Multiple imputation (MI) can be used to address missing data at Level 2 in multilevel research. In this article, we compare joint modeling (JM) and the fully conditional specification (FCS) of MI as well as different strategies for including auxiliary variables at Level 1 using either their manifest or their latent cluster means. We show with…

Loglinear smoothing (LLS) estimates the latent trait distribution while making fewer assumptions about its form and maintaining parsimony, thus leading to more precise item response theory (IRT) item parameter estimates than standard marginal maximum likelihood (MML). This article provides the expectation-maximization algorithm for MML estimation…

The main purpose of this study is to improve estimation efficiency in obtaining maximum marginal likelihood estimates of contextual effects in the framework of nonlinear multilevel latent variable model by adopting the Metropolis-Hastings Robbins-Monro algorithm (MH-RM). Results indicate that the MH-RM algorithm can produce estimates and standard…

Model-based multiple imputation has become an indispensable method in the educational and behavioral sciences. Mean and covariance structure models are often fitted to multiply imputed data sets. However, the presence of multiple random imputations complicates model fit testing, which is an important aspect of mean and covariance structure…

The article considers a test of specification for quantile regressions. The test relies on the increase of the objective function and the worsening of the fit when unnecessary constraints are imposed. It compares the objective functions of restricted and unrestricted models and, in its different formulations, it verifies (a) forecast ability, (b)…

The Programme for International Student Assessment comparative study of reading performance among 15-year-olds is reanalyzed using statistical procedures that allow the full complexity of the data structures to be explored. The article extends existing multilevel factor analysis and structural equation models and shows how this can extract richer…