependable Economical Economical Economical Stylish Stylish Stylish DemOgraphic Information: G.P.A. College Status less than 2.00 Freshman Single 2.01 to 2.40 Sophomore Married 2.41 to 2.80 Junior 2.81 to 3.00 Senior Male 3.01 to 3.40 Graduate Female 3.41 to 4.00 Have you bought a new car within the last 6 months? No Yes If yes, was it a compact or subcompact? No Yes Do you plan to buy a new car within the next 6 months? NO Yes APPENDIX B CONJOINT PROCEDURE AND ALGORITHM This appendix technically describes the computational operations of Richard Johnson's NMRG computer program (Johnson, 1975). It is in- cluded for technical completeness, although for most readers Chapter III is probably sufficient for purposes of understanding conjoint analysis. The program is written in FORTRAN IV with less than 200 statements. It is available from Richard M. Johnson, Vice President, Market Facts, Inc., 100 S. Wacker Drive, Chicago, IL, 60606. All material in this appendix is from Johnson, 1973 and 1975 or easily derivable from those sources. Initializing the conjoint analysis procedure is accomplished through specification of a coefficient matrix of dummy variables con- sisting of zeroes and ones to indicate the presence or absence in an object of each level of each attribute. The matrix‘would have a row (n) for each object and a column (p) for each attribute level. A unit element in cell position ij would indicate that object 1 possessed the jth attribute level. "A set of weights for each column is sought such that the weighted row sums of the coefficient matrix would be monotonic with the individual's rank order of preference among the Objects des- cribed by that matrix." Consider a coefficient matrix X of order n x‘p, and an unknown vector b of length p to contain part weights. Let the vector y of length n contain an individual's preference ratings. Let X.b - §. The problem then becomes finding a vector b such that the elements of the § vector are as nearly monotonic to the given vector y as possible. 82 83 As a measure of monotonicity, consider the measure 02 (Johnson, 1973): 2 2 - iEj Gij (§1-§j) ~ . 2 i1 (yi-yj) (l) O where: _ {1 if sign (§,—§J) - sign (yi-yj) (2) 6i 0 otherwise 3 Note that this definition of 6 forces the 62 statistic to zero for a perfect fit, and to one for a perfectly inverse relationship. The interpretation of 02 as the proportion of variation in the y's which is discordant with the y's is more easily seen through examination of the formula. The numerator is the sum of squared differences be- tween all pairs of y's that are discordant with the y's. The denomin- ator is simply a normalizing constant which constrains the range of 62 to the unit interval. The iterative procedure for the minimization of 92 consists of starting with an arbitrary vector b of the fOrm 1 x'p and modifying this vector successively. The direction of the modification indicated by gradient vectors. The gradient vector g corresponding to an iterative form of b is derived by differentiating 02 partially with respect to b’ (an iterative form of b). To indicate the form of the gradient, we set 2 u <3) 9 ‘T for scalars u and v, then 2 d9 1 du dv (4) db’ ' v2 (V db’ " “ db’) 84 using equations (1) and (3) and the transitive prOperty: (5) ._".1__ I A A v ij (Yi‘YJ)2 then du 22 Using x1 and x1 as the ith and jth rows of X and 9, and 9, as scalars du 22 With the same procedure: dv 22 (8) 3,?