Two bootstrap tests are proposed to test the independence hypothesis in a two-way cross table. Monte Carlo studies are used to compare the traditional asymptotic test with these bootstrap methods, and the bootstrap methods are found superior in two ways: control of Type I error and statistical power. (SLD)

Simulated data for factor analytic models is used in the evaluation of three methods for controlling Type I errors: (1) the standard approach that involves testing each parameter at the 0.05 level; (2) the Bonferroni approach; and (3) a simultaneous test procedure (STP). Advantages offered by the Bonferroni approach are discussed. (SLD)

Whether "more is ever too much" for the number of indicators per factor in confirmatory factor analysis was studied by varying sample size and indicators per factor in 35,000 Monte Carlo solutions. Results suggest that traditional rules calling for fewer indicators for smaller sample size may be inappropriate. (SLD)

Studied the relationship between internal test bias and regression slope differences. Monte Carlo simulation results indicate a strong relationship between internal test bias and slope differences, but this relationship does not imply that an absence of internal test bias leads to slope invariance or that slope differences imply internal test…

This article illustrates the use of the SAS system for Monte Carlo simulation work in structural equation modeling (SEM). Data generation procedures for both multivariate normal and nonnormal conditions are discussed, and relevant SAS codes for implementing these procedures are presented. A hypothetical example is presented in which Monte Carlo…

Rasch proposed an exact conditional inference approach to testing his model but never implemented it because it involves the calculation of a complicated probability. This paper furthers Rasch's approach by (1) providing an efficient Monte Carlo methodology for accurately approximating the required probability and (2) illustrating the usefulness…

In this article we analyze the dynamics of endowment spending and real endowment values using rules that tie endowment spending to inflation. Numerical examples demonstrate that under a pure inflation rule, spending rates tend to drift away over time from the appropriate rate, leading to either rising or falling real endowment values. Under a…

The purpose of this study was to investigate and compare the performance of a stepwise variable selection algorithm to traditional exploratory factor analysis. The Monte Carlo study included six factors in the design; the number of common factors; the number of variables explained by the common factors; the magnitude of factor loadings; the number…

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…

Many statistical tests are designed to test the different assumptions of the Rasch model, but only few are directed at detecting multidimensionality. The Martin-Lof test is an attractive approach, the disadvantage being that its null distribution deviates strongly from the asymptotic chi-square distribution for most realistic sample sizes. A Monte…

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…