Factor Score Regression (FSR) is increasingly employed as an alternative to structural equation modeling (SEM) in small samples. Despite its popularity in psychology, the performance of FSR in multigroup models with small samples remains relatively unknown. The goal of this study was to examine the performance of FSR, namely Croon's correction and…

Researchers often study dynamic processes of latent variables in everyday life, such as the interplay of positive and negative affect over time. An intuitive approach is to first estimate the measurement model of the latent variables, then compute factor scores, and finally use these factor scores as observed scores in vector autoregressive…

In education research test scores are a common object of analysis. Across studies test scores can be an important outcome, a highly predictive covariate, or a means of assigning treatment. However, test scores are a measure of an underlying proficiency we can't observe directly and so contain error. This measurement error has implications for how…

The problem of local item dependencies (LIDs) is very common in personality and attitude measures, particularly in those that measure narrow-bandwidth dimensions. At the structural level, these dependencies can be modeled by using extended factor analytic (FA) solutions that include correlated residuals. However, the effects that LIDs have on the…

Item-level fit analysis not only serves as a complementary check to global fit analysis, it is also essential in scale development because the fit results will guide item revision and/or deletion (Liu & Maydeu-Olivares, 2014). During data collection, missing response data may likely happen due to various reasons. Chi-square-based item fit…

The current study aims to evaluate the performance of three non-IRT procedures (i.e., normal approximation, Livingston-Lewis, and compound multinomial) for estimating classification indices when the observed score distribution shows atypical patterns: (a) bimodality, (b) structural (i.e., systematic) bumpiness, or (c) structural zeros (i.e., no…

A log-linear model (LLM) is a well-known statistical method to examine the relationship among categorical variables. This study investigated the performance of LLM in detecting differential item functioning (DIF) for polytomously scored items via simulations where various sample sizes, ability mean differences (impact), and DIF types were…

There has been some research in the use of propensity scores in the context of measurement error in the confounding variables; one recommended method is to generate estimates of the mis-measured covariate using a latent variable model, and to use those estimates (i.e., factor scores) in place of the covariate. I describe a simulation study…

Violations of normality and homogeneity are common in educational data. When this occurs, the use of parametric statistics may be inappropriate. A generalized form of nonparametric analyses based on the Puri and Sen L statistic provides an alternative approach. Using a chi-square distribution, this technique is easy to apply and has significant…

Linking score scales across different tests is considered speculative and fraught, even at the aggregate level (Feuer et al., 1999; Thissen, 2007). We introduce and illustrate validation methods for aggregate linkages, using the challenge of linking U.S. school district average test scores across states as a motivating example. We show that…

More robust and rigorous psychometric models, such as multidimensional Item Response Theory models, have been advocated for survey applications. However, item responses may be influenced by construct-irrelevant variance factors such as preferences for extreme response options. Through empirical and simulation methods, this study evaluates the use…

Precision is a key facet of test development, with score reliability determined primarily according to the types of error one wants to approximate and demonstrate. This article identifies and discusses several primary forms of reliability estimation: internal consistency (i.e., split-half, KR-20, a), test-retest, alternate forms, interscorer, and…

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…

In this paper, we present a flexible full-information approach to modeling multiple userdefined response styles across multiple constructs of interest. The model is based on a novel parameterization of the multidimensional nominal response model that separates estimation of overall item slopes from the scoring functions (indicating the order of…

The Mantel-Haenszel (MH) procedure is commonly used to detect items that function differentially for groups of examinees from various demographic and linguistic backgrounds--for example, in international assessments. As in some other DIF methods, the total score is used to match examinees on ability. In thin matching, each of the total score…