ESTIMATION OF 305 DAY MILK YIELD FROM ERREGULAR MLK RECORDS Thesis for the Degree of M.S. MICHIGAN STATE UNIVERSITY CURTIS C . MILLER 1 9 6 6 THESIS LIBRARY MiChiq‘lu I K. Unix/cu HI. '9’ E ‘ BINDING av : HMS 8: SUIS' f ' 800K BINDERV INC. LIBRARY BINDERS ESTIJ TIC; O: 505 DAY KILK YILLJ . ‘ .' ‘ ‘r‘ :1 1“" Al? ~'. \0 r> r, “(x/1 . "\ “_. .'. i“... iL\-<..;\:-JL 1i i .L i\ .KLVU 1.2.2 vi Curtis C. Miller . 3-1.: :18. .3 :33? .n < flax/2T ausnittea to tn: collcce oi quipulCure Ligiigau state University in rartial :ul4iilwent oi tne rewuirEMents :cr the jegree o: ueoartment 0: Dairy 1930 A I E ' /' . / /’{/ /,-. /, /’.)1’./-.’///;-'r//x Amérovec": - — —v' - — — '— ’— — ‘Vr't _' u "’1 ‘ ‘d—v- --.:"va -T ~"r . ' ..' :.|‘V"1 " V; " I- ...I v. ‘V .. lv“ - ‘ ‘; I. l'\ noflmflilOu 0: 30a DAY HLLR Iluba ‘V-I \._u I .‘i" (‘_'.~T . L, 3-” T- Yl' "‘ 4‘ " v‘, 'uf_' 1? Avg. l...(o-1:\'.r.J....z.$.\ .- 24.er “34901;“: bv Curtis C. Miller several methoes or estimating milK yield ror the lactation from various narts inclaCinq several intervals be- tween tests were evaluated on 58,840 comeleted records of Michigan Holstein cows calving between January, 1959, and Januarv, 1961. Three ratio procedures and linear regression were used to estimate total milk yield rrom the dirferent narts for two monthlv sets or bi—non hly data ana three monthlv sets or tri—monthlv data. The rirst ratio nrocecuie consisted or averages .‘ -\ estimates where the estimates were those obtain e by estimat- FD inq total mi k viela rrom the non—cumulative factors. These estimates orovieed error variances or 5al,395, and 502 lb milk for the tri-monthlv sets consisting or months l-4-7—lO, 2-5-8, anu 3-0—9 resnectivelv. The second ratio nrocedure consisted oi weighting each non—cumulative estimate according to its variance and nrovided error variances for the three tri-monthly sets l-4-7—lO, 2-5-8, and 3-6—9 oi 292,471 and 493 lb milk reSpectively. The third ratio nroceoure emnloved a single ratio or total to sum of nroouction on grouns of monthlv test days to estimate total viela. This orocedure J) nrovitefi error variances or 273,453 an; 475 la milk :or the tri-monthlv sets consisting of months 1-4-7—10, 2—b-o, and 3-c—Q respectivelv. :i—“OItElg estien cs ire“ h; Lego rgtie ‘roceSUrC: niovijef errar variances of 433,1’4 'n: 207 1% milk resnec ivclf for rrocefire: l,2, enf 3 Ecr the rental? art conteiai“; tn; first “onth e“ test as. 415, 1C1, a“? 123 ll ‘ilk fa: the ::"e three “r“CCClI€S “or ”he ~cutnl :ct consistiAj o? ”o t5: “—3-Z—3-lC. .11 error variances acre large: -nas t :.c oltaineg my lliiir rearzrs_on. for estimatins total .J 7 ”D O H (D U) U) H . O :3 H {.1 CI rt' 0 H m (D '— (D O (‘1 rl Q: P '6. D .J milk yiela fror various oarts inclucing several intervals between tests for tour age—season qrouns ESTIMA$ION OF 305 DAX'MILK YIELD FROM IRREGULAR MILK RECORDS BY Curtis C. Miller A THESIS Submitted to the College of Agriculture Michigan State University in partial fulfillment of the requiranents for the degree of MASTER.OF SCIENCE Department of Dairy 1966 Acknowledgements I wish to express my sincere anoreciation to Dr. Clinton 3. Heaeows for his encouragement and friendly guiuance during the investigation of the nroblem and his helnful suggestions during the writing of the thesis. The encouragement of Dr. Lon D. Ecsilliard was also anereciated. ii TABLE OF CONTESTS Page I;\:Tkj\ODUCTIO:.‘I O..........OOOOOOCOOOOOOOO......OOOOOOOCO l (A) PEN/Ids": OF LITE.;:PU£.\AL ......ooooooooooooooo00.00.000.00 Methods of Estimating Total Lactation Yield .. a Standard DHIA Method ......................... 3 si—Monthly Tests ............................. 4 Predicting Total Production From Parts ....... 8 Extension Factors and Their Derivation ....... 12 Ratio 00............OOOOOOOOO0.0.0.0....- 1-2 Regression .............................. 18 Comparison of Regression and Ratio Methods ... 22 SOURCE OF Dl-QT‘XO......OOOOOOOOOO.....OOOOOOOO.00...... 24 D:ETHODS &;D RESIJLTS 00.0.0.0.........OOOOOOOOOOOOOOOOO 25 Record Classification ........................ 25 Measuring Relationships of Parts to the Whole. 25 Ratios O......OOOOOOOOOOO......OOOOOOOOCOOOCOO 28 Standard DHIA.Method ......................... 32 Regression Coefficients for Estimating Total Yield 0.0...O00.0.0000.........OOOOOOCOOOOOO 33 Bi-Monthly and Tri-Monthly Results ........... 42 Average Production Within Age and Season ..... 43 Comparison of Methods ........................ 59 Ratio and Regression Methods ................. 59 Distribution of Errors ....................... 61 DISC‘JSSIO-q 0.....0...O.......OOOOOO......OOOOOOOOOOOOO 65 Relationship Between Various Parts and Total Yield ...O....00......0.000.000.0000...0.... 65 Precision of Various Methods Used to Extend Records 0.0.00.0...0.0.0.000.........OOOOOOO 67 Ratios O.......OCOOOOOOCOQOOOOOO0........ 67 Regression .............................. 7O Regression-Ratio Combinations ........... 72 DiStribution Of Errors ......OOOOOOOOOOOOOOOOO 73 Application of "Ten Test Date" Regression Factors to All Data ........................ 76 E‘PPLICf‘lTIOL‘I 01"? RESULTS .........COOOOOOOOOO00......... 77 SUI';E:ARY O......OOOOOOOOO0.00.0000........OOOOOOOOCOOOO 80 LITERATURE CITE-I) 0.000.000.0000......OOOOOOOOOOOOOOOOO 84 TABL E 1 LA ) 10 ll 12 Page Distribution of Records by Age and Season .... 26 Percent Cows in Milk on Each of 10 Test Dates ......OOOOO......OOCOOOOOOO0.00.0...O. 29 Correlations Beteen Milk Produced on Single Test-Days for Records with 10 Tests ........ 30 Correlations Between milk Produced on Single Test-Days (Dry Test Days Excluded) ......... 3l Means and Standard Deviations of fianthly Test Day Records of Milk Produced on Single and Cumulative Test Days (10 Test Days) .... 36 Milk Produced on Single Test Days (Dry Test Days EXClUded) OOOOOCOOOOCOOOOOOOOOO00...... 36 Regression Factors for Estimating Total Milk Yield from Cumulative Test-Day Records (10 TeSt DaYS) ......OOOOCOOO......OOCOOOOOOOOOO 37 Regression Factors for Estimating Total Milk Yield from Cumulative Test Day Records (Dry Test Days Excluded) ................... 37 Regression Factord for Estimating Total Milk Yield from a Single Monthly Test Using Data From Cows in Milk at Least Ten Test Dates 00............OOCOCOOOOOOOOOCOO0...... 3’3 Regression Factors for Estimating Total Milk Yield Erom a Single Monthly Test Record Using Data From All Cows in Milk on Test Date......OOOCOOCOOOOOCI......COOOCOOCOOCOO 33 Regression Factors for Estimating Total Milk Yield From Cumulative Test Day Records when First Month Records Are I‘EiSSing O0...............O.........OOOOOOOOO 39 Regression Factors for Estimating Total Milk Yield from Sequential Test-Dates Using Data Only From Cows in Milk at Least Ten 11eSt Dates O.....OOOOOOOOOOOOO...0.0.0.0.... 40 iv 14 15 17 18 23 21 22 TAB ES (Continued ......) Regression Factors for Estimating Total Milk Yield from Sequential Test-Dates When Last Months Data are Kissing Using Records of all Cows in Milk on Test Date o00.000.00.00000000000coo-000.000...000 Regression Factors for Estimating Total milk Yield irom Sequential Test-Dates When First Month's data are Kissing Using Records From all Cows in fiilk on Test Date ................ Regression Factors for Estimating Total milk Yield from sequential Bi—Aonthly and Tri— Eonthly Test-Lay Records ................... Regression Factors for Estimating Total Hi K Yield from Cumulative Bi—xontnly and Tri- xOnthly Test—Day Records ................... Regression Factors fior Estimating Total Milk Yield from Sequential Tri-flonthly Test Day Records when uata fr n One or Kore Test Dates are HiSSing oo...00.000000000000000... Test Date Means and Standard Deviations for Four Age-SeaSOn groups 000.000.00.0000000000 Regression Factors for Lstimating Total milk Yield from Cumulative Test-Day Records for Four Age-Season Groups ..................... Ragression Factors for Estimating Total Hilk Yield Cumulative Test pay Records when First tonth Records are missing for Four Age-Season Groups .......................... Regression Factors for Estimating Total Kilk Yield from a Single Honthly Test Record ror Four Age—Season Groups ..................... Regression Factors for Estimating Total Milk Yield from Sequential Test Day Data for ;?O1~lr 3&Qe-Season Groups ......OOOOOOOOOOOOOOO Regression factors for Estimating Total xilk Yield from Sequential Bi-Konthly Test Day Records for Four Age-Season Groups ......... Page 41 fl @ 47 49 m H 52 tn m LIST OF TABLES (Continued ........) F3 AJLE Page 24 Regression Factors for Estimating Total milk Yield from Sequential Tri-monthly Test Day Records for Four Age-Season Groups 00...........OOOCO......OCOOOOOOOOOO 57 25 Regression Factors for Estimating Total milk Yield from Cumulative Bi—Monthly Test Da‘z, Recoréls 00.00.0000.........OOOOOOOOOOOO 58 26 Regression Factors for Estimating Total Milk Yield from Cumulative Tri-Monthly Test Day Records OO.......OOOOOOOOOOOOOOOOOO.... SO 27 Comparisons of Deviations of Di ferences Between Estimates and Actual Values for Various Methods Used to Estimate Ten Month Total Ni k Production ............... 6O 28 A Comparison of Non-Cumulative Regression and Ratio :‘aCtorS ......OOOOOOOOOOOOO...... O» U) 29 A Comparison of Cumulative Regression and Ratio Factors ......................... 63 3O Frequencies of Estimated Value Deviations from Actual Values for Various Methods of Projecting Tri-Eonthly Testing Data to a Ten Month Total ...................... 65 31 Relative Efficiency of Various Methods in Estimating Ten Month Production from Three Tri-i’ionthly set-S Of Data . o . g o g Q g o o O O 69 32 Relative Efficiencies of Regression Factors Derived from Ten Month Data when Applied to all Cows in Milk on Test Data .......... 74 33 A Comparison of Efficiencies when Regression Factors are used to Extend Ratio Estimates to a Ten bionth BaSiS ......OOOOOOOOOOOOOOOO 75 vi IITRODUCTION management and selection decisions for the dairy herd are based on production of each cow and the herd. Decisions on daily feeding are based on production at that narticular time. Bulls are compared through the performance of their orogeny where each animal's oroduction is adjusted to a common age and constant length of lactation. In the culling of females from the herd, each animal is compared with the herd, again adjusting each animal to a common age and constant length of lactation. Traditionally, records have been adjusted to a common age using mature—equivalent factors and length of lactation has been 305 days, estimated from 10 monthly milk weights. Considerable time could he saved in choosing between bulls and culling of the herd could be much more timely if an accurate estimate of the total lactation could he obtained from a part record. Less frequent milk weights and butter- fat tests would reduce the cost of the testing prOgran. Total production has been estimated from part records by ratios and by regression. The ratio method relates the ratio of total production to a part for the lactation. The regression method takes into account some overall averagerflus anorooriate weights for each added oart. To estimate total yield from cumulative and non-cumulative oarts, uses either methoc. Regression coefficients have been formulated for estimating total yield from hi—monthly and tri-monthly tests. However, ratios have not been obtained for this ouroose, nor have regression factors been commuted for missing data. Seoarate regression factors for various age—season grouns are needed. There is also a need for commuting appro- oriate factors for the various combinations ofsequential data and for tri- and bi-monthly sets with missing observations, where a monthly set consists of a particular group of months. There are three tri—monthly sets, one consisting of months 1-4—7—10, another consisting of months 2-5-8 and the third consisting of months 3-b-9. The bi—monthly sets contain months 1-3-5—7-9 and 2—4-0-5-10. If ratios are to he used, there arises a question or handling additional data after the first estimate has been computed. Several possibilities exist for handling this situation: weight each non—c'mulative estimate equally, weight the non-cumulative estimates in orooortion to their relative orecision, or form one ratio from all availanle data each time new data are available. The Objectives of this study are: (a) to comoare the deviations from actual oroduction of total production esti— mated from various carts by several methods, and (b) to seek ways to include longer intervals between tests without in— creasing errors of estimate. REV I L51 0 i“ L ""'I'23.'