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…

In latent growth curve modeling (LGCM), overall fit indices have garnered increased disputation for model selection, and model fit evaluation based on the mean structure has becoming popularity. The present study developed a versatile fit index, named Weighted Root Mean Squared Errors (WRMSE), based on individual case residuals (ICRs) with the aim…

Ethnoracial identity refers to the racial and ethnic categories that people use to classify themselves and others. How it is measured in surveys has implications for understanding inequalities. Yet how people self-identify may not conform to the categories standardized survey questions use to measure ethnicity and race, leading to potential…

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…

This study examined the false positive (FP) rates and sensitivity of Bayesian fit indices to structural misspecification in Bayesian structural equation modeling. The impact of measurement quality, sample size, model size, the magnitude of misspecified path effect, and the choice or prior on the performance of the fit indices was also…

The p-factor is a construct that is thought to explain and maybe even cause variation in all forms of psychopathology. Since its 'discovery' in 2012, hundreds of studies have been dedicated to the extraction and validation of statistical instantiations of the p-factor, called general factors of psychopathology. In this Perspective, we outline five…

The Q-matrix played a key role in implementations of diagnostic classification models (DCMs) or cognitive diagnostic models (CDMs) -- a family of psychometric models that are gaining attention in providing diagnostic information on students' mastery of cognitive attributes or skills. Using two Monte Carlo simulation studies, this dissertation…

Measurement error affects the quality of population orderings of an index and, hence, increases the misclassification of the poor and the non-poor groups and affects statistical inferences from binary regression models. Hence, the conclusions about the extent, profile, and distribution of poverty are likely to be misleading. However, the size and…

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…

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…

Classification measures and entropy variants can be used as indicators of model fit for logistic regression. These measures rely on a cut-point, "c," to determine predicted group membership. While recommendations exist for determining the location of the cut-point, these methods are primarily anecdotal. The current study used Monte Carlo…

The application of diagnostic classification models (DCMs) in the field of educational measurement is getting more attention in recent years. To make a valid inference from the model, it is important to ensure that the model fits the data. The purpose of the present study was to investigate the performance of the limited information…

Researchers are often reluctant to rely on classification rates because a model with favorable classification rates but poor separation may not replicate well. In comparison, entropy captures information about borderline cases unlikely to generalize to the population. In logistic regression, the correctness of predicted group membership is known,…

Measures of agreement are compared to measures of prediction accuracy within a general context. Differences in appropriate use are emphasized, and approaches are examined for both numerical and nominal variables. General estimation methods are developed, and their large-sample properties are compared.

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…