In this chapter, we examine the use of special forms of correlated random e ects in the generalized linear mixed model (GLMM) setting. A special feature of our GLMM is the inclusion of random residual e ects to account for lack of t due to extra variation, outliers and other unexplained sources of variation. For random e ects, we consider, in particular, the correlation structure and improper p...

This article discusses the use of a symmetric multiplicative interaction effect to capture certain types of third-order dependence patterns often present in social networks and other dyadic datasets. Such an effect, along with standard linear fixed and random effects, is incorporated into a generalized linear model, and a Markov chain Monte Carlo algorithm is provided for Bayesian estimation an...

This paper is concerned with the selection and estimation of fixed and random effects in linear mixed effects models. We propose a class of nonconcave penalized profile likelihood methods for selecting and estimating important fixed effects. To overcome the difficulty of unknown covariance matrix of random effects, we propose to use a proxy matrix in the penalized profile likelihood. We establi...

Two efficient approaches are considered to deal with the difficulty in computing the intractable integrals when implementing Gibbs sampling in the nonlinear mixed effects model (NLMM) based on Dirichlet processes (DP). The first approach computes the Laplace's approximation to the integral for its high accuracy, low cost, and ease of implementation. The second approach uses the no-gaps algorith...

Psycholinguistic data are often analyzed with repeated-measures analyses of variance (ANOVA), but this paper argues that mixed-effects (multilevel) models provide a better alternative method. First, models are discussed in which the two random factors of participants and items are crossed, and not nested. Traditional ANOVAs are compared against these crossed mixed-effects models, for simulated ...

Psycholinguistic data are often analyzed with repeated-measures analyses of variance (ANOVA), but this paper argues that mixed-effects (multilevel) models provide a better alternative method. First, models are discussed in which the two random factors of participants and items are crossed, and not nested. Traditional ANOVAs are compared against these crossed mixed-effects models, for simulated ...