- ,, 6,, (x,- x,><9,— 9,) By substituting (7) and (8) into (4) we get, do2 2 (9) F- %2 (zv ,, 6,, and simplifying 2 Z _2u 2 <11) = 3- ‘ (x- x><9- 9)<6 —> v ij i x, 1y, 13 V So, the gradient vector e2 (12) g - ,2; i, (x,- x,><9,- 9,><6,,-e ) The program normalizes both b and g to have unit sums of squares at each stage and uses the current value of O as the "step size" with the recursive equation. bm.+l E bm - emam 85 where m is the iteration number. This process can be terminated after a limiting number of iterations. For example, when 0 fails to decrease, or the default option is reached. The default option for stabilization of O is thirty iterations. Fifteen iterations were utilized for this project with the average number of iterations required for O stabili- zation being eight with a range of one to fourteen. This is to be expected because the successively smaller modifications of X are based on the 0 value. In brief summary, the procedure for one iteration is as follOws: 1. For a given X, compute all pairs of distance values (91-9,) 2. Evaluate the sign of (91-9,) and cumulate the 611's 3. Calculate 92 and g as shown above 4. Normalize X and g to have equal sums of squares 5. Replace X by X - 9g There are also procedures for considering ties and missing data, neither of which posed a problem for this research. The respective procedures are presented by Johnson (1975). The following page is an example of the input for each individual. The example shown is for respondent number 001 from this sample. An Example To further clarify the mathematics shown above, the following example is included. In the present study there are four attributes with three levels each (see Chapter IV). The grand input matrix for each respondent could then be viewed as: 86 B S D P 1 2 3 4 5 6 7 8 9 10 11 12 1 B 2 3 4 S 5 6 7 D 8 9 10 P 11 12 The letters B, S, D, and P stand for brand, style, dependability, and price respectively. Each of the 3 x 3 cells above represents a single trade off matrix. Note that a trade off matrix with the same attribute on both axes is illegitimate. That is to say, the levels of an attribute cannot be traded off against itself. This eliminates the diagonal of the above matrix. Note also that the top and bottom sides of the matrix are redundant. In other words, style and brand are the same as brand and style. The trade off matrices used as input can be from either the top or bottom but not both. In other words, the input must be consis- tently from the top half or the bottom half. Noting the questionnaire in Appendix A, the bottom half is used for this study. The program is designed to accept row-wise or columndwise data, but again all