Skip to main content Accessibility help
×
Home
Hostname: page-component-66d7dfc8f5-czmr8 Total loading time: 0.665 Render date: 2023-02-08T17:55:04.476Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

Using quantile regression for fitting lactation curve in dairy cows

Published online by Cambridge University Press:  07 February 2019

Hossein Naeemipour Younesi
Affiliation:
Department of Animal Science, Ferdowsi University of Mashhad, 91779 Mashhad, Iran Department of Animal Science, University of Birjand, 97191 Birjand, Iran
Mohammad Mahdi Shariati*
Affiliation:
Department of Animal Science, Ferdowsi University of Mashhad, 91779 Mashhad, Iran
Saeed Zerehdaran
Affiliation:
Department of Animal Science, Ferdowsi University of Mashhad, 91779 Mashhad, Iran
Mehdi Jabbari Nooghabi
Affiliation:
Department of Statistics, Ferdowsi University of Mashhad, 91779 Mashhad, Iran
Peter Løvendahl
Affiliation:
Department of Molecular Biology and Genetics, Center for Quantitative Genetics and Genomics, Aarhus University, Blichers Alle 20, 8830 Tjele, Denmark
*
Author for correspondence: Mohammad Mahdi Shariati, Email: mm.shariati@um.ac.ir

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.

Type
Research Article
Copyright
Copyright © Hannah Dairy Research Foundation 2019 

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

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.2011-4663CrossRefGoogle ScholarPubMed
Akaike, H (1974) A new look at the statistical model identification. IEEE transactions on Automatic Control 19, 716723.10.1109/TAC.1974.1100705CrossRefGoogle Scholar
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/cjas87-067CrossRefGoogle Scholar
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)82959-6CrossRefGoogle Scholar
Beyerlein, A (2014) Quantile regression—opportunities and challenges from a user's perspective. American Journal of Epidemiology 180, 330331.10.1093/aje/kwu178CrossRefGoogle ScholarPubMed
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.Google Scholar
Briollais, L and Durrieu, G (2014) Application of quantile regression to recent genetic and-omic studies. Human Genetics 133, 951966.10.1007/s00439-014-1440-6CrossRefGoogle ScholarPubMed
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-GCrossRefGoogle Scholar
Chernozhukov, V and Hansen, C (2006) Instrumental quantile regression inference for structural and treatment effect models. Journal of Econometrics 132, 491525.CrossRefGoogle Scholar
Cobby, J and Le Du, Y (1978) On fitting curves to lactation data. Animal Science 26, 127133.Google Scholar
Dematawewa, C, Pearson, R and VanRaden, P (2007) Modeling extended lactations of Holsteins. Journal of Dairy Science 90, 39243936.10.3168/jds.2006-790CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.v41i2.71013CrossRefGoogle Scholar
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, 503517.10.1590/0001-3765201520130514CrossRefGoogle ScholarPubMed
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.Google Scholar
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.CrossRefGoogle ScholarPubMed
Gilmour, A, Gogel, B, Cullis, B, Welham, S & Thompson, R (2015) ASReml User Guide Release 4·1 Structural Specification. Hemel Hempstead: VSN International Ltd.Google Scholar
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)00128-1CrossRefGoogle Scholar
Huang, B and Lin, DY (2007) Efficient association mapping of quantitative trait loci with selective genotyping. The American Journal of Human Genetics 80, 567576.CrossRefGoogle ScholarPubMed
Koenker, R (2017) quantreg: Quantile Regression. R package version 5.33. Available at: http://CRAN.R-project.org/package=quantregGoogle Scholar
Koenker, R and Bassett, G (1978) Regression quantiles. Econometrica: Journal of the Econometric Society 46, 3350.10.2307/1913643CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.2010-3589CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.Google Scholar
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.CrossRefGoogle ScholarPubMed
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-XCrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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).Google Scholar
Papajcsik, I and Bodero, J (1988) Modelling lactation curves of Friesian cows in a subtropical climate. Animal Science 47, 201207.Google Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Sundrum, A (2015) Metabolic disorders in the transition period indicate that the dairy cows’ ability to adapt is overstressed. Animals 5, 9781020.10.3390/ani5040395CrossRefGoogle ScholarPubMed
Wei, Y, Pere, A, Koenker, R and He, X (2006) Quantile regression methods for reference growth charts. Statistics in Medicine 25, 13691382.CrossRefGoogle ScholarPubMed
Wilmink, J (1987) Adjustment of test-day milk, fat and protein yield for age, season and stage of lactation. Livestock Production Science 16, 335348.CrossRefGoogle Scholar
Wood, P (1967) Algebraic model of the lactation curve in cattle. Nature 216, 164165.CrossRefGoogle Scholar
Supplementary material: PDF

Naeemipour Younesi et al. supplementary material

Naeemipour Younesi et al. supplementary material 1

Download Naeemipour Younesi et al. supplementary material(PDF)
PDF 591 KB
2
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Using quantile regression for fitting lactation curve in dairy cows
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Using quantile regression for fitting lactation curve in dairy cows
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Using quantile regression for fitting lactation curve in dairy cows
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *