Consider the conventional multilevel model Y=C[gamma]+Zu+e where [gamma] represents fixed effects and (u,e) are multivariate normal random effects. The continuous outcomes Y and covariates C are fully observed with a subset Z of C. The parameters are [theta]=([gamma],var(u),var(e)). Dempster, Rubin and Tsutakawa (1981) framed the estimation as a…

In education research, small samples are common because of financial limitations, logistical challenges, or exploratory studies. With small samples, statistical principles on which researchers rely do not hold, leading to trust issues with model estimates and possible replication issues when scaling up. Researchers are generally aware of such…

In this article, a maximum likelihood (ML) approach for analyzing a rather general two-level structural equation model is developed for hierarchically structured data that are very common in educational and/or behavioral research. The proposed two-level model can accommodate nonlinear causal relations among latent variables as well as effects…

The question of how to analyze unbalanced hierarchical data generated from structural equation models has been a common problem for researchers and analysts. Among difficulties plaguing statistical modeling are estimation bias due to measurement error and the estimation of the effects of the individual's hierarchical social milieu. This paper…

Estimating item parameters from a two-parameter normal ogive model is considered using Gibbs sampling to simulate draws from the joint posterior distribution of ability and item parameters. The method gives marginal posterior density estimates for any parameter of interest, as illustrated using data from a 33-item mathematics placement…