We conducted an extensive Monte Carlo study of factor-rotation local solutions (LS) in multidimensional, two-parameter logistic (M2PL) item response models. In this study, we simulated more than 19,200 data sets that were drawn from 96 model conditions and performed more than 7.6 million rotations to examine the influence of (a) slope parameter…

Measurement error affects the quality of population orderings of an index and, hence, increases the misclassification of the poor and the non-poor groups and affects statistical inferences from binary regression models. Hence, the conclusions about the extent, profile, and distribution of poverty are likely to be misleading. However, the size and…

Cognitive diagnosis models (CDMs) are the statistical framework for cognitive diagnostic assessment in education and psychology. They generally assume that subjects' latent attributes are dichotomous--mastery or nonmastery, which seems quite deterministic. As an alternative to dichotomous attribute mastery, attention is drawn to the use of a…

Spatial regression models provide the opportunity to analyze spatial data and spatial processes. Yet, several model specifications can be used, all assuming different types of spatial dependence. This study summarizes the most commonly used spatial regression models and offers a comparison of their performance by using Monte Carlo experiments. In…

A Monte Carlo study was conducted to compare the performance of a level-specific (LS) fit evaluation with that of a simultaneous (SI) fit evaluation in multilevel confirmatory factor analysis (MCFA) models. We extended previous studies by examining their performance under MCFA models with different factor structures across levels. In addition,…

Factor mixture modeling (FMM) has been increasingly used to investigate unobserved population heterogeneity. This study examined the issue of covariate effects with FMM in the context of measurement invariance testing. Specifically, the impact of excluding and misspecifying covariate effects on measurement invariance testing and class enumeration…

This paper develops models to measure growth in student achievement with a focus on the possibility of differential growth in achievement for low and high-achieving students. We consider a gap-closing model that evaluates the degree to which students in a target group -- students in the bottom quartile of measured achievement -- perform better…

Despite broad applications of growth curve models, few studies have dealt with a practical issue -- nonnormality of data. Previous studies have used Student's "t" distributions to remedy the nonnormal problems. In this study, robust distributional growth curve models are proposed from a semiparametric Bayesian perspective, in which…

In item response theory (IRT) modeling, the Fisher information matrix is used for numerous inferential procedures such as estimating parameter standard errors, constructing test statistics, and facilitating test scoring. In principal, these procedures may be carried out using either the expected information or the observed information. However, in…

The usefulness of item response theory (IRT) models depends, in large part, on the accuracy of item and person parameter estimates. For the standard 3 parameter logistic model, for example, these parameters include the item parameters of difficulty, discrimination, and pseudo-chance, as well as the person ability parameter. Several factors impact…

In behavioral sciences broadly, estimating growth models with Bayesian methods is becoming increasingly common, especially to combat small samples common with longitudinal data. Although Mplus is becoming an increasingly common program for applied research employing Bayesian methods, the limited selection of prior distributions for the elements of…

Collection and analysis of longitudinal data is an important tool in understanding growth and development over time in a whole range of human endeavors. Ideally, researchers working in the longitudinal framework are able to collect data at more than two points in time, as this will provide them with the potential for a deeper understanding of the…

Path models with observed composites based on multiple items (e.g., mean or sum score of the items) are commonly used to test interaction effects. Under this practice, researchers generally assume that the observed composites are measured without errors. In this study, we reviewed and evaluated two alternative methods within the structural…

When researchers fit statistical models to multiply imputed datasets, they have to fit the model separately for each imputed dataset. Since there are multiple datasets, there are always multiple sets of model results. It is possible for some of these sets of results not to converge while some do converge. This study examined occurrence of such a…

This study examined the diagnostic accuracy associated with decision making as is typically conducted with curriculum-based measurement (CBM) approaches to progress monitoring. Using previously published estimates of the standard errors of estimate associated with CBM, 20,000 progress-monitoring data sets were simulated to model student reading…