A two-level data set can be structured in either long format (LF) or wide format (WF), and both have corresponding SEM approaches for estimating multilevel models. Intuitively, one might expect these approaches to perform similarly. However, the two data formats yield data matrices with different numbers of columns and rows, and their "cols :…

For efficiency, Computerized Adaptive Test (CAT) algorithm selects items with the maximum information, typically with a 50% probability of being answered correctly. However, examinees may not be satisfied if they only correctly answer 50% of the items. Researchers discovered that changing the item selection algorithms to choose easier items (i.e.,…

Lagrange multiplier (LM) or score tests have seen renewed interest for the purpose of diagnosing misspecification in item response theory (IRT) models. LM tests can also be used to test whether parameters differ from a fixed value. We argue that the utility of LM tests depends on both the method used to compute the test and the degree of…

Multidimensional item response theory (MIRT) models use data from individual item responses to estimate multiple latent traits of interest, making them useful in educational and psychological measurement, among other areas. When MIRT models are applied in practice, it is not uncommon to see that some items are designed to measure all latent traits…

The purpose of this study was to explore the influence of the number of targets specified on the quality of exploratory factor analysis solutions with a complex underlying structure and incomplete substantive measurement theory. Three Monte Carlo studies were performed based on the ratio of the number of observed variables to the number of…

In Ramsay curve item response theory (RC-IRT) modeling, the shape of the latent trait distribution is estimated simultaneously with the item parameters. In its original implementation, RC-IRT is estimated via Bock and Aitkin's EM algorithm, which yields maximum marginal likelihood estimates. This method, however, does not produce the…

The design of research studies utilizing binary multilevel models must necessarily incorporate knowledge of multiple factors, including estimation method, variance component size, or number of predictors, in addition to sample sizes. This Monte Carlo study examined the performance of random effect binary outcome multilevel models under varying…

Previous research in cognitive diagnostic assessment (CDA) of L2 reading ability has been frequently conducted using large-scale English proficiency exams (e.g., TOEFL, MELAB). Using CDA, it is possible to analyze individual learners' strengths and weaknesses in multiple attributes (i.e., knowledge, skill, strategy) measured at the item level.…

The study utilised a fine-grained diagnostic checklist to assess first-year undergraduates in Hong Kong and evaluated its validity and usefulness for diagnosing academic writing in English. Ten English language instructors marked 472 academic essays with the checklist. They also agreed on a Q-matrix, which specified the relationships among the…

The p-median offers an alternative to centroid-based clustering algorithms for identifying unobserved categories. However, existing p-median formulations typically require data aggregation into a single proximity matrix, resulting in masked respondent heterogeneity. A proposed three-way formulation of the p-median problem explicitly considers…

Cognitive diagnostic analyses have been advocated as methods that allow an assessment to function as a formative assessment to inform instruction. To use this approach, it is necessary to first identify the skills required for each item in the test, known as a Q-matrix. However, because the construct being tested and the underlying cognitive…

Monte Carlo studies of several fixed-effects methods for combining and comparing correlation matrices have shown that two refinements improve estimation and inference substantially. With rare exception, however, these simulations have involved homogeneous data analyzed using conditional meta-analytic procedures. The present study builds on…

The purpose of this study was to examine the impact of misspecifying a growth mixture model (GMM) by assuming that Level-1 residual variances are constant across classes, when they do, in fact, vary in each subpopulation. Misspecification produced bias in the within-class growth trajectories and variance components, and estimates were…

A Monte Carlo investigation of Markov chain matrices was conducted to create empirical distributions for two statistics created from the transition matrices. Curve fitting techniques developed by Karl Pearson were used to deduce if theoretical equations could be fit to the two sets of distributions. The set of distributions which describe the…

To assess the effect on discriminant analysis in terms of correct classification into two groups, the following parameters were systematically altered using Monte Carlo techniques: sample sizes; proportions of one group to the other; number of independent variables; and covariance matrices. The pairing of the off diagonals (or covariances) with…