~’;.:{TU;~;£ Methods of estimating total lactation yield standard DnIA method The standard 9313 method of comnuting total lacta— tion yield of a cow is tn test the animal one time nercalen— dar month within 3 days 0; a centering date tor the herd. r”he amount produced on test day is apolied back 15 days and ahead 15 days taking into account date 0: freshening and date dry or removed where annronriate. Production is cumulated to 305 days or to the end 03 the lactation. Campbell (1943), Erb et a1. (1952), Flanagan (1965), chowell (1927), O'Connor 3; El. (1960) and Rabild (1909) have resorted accuracies or estimating total lactation yield from this method compared to the actual daily milk weights. The DHIA method is somewhat costly and laborious. Therefore, as early as 1915, workers were attempting to determine some method of estimating the total lactation yield oi a cow from a partial record. Yapo (1915) concluded that the standard 331A7method mentioned above, represented tairly accurately the producing abilities or cows and that a continuous seven day test was not a satisfactory criterion by which to judge a cow‘s total yield. (1) 4 McDowell (1927) reported that the standard method varied on the average 2.91 percent from actual production. McCandlish and M'Vicar (1925) reported that the monthly method of testing produced results within two percent of the actual yield. Dick (1950) observed an error of 2.32 percent from actual production when cows were tested at 28 day inter- vals. Using 96 bi-monthly, monthly, and six week intervals of recording production, Cunningham (1965) measured correla- tions between these estimates and actual BOB-day milk pro- duction to be .99 for all three methods, .97 for bi-monthly and .98 for the other two methods. Actual data were milk weights each day for the entire lactation. Bi:Monthly Tests Erb 22.81- (1952), using 19 cows, reported that the calendar month method showed twice as much variation as the centering date (standard) method, but the former was not likely to be in error more than 1 five percent for fat-corrected milk in 25 percent of the records, nor more than t 12 percent in one percent of the records. The error could be reduced by less than one percent of that indicated for the 24 hour test by testing on a 48 hour basis and reduced less than two per- cent when the 96 hour test was compared with the 24 hour test. The percent error in estimating milk yield exceeded by 25 percent of the records was 2.4, 3.4, 5.6, 7.4, and 8.8 for the 30, 60, 90, 120, and 150 day testing intervals, reSpectively. These data further substantiated the belief that S cows tested at the first of a calendar month have an advantage over those always tested at the end of the month. These data on the 30 and 60 day intervals are in good agreement with McDowell (1927) and.McCandlish and M'Vicar (1925). McDowell (1927) found 3.8 percent error in estimates of fat when bi-monthly records were compared with monthly testing on 70 cows in the Minnesota Agriculture Experiment Station herd. This amounted to 6.65 lb fat per lactation on cows averaging 1.75 lb fat and five percent of the 70 cows had an error of 8.75 lb fat. As previously mentioned, McDowell (1927) concluded that the bi-monthly method would be in error 2.5 lb fat per lactation more than the standard method, but errors of both methods should be disregarded for all practical purposes. Gifford (1930), reporting on more than 100 AR Holstein and Guernsey records, stated that 69 percent of the estimates were within one standard error of estimate in com- paring bidmonthly with monthly records, 95 percent within . two standard errors and 99 percent were within three standard errors of the estimate. For two combinations of bi-monthly testing reported mean deviations for fat of -4.9 t .35 for odd numbered months and +2.4 t .38 for even numbered months. For convenience he further divided the records by levels of fat production, using groupings of 300-400, 500-600, 700-800, and 900 lb. Corrnlation coefficients between monthly and bi-monthly records ranged from .956 to .997. From these data, Gifford concluded that a bi-monthly form of testing is satis- factory. 6 McKellip and Seath (1941) reported a correlation coefficient of .97 between monthly and bi-monthly records. They concluded that bi-monthly tests when used with daily weights were practically as accurate as monthly records made by centering the tests and not using daily weights. COpeland (1928) reported that records made under a bi-monthly method show little deviation from those made by the usual monthly methods. He used 500 Jersey records and found the deviation of all records to be 7.21 lb fat. He found 258 bi-monthly records that exceeded the monthly records and 242 that were lower. Alexander and Yapp (1949) used 684 cows of five breeds to compare bi-monthly with monthly tests and found that 43.27 percent of all cows were within two percent error of the actual, 29.54 percent of the total were within 2.1 to 5.0 percent of the actual, 20.03 percent within 5.1 to 10.0 per- cent of the actual, and 7.16 percent of the 684 cows were above 10.0 percent of the actual production. For all breeds, the average production was 11,894 lb milk with the average of the negative deviates being 11,802 and the positive 12,383 for the standard method. The bi-monthly method showed 11,453 lb milk for all cows, 12,431 lb for those above the average and 11,453 lb for those below average. These figures represented an error percentage from the standard method of -3.7 for the overall group, +0.4 for those above and -5.0 for those below the overall average. The authors concluded that bi-monthly testing is 92.84 percent as dependable as the standard method and this difference is not sufficiently large to exclude the practical use of bi-monthly testing. 7 The first data involving records from more than one herd were reported by Bayley gg,gl. (1952). They used 1,255 Holstein records of 305 days or less, but not less than 150 days, in 42 herds and reported a slightly greater percent error in the estimates than previous workers. Bayley com- pared the two sets of bi-monthly records with the standard DHIA method and found that the set which includes the first month on test is somewhat more accurate than the remaining set for both milk and butterfat. The relative reliability of the first set, where "relative reliability“ was measured by the ratio of the mean squares of the two monthly sets, was reported as 101.0 percent and 104.0 percent for the first and second sets, reSpectively. The first set overestimated the milk record by an average of 69 lbs with a standard error of 2.8 lb. The second set underestimated the milk record by an average of 18 1b with a standard error of 3.4 lb. The fre- quency of errors larger than 10 percent for the first set was one in 78 and was one in 32 for the second set. The average percent error when bi-monthly records were compared with the standard method was 3.0 for all bi-monthly sets for milk and 4.0 for fat. Again, the first set was somewhat more accurate, being in error 2.8 percent for milk and 3.7 percent for fat while the second set was in error 3.2 percent and 4.4 percent for milk and fat. The workers concluded that bi- monthly testing should be satisfactory for sire provings and p0pulation studies, but it may be unsatisfactory for indivi- dual lactation records. 8 Flanagan (1965) employed the centering date method to predict lactation records of six different lengths from seven, 14, 30, 42, 60, and 90 day intervals. From daily records of 367 lactations of s pring-calving Shorthorn cows and 147 lactations of spring-calving Friesians he found that different factors should be used to compensate for the bias introduced by the three months of calving, and for each of seven lactation length classes. For all lactation lengths combined, he reported standard errors of estimate as 9.35 imperial gallons for seven day intervals, 13.43, 22.48, 29.75, 40.32, and 69.60 imperial gallons for l4,30,42,60 and 90 day intervals, reSpectively for the Friesian breed. When he used the 305 day standard error as the base, the standard error of cows tested at 90 day intervals was 34.5 percent of the base. Predictingigotal Production from Parts In the prediction of total lactation from one or more months of a cow's record the coefficient of correlation between the part and whole tells how valuable each part will be. The higher the correlation of production of a given month with the total yield, the more accurate is that seg— ment in estimating the record. Gaines (1927) found that a one or two day test during the fourth month of lactation provided the best indication of what the cow would produce during the lactation. Working with 80 Jersey and 80 Holstein records, Kennedy and Seath (1942) 9 reported that production by first calf heifers during the first four months was a good index of what the first lactation would be and that it was useful to predict the relative pro- duction of the second lactation. Coefficients of correlations between production in single months and total production for first lactation for Holsteins were .62 for the first month and .78 for the fourth month. The correlation between com- Iplete first and second lactations was .54. Madden 33 a1. (1955) reported repeatabilities, heritabilities, and genetic correlations for monthly and cumulative periods of milk production. Repeatabilities for milk and fat production in single months and for cumulative milk and fat production were 0.41, 0.32, 0.57, and 0.51, reSpectively. By intra-sire regression of daughters on dam, heritabilities were .076 for 275-305 to .390 for 1-30 days production for monthly data and .344 for 1-120 days to .632 for 1-274 days of cumulative production. Genetic correlations between cumulative parts and total milk and fat production were larger than 0.90. Selecting on the cumulative part record would improve production nearly as much as selecting on the complete record itself, with efficiency values ranging from 0.74 to unity. Reece (1942), working in New Jersey with 70 cows in the Experiment Station herd, concluded that the average fat test at the end of the second month of lactation was a good measure of the ability of a cow to secrete milk fat. Further- more, he found that almost as much accuracy was available by 10 the end of the sixth month of lactation as for 10 full months. He reported correlations with total production of 0.53 for the first month, .74, .80, .85, .87, and .93 for two through six cumulative months of the lactation. Voelker (1957) extended 1636 two—year-old records from the college herd at South Dakota and reported correla- tions of total production of .68 for the first month to .99 for nine cumulative months on test. Correlation coefficients increased to .89 for five cumulative months then remained the same for the next four months. The cumulative milk yield for the first 70 days of lactation was a good indication of total lactation yield, correlation coefficient of .80 reported by Rendel (1957), using 3109 production records from six breeds in Great Britain. Madden 33 a1. (1959) found the correlations between non-cumulative test-day production and total yield were higher for younger cows and that the highest values occurred between the fourth and seventh months, ranging from .71 to .93. Correlations between production on test dates varied from .38 to .89 for cows under two years old on 2x milking and from .23 to .88 for cows three years old and older. The highest correlations occurred between adjacent months. These results were similar to those reported earlier by Kennedy (1942), Voelker (1957), and Reece (1942) in the United States and Rendel (1957) in “reat Britain. Lamb (19oz) also reported relatively high correlations com- pared with the other months for the fourth, fifth, and sixth months individually with the total lactation yield. 