DETECT is a nonparametric "full" dimensionality assessment procedure that clusters dichotomously scored items into dimensions and provides a DETECT index of magnitude of multidimensionality. Four factors (test length, sample size, item response theory [IRT] model, and DETECT index) were manipulated in a Monte Carlo study of bias, standard error,…

Generalized Structured Component Analysis (GSCA) was recently introduced by Hwang and Takane (2004) as a component-based approach to path analysis with latent variables. The parameters of GSCA are estimated by pooling data across respondents under the implicit assumption that they all come from a single, homogenous group. However, as has been…

Mixture modeling is a widely applied data analysis technique used to identify unobserved heterogeneity in a population. Despite mixture models' usefulness in practice, one unresolved issue in the application of mixture models is that there is not one commonly accepted statistical indicator for deciding on the number of classes in a study…

This Monte Carlo study examined the impact of misspecifying the [big sum] matrix in longitudinal data analysis under both the multilevel model and mixed model frameworks. Under the multilevel model approach, under-specification and general-misspecification of the [big sum] matrix usually resulted in overestimation of the variances of the random…

This paper develops a model for longitudinal student achievement data designed to estimate heterogeneity in teacher effects across students of different achievement levels. The model specifies interactions between teacher effects and students' predicted scores on a test, estimating both average effects of individual teachers and interaction terms…

In meta-analysis, it is common to have dependent effect sizes, such as several effect sizes from the same sample but measured at different times. Cheung and Chan proposed the adjusted-individual and adjusted-weighted procedures to estimate the degree of dependence and incorporate this estimate in the meta-analysis. The present study extends the…

Covariance and correlation structure analytic techniques can be used to test whether a specified correlation structure is an adequate model of the population correlation structure. These procedures include: (1) normal theory (NT) and asymptotically distribution free (ADF) covariance structure analysis techniques; and (2) NT and ADF correlation…

A procedure proposed by H. F. Kaiser (1968) for averaging coefficients using the first eigenvalue of an intercorrelation matrix was studied via Monte Carlo methods. The study also assessed a modification of the Kaiser procedure and the use of Fisher's "z." Applications to sample size effects are discussed. (TJH)

While violation of the homogeneity of variance assumption has received considerable attention, violation of the assumption of normally distributed data has not received as much attention. As a result, researchers may have the mistaken impression that as long as the assumptions of independence of observations and homogeneity of variance are…

A likelihood ratio test, using Monte Carlo methods, is conducted to determine the number of classes appropriate to a certain data set when applying latent class analysis. Results confirm that the usually assumed null distribution is inappropriate. (TJH)

Two Monte Carlo studies investigated the effects of within-group covariance structure on subgroup recovery by 10 hierarchical clustering methods using 100 bivariate observations from 2 subgroups. Superior recovery was associated with within-group correlation that matched the direction of subgroup separation. (SLD)

Studied Type I error rates and relative power of structural means, multiple-indicator, multiple-cause, and multivariate analysis of variance approaches for testing construct mean differences within a one-factor, two-group design. Used Monte Carlo methods to investigate Type I error rates and a population analysis approach to study the power of…

An approach called generalizability in item response modeling (GIRM) is introduced in this article. The GIRM approach essentially incorporates the sampling model of generalizability theory (GT) into the scaling model of item response theory (IRT) by making distributional assumptions about the relevant measurement facets. By specifying a random…

This article describes several methods from discrete mathematics used to simulate and solve an interesting problem occurring at a holiday gift exchange. What is the probability that two people will select each other's names in a random drawing, and how does this result vary with the total number of participants? (Contains 5 figures.)