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Using quantile regression for fitting lactation curve in dairy cows

  • Hossein Naeemipour Younesi (a1) (a2), Mohammad Mahdi Shariati (a1), Saeed Zerehdaran (a1), Mehdi Jabbari Nooghabi (a3) and Peter Løvendahl (a4)...

Abstract

The main objective of this study was to compare the performance of different ‘nonlinear quantile regression’ models evaluated at the τth quantile (0·25, 0·50, and 0·75) of milk production traits and somatic cell score (SCS) in Iranian Holstein dairy cows. Data were collected by the Animal Breeding Center of Iran from 1991 to 2011, comprising 101 051 monthly milk production traits and SCS records of 13 977 cows in 183 herds. Incomplete gamma (Wood), exponential (Wilmink), Dijkstra and polynomial (Ali & Schaeffer) functions were implemented in the quantile regression. Residual mean square, Akaike information criterion and log-likelihood from different models and quantiles indicated that in the same quantile, the best models were Wilmink for milk yield, Dijkstra for fat percentage and Ali & Schaeffer for protein percentage. Over all models the best model fit occurred at quantile 0·50 for milk yield, fat and protein percentage, whereas, for SCS the 0·25th quantile was best. The best model to describe SCS was Dijkstra at quantiles 0·25 and 0·50, and Ali & Schaeffer at quantile 0·75. Wood function had the worst performance amongst all traits. Quantile regression is specifically appropriate for SCS which has a mixed multimodal distribution.