11 The younger cows tended to be more persistent than the older animals: correlations of first month with total milk declined from .68 for the first lactation, to .62 for the second, and to .54 for the third lactation and over. The middle months varied less than the first and last months of the lactation, but the younger cows were always highest and the older animals always lowest in production. This was al— so true for butterfat values. VanVleck and Henderson (1961d), in ascertaining the efficiency of intra-herd regression factors compared to those derived by ignoring herd effects, reported similar findings. They found correlations of .67 between first month and milk yield for total lactation for 9036 Holstein cows, and the correlation increased to .90 for the fifth month of lactation, then decreased to .52 for the tenth month. Again, the fourth and sixth months were also higher than all others except the fifth month, when herd effects were ignored. The correlation between part and whole for cumulative milk production increased from .67 for the first month to .99 for the ninth month. On an intra-herd basis, non-cumulative data provided correlations of .53 for the tenth month and .57 for the first month. Cumulatively, the correlation coefficients were .57 for the first month and .99 for the ninth month. These values were similar to those later reported by Lamb (1962). However Lamb's data were recorded by lactation number and the older animals had lower values, particularly in the first five months, than did the first lactation animals. The same pattern for fat was evident 12 in Lamb's (1962) data. Miller (196 cumulative factors for milk and fat of .92 between actual herd averages averages estimated from single days at various stages of the lactation. for milk and .62 for fat production dual cows. Extension Factors and Their 1 Two methods have been used 3 used Lamb‘s non— and reported a correlation from 553 herds and of test of 19,000 cows The correlation was .82 when computed for indivi- nerivations to derive factors for estimating production from parts for the total lactation (305 days). goth methods provide factors for estimating total production from data in a single month or from produc- tion cumulated from mo total production to a particular part. tion is y — the ratio of the comnl the prouuction for the represented by V a + record, a is the point 1’3 \l u- the y axis, and average change in y :0 actual production fiatios Turner 9 — “I“. (4.1% estimate 5:. st 1. length. Cannon is the .5 .L '.(‘. 305—day fat p re than one month, using the ratio of The projection ecua- is the estimated 305—day record, 9 is eted lactation to the part, and x is " v -.L t. The regression equation can be bx where y is the estimated 305-day where the regression line intercepts (fl regre sion coefficient measuring the so ”no “V 1 each unit change in x, and x is t for the part. csdale (1924) formulated rahos to ..J rocuction from ad recorcs of lesser \ A 'r \-\ (1924) selects at ransom 15 COWS of 13 three breeds and computed the errors resulting from estimating a 305-day record. They observed an average difference of 8.8 lb fat with the estimated records being larger for the “College Herd“ factors and a negative value of 3.0 lb fat when factors derived from DHIA data were used to extend records. They concluded that the errors in records calculated by ratio factors are small, and the factors could be used successfully. Turner and Ragsdale used over 3,000 Holstein lactation AR records to ascertain appropriate age and length factors which would allow them to compare daughters of 229 Holstein sires. Cannon used 400 Holstein records from the Iowa State College herd and 1289 lactation records of five breeds from the Iowa Dairy Herd Improvement Association to calculate cumulative factors to extend partial records to a 305 day basis. The conversion factors were based on the average rate of decline by using the ratio of total production during 365 days to the production at various monthly intervals. Turner (1926) illustrated how the exponential law could be employed in expressing in a quantitative form the persistency of milk and fat secretion and its application to the analysis of experimental data. His argument was that from a given maximum production for a month, the cause of variation in total yield of milk is due to the variation in the rateof decrease. He suggested that an index of persist- ency could be obtained from the ratio between total yearly yield and the maximum month's production. When this ratio l4 equals twelve for a yearly test or ten for ten months, the persistency percent is 100. This ratio applied to the maximum month's production provided an estimate of the 305- day production when ten months were used in the total. Turner concluded that when all other conditions are uniform, the monthly milk or fat production during the lactation period after the maximum is passed is a constant percentage of the preceeding month's production. Madden 23 a1. (1959) considered age, frequency of milking, and production levels in formulating factors to estimate total lactation records from parts. They used the first ten tests from lactations which had production recorded for at least ten different test dates and divided the data into lactations with the same milking frequencies (2X or 3X). They found that lactation curves for 2X and 3X for the same lactation appeared parallel, with the 3X curve being higher than the 2X curve. Earlier Madden 22 31. (1955) found lactation curves parallel for cows calving at less than three years of age, and for three, four, five, and six year olds, but the older cows differed from the younger animals in achieving a higher maximum but declining more rapidly. The curves crossed at about nine months in production. Average production on first test day for monthly age groups through six years of age differed significantly, but the means for ages under three years and means for three years and older did not differ within their respective groups. There was overlapping of average production between groups only at the 15 ages of 35 to 37 months. Of those animals calving between 35 and 36 months of age the percent of first lactations initiated was approximately equal to the percent of total lactations initiated. Twelve percent of the second lactations were initiated prior to 36 months and ten percent of the first lactations after 35 months. For this reason, they classi- fied the ages into less than 36 months and equal to or greater than 36 months. Madden gt Q1. (1959) concluded that the ratio method may appeal intuitively to many and that it is easy to develop and use although it tends to underestimate total production of low-producing cows and overestimate total production of high producing cows since the ratio method corrects only for incompleteness of the lactation and does not take into account the incomplete repeatability of the parts of the lactation. Lamb (1959) completed a comprehensive study of vari- ables affecting the relationship of the total to part produc- tion. He used 16,272 complete lactation records of four breeds in Michigan to study age and lactation number, season of calving, herd effect, and breed effect. First calf heifers did not decline in production as rapidly as older cows during the last months of the lactation. By grouping cows according to first, second, and third or more lactations and according to age by less than 36 months, 36 to 48 months, 48 to 60 months, and 60 months and over, he found the variability in ratios of total to part was larger for lactation number than 16 for age. This was true particularly for the first and last months of lactation. The component of variance for age dur- ing the center months was larger than the component for lactation: thus, age would be a better indicator for these months. He further stated that age correction factors should be used to extend first lactation records initiated after 36 months of age, since the factors for first lactation would overestimate production. Age correction factors also would be more realistic for animals with second lactations initiated prior to 36 months, since the factors based on lactation would tend to underestimate production. In all other cases, factors based on either age or lactation should work equally well. Lamb (1962) substantiated the previous work and suggested that at least two sets of age correction factors be used. Separate factors could be used for records initiated at less than 36 months, 37 to 47 months, and over 48 months, but it appears reasonable to use one set of factors for all cows calving at ages over 36 months. If one set of ratio factors were used, records for older cows would be overestimated while those for younger cows would be underestimated. These results were similar to those reported by Madden g5 21. (1959) for Holstein HIR data. Lamb (1959) classified records by four seasons, October-December, January-March, April-June, and July-September. Season appeared to account for almost as much variation as age, and Holsteins were least influenced by season of calving. 17 Two seasonal groups were used to develOp ratio factors - November-April and MaybOctober. Lamb's~ later work did not substantiate earlier results: he found the season adjustment was less important than adjustment for age. He also re- arranged the two seasonal groups to include April-July and AugustsMarch since differences between the factors of these groups were larger than between factors of the two previous groups. Lamb's (1959) work indicated no sizable variation in the relationship of total to part production among various classes of records. However, Jerseys tended to show the most herd differences of the four breeds included. Aulerich (1965) reported ratio factors for predicting total production from terminal incomplete lactations differed from those for non-terminal records. The terminal incomplete lactations were initiated at a lower milk yield than those of cows completing their records in the same age-season group, and they declined at a faster rate. A separate set of ratio factors was developed for cows having voluntarily terminal incomplete records. Cows removed voluntarily were culled for low production, old age, dairy purposes, or hard milking. The DHIA Newsletter (1965) includes a set of projec- tion factors for estimating 305-day milk production. These factors were based on a total of 162,191 DHIA lactations combining Michigan and Iowa data. The authors recommend the use of two age factors. disregarding season effects, since 18 previous research indicates that age is the most important cause of variation within breed in the projection factors. VanVleCK and Henderson (1961b) classified cows into 60 age classes, three seasons of calving and ten stages of lactation to ascertain the differences beteen ratio factors for each of the above effects. Their analysis of 177,575 Holstein records indicated that ratio factors for estimating total lactation yield from cumulative monthly records must be constructed simultaneously taking into account age at calving, season of calving, month of production, and whether the record is milk or fat. Ratio factors for adjusting monthly records to a common age and season and for estimating a total lacta- tion from a single monthly record must be constructed in the same manner. This method would require 3600 factors, too many to be practical. Therefore, the authors suggest using sixamonth age intervals which would reduce the number of factors to 1200. They remarked that correcting for age but not for season and then analyzing records within seasons would not be adequate because definite differences exist among seasons. Regression Gowen and Gowen (1922) to provide some means for mak- ing the seven day test more meaningful to farmers, used regression factors to estimate total lactation yield from the seven day totals. They reported Correlation coefficients of -.115 to .835 (with a weighted mean of .598) between seven-day 19 and 365-day totals for various age groups. In addition to formulating prediction equations for the same lactation, they predicted the succeeding lactation from a given record. They found that a seven day test predicted the 365-day record of which it ié a part more accurately than it predicts subsequent lactations. Fritz pg 21. (1960) investigated the importance of breed, herd, Iactation number, season of calving, and age at calving on the relationship between milk or fat production on test day and correSponding production for the complete lacta- tion. They computed apprOpriate regression factors for esti- mating 305-day records from parts. In this study, they used 11,420 Michigan DHIA-IBM records, including only those animals having at least ten consecutive test days. They reported that variation in fat production among seasons was significant only for the first test day of production and that herd differences in milk production were significant for the first test day of production. An examination of age and lactation numbers revealed that only seven percent of the first lactations were initiated after 36 months of age and five percent of the second lactations prior to 36 months of age. Intra-herd factors were compared visually with inter- herd factors and, although these results were not tested for significance, the authors reported a marked similarity between the two sets of factors, eSpecially for milk production. Since variation due to herd differences was not significant except for the first month of production, the authors suggested that 20 it may not be necessary to derive extension factors on an intra-herd basis to achieve sufficient maximum accuracy in extending records to 305 days. Correlations between cumula- tive test day production and the 305-day total, ignoring herd effects, also were reported and compared closely with others previously mentioned. To ascertain if separate extension factors are needed for low or high producing cows , Madden gt a1. (1959) fit quadratic regression equations of total on cumulative part production for various age-milking frequency groups. They reported that multiple correlation values were within .006 of the correlationsreported when production levels were not con- sidered. They developed regression factors for extending cumulative part records at two milking frequencies and two age groups. Except for young cows in the first month of the lactation, the differences between frequencies of milking within ages were non-significant. VanVleCK and Henderson (1961a) used 9,036 Holstein records from 375 New YOrk herds and reported regression factors for extending (1) single monthly records, (2) sequen- tial test day data, and (3) cumulative test day records to a ten month total on an intra—herd basis. Correlations between monthly and total production ranged from .53 for the tenth month to .85 for the fourth, fifth, and sixth months when used singly. Correlation coefficients for cumulative production ranged from .57 for the first month to .99 for the ninth month, and these were in general agreement with others previously 21 reporteC. The authors reported recression factors :or extend- a ten—month total :01 those H (3 U) (1. 