We present a bias-adjusted three-step estimation approach for multilevel latent class models (LC) with covariates. The proposed approach involves (1) fitting a single-level measurement model while ignoring the multilevel structure, (2) assigning units to latent classes, and (3) fitting the multilevel model with the covariates while controlling for…

Multiple imputation (MI) is a popular method for handling missing data. In education research, it can be challenging to use MI because the data often have a clustered structure that need to be accommodated during MI. Although much research has considered applications of MI in hierarchical data, little is known about its use in cross-classified…

When there are no personal consequences associated with test performance for examinees, rapid guessing (RG) is a concern and can differ between subgroups. To date, the impact of differential RG on item-level measurement invariance has received minimal attention. To that end, a simulation study was conducted to examine the robustness of the…

This study was conducted to analyze potential item parameter drift (IPD) impact on person ability estimates and classification accuracy when drift affects an examinee subgroup. Using a series of simulations, three factors were manipulated: (a) percentage of IPD items in the CAT exam, (b) percentage of examinees affected by IPD, and (c) item pool…

A valuable extension of the single-rating regression discontinuity design (RDD) is a multiple-rating RDD (MRRDD). To date, four main methods have been used to estimate average treatment effects at the multiple treatment frontiers of an MRRDD: the "surface" method, the "frontier" method, the "binding-score" method, and…

The multilevel latent class model (MLCM) is a multilevel extension of a latent class model (LCM) that is used to analyze nested structure data structure. The nonparametric version of an MLCM assumes a discrete latent variable at a higher-level nesting structure to account for the dependency among observations nested within a higher-level unit. In…

Survey data are often subject to various types of errors such as misclassification. In this article, we consider a model where interest is simultaneously in two correlated response variables and one is potentially subject to misclassification. A motivating example of a recent study of the impact of a sexual education course for adolescents is…

In education research, small samples are common because of financial limitations, logistical challenges, or exploratory studies. With small samples, statistical principles on which researchers rely do not hold, leading to trust issues with model estimates and possible replication issues when scaling up. Researchers are generally aware of such…

Given the importance of large-scale assessments to educational policy conversations, it is critical that subpopulation achievement is estimated reliably and with sufficient precision. Despite this importance, biased subpopulation estimates have been found to occur when variables in the conditioning model side of a latent regression model contain…

The Graded Response Model (GRM; Samejima, "Estimation of ability using a response pattern of graded scores," Psychometric Monograph No. 17, Richmond, VA: The Psychometric Society, 1969) can be derived by assuming a linear regression of a continuous variable, Z, on the trait, [theta], to underlie the ordinal item scores (Takane & de Leeuw in…

In multilevel modeling, group-level variables (L2) for assessing contextual effects are frequently generated by aggregating variables from a lower level (L1). A major problem of contextual analyses in the social sciences is that there is no error-free measurement of constructs. In the present article, 2 types of error occurring in multilevel data…

Rudner (2001, 2005) described an expected classification accuracy index for determining the asymptotic expectation of accuracy of classifications of examinees into score categories. This article expands on that exposition by evaluating the index as it is likely to be used in practice (as a point estimate of classification accuracy), provides a…

Cross-classified random effects modeling (CCREM) is used to model multilevel data from nonhierarchical contexts. These models are widely discussed but infrequently used in social science research. Because little research exists assessing when it is necessary to use CCREM, 2 studies were conducted. A real data set with a cross-classified structure…

Taxometric procedures provide an empirical means of determining which psychiatric disorders are typologically distinct from normal behavioral functioning. Although most disorders reflect extremes along continuously distributed behavioral traits, identifying those that are discrete has important implications for accurate diagnosis, effective…

Investigated the impact of categorization on confirmatory factor analysis parameter estimates, standard errors, and five ad hoc fit indexes through simulation studies. Results replicate some previous studies but also suggest that tests of parameter estimates will be underestimated and the amount of underestimation will increase as saturation…