This article discusses estimation of multilevel/hierarchical linear models that include cluster-level random intercepts and random slopes. Viewing the models as structural, the random intercepts and slopes represent the effects of omitted cluster-level covariates that may be correlated with...

Investigations of the effects of schools (or teachers) on student achievement focus on either (1) individual school effects, such as value-added analyses, or (2) school-type effects, such as comparisons of charter and public schools. Controlling for school composition by including student...

This text is a Stata-specific treatment of generalized linear mixed models, also known as multilevel or hierarchical models. These models are "mixed" in the sense that they allow fixed and random effects and are "generalized" in the sense that they are appropriate not only for continuous...

An additive multilevel item structure (AMIS) model with random residuals is proposed. The model includes multilevel latent regressions of item discrimination and item difficulty parameters on covariates at both item and item category levels with random residuals at both levels. The AMIS model is...

Group-level variance estimates of zero often arise when fitting multilevel or hierarchical linear models, especially when the number of groups is small. For situations where zero variances are implausible a priori, we propose a maximum penalized likelihood approach to avoid such boundary...

When fitting hierarchical regression models, maximum likelihood (ML) estimation has computational (and, for some users, philosophical) advantages compared to full Bayesian inference, but when the number of groups is small, estimates of the covariance matrix (Σ) of group-level varying...