Lecture on estimation and inference: Non-maximum likelihood estimation and statistical inference for linear and nonlinear mixed models
Seminar Room 1, Newton Institute
Traditionally linear and nonlinear mixed effects models are estimated by maximum likelihood assuming normal distribution. The goal of this lecture is to discuss non-iterative methods for estimation of linear mixed models and simplified methods for estimation of generalized linear and nonlinear mixed models. In particular, we will talk about testing the presence of random effects, often overlooked fundamental test in the framework of mixed effects model. Simplified methods for generalized linear mixed models (GLMM), such as conditional logistic regression models with random intercepts and Poisson model for count data will be discussed. Limitations of popular generalized estimating equation (GEE) approach are uncovered. On the other hand, it is shown that this approach is valid for Poisson mixed model. Fixed sample maximum likelihood approach is introduced and its statistical properties are investigated via statistical simulations. Open problems and future work on statistical inference for mixed models are outlined.