Measurement invariance (MI) is an essential part of validity evidence concerned with ensuring that tests function similarly across groups, contexts, and time. Most evaluations of MI involve multigroup confirmatory factor analyses (MGCFA) that assume simple structure. However, recent research has shown that constraining non-target indicators to…

A necessary step in applying bi-factor models is to evaluate the need for domain factors with a general factor in place. The conventional null hypothesis testing (NHT) was commonly used for such a purpose. However, the conventional NHT meets challenges when the domain loadings are weak or the sample size is insufficient. This article proposes…

This paper aims to advocate for a balanced approach to model fit evaluation in structural equation modeling (SEM). The ongoing debate surrounding chi-square test statistics and fit indices has been characterized by ambiguity and controversy. Despite the acknowledged limitations of relying solely on the chi-square test, its careful application can…

Measurement invariance holds when a latent construct is measured in the same way across different levels of background variables (continuous or categorical) while controlling for the true value of that construct. Using Monte Carlo simulation, this paper compares the multiple indicators, multiple causes (MIMIC) model and MIMIC-interaction to a…

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…

Monte Carlo methods are an accepted methodology in regards to generation critical values for a Maximum test. The same methods are also applicable to the evaluation of the robustness of the new created test. A table of critical values was created, and the robustness of the new maximum test was evaluated for five different distributions. Robustness…

Staggered adoption of policies by different units at different times creates promising opportunities for observational causal inference. Estimation remains challenging, however, and common regression methods can give misleading results. A promising alternative is the synthetic control method (SCM), which finds a weighted average of control units…

Prior studies investigating the effects of non-normality in structural equation modeling typically induced non-normality in the indicator variables. This procedure neglects the factor analytic structure of the data, which is defined as the sum of latent variables and errors, so it is unclear whether previous results hold if the source of…

Model fit indices are being increasingly recommended and used to select the number of factors in an exploratory factor analysis. Growing evidence suggests that the recommended cutoff values for common model fit indices are not appropriate for use in an exploratory factor analysis context. A particularly prominent problem in scale evaluation is the…

This study presents a new approach to synthesizing differential item functioning (DIF) effect size: First, using correlation matrices from each study, we perform a multigroup confirmatory factor analysis (MGCFA) that examines measurement invariance of a test item between two subgroups (i.e., focal and reference groups). Then we synthesize, across…

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…

Autocorrelation and partial autocorrelation, which provide a mathematical tool to understand repeating patterns in time series data, are often used to facilitate the identification of model orders of time series models (e.g., moving average and autoregressive models). Asymptotic methods for testing autocorrelation and partial autocorrelation such…

Researchers continue to be interested in efficient, accurate methods of estimating coefficients of covariates in mixture modeling. Including covariates related to the latent class analysis not only may improve the ability of the mixture model to clearly differentiate between subjects but also makes interpretation of latent group membership more…

High dimensional multivariate data, where the number of variables approaches or exceeds the sample size, is an increasingly common occurrence for social scientists. Several tools exist for dealing with such data in the context of univariate regression, including regularization methods such as Lasso, Elastic net, Ridge Regression, as well as the…

Sparse-rated data are common in operational performance-based language tests, as an inevitable result of assigning examinee responses to a fraction of available raters. The current study investigates the precision of two generalizability-theory methods (i.e., the rating method and the subdividing method) specifically designed to accommodate the…