0 ing part lactation reco ' the first ncntn are missili .4 re 51) situations when c.t 5. ’| In a later paper, Van71eck and Henderson (19016) con— parec the erficiencv oi using intra—herd regression :actors (I) Elf U) to those wnere herd effect. ignored. The IGCOILS were " 1') adjusted ror age at calving and eason of calving. The rela- tive efficiency (3) was Cerined as 120 (Vi/V2) where Vl was the residual variance of the sum of the first ten test records not accoun ed for by total regression and V2 was tne residual variance of total yield not accounted for by intra—herd regression. The relative efficiencies of the intra—herd factors ranged from 102 percent for the first nine sequential months to 15: percent for the tenth month alone. For most cases, ignorino herd effects was 10—20 percent less efficient than considering herd effects. Residual variances for regression ignoring herd effects for single month's records ranged :rom 1,73o for the fifth month to 6,443 for tne tenth month. For semuentia1 months, the variance ranged from 51 for the first ninesecuential months to 4,585 for the first month. For cumulative months the variance was highest for the first month and lowest at the ninth month. Bi—monthly residual variances, ignoring herd effects, were 165 and 171 for sequential monthly sets of odd numbered months and even numbered months of lactation reenactive1V. :or three tri- monthly sets variances were 573, 423, ant 393. Cumulative func- tionQ of these data gave the following variances: 214 and 213 ror H 22 sets one and two of bi-monthly records and 904, 457, and 421 for the three tri-monthly sets. The authors concluded that prediction of ten month milk yield by regression ignoring herd effects is more practical for most situations because of simplicity although the accuracy is slightly less in all situations than for the intra-herd predictions. ggmparison of the Ratio and Regression Methods Madden 25 a1. (1959) stated that the choice between the ratio and regression methods depends on the purpose for which the method is to be used and the ease of use. They indicated that the ratio method may have more appeal to many and would be easier to develop and use. The variation in the total production estimated by ratio is more nearly like the variation in actual total production. In addition to the adjustment for incompleteness accomplished by the ratio method, the regression method also adjusts for the unidentified sources of variation which make the part larger or smaller than average, and the total estimated by regression varies less than the actual total. The differences between these two methods are largest during the early months of the lacta- tion. Lamb (1959) reported that the value of the regression procedure is in its ability to correct for the incomplete repeatability of various portions of the lactation, whereas the advantages of the ratio procedure are its direct measure of the relationship of the partial lactation to its total, its simolicitv, ease of calculation, anu its availaoilitv from a single lactation. Harvev (l95b)£0uno that seharate equations are needed for each stage or lactation when the regression Dro- cedure is used because 0: the changinj parameter values. Ye note” that the efti“nte7 intercoft ajproacho* zero a: the 314th of lactation increase], cousin: :ifiilar'tie: to c:::t *eencon tn“ ratios on; regression coefificients. The differ— ence: getueen the use methods can be exoressed as (b-c)(x-x) where Q is the linear regression of total oroduction on a c is the ratio or the total to part, g is the actual oart, oartial milk oroluetion, anu E is the mean of the partial milK oroduction for the aotrooriate hreeC-age-season grouo. xaoeen gt 2;. (1959) found the differences (b-c) to be nega- tive anc largest in magnituoe curing the early (onathree) cumulative months, negative but smaller in magnitude during the milee months (four-six), and positive and small during the longer (seven—nine) cumulative months. SOURCE OF DATA Approximately 58,840 completed records of Holstein cows were selected from more than 500,000 records tested in Michigan DHIA between January, 1959, and October, 1961. The analyzed records in this study were obtained by selecting completed Holstein records which were included in a previous study (Aulerich, 1963). In the previous work, records of milk production were obtained from approximately 2,500,000 monthly reports of cows tested in Michigan DHIA.from January, 1959 to October, 1961. Only lactations initiated after January 1, 1959 and identified by herd number, cow number, date of calving, age at calving and breed were included. Each test day milk weight was recorded in tenths of pounds, and records in which the first test occurred more than 50 days after calving were excluded. From this group, records were chosen to include only those cows that had consecutive monthly production from calving until going dry. Records of cows leaving the herd for various reasons were excluded from this analysis. Likewise, lactations with data missing for one or more months were excluded. 24 METHODS AND RESULTS Record Classification Data were analyzed as a single group for the primary purpose of this study to compare various methods of estimat- ing production in the total lactation. For computing regres- sion coefficients, the data were categorized by two age groups (cows calving at less than 36 months of age and those calving at 36 months or over) and two seasons of calving (cows calving from April through July and those calving from August through March). The basis of these classifications is primarily Lamb's (1959 and l962)work. All ratio procedures were limited to include all cows in milk on test date and the comparison between regression and the ratio procedures was conducted on this basis rather than for each of the various age-season groups. Table 1 shows the classification of data as used for computing the age-season regression factors. Measuring Relationships of Parts to the Whole The value of any part in estimating the whole is determined by how closely the part is related to the whole. Simple product-moment correlations were used to measure this relationship. When several parts were included in the relation- ship, multiple correlation coefficients were used to eXpress the relationship between the parts combined and the whole, 25 26 TABLE 1 Distribution of Records by Age and Season Age at Calving Percent (.36 months --------------------------------------- 36.5 £f36 months --------------------------------------- 63.5 Season of Calying April - July --------------------------------------- 23.4 August - March ------------------------------------- 76.6 Age-Seasgnmggflgalvigg_ 436 months - April - July ------------------------- 8.6 4 36 months - August - March ----------------------- 27.9 .£?36 months - April - July ------------------------- 14.8 >36 months - August - March ----------------------- 48.7 27 partial correlation coefficients were used to express the highest order partial correlation coefficient between the parts (Xi) and the whole (Y). Most data used in previous reports have had the re- striction that the first ten consecutive months of test be in- cluded. To determine whether the relationships of part to whole were similar in these cases to those instances where animals terminate their record by going dry prior to the com- pletion of the first ten test dates, correlations were com- puted for both situations. Aulerich (1965) suggested that ratios may differ for terminated records after plotting the lactation curves for the two groups. She stated that involuntary tenninal records were similar to the complete records and that these data should be extended using the non-terminal factors. She further reported that voluntarily tenninal incomplete lacta- tions should be extended using another set of factors. There- fore, she develOped a separate setof ratios for these records. ) This could also be accomplished for animals going dry prior to 305 days. Table 2 shows the percent and numbers of animals in milk for each of the ten test dates. These data indicate that 18 percent of the cows go- ing dry prior to 305 days terminate their records between the ninth and tenth month of lactation. Table 3 shows the simple correlations between milk produced on individual test days and the production for the 28 total lactation for records including the first ten tests. Table 4 provides corresponding correlations between various parts and the total production for all cows in milk on test day. Estimating 305-Day Records from Various Parts of the Lactation is; 1.92 The ratios, which were extensively developed by Lamb (1962), Madden gt a1. (1955) and Aulerich (1965), are a pOpular form of extending records. Two forms of ratios have been developed, (1) cumulative ratio factors which extend the total production to date to the whole, and (2) non-cumulative ratios which extend single month's production to the total. A linear function of the ratios to extend records from two or more nonadjacent test dates can be expressed as -1 1)- R1 = (Rj amounts produced on two non-adjacent months. + Rk- 1 where R1 3 ratio to extend the sum of R ratio used to extend on non-cumulative basis the J jth test R the kth test. ratio used to extend on non-cumulative basis This ratio may be useful where some tests are missing. Another method of using ratios is to average estimates from individual test days. This could be accomplished by dividing the estimate by the number of ratios used, thus, weighting equally each ratio. This can be expressed as 29 TABLE 2 Percent Cows in Milk on Each of 10 Test Dates Month of Test 4 5 6 7fi_ 8 9 10 Percent 99.8 99.5 99.3 99.0 98.3 97.4 82.0 Percent Cows Reported Dry the First Time for Each of 10 Test Dates Percent 1.34 1.28 1.01 1.76 3.81 20.2 70.4 Total 17.99 TABLE 3 Correlations Between Milk Produced on Single Test-Days for Records with 10 Tests W Month of Test ionth of Test 1 2 3 4 5 6 7 8 9 10 Total 1 1.0 .75 2 .82 1.0 .85 3 .75 .87 1.0 .88 4 .69 . 82 .88 1.0 .90 5 .64 .76 .82 .87 1.0 .91 6 .58 .60 .76 .81 .87 1.0 .90 7 .50 .61 .67 .74 .80 .86 1.0 .87 8 .39 .49 .56 .62 .69 .76 .84 1.0 .81 9 .24 .32 .38 .44 .50 .58 .66 .80 1.0 .67 10 .13 .20 .24 .29 .35 .42 .50 .63 .81 1.0 .53 31 TABLE 4 Correlations Between Milk Produced on Single Test—Days (Dry Test Days Excluded) Month of Test Month of Testfi 1 2 3 4 5 6 7 8 9 10 Total 1 1.0 .71 2 .81 1.0 .82 3 .75 .87 1.0 .85 4 .69 .82 .88 1.0 .88 5 .64 .76 .82 .87 1.0 .89 6 .56 .68 .75 .81 .87 1.0 .89 7 .47 .59 .65 .72 .78 .86 1.0 .87 8 .34 .45 .51 .58 .65 .73 .83 1.0 .80 9 . .20 .29 .35 .41 .47 .55 .65 .81 1.0 .66 10 .13 .20 .24 .29 .35 .42 .50 .63 .81 .53 32 (R1A1+R2x2 + R3x3) / 3 where R1, R2, R3 are the non-cumulative ratio factors for any three test days and X , X2, X are the 3 corresponding amounts of milk for each of the test days. To weight each estimate of total production by the inverse of its error variance can be expressed as follows: Z". (RiY/(l—rfy) e'fyj/E [1- / l-rizy) ?‘ Ty] where R1 = non-cumulative factor for extending records for the ith test date riy= correlation between the ith part and the total A 2 _ a_.iy= total variance of 305-day lactations. Standard DHIA.Method The DHIA.Handbook provides a centering date table for bi—monthly testing which functions in the same manner as the regular monthly testing program. Each bi-monthly testing period is divided as nearly as possible into two equal groups of time, half of the time occurring prior to the test date and half the time falling after the test date. Many states have used a bi-monthly system to provide a low cost testing prOgram. The model for the DHIA procedure can be written: a y = B X + B l 1 .2X2 + 82X3 + B X + B X where the values of 31 2 4 3 5 and B depend on the stage of lactation when the animal is 3 first tested and the Xi represent the milk weights on test days. The value of 82 is 2.0 since each test represents two monthly tests. 