Profile-Likelihood Approach for Estimating Generalized Linear Mixed Models With Factor Structures

Minjeong Jeon, Sophia Rabe-Hesketh
2012 Journal of educational and behavioral statistics  
In this article, the authors suggest a profile-likelihood approach for estimating complex models by maximum likelihood (ML) using standard software and minimal programming. The method works whenever setting some of the parameters of the model to known constants turns the model into a standard model. An important class of models that can be estimated this way is generalized linear mixed models with factor structures. Such models are useful in educational research, for example, for estimation of
more » ... alue-added teacher or school effects with persistence parameters and for analysis of large-scale assessment data using multilevel item response models with discrimination parameters. The authors describe the profile-likelihood approach, implement it in the R software, and apply the method to longitudinal data and binary item response data. Simulation studies and comparison with gllamm show that the profile-likelihood method performs well in both types of applications. The authors also briefly discuss other types of models that can be estimated using the profile-likelihood idea. Here, w mij is a vector of covariates and known constants associated with the random effect or latent variable mj and m is a vector of coefficients that we will refer to as factor loadings. As we will see in the applications, models with further levels of nested and/or crossed random effects (e.g., students nested within middle school and high school) with factor structures can also be estimated. When the factor loadings are set to known constants, we can define covariates z mij ¼ w 0 mij m and the model becomes a standard generalized linear mixed model. Profile-Likelihood Approach 519
doi:10.3102/1076998611417628 fatcat:cwlbxgio4rh7pchbxgasmhtuem