Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-27T22:13:08.688Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis of water intake, dry matter intake and daily milk yield using different error covariance structures

Published online by Cambridge University Press:  01 November 2008

E. Kramer ,
E. Stamer ,
J. Spilke  and
J. Krieter
E. Kramer*
Affiliation:
Institute of Animal Breeding and Husbandry, Christian-Albrechts-University, D-24118 Kiel, Germany
E. Stamer
Affiliation:
TiDa Tier und Daten GmbH, D-24259 Westensee/Brux, Germany
J. Spilke
Affiliation:
Biometrics and Informatics in Agriculture Group, Martin-Luther-University, D-06108 Halle/Saale, Germany
J. Krieter
Affiliation:
Institute of Animal Breeding and Husbandry, Christian-Albrechts-University, D-24118 Kiel, Germany
*
E-mail: [email protected]
Get access

Abstract

The aim of the present study was to investigate the daily measured traits milk yield, water intake and dry matter intake with fixed and random regression models added with different error covariance structures. It was analysed whether these models deliver better model fitting in contrast to conventional fixed and random regression models. Furthermore, possible autocorrelation between repeated measures was investigated. The effect of model choice on statistical inference was also tested. Data recording was performed on the Futterkamp dairy research farm of the Chamber of Agriculture of Schleswig-Holstein. A dataset of about 21 000 observations from 178 Holstein cows was used. Average milk yield, water intake and dry matter intake were 34.9, 82.4 and 19.8 kg, respectively. Statistical analysis was performed using different linear mixed models. Lactation number, test day and the parameters to model the function of lactation day were included as fixed effects. Different structures were tested for the residuals; they were compared for their ability to fit the model using the likelihood ratio test, and Akaike’s and Bayesian’s information criteria. Different autocorrelation patterns were found. Adjacent repeated measures of daily milk yield were highest correlated (p1 = 0.32) in contrast to measures further apart, while for water intake and dry matter intake, the measurements with a lag of two units had the highest correlations with p2 = 0.11 and 0.12. The covariance structure of TOEPLITZ was most suitable to indicate the dependencies of the repeated measures for all traits. Generally, the most complex model, random regression with the additional covariance structure TOEPLITZ(4), provided the lowest information criteria. Furthermore, the model choice influenced the significance values of one fixed effect and therefore the general inference of the data analysis. Thus, the random regression + TOEPLITZ(4) model is recommended for use for the analysis of equally spaced datasets of milk yield, water intake and dry matter intake.

