The use of MIXED models in the analysis of animal experiments with repeated measures data

Abstract

The analysis of data containing repeated observations measured on animals (experimental unit) allocated to different treatments over time is a common design in animal science. Conventionally, repeated measures data were either analyzed as a univariate (split-plot in time) or a multivariate ANOVA (analysis of contrasts), both being handled by the General Linear Model procedure of SAS. In recent times, the mixed model has become more appealing for analyzing repeated data. The objective of this paper is to provide a background understanding of mixed model methodology in a repeated measures analysis and to use balanced steer data from a growth study to illustrate the use of PROC MIXED in the SAS system using five covariance structures. The split-plot in time approach assumes a constant variance and equal correlations (covariance) between repeated measures or compound symmetry, regardless of their proximity in time, and often these assumptions are not true. Recognizing this limitation, the analysis of contrasts was proposed. If there are missing measurements, or some of the data are measured at different times, such data were excluded resulting in inadequate data for a meaningful analysis. The mixed model uses the generalized least squares method, which is generally better than the ordinary least squares used by GLM, if the appropriate covariance structure is adopted. The presence of unequally spaced and/or missing data does not pose a problem for the mixed model. In the example analyzed, the first order ante dependence [ANTE(1)] covariance model had the lowest value for the Akaike and Schwarz’s Bayesian information criteria fit statistics and is therefore the model that provided the best fit to our data. Hence, F values, least square estimates and standard errors based on the ANTE (1) were considered the most appropriate from among the five models demonstrated. It is recommended that the mixed model be used for the analysis of repeated measures designs in animal studies. Key words: Repeated measures, General Linear Model, Mixed Model, split-plot, covariance structure