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Corresponding author

Author for correspondence: Mohammad Mahdi Shariati, Email: mm.shariati@um.ac.ir

References

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Adediran, S, Ratkowsky, D, Donaghy, D and Malau-Aduli, A (2012) Comparative evaluation of a new lactation curve model for pasture-based Holstein-Friesian dairy cows. Journal of Dairy Science 95, 53445356.10.3168/jds.2011-4663
Akaike, H (1974) A new look at the statistical model identification. IEEE transactions on Automatic Control 19, 716723.10.1109/TAC.1974.1100705
Ali, T and Schaeffer, L (1987) Accounting for covariances among test day milk yields in dairy cows. Canadian Journal of Animal Science 67, 637644.10.4141/cjas87-067
Ali, A and Shook, G (1980) An optimum transformation for somatic cell concentration in Milk1. Journal of Dairy Science 63, 487490.10.3168/jds.S0022-0302(80)82959-6
Beyerlein, A (2014) Quantile regression—opportunities and challenges from a user's perspective. American Journal of Epidemiology 180, 330331.10.1093/aje/kwu178
Boujenane, I (2013) Comparison of different lactation curve models to describe lactation curve in Moroccan Holstein-Friesian dairy cows. Iranian Journal of Applied Animal Science 3, 817822.
Briollais, L and Durrieu, G (2014) Application of quantile regression to recent genetic and-omic studies. Human Genetics 133, 951966.10.1007/s00439-014-1440-6
Buchinsky, M (1995) Estimating the asymptotic covariance matrix for quantile regression models a Monte Carlo study. Journal of Econometrics 68, 303338.10.1016/0304-4076(94)01652-G
Chernozhukov, V and Hansen, C (2006) Instrumental quantile regression inference for structural and treatment effect models. Journal of Econometrics 132, 491525.
Cobby, J and Le Du, Y (1978) On fitting curves to lactation data. Animal Science 26, 127133.
Dematawewa, C, Pearson, R and VanRaden, P (2007) Modeling extended lactations of Holsteins. Journal of Dairy Science 90, 39243936.10.3168/jds.2006-790
Dijkstra, J, France, J, Dhanoa, M, Maas, J, Hanigan, M, Rook, A and Beever, D (1997) A model to describe growth patterns of the mammary gland during pregnancy and lactation. Journal of Dairy Science 80, 23402354.
Elahi Torshizi, M, Aslamenejad, A, Nassiri, M and Farhangfar, H (2011) Comparison and evaluation of mathematical lactation curve functions of Iranian primiparous Holsteins. South African Journal of Animal Science 41, 104115.10.4314/sajas.v41i2.71013
Ferreira, AG, Henrique, DS, Vieira, RA, Maeda, EM and Valotto, AA (2015) Fitting mathematical models to lactation curves from Holstein cows in the southwestern region of the state of Parana, Brazil. Anais da Academia Brasileira de Ciências 87, 503517.10.1590/0001-3765201520130514
Friggens, NC and Løvendahl, P (2008) The potential of on-farm fertility profiles: In-line progesterone and activity measurements. In Fertility in dairy cows: bridging the gaps. In Royal, M.D., Friggens, N.C. and Smith, R.F. (eds), British Society of Animal Science. UK, Cambridge: Cambridge University Press, pp. 7278.
Friggens, N, Ridder, C and Løvendahl, P (2007) On the use of milk composition measures to predict the energy balance of dairy cows. Journal of Dairy Science 90, 54535467.
Gilmour, A, Gogel, B, Cullis, B, Welham, S & Thompson, R (2015) ASReml User Guide Release 4·1 Structural Specification. Hemel Hempstead: VSN International Ltd.
Heringstad, B, Klemetsdal, G and Ruane, J (2000) Selection for mastitis resistance in dairy cattle: a review with focus on the situation in the Nordic countries. Livestock Production Science 64, 95106.10.1016/S0301-6226(99)00128-1
Huang, B and Lin, DY (2007) Efficient association mapping of quantitative trait loci with selective genotyping. The American Journal of Human Genetics 80, 567576.
Koenker, R (2017) quantreg: Quantile Regression. R package version 5.33. Available at: http://CRAN.R-project.org/package=quantreg
Koenker, R and Bassett, G (1978) Regression quantiles. Econometrica: Journal of the Econometric Society 46, 3350.10.2307/1913643
Leclerc, H, Duclos, D, Barbat, A, Druet, T and Ducrocq, V (2008) Environmental effects on lactation curves included in a test-day model genetic evaluation. Animal: An International Journal of Animal Bioscience 2, 344353.
Løvendahl, P and Chagunda, M (2011) Covariance among milking frequency, milk yield, and milk composition from automatically milked cows. Journal of Dairy Science 94, 53815392.10.3168/jds.2010-3589
Macciotta, NPP, Vicario, D and Cappio-Borlino, A (2005) Detection of different shapes of lactation curve for milk yield in dairy cattle by empirical mathematical models. Journal of Dairy Science 88, 11781191.
Madsen, P & Jensen, J (2008) A user's guide to DMU: a package for analysing multivariate mixed models, version 6, release 4. Danish Institute of Agricultural Sciences, Tjele, Denmark.
Madsen, P, Shariati, MM and Ødegård, J (2008) Genetic analysis of somatic cell score in Danish Holsteins using a liability-normal mixture model. Journal of Dairy Science 91, 43554364.
Nash, D, Rogers, G, Cooper, J, Hargrove, G, Keown, JF and Hansen, L (2000) Heritability of clinical mastitis incidence and relationships with sire transmitting abilities for somatic cell score, udder type traits, productive life, and protein yield. Journal of Dairy Science 83, 23502360.10.3168/jds.S0022-0302(00)75123-X
Ødegård, J, Heringstad, B and Klemetsdal, G (2004) Bivariate genetic analysis of clinical mastitis and somatic cell count in Norwegian dairy cattle. Journal of Dairy Science 87, 35153517.
Olori, V, Brotherstone, S, Hill, W and McGuirk, B (1999) Fit of standard models of the lactation curve to weekly records of milk production of cows in a single herd. Livestock Production Science 58, 5563.
Pakdel, A, Heydaritabar, M and Nejati Javaremi, A (2010) The feasibility of nonlinear models to describe the milk somatic cell score of Iranian holstein cows throughout different lactation periods. Iranian Journal of Animal Science 41, 185192 (in Persian).
Papajcsik, I and Bodero, J (1988) Modelling lactation curves of Friesian cows in a subtropical climate. Animal Science 47, 201207.
Quinn, N, Killen, L and Buckley, F (2005) Empirical algebraic modelling of lactation curves using Irish data. Irish Journal of Agricultural and Food Research 44, 113.
Rodriguez-Zas, SL, Gianola, D and Shook, GE (2000) Evaluation of models for somatic cell score lactation patterns in Holsteins. Livestock Production Science 67, 1930.
Rupp, R and Boichard, D (1999) Genetic parameters for clinical mastitis, somatic cell score, production, udder type traits, and milking ease in first lactation Holsteins. Journal of Dairy Science 82, 21982204.
Scott, T, Yandell, B, Zepeda, L, Shaver, R and Smith, T (1996) Use of lactation curves for analysis of milk production data. Journal of Dairy Science 79, 18851894.
Sundrum, A (2015) Metabolic disorders in the transition period indicate that the dairy cows’ ability to adapt is overstressed. Animals 5, 9781020.10.3390/ani5040395
Wei, Y, Pere, A, Koenker, R and He, X (2006) Quantile regression methods for reference growth charts. Statistics in Medicine 25, 13691382.
Wilmink, J (1987) Adjustment of test-day milk, fat and protein yield for age, season and stage of lactation. Livestock Production Science 16, 335348.
Wood, P (1967) Algebraic model of the lactation curve in cattle. Nature 216, 164165.
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Journal of Dairy Research
  • ISSN: 0022-0299
  • EISSN: 1469-7629
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