Inferences in generalized linear longitudinal mixed models

Abstract

AbstractWithout realizing the fact that the time‐dependent covariates corresponding to the repeated discrete responses under a generalized linear longitudinal model (GLLM) cause non‐stationary (time dependent) correlations for the repeated responses, many existing studies use a stationary (either “working” or true) correlation structure to develop certain estimating equations for the regression effects involved in the model. By constructing suitable non‐stationary correlation structures both for longitudinal count and binary data, this article first demonstrates that the stationary correlations based estimation approaches may yield inefficient regression estimates. For efficient estimation, the article then suggests a true non‐stationary correlation structure based generalized quasi‐likelihood (GQL) estimation approach, where non‐stationary correlation structure is identified by exploiting the estimated lag correlations of the responses. A generalization of the GLLM to the familial‐longitudinal set up both for count and binary data is also discussed, where the data exhibit familial as well as non‐stationary longitudinal correlations, the familial correlations among the responses of the family members are being generated through a random common family effect. The GQL estimating equations are provided for the estimation of the regression and the variance component parameters of this generalized linear longitudinal mixed model (GLLMM), whereas the longitudinal correlations are estimated by solving suitable moment estimating equations. The Canadian Journal of Statistics 38: 174–196; 2010 © 2010 Statistical Society of Canada