Generalized quasi-linear mixed-effects model

The generalized linear mixed model (GLMM) is one of the most common method in the analysis of longitudinal and clustered data in biological sciences. However, issues of model complexity and misspecification can occur when applying the GLMM. To address these issues, we extend the standard GLMM to a nonlinear mixed-effects model based on quasi-linear modeling. An estimation algorithm for the proposed model is provided by extending the penalized quasi-likelihood and the restricted maximum likelihood which are known in the GLMM inference. Also, the conditional AIC is formulated for the proposed model. The proposed model should provide a more flexible fit than the GLMM when there is a nonlinear relation between fixed and random effects. Otherwise, the proposed model is reduced to the GLMM. The performance of the proposed model under model misspecification is evaluated in several simulation studies. In the analysis of respiratory illness data from a randomized controlled trial, we observe the proposed model can capture heterogeneity; that is, it can detect a patient subgroup with specific clinical character in which the treatment is effective.