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…

Computer-based and web-based testing have become increasingly popular in recent years. Their popularity has dramatically expanded the availability of response time data. Compared to the conventional item response data that are often dichotomous or polytomous, response time has the advantage of being continuous and can be collected in an…

The unstructured multiple-attempt (MA) item response data in virtual learning environments (VLEs) are often from student-selected assessment data sets, which include missing data, single-attempt responses, multiple-attempt responses, and unknown growth ability across attempts, leading to a complex and complicated scenario for using this kind of…

Student assessment nonparticipation (or opt out) has increased substantially in K-12 schools in states across the country. This increase in opt out has the potential to impact achievement and growth (or value-added) measures used for educator and institutional accountability. In this simulation study, we investigated the extent to which…

To date, small sample problems with latent growth models (LGMs) have not received the amount of attention in the literature as related mixed-effect models (MEMs). Although many models can be interchangeably framed as a LGM or a MEM, LGMs uniquely provide criteria to assess global data-model fit. However, previous studies have demonstrated poor…

A new variant of the iterative "data = fit + residual" data-analytical approach described by Mosteller and Tukey is proposed and implemented in the context of item response theory psychometric models. Posterior probabilities from a Bayesian mixture model of a Rasch item response theory model and an unscalable latent class are expressed…

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…

A challenge associated with traditional mixture regression models (MRMs), which rest on the assumption of normally distributed errors, is determining the number of unobserved groups. Specifically, even slight deviations from normality can lead to the detection of spurious classes. The current work aims to (a) examine how sensitive the commonly…

Conventional differential item functioning (DIF) detection methods (e.g., the Mantel-Haenszel test) can be used to detect DIF only across observed groups, such as gender or ethnicity. However, research has found that DIF is not typically fully explained by an observed variable. True sources of DIF may include unobserved, latent variables, such as…

Under the No Child Left Behind Act, large-scale test score trend analyses are widespread. These analyses often gloss over interesting changes in test score distributions and involve unrealistic assumptions. Further complications arise from analyses of unanchored, censored assessment data, or proportions of students lying within performance levels…

For the past 25 years, methodological advances have been made in missing data treatment. Most published work has focused on missing data in dependent variables under various conditions. The present study seeks to fill the void by comparing two approaches for handling missing data in categorical covariates in logistic regression: the…

Properties of the Spearman correction for attenuation were investigated using Monte Carlo methods, under conditions where correlations between error scores exist as a population parameter and also where correlated errors arise by chance in random sampling. Equations allowing for all possible dependence among true and error scores on two tests at…

Studied the problem of missing data at the second level of a two-level hierarchal data structure using data generated to simulate the 1982 High School and Beyond data set with five different missing data treatments: listwise deletion, overall mean substitution, group mean substitution, the EM algorithm, and multiple imputation. (SLD)

One theoretical feature that makes item response theory (IRT) models those of choice for many psychometric data analysts is parameter invariance, the equality of item and examinee parameters from different examinee populations or measurement conditions. In this article, using the well-known fact that item and examinee parameters are identical only…

Response bias has long been recognized as an issue in the behavioral and social sciences, especially in cross-cultural research. Transforming raw data into ipsatized data, individual scores subject to a constant sum constraint, is proposed to be an effective measure to minimize response bias. One major problem of applying ipsatized data is that…