33 _Reg£ession Coefficients for Estimating Total Yield The least squares normal equations were solved to estimate the desired regression coefficients. The right and left hand sides of these equations were made up of the total sums of squares and cross-products corrected for means. Algebraically, the estimates are obtained from: ta ==éé ciJ . ij where bi is the estimated partial regression j=1 coefficient of total production on production in part i of the lactation. ciJ is the element of the inverse of the matrix of sums of squares and products involving production parts i and J'. Mj is the corrected sum of products of total produc- tion and production in part 3. The standard error of the regression coefficient is estimated as Sb =\’c1182 where 82 is the error variance or i (1-R§)3§2 where R% is the square of the multiple correlation andf&2 is the estimated variance of the total yield. VanVleck and Henderson (l961d) concluded that this method is more practical for most situations if herd effects are ignored. An example of the use of regression factors to esti- mate total yield from a test-day of a single record is as follows: $b= total lactations for the breed + bi (test day production - breed average production for that test day or " "' ) Y = Y + . = o bl(Xi xi 34 Regression coefficients and their standard errors, standard errors of estimated yields, and correlations of various parts with total production were computed for single months, sequential months, cumulative months, and different types of both bi-monthly and tri-monthly testing. Most work to date has been based on records contain- ing at least ten test dates, with the exception of that of Madden §§_al. (1955) who included completed records of 243 or more days in length. To ascertain whether or not this type of restriction affects the factors, the regression factors in this study were computed in the two ways, one including those records containing at least ten consecutive test dates and the other also including records terminated by dry period prior to 305 days. Table 5 shows the means and standard deviation of monthly test day records and the cumulative production for those animals in milk at least ten consecutive test dates. A total of 48,257 records was used in this category, with the average age being 47 months. Table 6 contains correSponding values for data including all cows in milk on test date. Tables 7 and 8 contain regression coefficients for estimating total milk yield for the lactation from cumulative test data for both situations. The standard errors of esti— mates are smaller for the data where ten consecutive test dates are used than for records of all cows in milk on test day. 35 Tables 9 and 10 compare similar regrission co- efficients when the production in single months is used to project the total yielc. Since all cows in milk on the tenth test day are the same animals in milk ten consecutive test sates, the results for these two cases are identical, but results IOI the two methods diverge from the tenth to the first test month's cata. Tasle ll contains the rec ession coefficients ror extending records when the first month's data are missing. The number of animals included in ‘ne estiaates is the sane as the number of animals in milk at least ten consecutive Cites. Thus far, all factors have been simole regressions where only one part is used to estimate total production. Tables 12 and 13 are results of multiple linear regressions 'l where two or more parts are involved. This can be represented \ as follows: Y = + ‘To 21'- + "3- '3{ ... “a 3; where- represents - I ‘ 1 V7—l“ ‘\ —3 ‘\ - l‘1 *1. d} 5...] C. n U) :1) H (9 O O 3 £3 rl” ‘1 l» I O *1 L- L) (1' D“ (n L“ ('1‘ U) 0 z in (J r: ,1} \ (T (1 f) (1 rt (1‘ U} ”U , ) t (‘J |_..J p3 -, ' z ‘ .2 ' . 2.. - . A . ..L. ',- .‘ J- 4 _. aVailaole for the "lfSo ten consecutive test ta I_J (D data available on a particular test date."Tau 12 lists cats ..‘. ‘ . . __ ._ - i 1‘ ‘_ _' _ "I: \ - v“ \fi. , ‘ o _4‘- ’3 ‘v_ for situations where records ior one or more Beuddfltlui test ’, .) ‘m‘J. ; .. . ' -- -' . - - ' -. ..-l __' - dates at the end or lCCtltlQn are hissing. ingle 1 Table 14 contains values used to extend part records ' .L-‘. .---_ 4. .-..t in the iiist hart 36 TABLE 5 Means and Standard Deviations of Monthly Test Day Records of Milk Produced on Single and Cumulative Test Days (10 Test Days) ‘-~ Month of Test 1 2 3 4 5 6 7 8 9 10 Single Months 51.3 51.0 46.9 43.3 40.4 37.9 35.3 32.4 28.1 23.7 Std. Dev. 12.6 12.7 11.9 10.9 10.1 9.5 9.0 8.7 9.0 9.2 Cum.Mos. Means 51.3 102.3 149.2 192.5 232.9 270.8 306.1 338.5 366.6 390.4 Total 390.4 Std.Dev. 84.0 305 Day (Actual) 11907 TQflE6 Milk Produced on Single Test Days (Dry Test Days Excluded) Month of Test 1 2 3 4 5 6 7 8 9 10 Mean 51.2 50.6 46.4 42.7 39.8 37.1 34.3 30.9 26.9 23.7 Std.Dev.12.7 12.8 12.0 11.0 10.2 9.7 9.4 9.4 9.5 9.2 37 Txms7 Regression Factors for Estimating Total Milk Yield from Cumulative Test-Day Records (10 Test Days) .— .4 ant fl" Month of Test 1 2 3 4 5 6 7 8 9 b‘ 4.97 2.91 2.12 1.72 1.48 1.31 1.19 1.11 1.05 Std.b .020 .009 .005 .004 .003 .002 .001 .001 .001 r .75 .84 .88 .91 .93 .95 .97 .98 .99 A 0‘; 55.9 46.2 39.9 34.8 30.0 25.4 20.6 15.2 8.3 —— Regression Factors for Estimating Total Milk Yield From Cumulative Test Day Records (Dry Test Days Excluded) W ...—.2- mm Month of Test 1 2 3 4 5 6 7 8 9 b 4.98 2.93 2.15 1.74 1.49 1.32 1.21 1.12 1.06 Std.b .020 .009 .006 .004 .003 .002 .002 .001 .001 .71 .80 .85 .88 .91 .93 .95 .97 .99 r A 6; 62.9 53.6 47.6 41.7 36.6 31.6 26.1 19.3 10.8 b = Regression coefficient a r 3 Correlation between that month and the total d3 Iflnovon Std b Std. error of regression coefficient 38 TABLE 9 Regression Factors for Estimating Total Milk Yield From A Single Monthly Test Using Data Only From Cows in Milk at Least Ten Test Dates ”.m. m-w T 1‘ .- .- ‘ m __: ___ fizz—fl Month of Test 1 2 3 4 5 6 7 8 9 10 b 4.97 5.58 6.23 6.96 7.54 7.94 8.10 7.79 6.27 4.80 Std.b .020 .016 .015 .015 .016 .017 .021 .026 .032 .035 .75 .85 .88 .90 .91 .90 .87 .81 .67 .53 r B 6;_ 55.9 44.7 39.8 36.5 35.2 36.6 41.2 49.2 62.4 71.5 TABLE 10 Regression Factors for Estimating Total Milk Yield From A Single Monthly Test Record Using Data From All Cows In Milk on Test Date Month of Test 1 2 3 4 5 6 7 8 9 10 b 4.98 5.68 6.34 7.09 7.66 8.03 8.05 7.34 5.94 4.80 Std.b .020 .017 .016 .016 .016 .017 .019 .023 .028 .035 r .71 .82 .85 .88 .89 .89 .87 .80 .66 .53 a; (52.9 51.5 46.5 41.8 39.3 39.2 42.7 51.4 63.5 71.5 39 TABLE 11 Regression Factors for Estimating Total Milk Yield From Cumulative Test Day Records When First Month Records are Missing Test 10 9 8 7 6 5 4 3 2 b 4.80 3.05 2.50 2.15 1.87 1.64 1.44 1.26 1.11 Std.b .035 .017 .011 .007 .005 .003 .002 .001 .001 r .53 .63 .73 .81 .88 .92 .96 .98 .99 71.5 65.4 57.3 48.8 40.6 32.7 24.8 17.1 9.4 40 J moo. woo. woo. woo. woo. woo. woo. moo. moo. Q .oum e.m oo.a mm.a eo.a mm. mm. mm. mm. oo.H oo.a mm. s o ado. ado. mac. mao. NHo. Hao. 0H0. >00. 9 .oum m.HH mm. mm.m HH.H oo.H mm. mm. mm. mm. mm. D m 5H0. omo. mao. mac. mac. vao. 0H0. Q .pum mda mm. 32m «64 404 so. mm. mm. mm. s s Hmo. «No. mmo. Hmo. mao. mao. D .pum H.Hm em. mm.m mm.a HH.H am. am. he. s o mmo. mmo. mmo. Nmo. mac. 9 .pum 0.8m mm. mm.m mo.a mo.H mm. mm. s m mmo. omo. smo. omo. n.6um m.am mm. Hm.m mo.a mm. mm. s m mmo. Hmo. mmo. Q .pum 4.6m om. aa.a os.a so. a m smo. mmo. s .pum o.¢v mm. on.v mo.H Q m owe. 9 .6pm m.mm mm. hm.v 9 H mu m m m k 6 m a m N a “was ‘ MO mSUCOE Hmaucmsgmm mmumo paws awe ummmu um sass 6H mzoo Bosh mace sumo mCflmD mmDMQIUmmB HmfiucmSWmm Scum tame» xaaz Hmuoe mcfiumfiaumm How muouumm coflmmmumwm NH mamme . woo. woo. moo. moo. ooo. moo. poo. ooo. moo. n.oum o.s oo.a oo.a Hm.a mm. mm. so. om. ao.a mo.a mm. a o ado. mao. mao. mao. vao. mao. ado. moo. n.oum o.mH om. mo.~ oo.a Ho. oo. oo. mo. No.a oo. 9 m mao. moo. mmo. omo. oao. oHo. mao. n.6um o.om so. aa.m om.a mo. om. no. mm. on. n s emo. omo. omo. amo. Hmo. mao. n.oum s.om mo. ms.m 64.4 mo.a mm. mm. mo. n o omo. Hmo. omo. moo. mao. n.6um H.~m mo. mo.m mo.H mo.a mo. me. n m omo. mmo. omo. Nmo. n.6um o.km oo. sa.¢ Hk.a mo. me. a a Nmo. emo. mmo. n.6um m.aa so. mm.a os.a me. n m mmo. vmo. n.6um s.om ms. mo.o oo. n N omo. n.6um o.mo as. oo.v n a MN .m o o s o m a m m H umms mo abuses HmHucmsgmm 1|Ill|lll “I “In! sumo pmmB co xawz cH wzoo dad mo mpuoomm mcamo moammwz_mna sumo mnucozeummq coca mmumolumme assucmogmm eoum pHmHM xHHE Hmuoa mcHDMEHumm now muouumm conmmummm md MAM4B 42 Bi-Monthly and Tri-Monthly Results It appears from previously mentioned results that it may be necessary to compute regression coefficients to ex- tend records which have only various portions of the data normally available for computation of the tri-monthly and bi- monthly records. For example, if a cow has no production on her first test day, she still fits into the first bi-monthly or tri-monthly set but with the first test date's data missing. If a full complement of monthly data are needed to extend the production to a 10 month basis, records with miss- ing monthly results would be excluded from the program. How- ever, if regression factors are available for extending a particular incomplete tri-monthly set, the data could be sal- vaged. The number of combinations of months varies from those situations where all months are available to those where only one is available. For tri-monthly testing, the monthly set using four test dates (1-4—7-10) would have a total of 15 combinations of incomplete data when single months are in- cluded: the other two sets have a total of seven combinations each. However, since the single months and the complete com- pliment of dates are already computed, it is necessary only to solve for ten additional factors for the 1-4-7-10 combina- tion and three additional factors for each of the other two sets, 2—5—8 and 3-6-9 combinations. Table 15 lists the simultaneous values for both tri- monthly and bi—monthly testing systems. These data contain all records available on test date. The correSponding cumulative A"? .1 figures for both bi- anw trl—monthly testing are shown in .1 7 shows the regression values to s (I) I.) (D Taole 1;. Taol ‘1 |’ EL 1. ( \u igned for the various “incomolete” monthly sets for each or the three sets of tri-monthlv data. The ntnoer of con- 1 binations that could result ror seen or the tw. bi-nonthlv J sets is ouite large (.t least 30). dowever, many of these (I will rail into the single month category or into one of the above listed tri-nonthlv results. - h "7 ‘-I a. ' '~ ' i . - ‘ ‘. Lverace crocuCtion 71thln :.e a:o Seasou m Means of total production were highest for animals initiating lactations at 35 or more months of age and from August to march, and were lowest for those animals freshen— ing curing April—July at ages less than :8 months. The younger cows reached peak prouuction at lower levels anu did not dininish in production as rapidly as the older animals. Table 18 gives the means and standard deviations for the four age—season groups for ten months during the lactation. Table 19 shows the regr-ssion factors for estimating total yield from cumulative test days data. Differences in these factors point to differences in proouction levels of aged cows and youn: animals. Larger factors are required for the younger animals early in the lactation: but as pro- duction accumulates, factors for different ages converge. Table 20 is a table of regression factors for the four age—season grouos for extending cumulative part records to a ten month basis when data are missing ror the first month. 44 woo. woo. moo. moo. moo. woo. woo. hoo. moo. Q .oum «.5 mm. mm. mm. mm. mm. mm. vo.a wo.a mH.H no.a Q m r. . oao. sac. mao. mao. mHo. eao. mao. oao. Q .num v.ma mm. em. mm. mm. so. mo.a mH.H Nv.H em.m Q m mao. omo. mmo. mmo. mmo. Ono. oao. Q .Uum m.hH mm. am. mm. mm. mm. om.a oh.a Qa.m Q h omo. mmo. mmo. mmo. mmo. mmo. Q .Uum o.¢m om. om. no. em. mH.H mm.a Ho.¢ Q o mmo. mmo. hmo. hmo. omo. Q .Upm o.Qm mm. as. am. vo.Q ho.m oo.m Q m mmo. veo. wvo. omo. Q .oum H.mm mm. mm. oe. mm.H mo.o Q avo. emo. mvo. Q .oum H.mv am. mo.l mo. mm.h Q mmo. mmo. Q .oum m.mo no. av.l Ho.o Q N mmo. Q .oum m.ah mm. om.