cases must be consistent. Rowiwise input was used for this data base. Specification of the X matrix simply involves specifying the location of the respondent's rank ordering in the overall matrix. For 87 example, the first respondent filled in the first trade off matrix for style and brand as shown below. Chevette Pinto Vega Modern Style and Lines 3 2 1 Average Styling 6 5 4 Constant Style that 9 8 7 is Functional This translates to a column vector (y) as follows: :NmObUIGI-‘Nwl The X matrix, with dimensions of 9 x 12, would appear as follows: T100 100 000 006‘ 010 100 000 000 001 100 000 000 100 010 000 000 010 010 000 000 001 010 000 000 100 001 000 000 010 001 000 000 001 001 000 000 — _l To illustrate, the first row of the X matrix: 100 100 000 000 would be interpreted as identifying the first number in the y vector (3) as being located in the first column and the fourth row of the grand matrix. Referring back to the grand matrix, the first column and fourth row is the intersection Brand 1 and the first level of the attribute 88 style. Each number in the y vector can be located in the grand matrix by using the above procedure. The scheme outlined above for specifying the X matrix would require nine cards for each trade-off matrix, which for this study would total 54 cards for all six trade-off matrices. Constant use of the program is more efficient if the cards are simply accessed from tape rather than separately punched for each project. The following page is an example of the output for each respon- dent. The example shown is for respondent number 001 from this sample. To clarify the interpretation of the sample output, Iteration simply refers to the number of the iteration and the corresponding theta and tau values. Recall that theta has an inverse relationship to tau. A lower theta value (or a higher tau value), indicates more consistent responses to the trade-off matrix. The iterative procedure seeks a best fitting function using theta as a criterion, and in the case of respondent 001, after 15 iterations settles at a value of 0.04706 for theta and 0.73148 for tau. The variable number refers to the attribute level as specified in the grand matrix. Again referring back to the grand matrix, it can be seen that variable numbers 1, 2, and 3 correspond to the brands Chevette, Pinto and Vega respectively. variables 4, 5, and 6 corres- pond to the three levels of style, 7, 8, and 9 correspond to the levels of dependability, and 10, 11, and 12 correspond to the levels of price. The Additive and Multiplicative columns on the printout are the utility values for each of the variables (attribute levels). For example, the additive utility for variable 1 (Chevette) is 0.07630, the additive 89 SAMPLE OUTPUT FROM NON-METRIC REGRESSION PROGRAM ID - 001 ITERATION THETA TAU 1 0.93953 -0.60185 2 0.52517 0.49074 3 0.17703 0.75926 4 0.10039 0.92593 5 0.06111 0.79630 6 0.05985 0.94444 7 0.04620 0.71296 8 0.04998 0.69444 9 0.05036 0.71296 10 0.04971 0.69444 11 0.04841 0.73148 12 0.04846 0.69444 13 0.04776 0.73148 14 