Covariance structure selection in linear mixed models for longitudinal data.

摘要

Linear mixed models are frequently used to analyze data with random effects and/or repeated measures in longitudinal data analysis. In order to implement linear mixed models, one of the important steps is to choose a covariance structure. Information criteria, such as the Akaike Information Criterion (AIC) and Schwarz's Bayesian Criterion (BIC) (Schwarz, 1978), are often used by statisticians to guide selection of covariance structure. However, these criteria do not always point to the true covariance structure: Hurvich and Tsai's Criterion (AICC) (Hurvich and Tsai, 1989), and Hannan and Quinn's Information Criterion (HQIC) (Hannan and Quinn, 1979), and Bozdogan's Criterion (CAIC) (Bozdogan, 1987) as well as AIC and BIC were used to select the covariance structure in our study. Performance of these criteria in selecting the true covariance structure was evaluated via a simulation study, focusing on the equal replication case, with varying numbers of subjects per treatment and measurements per subject. Type I error rates are presented for the fixed effects using the covariance structures identified using the various criteria. Twelve different covariance structures are researched in this study, including six spatial covariance structures.;Success of these five ICs in selecting the correct covariance structure increased as number of subjects and number of observations per subject increased. We found from this study that the Type I error rates for the best IC models were always higher than the target values, but approached the nominal significance level as the number of observations per subject increased.;Alternative graphical diagnostic methods such as the ordinary scatterplots matrix (OSM) (Zimmerman, 2000, 2001)) and partial regression-on-intervenors scatterplot matrix (PRISM) for choosing the covariance structure are also discussed.