A theorem is presented that describes conditions under which measurement invariance is consistent with predictive invariance for the linear case. These two forms of invariance are shown to be inconsistent under realistic conditions, and the duality is illustrated with simulated data. Implications for group differences research are discussed. (SLD)

The analysis of contingency tables via set correlation allows the assessment of subhypotheses involving contrast functions of the categories of the nominal scales. The robustness of such methods with regard to Type I error and statistical power was studied via a Monte Carlo experiment. (TJH)

Effects of overextracting factors and components within and between maximum likelihood factor analysis and principal components analysis were examined through computer simulation of a range of factor and component patterns. Results demonstrate similarity of component and factor scores during overextraction. Overall, results indicate that…

In this simulation study, we investigate the power and Type I error rate of a procedure based on the mean and covariance structure analysis (MACS) model in detecting differential item functioning (DIF) of graded response items with five response categories. The following factors were manipulated: type of DIF (uniform and non-uniform), DIF…

Cross-classified random effects modeling (CCREM) is used to model multilevel data from nonhierarchical contexts. These models are widely discussed but infrequently used in social science research. Because little research exists assessing when it is necessary to use CCREM, 2 studies were conducted. A real data set with a cross-classified structure…

The present study compares the performance of phi coefficients and tetrachorics along two dimensions of factor recovery in binary data. These dimensions are (1) accuracy of nontrivial factor identifications; and (2) factor structure recovery given a priori knowledge of the correct number of factors to rotate. (Author/LMO)

The utility of the three-form design coupled with maximum likelihood methods for estimation of missing values was evaluated. Simulation studies demonstrate that maximum likelihood estimation and multiple imputation methods produce the most efficient and least biased estimates of variances and covariances for normally distributed and slightly…

Examined several hypotheses about the suitability of the noncentral chi square in applied research using Monte Carlo simulation experiments with seven sample sizes and three distinct model types, each with five specifications. Results show that, in general, for models with small to moderate misspecification, the noncentral chi-square is well…

Procedures for implementing parallel analysis (PA) criteria in practice were compared, examining regression equation methods that can be used to estimate random data eigenvalues from known values of the sample size and number of variables. More internally accurate methods for determining PA criteria are presented. (SLD)

It is suggested that using an unbiased estimate of the weight matrix may eliminate the small or intermediate sample size bias of the asymptotically distribution-free (ADF) test statistic. Results of simulations show that test statistics based on the biased estimator or the unbiased estimate are highly similar. (SLD)

Analytical solutions for point and variance estimators of the mediated effect, the ratio of mediated to direct effect, and the proportion of the total effect mediated were determined through simulation for different samples. The sample sizes needed for accuracy and stability are discussed with implications for mediated effects estimates. (SLD)

Five methods for testing the hypothesis of independence between two sets of variates were compared through simulation. Results indicate that two new methods, based on robust measures reflecting the linear association between two random variables, provide reasonably accurate control over Type I errors. Drawbacks to rank-based methods are discussed.…

Using a Monte Carlo simulation, a bootstrap procedure was evaluated for setting a confidence interval on the unrestricted population correlation (rho) assuming various degrees of incomplete truncation on the predictor. Sample size was the most important factor in determining accuracy and stability. Sample size should be at least 50. (SLD)

The likelihood ratio test statistic G[squared](dif) is widely used for comparing the fit of nested models in categorical data analysis. In large samples, this statistic is distributed as a chi-square with degrees of freedom equal to the difference in degrees of freedom between the tested models, but only if the least restrictive model is correctly…

Numerous studies have shown increasing item reliabilities as an effect of the item position in personality scales. Traditionally, these context effects are analyzed based on item-total correlations. This approach neglects that trends in item reliabilities can be caused either by an increase in true score variance or by a decrease in error…