The present work focuses on the performance of two types of shrinkage priors--the horseshoe prior and the recently developed regularized horseshoe prior--in the context of inducing sparsity in path analysis and growth curve models. Prior research has shown that these horseshoe priors induce sparsity by at least as much as the "gold…

The Schwarz or Bayesian information criterion (BIC) is one of the most widely used tools for model comparison in social science research. The BIC, however, is not suitable for evaluating models with order constraints on the parameters of interest. This article explores two extensions of the BIC for evaluating order-constrained models, one where a…

This article reviews and compares recently proposed factor analytic and item response theory approaches to the study of invariance across groups. Two methods are described and contrasted. The alignment method considers the groups as a fixed mode of variation, while the random-intercept, random-loading two-level method considers the groups as a…

Hierarchical or multilevel linear models are widely used for longitudinal or cross-sectional data on students nested in classes and schools, and are particularly important for estimating treatment effects in cluster-randomized trials, multi-site trials, and meta-analyses. The models can allow for variation in treatment effects, as well as…

Intra-individual variability over a short period of time may contain important information about how individuals differ from each other. In this article we begin by discussing diverse indicators for quantifying intra-individual variability and indicate their advantages and disadvantages. Then we propose an alternative method that models…

Markov chain Monte Carlo (MCMC) methods enable a fully Bayesian approach to parameter estimation of item response models. In this simulation study, the authors compared the recovery of graded response model parameters using marginal maximum likelihood (MML) and Gibbs sampling (MCMC) under various latent trait distributions, test lengths, and…

In sequential mastery testing (SMT), assessment via computer is used to classify examinees into one of two mutually exclusive categories. Unlike paper-and-pencil tests, SMT has the capability to use variable-length stopping rules. One approach to shortening variable-length tests is stochastic curtailment, which halts examination if the probability…

According to Kenny and McCoach (2003), chi-square tests of structural equation models produce inflated Type I error rates when the degrees of freedom increase. So far, the amount of this bias in large models has not been quantified. In a Monte Carlo study of confirmatory factor models with a range of 48 to 960 degrees of freedom it was found that…

Maximum likelihood and least-squares estimates of parameters from the logistic regression model are derived from an iteratively reweighted linear regression algorithm. Empirical Bayes estimates are derived using an m-group regression model to regress the within-group estimates toward common values. The m-group regression model assumes that the…

This paper investigates methods that avoid using multiple groups to represent the missing data patterns in covariance structure modeling, attempting instead to do a single-group analysis where the only action the analyst has to take is to indicate that data is missing. A new covariance structure approach developed by B. Muthen and G. Arminger is…

A class of two-stage models is developed to accommodate three common characteristics of behavioral data: (1) its multivariate nature; (2) the typical small sample size; and (3) the possibility of missing observations. The model, as illustrated, permits estimation of the full spectrum of plausible measurement error structures. (SLD)

Through a large-scale simulation study, this article compares item parameter estimates obtained by the marginal maximum likelihood estimation (MMLE) and marginal Bayes modal estimation (MBME) procedures in the 3-parameter logistic model. The impact of different prior specifications on the MBME estimates is also investigated using carefully…

The accuracy of the Markov Chain Monte Carlo (MCMC) procedure Gibbs sampling was considered for estimation of item parameters of the two-parameter logistic model. Data for the Law School Admission Test (LSAT) Section 6 were analyzed to illustrate the MCMC procedure. In addition, simulated data sets were analyzed using the MCMC, marginal Bayesian…

Used simulations of computerized adaptive tests to evaluate results yielded by four commonly used ability estimation methods: maximum likelihood estimation (MLE) and three Bayesian approaches. Results show clear distinctions between MLE and Bayesian methods. (SLD)

Expected a posteriori has a number of advantages over maximum likelihood estimation or maximum a posteriori (MAP) estimation methods. These include ability estimates (thetas) for all response patterns, less regression towards the mean than MAP ability estimates, and a lower average squared error. R. D. Bock and R. J. Mislevy (1982) state that the…