Growth curve models are widely used for investigating growth and change phenomena. Many studies in social and behavioral sciences have demonstrated that data without any outlying observation are rather an exception, especially for data collected longitudinally. Ignoring the existence of outlying observations may lead to inaccurate or even…

This article introduces an entropy-based measure of data-model fit that can be used to assess the quality of logistic regression models. Entropy has previously been used in mixture-modeling to quantify how well individuals are classified into latent classes. The current study proposes the use of entropy for logistic regression models to quantify…

Models of category learning have been extensively studied in cognitive science and primarily tested on perceptual abstractions or artificial stimuli. In this paper, we focus on categories acquired from natural language stimuli, that is, words (e.g., "chair" is a member of the furniture category). We present a Bayesian model that, unlike…

With the development of technology-enhanced learning platforms, eye-tracking biometric indicators can be recorded simultaneously with students item responses. In the current study, visual fixation, an essential eye-tracking indicator, is modeled to reflect the degree of test engagement when a test taker solves a set of test questions. Three…

Multilevel data are a reality for many disciplines. Currently, although multiple options exist for the treatment of multilevel data, most disciplines strictly adhere to one method for multilevel data regardless of the specific research design circumstances. The purpose of this Monte Carlo simulation study is to compare several methods for the…

As a method to shorten the test time of the Force Concept Inventory (FCI), we suggest the use of computerized adaptive testing (CAT). CAT is the process of administering a test on a computer, with items (i.e., questions) selected based upon the responses of the examinee to prior items. In so doing, the test length can be significantly shortened.…

Simulation studies use computer-generated data to examine questions of interest that have traditionally been used to study properties of statistics and estimating algorithms. With the recent advent of powerful processing capabilities in affordable computers along with readily usable software, it is now feasible to use a simulation study to aid in…

Stan is a flexible probabilistic programming language providing full Bayesian inference through Hamiltonian Monte Carlo algorithms. The benefits of Hamiltonian Monte Carlo include improved efficiency and faster inference, when compared to other MCMC software implementations. Users can interface with Stan through a variety of computing…

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…

The variance formula derived for a two-stage sampling design without replacement employs the joint inclusion probabilities in the first-stage selection of clusters. One of the difficulties encountered in data analysis is the lack of information about such joint inclusion probabilities. One way to solve this issue is by applying Hájek's…

Purpose: Critical differences state by how much 2 test results have to differ in order to be significantly different. Critical differences for discrimination scores have been available for several decades, but they do not exist for speech reception thresholds (SRTs). This study presents and discusses how critical differences for SRTs can be…

There is an increasing interest in reporting test subscores for diagnostic purposes. In this article, we review nine popular R packages (subscore, mirt, TAM, sirt, CDM, NPCD, lavaan, sem, and OpenMX) that are capable of implementing subscore-reporting methods within one or more frameworks including classical test theory, multidimensional item…

Test score distributions of schools or demographic groups are often summarized by frequencies of students scoring in a small number of ordered proficiency categories. We show that heteroskedastic ordered probit (HETOP) models can be used to estimate means and standard deviations of multiple groups' test score distributions from such data. Because…

The main purpose of this quantitative-qualitative content analysis study was to compare IELTS and TOEFL listening and reading tests based on the representation of the learning objectives of Revised Bloom's taxonomy. To this end, 12 Academic IELTS listening and reading tests and 12 TOEFL iBT listening and reading tests were analyzed qualitatively…

In applications of item response theory (IRT), an estimate of the reliability of the ability estimates or sum scores is often reported. However, analytical expressions for the standard errors of the estimators of the reliability coefficients are not available in the literature and therefore the variability associated with the estimated reliability…