Appropriate Covariance Structure for Linear Mixed Model in the Animal Experiments with Repeated Measurement Data

Abstract

Working on repeated measurement analysis in animal experimental data, the linear model become less appropriate, because by assuming the error variances being independent and homogeneous might be violated. Thus, this study intends to develop linear mixed model for animal experiments with repeated measurement data. The work of this study was aimed to determine the covariance structure for linear mixed model using animal experiments with repeated measurement data. The study presented general form of variance-covariance structure in case of repeated measures data and general form of parameter estimation. Data from comparing effects of treatment (diet) on cumulative gas production in case of equal time spacing, unequal time spacing and unbalance data were used to demonstrate mixed model methodology and analyze repeated measurement data. The results of the estimates of correlation coefficients and variance-covariance matrix for all three cases revealed that the variances and correlations within the same animal were different over time. This structure was satisfied with ANTE(1) model. By comparing seven covariance structures (SIMPLE, CS, AR(1), UN, CHS, ARH(1) and ANTE(1)) using MIXED procedure, the ANTE(1) covariance structure from fitted the data was the best choice based on four fit indices criteria (-2RLL, AIC, AICC and BIC) and F-test of fixed effects. Therefore, the ANTE(1) structure was an appropriate covariance structure to describe repeated measurement data from the animal experiments in case of equal time spacing, unequal time spacing and unbalance data under heteroscedasticity and correlated data over time.