Keywords

dairy cowerror covariance structuremodel fit
Type
Full Paper
Information
animal , Volume 2 , Issue 11 , November 2008 , pp. 1585 - 1594
Copyright
Copyright © The Animal Consortium 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akaike H 1973. Information theory and an extension of the maximum likelihood principle. Proceedings of the Second International Symposium on Information Theory (ed. BN Petrov and F Csaki), pp. 267–281. Akademiai Kiado, Budapest, Hungary.Google Scholar
Ali, TE, Schaeffer, LR 1987. Accounting for covariances among test day milk yields in dairy cows. Canadian Journal of Animal Science 67, 637–644.CrossRefGoogle Scholar
Bonham, CD, Reich, RM 1999. Influence of spatial autocorrelation on a fixed-effect model used to evaluate treatment of oil spills. Journal of Applied Mathematics and Computation 106, 149–162.CrossRefGoogle Scholar
Coffey, MP, Simm, G, Brotherstone, S 2002. Energy balance profiles for the first three lactations of dairy cows estimated using random regression. Journal of Dairy Science 85, 2669–2678.CrossRefGoogle ScholarPubMed
Collard, BL, Boettcher, PJ, Dekkers, JCM, Petitclerc, D, Schaeffer, LR 2000. Relationships between energy balance and health traits of dairy cattle in early lactation. Journal of Dairy Science 83, 2683–2690.CrossRefGoogle ScholarPubMed
DeLaval 2008. Somatic cell counter DCC. Retrieved March 08, 2008, from http://www.delaval.com/Products/Milking/Cell-counter-DCC/default.htmGoogle Scholar
de Vries, MJ, van der Beek, S, Kaal-Lansbergen, LMTE, Ouweltjes, W, Wilmink, JBM 1999. Modeling of energy balance in early lactation and the effect of energy deficits in early lactation on first detected estrus postpartum in dairy cows. Journal of Dairy Science 82, 1927–1934.CrossRefGoogle ScholarPubMed
Grossman, M, Koops, WJ 1988. Multiphasic analysis of lactation curves in dairy cattle. Journal of Dairy Science 71, 1598–1608.CrossRefGoogle Scholar
Hüttmann H 2007. Analyse der Futteraufnahme und der Energiebilanzmerkmale bei hochleistenden, erstlaktierenden Milchkühen. Schriftenreihe des Instituts für Tierzucht und Tierhaltung der Christian-Albrechts-Universität zu Kiel. Band 164.Google Scholar
Jamrozik, J, Schaeffer, LR 1997. Estimates of genetic parameters for a test day model with random regressions for yield traits of first-lactation Holsteins. Journal of Dairy Science 80, 762–770.CrossRefGoogle ScholarPubMed
Jennrich, RI, Schluchter, MD 1986. Unbalanced repeated-measures models with structured covariance matrices. Biometrics 42, 805–820.CrossRefGoogle ScholarPubMed
Kirkpatrick, M, Hill, WG, Thompson, R 1994. Estimating the covariance structure of traits during growth and ageing, illustrated with lactation in dairy cattle. Genetics Research 64, 57–69.CrossRefGoogle ScholarPubMed
Koenen, EPC, Veerkamp, RF 1998. Genetic covariance functions for live weight, condition score, and dry-matter intake measured at different lactation stages of Holstein Friesian heifers. Livestock Production Science 57, 67–77.CrossRefGoogle Scholar
König, S, Köhn, F, Kuwan, K, Simianer, H, Gauly, M 2006. Use of repeated measures analysis for evaluation of genetic background of dairy cattle behavior in automatic milking systems. Journal of Dairy Science 89, 3636–3644.CrossRefGoogle ScholarPubMed
Kramer, E, Stamer, E, Mahlkow, K, Lüpping, W, Krieter, J 2008. Relationship between water intake, dry matter intake and daily milk yield on a German research farm. Livestock Science 115, 99–104.CrossRefGoogle Scholar
Littell, RC, Henry, PR, Ammerman, CB 1998. Statistical analysis of repeated measures data using SAS procedures. Journal of Animal Science 76, 1216–1231.CrossRefGoogle Scholar
Littell, RC, Milliken, GA, Stroup, WW, Wolfinger, RD, Schabenberger, O 2006. SAS for mixed models, user mannual . SAS Inc., Cary, NC, USA, pp. 174–203.Google Scholar
Liu, YX, Zhang, J, Schaeffer, LR, Yang, RQ, Zhang, WL 2006. Optimal random regression models for milk production in dairy cattle. Journal of Dairy Science 89, 2233–2235.CrossRefGoogle ScholarPubMed
López-Romero, P, Carabaño, MJ 2003. Comparing alternative random regression models to analyse first lactation daily milk yield data in Holstein-Friesian cattle. Livestock Production Science 82, 81–96.CrossRefGoogle Scholar
Mielenz, N, Spilke, J, Krejcova, H, Schüler, L 2006. Statistical analysis of test-day milk yields using random regression models for the comparison of feeding groups during the lactation period. Archives of Animal Nutrition 60, 341–357.CrossRefGoogle Scholar
Murphy, MR, Davis, CL, McCoy, GC 1983. Factors affecting water consumption by Holstein cows in early lactation. Journal of Dairy Science 66, 35–38.CrossRefGoogle ScholarPubMed
Ordolff, D 2005. On-farm analysis of milk: a promising challenge. In Precision livestock farming ‘05 (ed. S Cox), pp. 157–161. Wageningen Academic Publishers, The Netherlands.Google Scholar
Pitt, MA, Myung, IJ, Zhang, S 2002. Toward a method of selecting among computational models of cognition. Psychological Review 109, 472–491.CrossRefGoogle Scholar
Rosário, MF, Silva, MAN, Coelho, AAD, Savino, VJM 2007. Estimating and predicting feed conversion in broiler chickens by modeling covariance structure. International Journal of Poultry Science 6, 508–514.CrossRefGoogle Scholar
SAS Institute Inc. 2005. SAS/STAT user’s guide version 9.0 . SAS Inc., Cary, NC, USA.Google Scholar
Sawalha, RM, Keown, JF, Kachman, SD, van Vleck, LD 2005a. Evaluation of autoregressive covariance structures for test-day records of Holstein cows: estimates of parameters. Journal of Dairy Science 88, 2632–2642.CrossRefGoogle ScholarPubMed
Sawalha, RM, Keown, JF, Kachman, SD, van Vleck, LD 2005b. Genetic evaluation of dairy cattle with test-day models with autoregressive covariance structures and with a 305-d Model. Journal of Dairy Science 88, 3346–3353.CrossRefGoogle ScholarPubMed
Schaeffer, LR 2004. Application of random regression models in animal breeding. Livestock Production Science 86, 35–45.CrossRefGoogle Scholar
Schaeffer LR and Dekkers JCM 1994. Random regressions in animal models for test-day production in dairy cattle. Proceedings of the 5th World Congress of Genetics Applied to Livestock Production, vol. 18, pp. 443–446. Guelph, Canada.Google Scholar
Schwarz, G 1978. Estimating the dimension of a model. Annals of Statistics 6, 461–464.CrossRefGoogle Scholar
Stamer E 1995. Futteraufnahmeverhalten von Milchkühen – Analyse der Zeitstruktur und Nutzungsmöglichkeiten. Schriftenreihe des Institutes für Tierzucht und Tierhaltung der Christian-Albrechts-Universität zu Kiel, Band 85.Google Scholar
Svennersten-Sjaunja, K, Sjögren, M, Andersson, I, Sjaunja, LO 2005. Milk analyses: a comparison between a simple IR-instrument for use on farm level and available IR-methods. In Precision livestock farming ‘05 (ed. S Cox), pp. 141–147. Wageningen Academic Publisher, The Netherlands.Google Scholar
Sylvestre, AM, Petim-Batista, F, Colaco, J 2006. The accuracy of seven mathematical functions in modeling dairy cattle lactation curves based on test-day records from varying sample schemes. Journal of Dairy Science 89, 1813–1821.CrossRefGoogle Scholar
van der Werf J 2001. Random regression in animal breeding. Course notes. Jaboticabal, SP Brazil, November 2001.Google Scholar
Veerkamp, RF, Thompson, R 1999. A covariance function for feed intake, live weight, and milk yield estimated using a random regression model. Journal of Dairy Science 82, 1565–1573.CrossRefGoogle ScholarPubMed
Wilmink, JBM 1987. Adjustment of test-day milk, fat and protein yield for age, season and stage of lactation. Livestock Production Science 16, 335–348.CrossRefGoogle Scholar
Wood, PDP 1967. Algebraic model of the lactation curve in cattle. Nature 216, 164–165.CrossRefGoogle Scholar
Woodford, ST, Murphy, MR, Davis, CL 1984. Water dynamics of dairy cattle as affected by initiation of lactation and feed intake. Journal of Dairy Science 67, 2336–2343.CrossRefGoogle ScholarPubMed