Linear mixed-effects models and least confounded residuals in the modelling of Holstein calves’ performance
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Abstract
Some experimental studies are carried out considering a longitudinal feature. In view of this, the classical regression models are not able to handle with it, since the independence assumption between the observations is violated. To handle with this kind of data it was proposed the called linear mixed-effects models, where it is possible to model the response variable taking into account the correlation between the observations, and even between the response variables, when there are two or more of them in study, setting a bivariate or multivariate scenario, respectively. For the diagnosis of the linear mixed-effects models the least confounded residuals are quite recommended due to their lower bias in relation to other types of residuals, but it is not so used in the literature. Using a data set of dairy calves’ performance according to three different diets over eight weeks, the linear mixed-effects models theory under univariate and bivariate approach was applied alongside the least confounded residuals in the diagnosis of the model for both approaches. Comparing the univariate and bivariate approaches, the last one was more informative presenting lower standard errors’ values for its estimates, while the least confounded residuals was more efficient than the classical residuals present in the literature.
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References
Bagheri, N, Alamouti, A., Norouzian, M., Mirzaei, M & Ghaffari, M. Effects of wheat straw particle size as a free-choice provision on growth performance and feeding behaviors of dairy calves. Animal 15, 100128 (2021).
Berends, H, Van den Borne, J., Mollenhorst, H, Van Reenen, C., Bokkers, E. & Gerrits, W. Utilization of roughages and concentrates relative to that of milk replacer increases strongly with age in veal calves. Journal of dairy science 97, 6475–6484 (2014).
Castells, L., Bach, A, Araujo, G, Montoro, C & Terré, M. Effect of different forage sources on performance and feeding behavior of Holstein calves. Journal of Dairy Science 95, 286–293 (2012).
Engelking, L., Matsuba, T, Inouchi, K, Sugino, T & Oba, M. Effects of feeding hay and calf starter as a mixture or as separate components to Holstein calves on intake, growth, and blood metabolite and hormone concentrations. Journal of dairy science 103, 4423–4434 (2020).
Henze, N. & Zirkler, B. A class of invariant consistent tests for multivariate normality. Communications in statistics-Theory and Methods 19, 3595–3617 (1990).
Hilden-Minton, J. A. Multilevel diagnostics for mixed and hierarchical linear models (University of California, Los Angeles, 1995).
Laird, N. M. & Ware, J. H. Random-effects models for longitudinal data. Biometrics, 963–974 (1982).
Lehmann, E. L. & Romano, J. P. Testing statistical hypotheses (Springer, 1986).
Loy, A. & Hofmann, H. HLMdiag: A suite of diagnostics for hierarchical linear models in R. Journal of Statistical Software 56, 1–28 (2014).
Loy, A., Hofmann, H. & Cook, D. Diagnostics for mixed/hierarchical linear models. Iowa State University (2013).
Movahedi, B, Foroozandeh, A. & Shakeri, P. Effects of different forage sources as a free-choice provision on the performance, nutrient digestibility, selected blood metabolites and structural growth of Holstein dairy calves. Journal of animal physiology and animal nutrition 101, 293–301 (2017).
Omidi-Mirzaei, H, Azarfar, A, Mirzaei, M, Kiani, A&Ghaffari, M. Effects of forage source and forage particle size as a free-choice provision on growth performance, rumen fermentation, and behavior of dairy calves fed texturized starters. Journal of dairy science 101, 4143–4157 (2018).
Oskrochi, G., Lesaffre, E., Oskrochi, Y. & Shamley, D. An application of the multivariate linear mixed model to the analysis of shoulder complexity in breast cancer patients. International journal of environmental research and public health 13, 274 (2016).
Overvest, M., Bergeron, R, Haley, D. & DeVries, T. Effect of feed type and method of presentation on feeding behavior, intake, and growth of dairy calves fed a high level of milk. Journal of Dairy Science 99, 317–327 (2016).
Poczynek, M. et al. Partial corn replacement by soybean hull, or hay supplementation: Effects of increased NDF in diet on performance, metabolism and behavior of pre-weaned calves. Livestock Science 231, 103858 (2020).
Rousseeuw, P. J., Ruts, I. & Tukey, J. W. The bagplot: a bivariate boxplot. The American Statistician 53, 382–387 (1999).
Schwarz, G. Estimating the dimension of a model. The annals of statistics, 461–464 (1978).
Shapiro, S. S. & Wilk, M. B. An analysis of variance test for normality (complete samples). Biometrika 52, 591–611 (1965).
Singer, J. M., Nobre, J. S. & Rocha, F. M. Diagnostic and treatment for linear mixed models in Session CPS203 Proceedings of the ISIWorld Statistics Congress (59), Hong Kong). Hong Kong, República Popular China (2013).
Stamey, J., Janovick, N., Kertz, A.&Drackley, J. Influence of starter protein content on growth of dairy calves in an enhanced early nutrition program. Journal of Dairy Science 95, 3327–3336 (2012).
Verbeke, G., Molenberghs, G. & Verbeke, G. Linear mixed models for longitudinal data (Springer, 1997).
Zhu, X. et al. Comparison of four methods for handing missing data in longitudinal data analysis through a simulation study. Open Journal of Statistics 4, 933 (2014).