¢ Q Q g m oa m m N. o m w m N umme ‘ mo mQQGOE Hmapcmswmm Ill mumo umma so xHHE CH mzou Has Some monoumm msHmD mcammez 0H4 mumn m.Qucoz umuam chB mmumalumma Hmfiucwswmm scum came» sees amuoe mceumEHpmm no“ muouumm GOemmmummm vH mflmde oao. mao. oao. n .oum Q.oa no. vo.m oH.m om.m n m an. «Ho. oao. a .oum m.ma so. ms.m em.m mo.m n m moo. «Ho. Hao. moo. n .oum o.ma mm. mo.a Ha.m .. efl.m Ho.a a a manucosufine 5 'l’ ‘1 [Ill 4 I moo. ado. Nao. ado. boo. n .oum >.HH mo. Q¢.Q oo.a eo.m eo.m mm.m n m umm poo. an. ado. moo. ooo. p .oum m.ma mo. m¢.m vo.m om.H oo.m nm.a Q Q umm sanucosram w» m oa m m N. o m e m m H umma C mo Qucoz noncomm mmolumwe haQQGOEIHHB Ucm macucozlwm Hmflpcmdwmm Eon“ Gamay xaez Hmuoe mceumfieumm “0m muouumm conmmummm ma MdmflB 46 TABLE 16 Regression Factors for Estimating Total Milk Yield From Cumulative Bi-Monthly and Tri-Monthly Test-Day Records m Bi-Monthly Tri-Monthly Monthly Sets 1 2 l 2 3 b 1.93 2.00 2.52 3.00 3.19 Std. b .001 .001 .002 .003 .003 R .99 .99 .98 .97 .97 32 14.4 13.0 17.2 20.3 20.0 47 oao. mao. n .oum m.em om. mv.e mm.m a . muo «Ho. oQo. n cum m.mm mm. os.m Hm.m a mum omo. oao. p .eum m.om so. Qa.m oa.m n osm hao. oao. n .oum o.o~ em. mm.m oe.m a mum NHO. Q. oUum o.mm om. oo.e a mum Hmo. p .oum m.em mm. ne.m a mum mmo. mmo. s .opm m.oe mo. NH.H mm.s n oaun mao. who. a .oum m.om so. mo.m Hm.o n oH'w oao. mao. a .oum m.om mm. om.v v~.¢ a sue Hmo. oao. n .oum o.m¢ om. om.m oo.v a oana mHo. oao. p .oum H.om «o. em.o He.m n nus Hmo. oao. n .oum o.oe mo. oo.o om.a 9 «aa «so. oHo. oao. n .oum m.vm so. me.a mH.m sm.m n oansua mHo. mao. vao. p .oum H.mm om. oo.a ea.m oo.e a oaueue oao. mHo. oQo. a .oum m.om om. oo.~ mm.¢ No.m n oHuqu mao. oao. Hoo. n .opm m.vm om. eo.¢ mo.m om.a p envua mocmsvmm Mo m 3 m o s o m 1v m a 039 -(.. 0 QCOE EOH .m UHG H” mcmeHz mum mmuma puma mnoz no 0:0 Eoum sumo cmcz monouwm man umma hasucozraua Hmaucmsvmm MHHE Hmpoa mcHQMEwumm How muouumm conmwummm ha Mdmfie I \l ..‘5 I lll‘!‘.l‘l\lllu.’|| ’I'all . ‘I’I‘lll' 1 ll‘l'll 48 Table 21 shows both correlations between part and total and the regression factors for extending single month's data to a ten month basis. Correlations are higher for younger animals than for older animals within a particular season of calving. The differences are larger in the early months of lactation than for the middle or last months of the record. Table 22 contains regression factors for estimating total lactation yield from sequential test-day data for the four age-season groups. Again the correlations between the estimate and actual are higher during the early parts of lactation for younger animals than for older cows. Table 23 lists the regression factors for estimat- ing total milk yield from sequential bi-monthly data for four age-season groups. Correlations between these estimates and the actual values are also included. Table 24 contains regression coefficients for esti- mating total yield from tri-monthly data. The correlations between the estimate and actual production using the first, fourth, seventh, and tenth month's data are as high or higher than the other two test sets for all four age- season groups, while the third set is as low or lower than the other two for the same age-season group. Regression factors to estimate total production from both bi-monthly and tri-monthly cumulative data are included in Tables 25 and 26. 49 m.mo¢ >.mom m.mmm m.amm m.omm m.0mm o.oam m.voa o.¢aa m.nm momma msucoz m>eumadesu m.mo m.m o.w m.m m.m o.m m.m v.oa H.HH o.ma o.aa .>wo .oum m.mov Q.mm m.om 0.0m o.vm Q.om w.o¢ m.mg m.om o.om m.om mQucoE oaocem Qmpoe oa m m o o m w m m H .IL msucoa sasoiawume masses omum Aoo m.mmm m.omm o.aom Q.o>m h.omm o.aom m.¢oa m.oNQ o.om m.mv cmmz mQucOE m>eumasesu m.mo m.m m.m m.o H.o m.m m. o g. m H.0H o.oa g.oa .>mQ .oum m.mmm o.¢m s.mm m.am e.mm Q.mm s. om a. om .m.oe m.me m.me sumo: mamcem Hopes OH 0 m .I.h| o m e m m H mQQco; Qunmzlumsmsa mQQQOE om av ?Qv m.NQv m.mmm o.oom m.omm N.m N m.mvm m.mom m.oma m.moa m.vm mammz Qucofi 0>Humasesu v.mm o.m o.m m.m w.m o.m Q.oa o.oa m.QQ m.QH v.HH .>mQ .oum m.NHv N.mm o.mm m.mm o.om v.o¢ m.me. N.o¢ 0.0m ¢.gm m.mm Qucoz maocwm Hence OH 0 m o o m .e m m H mQucoz Quumzlum9054 mQUCOE omdN Amv mdsoww COmmmmImmd wsom wow m20ephe>mo osmosmum ocm_mcmm: mung page ma m Amara. 50 v.mmm ¢.hmm 0.00m N.OBN m.®mm h.mom b.05H m.NmH ¢.Hm m.mv c002 mQQCOE m>HQMHSESU m.qs m.m n.e m.» o.» m.m o.o s.m v.oa m.HH H.HH .>mn .oum v.mmm o.mm e.s~ o.om e.am H.mm o.mm m.sm m.a¢ o.me m.mv msucos madcam Qmuoe oH m .1: mo int} o m |I.e m m H mnucos sensuaauaa mcucos omuv Qoo g [IRE ... omscwpcoo ma mamas 51 TAALE l9 Regression Factors For Estimating Total Milk Yield From Cumulative Test—bay Records for Four Age-Season Groups Age-Season Groups Cumulated & 36 months <36 months & 30 months C 36 months Months of Aug.-mar. Aug.-Mar. April-July April-July Test 1 5.20 5.56 4.55 4.97 2 3.14 3.21 2.87 2.91 3 2.28 2.32 2.14 2.13 4 1.84 1.85 1.74 1.73 5 1.56 1.56 1.50 1.49 6 1.37 1.37 1.34 1.33 7 1.23 1.23 1.23 1.22 8 1.13 1.13 1.14 1.14 9 1.06 1.06 1.06 1.06 52 T135143 20 Regression Factors for Estimating Total Milk Yield From Cumulative Test Day Records Jhen First Month Records are Missing for Four Age-Season Groups W Month of 7, 36.months <36 months )36 months 4 36 months Test Aug.-Mar. Aug.-Mar. April-July April-July 2 1.10 1.11 1.10 1.11 3 1.23 1.25 1.23 1.26 4 1.39 1.43 1.39 1.43 5 1.59 1.65 1.60 1.63 6 1.82 1.91 1.78 1.85 7 2.10 2.24 2.06 2.13 8 2.45 2.65 2.46 2.62 9 3.05 3.30 3.14 3.40 10 4.97 5.35 5.09 5.42 t) 5. ( TABLE 21 Regression Factors for Estimating Total Milk Yield from a Single Monthly Test Record for Four Age-Season f‘ urOUpS Month of )36 months <36 months .936 months <36 months Test Aug.-Mar. ___§gg;:fl§§. April-July April—July l b 5.20 5.56 4.55 4.97 r .71 .77 .0d .74 2 b 5.63 6.13 5.26 5.45 r .63 .36 .81 .64 3 b 6.30 6.63 5.93 6.23 r .87 .69 .84 .87 4 b 6.93 7.27 6.49 6.82 r .09 .91 .86 .89 5 b 7.39 7.72 7.27 7.65 r .90 .91 .8Q .90 6 b 7.75 8.06 7.66 8.19 r .90 .91 .88 .30 7 b 7.80 8.24 7.90 8.50 r .83 .89 .86 .87 8 b 7.42 7.92 7.76 8.24 r .33 .83 .32 .83 9 b 6.08 6.53 6.58 7.24 r .70 .71 .73 .75 10 b 4.97 5.35 5.09 5.42 5 mm. mo.a mo.Q oo.a oo.a oo.H gm. oo.H No.Q mm. m mo. mv.N QN.H mo.a mo.a mm. mm. mo.Q mm. m no. mo.N mm.a QN.Q mm. mm. No. mm. o no. ma.” oo.a oQ.H om. om. m. o om. om.m mo.Q oa.a no. om. m gm. oo.m mo.a ma.a om. v am. m.v gm.a m0. m on. Qa.m oN.Q N no. om.n a m o m o o m v m N H Quwmfiuumsmoom mQucoe om V AQV mm. mm.a No.a Qo.a mm. mm. mm. mm. Ho.H mm. 0 mm. om.N QH.H Ho.a so. me. No. oo.a mm. m mo. om.N mm.a mo.H mm. mm. mm. 00. h om. oN.m om.Q vH.Q Nm. mm. mm. o mm. om.m vF.Q mo. oo.H Hm. m No. Hm.m om.Q QN.H Hm. v mm. Ho.v mm.a mm. m we. vo.v hN.H N am. oN.m a m m m h o m g m N H ammu.m0 mQQCOE .gmm Quu Enumoosm msucoe omm. “no moose cemmmmlmmd mdoouo COmmmmlmmd usom mom mama >mo ammo Hmeucmsgmm Eowm pamflw xaez Houoe oceQMEHumm wow mucuumm cofimmmummm NN mande 55 mm. mo.a mQ.Q om. om. mm. no. no. mo. oo.a m mm. No.N 4N.a mo.Q mm. mo.a No. No. No. m mm. mm.N mo.a HH.H bO.H om. no mm. o om. om.m om.a mN.H No. no. om. o mm. No.m mo.a oQ.Q mm. mm. m Nm. mm.m .m.H oO.H an. v mm. on.m om.a go. m mm. mg.v mN.H N on. om.e H s o m a o m e m N H mastoid? masons Ru :3 :m. mm.Q Ho.a mm. mm. No.a om. mm. mm. mm. 0 mm. N0.N mo.Q om. om. No.H no. mm. mm. o no. ma.m om.a mm. mo.a on. m. mm. o om. N¢.m Nv.a ON.H mm. on. mm. o gm. em.m ow.a oQ.Q m\. mm. m Hm. o¢.m mo.a vo.a gm. w om. oo.m ho.a No.Q m Nm. nN.e Nv.Q N no. mm.v Q m m m o m m g m N a Home MO mecoe.wmm maobuaeuma. mnucoe om \A ADV dsowo COmmmmlmmw omscaucou NN HQM¢B 56 TABLE 23 Regression Factors for Estimating Total Milk Yield from Sequential Bi-Monthly Test Day Records For Four Age-Season Groups .._— ———— Age—Season Group )36 months <36 months $36 months <36 months Aug.-Mar. Aug.—Ear. April-July April-July Seq.month Monthly sets* of test 1 2 1 2 1 1 2 l 1.40 1.35 1.38 1.42 2 2.16 2.11 2.22 2.21 3 1.99 1.98 2.08 1.97 4 2.03 1.96 2.08 1.96 5 2.02 2.06 2.03 2.00 6 2.03 1.95 2.03 2.02 7 2.03 2.03 2.04 2.04 8 1.96 2.22 1.90 2.08 9 2.30 2.42 2.25 2.52 10 1.45 1.37 1.48 1.34 R .99 .99 .99 -.99 .99 .99 .99 .99 * 1 is 1—3-5-7-9 monthly set 2 is 2-4-6-8-10 monthly set umm sanucos onoum mg m umm manages mnmuN me N pom sarucoe oaueuvua me Q . 57 no. mm. mm. mm. mm. am. no. no. mm. mm. mm. mo. m oo.a Ho.Q N>.H am.a oa me.N sm.N mm.N oo.N o mo.v ov.m mo.e mm.m o sN.m No.m mm.m mo.m s ea.m oa.m 4Q.m mN.m o eo.N mo.N ms.N oo.N m oo.m . oa.m so.N oa.m v Hm.m No.m mN.m mo.m m oo.N Ns.N me.N om.N N mo.a om.a es.a oe.a a m N H m N a . m N a m N a comma mo wmumm manages runes .wmm masouawums .sasouawnea ».nmsn.ose .umsu.os¢ mQuCOE omV mauCOE omA mQQCOE mmV mQucoe “105$ Q5080 GOmmmmlmmrN museum semmmmlmmd Hoom Mom monoumm >mo ummB wanucozlawe HmwpcmSWmm Eoum mama» xQHz Hopes mowumsauwm now muouomm conmmwmmm no. mm. mm. 00. mm. mm. no. hm. hm. hm. mm. mm. m 1'; bl!" '. '1 I D|||1l mQ.m om.N om.N ma.m Qo.m Hm.N Qa.m gm.N mv.N Qa.m om.N mm.N Q m N a m N H m N a m N Q umme mo Qucoa masleewoa. wasolaewom - nastiness .nmzn.ms¢ moose mQucoe onN mQusoa omM msucos om! mnucoe omA. cemmmmlmma. 1 {ll 1“" . 15.411 A 1411 1‘11 O . ‘1 ‘il‘ .Il‘xl‘ mpwoomz woo pmwe Nabucomlene m>eumaseso Eoww pamew mafia Hmuoe useumeNumm new muouumm COHmmmHmmm mm mqmdfi JJ r3 mm. mm. mm. mm. mm. mm. mm. mm. m mm.H gm.H mm.a mm.H mm.H mm.a hm.H mm.a Q N H N a N H N H ummfi umm 3:202 mo cocoa... maool.wnm¢ . >a5olafiwne ,mesrwmom .Hmzr.ms¢ ozone mQQCOE omV mQQCOE om“. mQQQOE omV mQQCOE mmM. GOmmmmlmma. monoumm hmo umma NHQuCOEIHm m>HumaoeoU EOHM mama» xawz Qmuoe chQMEHumm now mwouumm CONmmmHmmm mN mqmdB CCE-CE’ARISOLJ CE" .‘iI‘JTElCi/S Hadden 25 21. (1959) have shown that differences between regression and ratio factors are largest during the early cumulative months of lactation and smallest in the latter stages (7—9 cumulative months» To express these "I I 1 MW ferences as a relationship between the estimated and actual performance, the standard error of estimate was used for regression for ratios or other schemes, the variance of the difference, Harvey (1956) explained that the in- creased variance of the difference between estimated and actual total production becomes (b-c)207X2 where 32 equals the variance of cumulative part production. Correlations between estimated and actual produc- tion and standard errors of the estimates are shown in Table 27 for four methods, regression, average estimates by ratios, proportionally weighted ratios, and the cumula- tive non-adjacent month ratios. Correlations and standard errors of estimates also are included when total production is estimated by the JHIA.method as eXplained earlier in this paper. Only those sets having a complete complement of test dates were used for the HHIA procedures. Ratio and Regression Hethods Non—cumulative and cumulative ratio and regression factors were compared to point out where the two varied and by how much. The regression factors have ignored herd effects; therefore, these results will not coincide with 60 --- ---- no. o.me ms. m.NN ea. n.om om. m.Ne cause --- ---- no. m.wN so. m.mm no. N.aN Na. m.om cause mm. o.HmH «a. m.Hm Ho. H.No ma. H.aN Ha. N.am cause mm. m.HN oa. H.NN ow. N.o¢ ma. N.oN em. N.oN swam on oH-N-e oH-N N-e oH-¢ om. N.oH swan Na. N.em so. N.oe ma. H.am ma. o.Nm --- ---- --- ---- --- ---- No. o.e¢ mm. o.oN om. N.eN on cause om. o.eN no. o.Nm so. m.mm Ha. o.Nm --- ---- --- ---- --- ---- as. o.Ne so. N.¢N om. H.NH Ago cause no. n.oN «a. o.aN om. m.m¢ so. m.om No. n.3n ow. n.oe 3N. N.HN ow. H.Ne em. o.oN om. N.oH Ago ensue as. a.oN oa. m.¢N ow. o.Ne «a. H.om No. N.N¢ om. m.He 3N. a.No mo. o.o¢ oa. N.¢N so. o.mH Amy “was oH-e-H oH-N-H oH-H N-H 4 H1. 3-3 N-¢-H oH-N-e-H vogumz_ sumo mo mumm hQQuaoz aouuosooum saws sauce sumo: awe ouuaaumm ou HON meHd> ngo¢ flan“ MOM—39mm .GOOBUGm QQOGOHOMMHQ NN mum<fi pomp aonuuz m50fiwm> mo msoauwa>mn mo maomwummaoo 608 ommwuo>w mmumawumo owuww m>auwaosootaoz Ago moaweum> uouwm mow ou wawpuouuw cause 0>Huwfiosoonaoz on sump mQusoa ummu unwommpw do: m>wuwassou Eoum cashew owuwu mQu we mowumm any .uamgoammmoo .uwmu wauuwm mQu we .uwmm Auv no. ¢.HN «Hun ow. ¢.Nn Nm. ¢.om em. ¢.Nn no. ¢.NN owumm om. o.m¢ mm. o.¢m «a. o.Qm mm. N.NN oaumm mo. Q.NoQ mm. m.m¢ Nm. ¢.Nm mm. ¢.5¢ mm. w.mN mm. o.¢m no. w.HN owuwm om. m.mm mm. N.om mm. m.oq ca. w.¢m no. m.nN cm. N.om no. Q.aQ wwmm m b one mum cum mnoum um. N.NN 04 main 32m ms; >04 mo.m No.m sea 3K moflumm oo.a NH.H HN.H mm.H ow.a vh.a mH.N mm.m mm.v mnouumm .ummm m m h o m w m N H pozumfi UmmB m0 mLuCOE muouomm OHumm 0cm conmmnmmm m>HuMH3ESU mo conflumdfioo a mm mumdh Hex: mméa wm.ma moéa mm.oa mm.m Norm mm.m mmK ow.» moflumm omé sod va mo.m mod mpg. 00;. vmro mofi mm.v mnouomm .nmmm oH m m n o m e m N a posses. umma mo mnucos muouumm ofiumm pom soflmmmummm m>Hu0H58501com mo comaummfioo s mm magma; -63a_ an. N¢.