Estimating a three-level latent variable regression model with cross-classified multiple membership data

TL;DR: This research inquiry examined two-level MMrem parameter estimate biases and inferential errors using a Monte Carlo simulation study and showed that estimates of fixed effect parameters and the level-one variance component were robust to level-two residual non-normality.

TL;DR: These Bayesian models identified factors affecting academic performance of college students while accounting for university instructors and majors as random effects and adjust for residency status, academic level, number of classes, student athletes, and disability residence services.

TL;DR: This study proposes a multiple membership growth curve model (MM-GCM), which offers some advantages to other similar modeling approaches, including greater flexibility in modeling the intercept at the time-point most desired for interpretation.

TL;DR: This study sought to examine the consequences of ignoring individual mobility across clusters when estimating a 3L-PGM in comparison to a new multiple membership PGM, which was extended to handle multiple membership data structures frequently found in the social sciences.

TL;DR: In this paper, the authors consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined and derive a measure pD for the effective number in a model as the difference between the posterior mean of the deviances and the deviance at the posterior means of the parameters of interest, which is related to other information criteria and has an approximate decision theoretic justification.

TL;DR: In this paper, Hierarchical Linear Models: Applications and Data Analysis Methods are used for data analysis in the context of statistical data analysis, and the authors propose a hierarchical linear model.

TL;DR: The posterior mean deviance is suggested as a Bayesian measure of fit or adequacy, and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages.

TL;DR: In this paper, a folded-noncentral-$t$ family of conditionally conjugate priors for hierarchical standard deviation parameters is proposed, and weakly informative priors in this family are considered.