Comparison of different covariance structure used for experimental design with repeated measurement

This study was conducted to compare performance of univariate and multivariate approaches used for analyzing experiments with repeated measurement and determine the best covariance structure for the data studied. In this study, univariate ANOVA, Geisser-Greenhouse Epsilon and Huynth-Feldt Epsilon were used as univariate approaches while profile analysis, Containment, Satterthwaite and Kenward-Roger approaches in general linear mixed model were applied as multivariate approaches. Annual amounts of wheat production from 65 provinces in seven geographical regions of Turkey from 1982 to 1999 were used as research material. A total of 1170 production values were obtained. In General Linear Model, nine various covariance structures (CS, CSH, UN, HF, AR (1), ARH (1), ANTE (1), TOEP and TOEPH) were applied. AIC and AICC criteria were used to determine the most appropriate covariance pattern for fitting data. In the study, "spherity assumption" for amounts of wheat production of provinces was violated. Application of Containment, Satterthwaite and Kenward-Roger approaches in general linear model and determination of covariance structure with the best fit were provided. According to AIC and AICC fitting criteria, it was determined that CS covariance structure gave the best fit to data set. As a result, covariance structure is compound symmetry (CS) in standard univariate ANOVA, and unstructured (UN) covariance structure in MANOVA. However, determination of the most appropriate covariance structure for data set is possible in multivariate general linear model. Containment, Satterthwaite, and Kenward-Roger approaches gave similar results since total sample size was sufficient. On the other hand, usage of Containment, Satterthwaite and Kenward-Roger approaches in analyzing experiments with repeated measurement were suggested to allow selection of the most suitable covariance structure for data set