A Stepwise Algorithm for Generalized Linear Mixed Models

Stepwise regression includes regression models in which the predictive variables are selected by an automated algorithm. The stepwise method involves two approaches, namely, backward elimination and forward selection. Currently, SAS has several regression procedures capable of performing stepwise regression. Among them are REG, LOGISTIC, GLMSELECT and PHREG. PROC REG handles linear regression model but does not support a CLASS statement. PROC LOGISTIC handles binary responses and allows for logit, probit and complementary log-log link functions. It also allows for CLASS statements. The GLMSELECT procedure performs selections in the framework of general linear models. It allows for a variety of model selection methods, including the LASSO method of Tibshirani (1996) and the related LAR method of Efron et al. (2004). GLMSELECT supports a CLASS statement. PHREG is appropriate for proportional hazard survival regression. We present a stepwise algorithm for Generalized Linear Mixed Models for both marginal and conditional models. We illustrate the algorithm using data from a longitudinal observational study aimed to investigate parents’ beliefs, behaviors, feeding practices that associate positively or negatively with indices of sleep quality.