In Bayesian statistics, the most widely used criteria of Bayesian model assessment and comparison are Deviance Information Criterion (DIC) and Watanabe-Akaike Information Criterion (WAIC). A multilevel mediation model is used as an illustrative example to compare different types of DIC and WAIC. More specifically, the study compares the…

The year 2022 is the 20th anniversary of Joseph Schafer and John Graham's paper titled "Missing data: Our view of the state of the art," currently the most highly cited paper in the history of "Psychological Methods." Much has changed since 2002, as missing data methodologies have continually evolved and improved; the range of…

We consider two-level models where a continuous response R and continuous covariates C are assumed missing at random. Inferences based on maximum likelihood or Bayes are routinely made by estimating their joint normal distribution from observed data R[subscript obs] and C[subscript obs]. However, if the model for R given C includes random…

In this paper, we analyze a two-level latent variable model for longitudinal data from the National Growth of Health Study where surrogate outcomes or biomarkers and covariates are subject to missingness at any of the levels. A conventional method for efficient handling of missing data is to reexpress the desired model as a joint distribution of…

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 [sigma] of group-level varying coefficients are often degenerate. One can do better, even…

There is a dearth of research on Tier 1 instruction designed to improve the mathematics achievement of English learners. This study examined the impact of a core kindergarten mathematics curriculum on the mathematics achievement of Spanish-speaking English learners (SS-ELs). Secondary aims tested for differential response to the curriculum among…

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; Cai, 2008, 2010a, 2010b). Results indicate that the MH-RM algorithm can…

This paper extends single-level missing data methods to efficient estimation of a "Q"-level nested hierarchical general linear model given ignorable missing data with a general missing pattern at any of the "Q" levels. The key idea is to reexpress a desired hierarchical model as the joint distribution of all variables including…

A multilevel latent transition analysis (LTA) with a mixture IRT measurement model (MixIRTM) is described for investigating the effectiveness of an intervention. The addition of a MixIRTM to the multilevel LTA permits consideration of both potential heterogeneity in students' response to instructional intervention as well as a methodology for…