0.04769 0.69444 15 0.04706 0.73148 VARIABLE ADDITIVE MMLTIPLICAIIVE 1 0.07630 1.07928 2 0.07630 1.07929 3 0.07631 1.07930 4 0.03265 1.03319 5 0.10768 1.11369 6 0.08850 1.09262 7 0.70302 2.01984 8 0.07630 1.07929 9 -0.55041 0.57671 10 0.31607 1.37173 11 0.17931 1.19639 12 0.26647 0.76608 90 utility of variable 4 (constant style that is functional) is 0.03265, and so forth. Recall from Chapter III that the multiplicative utilities are simply the logarithms of the additive utilities. Computer Algorithm The following algorithm is the NMRG program as set up on the IBM computer at Ravier University. R, M. JOHNSON/ MARKET FACTS / AUGUST,1973 THIS PROGRAM PERFORMS NONMETRIC REGRESSION TO MINIMIZE THE THETA CRITERION. IT HAS A SPECIAL FEATURE WHICH ALLOWS IT TO COMPUTE A SINGLE SET OF WEIGHTS WHICH PROVIDE THE BEST FIT TO SEVERAL BLOCKS OF DATA SIMULTANEOUSLY. EACH BLOCK MUST CONTAIN N OBSERVATIONS. ORDER COMPARISONS ARE ONLY MADE WITHIN BLOCKS. A.SECOND FEATURE ALLOWS WEIGHTING 50 AS TO PAY GREATER ATTENTION TO FITTING INPUT VALUES WITH SMALLER.MAGNITUDES ( SUCH AS FIRST,SECOND, ETC. RANK ORDERS WHEN USING PREFERENCE INPUT DATA). CURRENT RESTRICTIONS ARE 10 BLOCKS,50 OBSERVATIONS PER.BLOCK. AND 20 INDEPENDENT VARIABLES. INPUT ORDER: 1) CONTROL CARD(1615) A) NUMBER OF OBSERVATIONS PER.BLOCK (N) B) NUMBER OF INDEPENDENT VARIABLES (M) C) NUMBER OF BLOCKS ( NBLKS DEFAULT-1) D) ITERATION LIMIT ( DEFAULT-30) E) WEIGHTING OPTION(1 IF WEIGHTING DESIRED, O OTHERWISE) F) TIES OPTION (NORMALLY O, 1 IF TIES NOT TO BE FORCED) G) CARD OUTPUT OPTION (ADDITIVE) 1- CARD OUTPUT H) SUPPRESS PRINT OPTION AFTER.WEIGHTS 1- SUPPRESS 2) INITIAL WEIGHTS( ONE CARD, 4OF2.1) 3) DATA CARDS IN FORMAT(4OF2.0), EACH CARD CONTAINING ALL DATA FOR A.SINGLE OBSERVATION: IM INDEPENDENT VARIABLES FOLLOWED BY A DEPENDENT VARIABLE. ALL CARDS FOR.A BLOCK MUST BE TOGETHER IN THE DECK. A.ZERO VALUE FOR.THE DEPENDENT VARIABLE RESULTS IN THAT OBSERVATION NOT BEING USED IN THE COMPUTATION. 0001 0002 0003 0004 0005 0006 0007 0008 0009 0010 0011 0012 0013 0014 0015 0016 0017 0018 0019 0020 0021 0022 0023 0024 0025 0026 0027 0028 0029 0030 10 998 20 91 SHORT BLocxs CAN BE FILLED OUT WITH BLANK DATA CARDS. OUTPUT CONSISTS OF THE VALUE OF THETA ACHIEVED BY EACH ITERATION, A A SET OF WEIGHTS APPROPRIATE FOR AN ADDITIVE MODEL, AND A SET OF WEIGHTS APPROPRIATE FOR A MULTIPLICATIVE MODEL OBTAINED BY TAKING ANTILOGS OF THE FIRST SET. DIMENSION x(10, 36) ,IY(lO) ,YHAT(10) ,w(12) ,G(36) ,D(36) ,GNUM(36) DIMENSION GDEN(36) ,Sl(12) INTEGER*2 DATA(66,10,37) READ(5-,901) N,M,NBIKS,ITRLIM,IWT,ITIES,ICARD,ISUP IF(NBLKS .LT. 1) NBLKs-l IF(ITRLIM.LT.1) ITRLIM-30 IF(IWT .LT. 0) INT-=0 WRITE(6,914) WRITE(6,901)N,M,NBIKS,ITRLIM,IWT ,ITIES,ICARD,ISUP NMlaN-l MPl-=M+l MMI=M-1 WEIGHT-1 READ(5,9OS) (WU) .J-1.M) WRITE(6,903) (W(J).J=1.M) DO 10 I-1,NBLKS D0 10 J-1,N READ(11,912,END-999) ID, (DATA(I,J,R) ,K-1,MP1) WRITE(6,914) WRITE(6,998)ID F0RMAT<5x,'ID - ' ,A5) WRITE(6,900) DO 1000 ITER-1,ITRLIM DO 20 I-1,M GNUM(I)-0. CDEN(I)-0. SNUM-o. SDEN-O. TAUNUM=0 TAUDEN-o 0031 0032 0033 0034 0035 