~ oo.HH ms.mn ss.wm N¢.HH ea. as. maoammouwom as. oo.N mo.o~ oo.mm oN.Nm om.NH mm.N on. madame .uuz mm. oN.H oN.os oH.mn mm.mm mN.NH . Nw.s mN. oauam mwmum>¢ adv mm N.mH o. o.N m.os m.am n.mm s.HH s.H N.. aoammouwmm N.HN n. s.N m.NH N.Hm 0.0m o.as N.N n. «cause .uuz a.HN N. H.H a.m n.mm a.Nm H.HH e.H N. cause m-o-m sow engages Auv mm“ H.mH m. N.H a.oH o.Nn N.wm m.o~ m.H N. scammmuwum N.NN N. N.H N.m o.mm a.wm o.ss N.H m. moaumm .euz m.sN m. N.s m.oH m.nm N.wm ¢.HH N.H N. oaumm m-m-N sum manages “no mm o.ns 0N. m. o.m~ N.am m.Nm a.m~ «N. Nmo. scammmuwmm H.NH N. s.N m.HN H.Hm N.om m.¢~ .o.N Na. moaumm .uuz N.os en. em.N NN.oH em.sm. Na.mm RN.sH sm.N em. oaumm . 0H-N-s-s “an assume: Ame mm .>ma .>ma .aum .>ma .aum .>ma .uum .>mn .eum .>mn .eam .>mn .aum .>mn .uum .>on..eum vogue: .eumm- use» «was as on N- N- as a- a- o» o H o» o N on H m on N min.1. mmfluowmuwu coausnMMumHQ stuoz HmuoH susoz_amH a ou mama wsHumma hafiusozwwua manuomnoum mo mposuuz mDOfium> you mmDHm> Hmsuo< scum macaumw>mn msam> pwumEHumm mo mmfiocmskum om mumfifi 64 were more alike than for the other two methods. For example, the mean i one standard deviation for the regression method included 72.1 percent, 75.1 percent, and 73.6 percent of the observations for the three sets whereas the ratio method included 69.7 percent, 74.2 percent, and 76.4 percent. The weighted ratios included 68.8 percent, 76.9 percent and 67.8 percent for the three monthly sets, being about as in- consistent as the ratios. The ratio method overestimates the production 46.8 percent of the time, weighted ratios 46.7 percent and regression 43.5 percent of the time. 65 DISCUSSION Eelstionship Eta-tween "JarioysPartg and Total Yield The primary interest is in tri-monthly testing. Therefore, while data are included for sequential, cumula- tive, single months, bi-monthly, and tri-monthly data, most discussion will center around the tri-monthly figures. Results are similar for the other methods and will be dis- cussed only when they differ from the tri-monthly findings. Correlations of .89 between single monthly parts and total are highest for the fifth and sixth single months of production when all records available on test day are used. The corresponding values for data restricted to only animals in milk ten test dates are .91 and .90 for the fifth and sixth months, reSpectively. In the latter case, the fourth month is as highly correlated to the total as the sixth month. All correlations of part with whole are higher for the restricted data than for data where all ani— mals are included. This would indicate that the record of an animal going dry prior to having ten full months of production tends to deviate both plus and minus from the average lactation curve more than the records of counterparts. Regression and correlation coefficients reported here for animals in milk at least ten test dates are similar to those reported previously by Madden gt a1. (1959) but the correlations 66 are somewhat higher than those reported by VanVleck and Henderson (1961d). Largest differences between these figures and VanVleck's occur early in the lactation, with values reported here somewhat larger for the early months (e.g. .75 vs. .67 for the first month). Lamb (1962) reported correlations between monthly production and total lactation yield in three different age groups. The highest correlation for any age group between the first month and total yield was . 8 for the animals in their first lactations. Table 4 shows this value for all cows (average age 47 months) to be .71. Similar differences occurred in the other nine single months. Lamb (1962) found that the highest correlations occurred in the fourth and fifth months of production but these were slightly less than values reported in this study (.36 vs. .88 for the fourth month and .86 vs. .39 for the fifth month.) Lamb (1962) in— cluded only animals completing the first ten months of pro- duction. As could be expected, the highest correlations be- tween parts occurred between adjacent months of the lactation and the lowest occurred between the parts most distant. The lowest correlation involving the first month is with the ltenth month L13). These correlations of parts are of value in determining what combination of months will provide the best information about the total. Perhaps this can best be seen in one of the tri-monthly combinations where the monthly set is 3-6-9. The standard error of estimate when all three 67 months were used was 19.1: however, the standard errors for the 3-9, 6-9, and 3-6 combinations were 25.9, 34.8, and 30.2 lb, respectively. 0f the three months used, th e sixth month is most closely correlated with the total .39, .85, and .66 for months 6, 3 and 9, respectively. However, when the sixth month is dropped from the combination, the stand- ard error is smaller than when either the third or ninth month is dr0pped. The squared multiple correlation (R2) is affected similarly and is .34 when month three is excluded, .89 when month nine is excluded and .91 with month six ex- cluded. These differences may be explained partially by production in the sixth month being more highly correlated with production in the third or ninth month than is production in the third with the test in the ninth. Correlations between various parts are generally higher for the "ten consecutive test" groups than for the group including all animals in milk on test day. This is eSpecially true for the sixth through ninth months of lacta- tion, and in particular when correlated with the earlier months in the lactation. Precision of Various vethods Used to Extend Records Ratios Ratios for cumulative test days in non—adjacent monthswhich are linear combinations of the ratios for indivi- dual test days, were used to extend various parts to a ten- month basis. Correlations between these estimates and actual 68 production were similar to but never greater than those obtained by multiple linear regression. Variance of the deviations of estimates from actual production was used as a basis of comparison. Weighting the individual estimate with the inverse of its "variance of estimate" also was used to combine ratios to extend partial records. This method used as many weighted ratios as there were months in the monthly set to be used in making the estimate. In general, the variances of the deviations were similar for these two methods, with errors of estimate of one method smaller for a given monthly set and the other more precise for another set. The single ratio was more precise for five of the eleven combinations in the 1-4-7-10 monthly set and for two of four combinations for each of the other two monthly sets. The single ratio method was more precise in all three sets when the full complement of months was in- cluded for that set: however, this superiority was small. Table 31 shows the errors of estimate of these methods to the standard deviation from regression with the single ratio being about two percent more efficient for the three sets of monthly data. Since 82.0 percent, 94.7 percent, and 93.3 percent of the animals are in milk ten, nine and eight months, reSpectively, logically more emphasis can be placed on the sets that include these months than for those sets containing lesser numbers of months. 69 Relative Efficien y of Various fiethods in Estimating Ten Month Production From Three Tri—Ionthly Sets of Data Method Monthly sets 1(a) 2(b) 3(c) Regression 100 100 100 Ratio 80.6 (d) 80.2 76.5 Inv. of Var. 77.3 79.2 74.0 DHIA 77.3 74.5 79.5 (a) set 1 is 1—4-7-10 months (b) set 2 is 2-5-8 months (c) set 3 is 3-6—9 months (d) This is eXpressed as percent efficiency (E) compared to the regression estimate where E = 100 (residual variance of regression/residual variance of ratio). 70 Then the single ratio should be used in preference to the weighted ratios for extending the part records. How— ever, to be able to project the ten-month total early in the laction is always important when either set in the prefer— ence is for the set that is easiest to obtain in a particular situation. The equally weighted ratios provided the least pre- cise estimates of any ratio method employed. There were only a few isolated instances where equally weighted ratios provided estimates as precise as either of the other two ratio schemes. Regr~ss10n When multiple linear regression is used, the stand- ard errors of estimates are lower than those of any other method. The precision of the estimates for any one monthly set is related to the am unt of data available for that set, but some combinations involving the same number of variables are more precise than others in estimating the total produc- tion. The 1-4-10 monthly combination is the most precise of the three-variable sets in the 1-4-7-10 category. The 2-8 combination is most efficient of the two-variable sets from months 2-5—8 and the 3-9 set is the most precise of the three two-variable combinations in the 3-6-9 set. It was postulated that regression factors and corre- lations derived from data where only records at least ten consecutive months in length were used would provide results 7l inapprOpriate for the entire population. However, this was not the case when the regression factors derived from the ten-month data were applied to all cows in milk on test day. The residual variances were almost identical for both pOpula- tions. This can be explained partially by the fact that 80 percent of those cows going dry prior to ten test dates went dry after the ninth test but prior to the tenth test date. Major discrepancies could occur only when the tenth test date alone was used to project a record since this was the month most cows were included in one group but not the other. But the lactation curve for the group going dry after the ninth test date was more like the curve for all cows in milk on last test date than for any of the other dry cow groups. For this reason, these records could not change the standard error of estimate very much. Differences of the other groups of dry cows could change the standard error, but their number was so few that it was not an effective force in changing the results. The possibility of develOping a separate set of regression factors to be used for extending the records of dry cows is not excluded. The standard error of estimate for dry cows only would certainly be quite high if one applied the factors developed for either the ten test day data or the group involv- ing all cows. The use of separate regression factors is not very practical since just when a cow will go dry is not known at any given stage of the lactation. However to re—estimate the total lactation yield for dry cows after they go dry would be more accurate if any form of testing other than \ [\7 monthly testing is being used. Table 32 contains the efficiencies of the ten test date factors applied to all data. Relative efficiency is defined as the ratio of the error variance in the actual data to the error variance obtained when the 10 month data figures were applied to all data multiplied by 100. :ewression-Ratio combinations The ratio method is advantageous in that it does not include a be 0 effect. Regression factors can be Cevelonea which account for herd differences (VanVleCk and Henderson, l9éld), but this method is rather cumbersome. The ratios provide a simpler relationship of the part to the whole, but these ratios when applied to all data lead to over and under- estimates as noted by Harvey (1956). Thus, ratios are some— what easier to use, butthe regression factors provide esti- mates closer to the actual production values. This led to the development or a set of regression factors that could be applied to the ratio estimates to provide an estimate of final production. This would allow ratios to be used for estimation in practical situations: but when more precise figures are required, the estimates could then be weigh ed and combined. These regression factors also give some in- sight to the precision of existing ratios. Table 33 snows tne regression coefficients required to adjust the ratio estimate. For situations where the estimate by ratio was already highly correlated ( .97) with the actual value, the addition of the 73 regression factor did little to reduce the error of the esti- mate. Such was the case for the 1-4—7—10 estimate by ratio. The estimate by ratio was correlated with the actual value .98 and had a standard error of estimate of 16.7. When the additional step was added, the correlation remained the same (D and the standard error also remained nearly the same. Th regression coefficient in this case was almost unity, .993. The facts differed when the estimate by ratio was from one month such as the first. Here the correlation between the estimate by ratio and actual value was .71 and the standard error of the estimate was 71.2; when the regression factor was used to extend this record, the correlation was still .71 but the standard error of estimate was reduced to 62.9. The regression coefficient used in this case was .65. Distribution o§_Errors all methods tend to overestimate the ten month pro- duction and the average estimate by regression method is nearer the actual average for the ratio combinations. The more information available the more precise is the estimate for both. On a 305 day basis the ratios overestimated 35 per- fl‘ [—»\ cent of the records b; 613 lb of milk and underestimated so percent by the same amount. The proportionately weighted ratios estimated 71 percent of the observations within 619 lb of the actual production, and regression method estimated 73 percent of the observations within 543 lb of the actual produc— tion when the tri-monthly system of testing was employed, with 74 ‘TKELE 32 Relative Efficiencies of Regression Factors Derived From Ten fionth Data when Aoplied to all Cows in milk on Test Data ...