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. 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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