The multidimensional mixture data structure exists in many test (or inventory) conditions. Heterogeneity also relatively exists in populations. Still, some researchers are interested in deciding to which subpopulation a participant belongs according to the participant's factor pattern. Thus, in this study, we proposed three analysis procedures…

Words read correctly per minute (WCPM) is the reporting score metric in oral reading fluency (ORF) assessments, which is popularly utilized as part of curriculum-based measurements to screen at-risk readers and to monitor progress of students who receive interventions. Just like other types of assessments with multiple forms, equating would be…

Multiple imputation (MI) is one of the recommended techniques for handling missing data in ordinal factor analysis models. However, methods for computing MI-based fit indices under ordinal factor analysis models have yet to be developed. In this short note, we introduced the methods of using the standardized root mean squared residual (SRMR) and…

When scores are used to make decisions about respondents, it is of interest to estimate classification accuracy (CA), the probability of making a correct decision, and classification consistency (CC), the probability of making the same decision across two parallel administrations of the measure. Model-based estimates of CA and CC computed from the…

Equating is a statistical procedure used to adjust for the difference in form difficulty such that scores on those forms can be used and interpreted comparably. In practice, however, equating methods are often implemented without considering the extent to which two forms differ in difficulty. The study aims to examine the effect of the magnitude…

Recent approaches to the detection of cheaters in tests employ detectors from the field of machine learning. Detectors based on supervised learning algorithms achieve high accuracy but require labeled data sets with identified cheaters for training. Labeled data sets are usually not available at an early stage of the assessment period. In this…

For large-scale assessments, data are often collected with missing responses. Despite the wide use of item response theory (IRT) in many testing programs, however, the existing literature offers little insight into the effectiveness of various approaches to handling missing responses in the context of scale linking. Scale linking is commonly used…

We develop a "latent variable forest" (LV Forest) algorithm for the estimation of latent variable scores with one or more latent variables. LV Forest estimates unbiased latent variable scores based on "confirmatory factor analysis" (CFA) models with ordinal and/or numerical response variables. Through parametric model…

Identifying items with differential item functioning (DIF) in an assessment is a crucial step for achieving equitable measurement. One critical issue that has not been fully addressed with existing studies is how DIF items can be detected when data are multilevel. In the present study, we introduced a Lord's Wald X[superscript 2] test-based…

The presence of rapid guessing (RG) presents a challenge to practitioners in obtaining accurate estimates of measurement properties and examinee ability. In response to this concern, researchers have utilized response times as a proxy of RG and have attempted to improve parameter estimation accuracy by filtering RG responses using popular scoring…

Multilevel structural equation models (MSEMs) are well suited for educational research because they accommodate complex systems involving latent variables in multilevel settings. Estimation using Croon's bias-corrected factor score (BCFS) path estimation has recently been extended to MSEMs and demonstrated promise with limited sample sizes. This…

Oftentimes in many fields of the social and natural sciences, data are obtained within a nested structure (e.g., students within schools). To effectively analyze data with such a structure, multilevel models are frequently employed. The present study utilizes a Monte Carlo simulation to compare several novel multilevel classification algorithms…

Despite the existence of many methods for determining the number of factors, none outperforms the others under every condition. This study compares traditional parallel analysis (TPA), revised parallel analysis (RPA), Kaiser's rule, minimum average partial, sequential X[superscript 2], and sequential root mean square error of approximation,…

Simulation studies involving mixture models inevitably aggregate parameter estimates and other output across numerous replications. A primary issue that arises in these methodological investigations is label switching. The current study compares several label switching corrections that are commonly used when dealing with mixture models. A growth…

Although parallel analysis has been found to be an accurate method for determining the number of factors in many conditions with complete data, its application under missing data is limited. The existing literature recommends that, after using an appropriate multiple imputation method, researchers either apply parallel analysis to every imputed…