—.- .--- - - 1 Single Standard Error Standard Error Relative Eonths of Applied of Actual Efficiency* Estimates Estimates (lb milk) (lb milk) 9 63.6 63.5 99.8 8 51.6 51.4 99.4 7 42.8 42.7 99.8 6 39.2 39.2 100.0 5 39.3 39.3 100.0 4 41.9 41.8 99.7 3 46.5 46.5 100.0 2 51.6 51.5 99.3 1 62.9 62.9 100.0 Sequential Months 2-5-8 19.2 19.2 100 * Rel. Eff. = Resid. var. actual x 100 Resid. var. applied u ..... 75 TABLE 33 A Comparison of Efficiencies When Regression Factors Are Used to Extend Ratio Estimates to a Ten month Basis Monthly Set Method Regr.Coeff£a) R(b) Eiigr(c)§ff. 1—4-7-10 Ratio (Cumulative) .99 .99 16.7 100 1-4-7-10 Equally Weighted .94 .95 24.7 100 Ratios 1-4-7-10 Weighted Ratios .96 .97 17.1 100 (PrOportionally) 2—5-8 Ratio .95 .97 20.4 113 3-6-9 Ratio .92 .97 20.0 119 1 Ratio .65 .70 62.9 123 2 Ratio .74 .81 51.5 122 3 Ratio .77 .85 46.5 152 4 Ratio .80 .88 42.0 123 5 Ratio .80 .89 34.5 166 6 Ratio .79 .89 39.2 133 7 Ratio .73 .87 42.7 144 8 Ratio .59 .80 51.5 185 9 Ratio .42 .66 63. 259 10 Ratio .28 .53 71.5 340 % Eff. = Resid. var. ratio est.X 100 Resid. var. ratio regr. Est. a) Regr. Coeff. is the factor used to project the ratio estimate to a more accurate ten month basis. b) R is the correlation coefficient between the new estimates and the actual values. c) Std. Error is the residual variance of the new estimate. 76 a comolete complement of months. This amounted to only 67 lb milk difference between the wo extreme methods for about the same percent of the animals. The ratios could be enoloyed to estimate total pro— duction from oart records with almost the same accuracy and be almost as precise as regression. All methods estimate more records within one and two standard deviations of the actual amounts than would be exoected from normal distribu- tion theory. pnplication of “Ten Test Date” Regression Eactors to All Data The standard errors of estimate from regression factors where all cows are in milk at least ten consecutive test dates are smaller than corresnonding values for the situation where all cows in milk on test data are inclue d. while the former factors do not aooly to the entire nooula— tion quite as well as do those develooed when all cows are included, they no orovide more precise estimates than other methods. This would indicate that at the early stages of lactation, when which animals will go dry orior to 305 days or at what time are not yet known, the overall factors are best used to estimate nroduction for ten months. however, at com- oletion of the individual cow's lactation, an aporOpriate set of regression or ratio factors could be abolied, the exact factors deoending on the length of the record. The appro— oriateness of a method depends on the information desired. If an estimate is required early in the lactation, then the 77 overall factorshould be used to provide the smallest number of errors. If it is possible to wait until the record is com- plete, it may be more desirable to re-compute the ten month total from the appropriate set of regression factors. Since a large number of animals complete ten test dates, it would appear more feasible to begin by using the factors developed exclusively from those animals. Thus, 60 percent of the observations would already be predicted with the apprOpriate factors. The separate regression factors for various lengths of lactations have not been included in this study: however, ratios are available for this purpose (Aulerich, 1965). m--‘--. - N. ‘ {'.1-- «n— .1 ~'-.- ~ . --- rn-‘w if“ L'le.‘:..L.LUL. Cl; $s1—‘JOJULJ‘LiJ Several methods of extending part records of various lengths have been presented. The regression factors are more precise in estimating the total lactation yield from part records on a cumulative, non-cumulative, or sequential basis than any of the ratio methods. The ratio methods, of which two were discussed in detail, are equally precise in most cases but both less precise than the regression factors. The more information available the more precise are the factors in estimating total yield from part records. The ratios, while not quite as precise as regression factors, are easier to com- pute and may be somewhat easier to use for practical situations than are the regression factors. There are several purposes for using these factors in a production testing program. One is the application to a 78 shorter interval testing program such as a bi-monthly or tri- monthly program. another is to estimate production of ani- mals at an early date in order to provide early information about sires for a sire proving program and particularly for a young sire program. The phenotypic correlations between parts and the whole indicate that partial records can be ex- tended with considerable accuracy: however, Lamb (1962) report— ed that genetic progress per year will not be as rapid as if the complete records were used. This reduced accuracy may be offset if the generation interval is decreased sufficiently. The cost of testing has been postulated to be a con- tributing factor to the relatively low percentage of herds enrolled in a production testing program. A less costly pro- gram, such as bi-monthly or tri-monthly testing could raise this percentage. To date, much information has been reported concerning the practical use of a bi-monthly program: however, most work has centered around the accuracy of the results only after the five tests have been reported. The use of either regression or ratio factors to extend a record to a ten-month basis each time the animal is tested may provide sufficient information to the participating herd owner to keep him in- terested in a testing program. Each time any additional data are available on the animal, a new, more accurate estimate can be computed. This not only will provide information which the herd owners can use each month in ranking their herds, but a1- so these data will be available at all times for use in sum- marizing sires. 79 most work available on bi-monthly tests assumes a full complement of monthly tests, but a substantial percent— age of all cows terminate their records prior to having com- pleted ten full months. For these situations and those where the animal is not tested for a particular month for some un- known reason, additional factors must be used. The results H) 0 this study provide regression factors for all combinations of data available from each of three monthly sets of a.tri- monthly testing program. These factors and the resulting estimates must be included in the evaluation of a particular type of testing program if it is to be used in a practical manner. Finally, ratios because of their simplicity may be more desirable for practical use. However, in order to pro- vide a more precise estimate for sire summaries, to extend these estimates to a final ”ratio—regression" estimate may be desirable. SUMMARY Data from 58,840 completed records of Kichigan Holstein cows calving between January, 1959 and January, 1961 were used to evaluate several methods of estimating total lactation milk yield from various parts and to compare esti- mates obtained from several testing intervals with actual DHIA data. Simple correlations were calculated between each of the various parts and between each part and total milk yield from only those records consisting of 10 consecutive test date data and from all records containing test date data through the last test date involved. Simple correlations were calculated between each of the various parts and between each part and total milk yield for each of 4 age-season groups. Three ratio methods and linear regression were used to estimate total milk yield from the different parts. The non-cumulative ratio was used to estimate total yield from each part, and these estimates were weighted equally or weighted according to the variance of each individual esti- mate to form pooled estimates. The third ratio method in- volved the formation of a single cumulative ratio from data in the non-cumulative months. Total DHIA yield was obtained after summing data for each cow over all test dates. 80 Bl Total milk yield was estimated from each set of data obtained by two different bi-monthly testing plans and three different tri—monthly testing plans, as well as from all pos- sible partial sets of data for each plan. Total milk yield was also calculated by the linear regression of sequential, cumulative, and non-cumulative yield on time. Regression factors for each case were obtained for each of 4 age-season groups. Regression ’actors to estimate total milk yield were computed from only those records consisting of 10 consecutive test date data and from all records containing test date data through the last concerned test date. Simple linear regression factors were obtained to estimate total milk yield from the ratio estimates for each set of bi-monthly and tri—monthly data. Correlations between single monthly parts and total milk yield were highest for the middle months (5 and 6) and lower for either extreme from these months, with the tenth month being the lowest correlated single month with total yield (0.53). Correlations were higher between each single monthly part and total milk yield for data including only ten consecutive test dates than for data including all cows in milk on test date. The greatest differences occurred at the early months of lactation and converged as the monthly number increased. Simple correlations between various parts were highest for adjacent months, again, the data restricted to ten 32 consecutive test dates were higher correlated than the un— restricted data. Bstimates obtained by the equally weighted ratios were less precise than estimates from either of the other ratio methods. The latter estimates were equally precise, but were less precise than estimates obtained by linear regression. Estimates obtained from the more precise ratio method were within 509,653, and 655 lb milk of actual values for tri-monthly sets consisting of months 1—4-7-10, 2—5-8, and 3—6-9, respectively. Bi—monthly estimates from the same ratio methods were within 144 and 135 lb. milk of actual values for bi-monthly sets consisting of months l-3-5-7-9 and 2-4-6-8-10, respectively. Means of total production were highest for animals initiating lactations at 36 or more months of age and from August—March and were lowest for animals calving during April-July at ages less than 35 months. The younger cows reached peak production at lower levels and did not diminish production as rapidly as the older animals. Larger regres— sion factors were required to estimate total milk yield for younger cows from cumulative production in the early months of lactation and become about equal during the middle and latter months of lactation. Regression factors to estimate total milk yield from various parts are more precise when obtained from data includ- ing only those animals in milk ten consecutive test dates. 83 However, all cows will not be in milk the full ten months of lactation thus, it may be desirable to recompute the total milk yield using the appropriate regression factors after the cow has gone dry. Application of simple linear regression to the ratio estimates provides a more precise estimate of total milk yield than does the ratio estimate alone. The efficien- cy of doing this in terms of the residual variance decreases as additional monthly data become available. Efficiency values range from 3407 when month one alone is used to pre- dict total milk yield to 100% for tri-monthly sets of data consisting of months 1-4-7-10. Comparable results for monthly sets 2-5-8 and 3-6-9 are 113% and 119%, respectively. LITH.§.1TJ.LKH CITED Alexander, M.H. and Yapp, H.fi. (1949). Comparison of Methods of Estimating Milk and bat Production in Dairy Cows. J. Dairy Sci., 32:621. Aulerich, C. (1965). Differences in Extending Tenminal and Non-Terminal Incomplete Lactations to 305 Days. Un- published M.S. Thesis, Michigan State University Library, East Lansing. ‘ayley, N.D., Liss, R.M. and Stallard, J.E. 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