0036 0037 0038 0039 0040 0041 0042 0043 0044 0045 0046 0047 0048 0049 0050 0051 0052 0053 0054 0055 0056 0057 0058 0059 0060 0061 0062 0063 0064 24 30 40 43 45 92 DO 105 IBLOCK=1,NBLKS DO 24 I=1,N IY(I)-DATA(IBLOCK,I,MP1) DO 24 J=1,M X(I,J)=DATA(IBLOCK,I,J) DO 30 I=1,N YHAT(I)=0. DO 30 J-1,M YHAT(I)-YHAT(I)+X(I,J*W(J) DO 103 I-1,NM1 IF(IY(I).EQ.0) GO TO 103 IPI-I+1 DO 100 J=IP1,N IF(IY(J).EQ.0) IDIF=IY(I)-IY(J) DIF=YHAT(I)-YHAT(J) PROD-IDIF*DIF PROD=-l.*PROD IF(IDIF .EQ. o DIF2-DIF*DIF DO 40 L-1,M D(L)=X(I,L)-X(J,L) IF(IWT.EQ.O) GO TO 43 FI=FLOAT(IY(I)) FJ=FLOAT(1Y(J)) WEIGHT=1./FI/FJ CONTINUE IF(PROD .GT. 0.) GO TO 50 SNUM=SNUM+WEICHT*DIF2 TAUNUM-TAUNUM+1 DO 45 L-1,M GNUM(L)-GNUM(L)+DIF*D(L) GO TO 100 .AND. ITIES .EQ. 1) GO TO 100 +*WEIGHT GO TO 100 50 SDEN-SDEN+WEIGHT*DIF2 0065 0066 0067 0068 0069 0070 0071 0072 0073 0074 0075 0076 0077 0078 0079 0080 0081 0082 0083 0084 0085 0086 0087 0088 0089 0090 0091 0092 0093 0094 0095 0096 0097 55 93 TAUDEN-TAUDEN+1 DO 55 L31,M GDEN(L)-GDEN(L)+DIF*D(L) +*WEIGHT 100 CONTINUE 103 CONTINUE 105 CONTINUE THETA2=SNUM/ (SNUM+SDEN) THETA=SQRT(THETA2) TAU=(TAUDEN-TAUNUM)/(TAUDEN+TAUNUM) WRITE(6,902) ITER,THETA + ,TAU 110 125 130 1000 1001 205 D0 110 LP1,M G(L)-GNUM(L)-THETA2*(GNUM(L)+GDEN(L)) SUMw2=1.0E—20 SUMGZ-1.0E-20 DO 125 I-1,M SUMWZ-SUMW2+W(I)*W(I) SUMCZ-SUMCZ+G(I)*G(I) SUMW2=SQRT(SUIM2) SUMczasORT(SUM02) Do 130 I-1,M W(I)=w(I)/SUMw2-(SQRT(THETA))*C(I)/SUM02 CONTINUE CONTINUE WRITE(6,914) WRITE(6,904) DO 205 J-1,M 81(J)-EXP(W(J)) WRITE(6,902) J,W(J),Sl(J) IF(ICARD.NE.O) WRITE(7,913) ID,W IF(ICARD.NE.0) WRITE(7,913) ID,Sl IF (ISUP.NE.0) GO TO 1 D0 200 IBLOCK-1,NBLKS DO 124 I-1,N 0098 0099 0100 0101 0102 0103 0104 0105 0106 0107 0108 0109 0110 0111 0112 0113 0114 0115 0116 0117 0118 0119 0120 0121 0122 0123 0124 0125 0126 0127 0128 0129 0130 0131 0132 124 150 160 399 200 5000 900 901 902 903 904 905 906 907 910 94 IY(I)-DATA(IBLOCK,I,MP1) DO 124 J-1,M X(I,J)-DATA(IBLOCK,I,J) WRITE(6,907) WRITE(6,901) (IY(I),I=1,N) DO 150 I—1,N YHAT(I)=0. DO 150 J-l,M YHAT(I)-YHAT(I)+X(I,J)*W(J) DO 160 J-IP1,N IP1-I+1 DO 160 J-IP1,N IF(IY(I) .CT. S=YHAT(I) YHAT(I)=YHAT(J) YHAT(J)-S IJ=IY(I) IY(I)-IY(J) IY(J)-IJ CONTINUE WRITE(6,906) DO 399 I-1,N WRITE(6,902) CONTINUE CONTINUE GO TO 1 FORMAT(///.' FORMAT(1615) FORMAT(110,7F10.5) FORMAT(10F12.6) FORMAT(///,' FORMAT(40F2.1) FORMAT(///,' DEPENDENT 6 PREDICTIONS SORTED BY DEPENDENT') FORMAT(///' INPUT DATA') FORMAT(10F1.0,F2.0) IY(J)) GO TO 160 IY (I) ,YHAT(I) ITERATION THETA') VARIABLE ADDITIVE MULTIP') 0133 0134 0135 0136 0137 0138 95 911 FORMAT(16F5.0) 912 FORMAT(A3,2X,3711) 913 FORMAT(A3,2X,12F6.3) 914 FORMAT('1') 999 CALL EXIT END BIBLIOGRAPHY 96 BIBLIOGRAPHY Ahtola, 0111 T. "Vector MOdel Preferences: An Alternative to the Fishbein MOdel." Journal of Marketing Research (Feb., 1975), pp. 52-59 I American Telephone and Telegraph,.Marketing Department/Research Section. "Dataspeed 40 Market Study, Morristown, New Jersey, January, 1974, pp. 7-14. Bass, Frank M. and Wilkie, William L. 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