Marginal maximum likelihood, a common estimation method for item response theory models, is not inherently a Bayesian procedure. However, due to estimation difficulties, Bayesian priors are often applied to the likelihood when estimating 3PL models, especially with small samples. Little focus has been placed on choosing the priors for marginal…

A full structural equation model (SEM) typically consists of both a measurement model (describing relationships between latent variables and observed scale items) and a structural model (describing relationships among latent variables). However, often researchers are primarily interested in testing hypotheses related to the structural model while…

A linear model is often used to find the effect of a binary treatment D on a noncontinuous outcome Y with covariates X. Particularly, a binary Y gives the popular "linear probability model (LPM)," but the linear model is untenable if X contains a continuous regressor. This raises the question: what kind of treatment effect does the…

Normative studies are needed to obtain norms for comparing individuals with the reference population on relevant clinical or educational measures. Norms can be obtained in an efficient way by regressing the test score on relevant predictors, such as age and sex. When several measures are normed with the same sample, a multivariate regression-based…

The recently proposed "continuous-time latent curve model with structured residuals" (CT-LCM-SR) addresses several challenges associated with longitudinal data analysis in the behavioral sciences. First, it provides information about process trends and dynamics. Second, using the continuous-time framework, the CT-LCM-SR can handle…

Variability is underemphasized in domains such as engineering. Statistics and data science education research offers a variety of frameworks for understanding variability, but new frameworks for domain applications are necessary. This study investigated the professional practices of working engineers to develop such a framework. The Neglected,…

Lagged dependent variables (LDVs) are often used as predictors in ordinary least squares (OLS) models in the social sciences. Although several estimators are commonly employed, little is known about their relative merits in the presence of classical measurement error and different longitudinal processes. We assess the performance of four commonly…

Researchers across many fields have called for greater attention to heterogeneity of treatment effects--shifting focus from the average effect to variation in effects between different treatments, studies, or subgroups. True heterogeneity is important, but many reports of heterogeneity have proved to be false, non-replicable, or exaggerated. In…

Item response tree (IRTree) models are a flexible framework to control self-reported trait measurements for response styles. To this end, IRTree models decompose the responses to rating items into sub-decisions, which are assumed to be made on the basis of either the trait being measured or a response style, whereby the effects of such person…

Background: This paper develops a new method to estimate quasi-experimental evaluation models when it is necessary to control for measurement error in predictors and individual assignment to the treatment group is based on these same fallible variables. A major methodological finding of the study is that standard methods of estimating models that…

Multiple regression is often used to compare the importance of two or more predictors. When the predictors being compared are measured with error, the estimated coefficients can be biased and Type I error rates can be inflated. This study explores the impact of measurement error on comparing predictors when one is measured with error, followed by…

Educational researchers are often interested in phenomena that unfold over time within a person and at the same time, relationships between their characteristics that are stable over time. Since variables in a longitudinal study reflect both within- and between-person effects, researchers need to disaggregate them to understand the phenomenon of…

Modest correlations between teacher-assigned grades and external assessments of academic achievement (r = 0.40-0.60) have led many educational stakeholders to deem grades subjective and unreliable. However, theoretical and methodological challenges, such as construct misalignment, data unavailability and sample unrepresentativeness, limit the…

The present simulation study indicates that a method where the regression effect of a predictor (X) on an outcome at follow-up (Y1) is calculated while adjusting for the outcome at baseline (Y0) can give spurious findings, especially when there is a strong correlation between X and Y0 and when the test-retest correlation between Y0 and Y1 is…

We consider two-level models where a continuous response R and continuous covariates C are assumed missing at random. Inferences based on maximum likelihood or Bayes are routinely made by estimating their joint normal distribution from observed data R[subscript obs] and C[subscript obs]. However, if the model for R given C includes random…