Although statistical practices to evaluate intervention effects in SCEDs have gained prominence in the recent times, models are yet to incorporate and investigate all their analytic complexities. Most of these statistical models incorporate slopes and autocorrelations both of which contribute to trend in the data. The question that arises is…

Latent transition analysis is an informative statistical tool for depicting heterogeneity in learning as latent profiles. We present a Monte Carlo simulation study to guide researchers in selecting fit indices for identifying the correct number of profiles. We simulated data representing profiles of learners within a typical pre- post- follow…

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…

When a response pattern does not fit a selected measurement model, one may resort to robust ability estimation. Two popular robust methods are biweight and Huber weight. So far, research on these methods has been quite limited. This article proposes the maximum a posteriori biweight (BMAP) and Huber weight (HMAP) estimation methods. These methods…

Longitudinal data structures are frequently encountered in a variety of disciplines in the social and behavioral sciences. Growth curve modeling offers a highly extensible framework that allows for the exploration of rich hypotheses. However, owing to the presence of interrelated sources of potential data-model misfit at multiple levels, the…

Standard methods for the meta-analysis of medical tests, without assuming a gold standard, are limited to dichotomous data. Multivariate probit models are used to analyse correlated dichotomous data, and can be extended to model ordinal data. Within the context of an imperfect gold standard, they have previously been used for the analysis of…

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…

A Monte Carlo simulation was performed to compare methods for handling missing data in growth mixture models. The methods considered in the current study were (a) a fully Bayesian approach using a Gibbs sampler, (b) full information maximum likelihood using the expectation-maximization algorithm, (c) multiple imputation, (d) a two-stage multiple…

Many statistical methods (estimators) are available for estimating the consensus value (or average effect) and heterogeneity variance in interlaboratory studies or meta-analyses. These estimators are all valid because they are developed from or supported by certain statistical principles. However, no estimator can be perfect and must have error or…

Markov chain Monte Carlo is a key computational tool in Bayesian statistics, but it can be challenging to monitor the convergence of an iterative stochastic algorithm. In this paper we show that the convergence diagnostic [R-hat] of Gelman and Rubin (1992) has serious flaws. Traditional [R-hat] will fail to correctly diagnose convergence failures…

When working with multimodal Bayesian posterior distributions, Markov chain Monte Carlo (MCMC) algorithms have difficulty moving between modes, and default variational or mode-based approximate inferences will understate posterior uncertainty. And, even if the most important modes can be found, it is difficult to evaluate their relative weights in…

In this article, the beta-binomial model for count data is proposed and demonstrated in terms of its application in the context of oral reading fluency (ORF) assessment, where the number of words read correctly (WRC) is of interest. Existing studies adopted the binomial model for count data in similar assessment scenarios. The beta-binomial model,…

This study proposes a two-stage causal modeling with instrumental variables to mitigate selection bias, provide correct standard error estimates, and address nonnormal and missing data issues simultaneously. Bayesian methods are used for model estimation. Robust methods with Student's "t" distributions are used to account for nonnormal…

A Monte Carlo simulation study was conducted to compare fit indices used for detecting the correct latent class in three dichotomous mixture item response theory (IRT) models. Ten indices were considered: Akaike's information criterion (AIC), the corrected AIC (AICc), Bayesian information criterion (BIC), consistent AIC (CAIC), Draper's…

Standard item response theory (IRT) models have been extended with testlet effects to account for the nesting of items; these are well known as (Bayesian) testlet models or random effect models for testlets. The testlet modeling framework has several disadvantages. A sufficient number of testlet items are needed to estimate testlet effects, and a…