In the article "Exploring the Sensitivity of Horn's Parallel Analysis to the Distributional Form of Random Data," Dinno (this issue) provides strong evidence that the distribution of random data does not have a significant influence on the outcome of the analysis. Hayton appreciates the thorough approach to evaluating this assumption, and agrees…

The noncentral chi-square approximation of the distribution of the likelihood ratio (LR) test statistic is a critical part of the methodology in structural equation modeling. Recently, it was argued by some authors that in certain situations normal distributions may give a better approximation of the distribution of the LR test statistic. The main…

Conducted simulations to explore methods for comparing bivariate distributions corresponding to two independent groups, all of which are based on Tukey's "depth," a generalization of the notion of ranks to multivariate data. Discusses steps needed to control Type I error. (SLD)

Meehl's taxometric method was developed to distinguish categorical and continuous constructs. However, taxometric output can be difficult to interpret because expected results for realistic data conditions and differing procedural implementations have not been derived analytically or studied through rigorous simulations. By applying bootstrap…

An alternative for analyzing responses to Likert Scales is proposed, using additive conjoint measurement. It assumes that subjects can report their attitudes toward stimuli in rank order. Neither within-subject nor between-subject distributional assumptions are made. Nevertheless, interval level stimulus values and response category boundaries are…

This paper illustrates an application of Efron's bootstrap to the repeated measures design. While this approach does not require parametric assumptions, it does utilize distributional information in the sample. By appropriately resampling from study data, the bootstrap may determine accurate sampling distributions for estimators, effects, or…

Mardia's measure of multivariate kurtosis has been implemented in many statistical packages commonly used by social scientists. It provides important information on whether a commonly used multivariate procedure is appropriate for inference. Many statistical packages also have options for missing data. However, there is no procedure for applying…

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…

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)

A method is presented that eliminates some interpretational limitations arising from assumptions implicit in the use of arbitrary rules of thumb to interpret exploratory factor analytic results. The bootstrap method is presented as a way of approximating sampling distributions of estimated factor loadings. Simulated datasets illustrate the…

Use of confirmatory factor analysis (CFA) with nonzero latent means in testing six different measurement models from classical test theory is discussed. Implications of the six models for observed mean and covariance structures are described, and three examples of the use of CFA in testing the models are presented. (SLD)

To assess problems in hypothesis testing and model comparisons based on normed indices caused by latent class models with sparse contingency tables, a simulation was carried out investigating the distributions of the likelihood ratio statistic, the Pearson statistic chi-square, and a new goodness of fit statistic. (SLD)

The general-information-theoretic approach was used to identify informational overlap and asymmetry between variables, using affective, cognitive, and behavioral measures. Using the chi-squared test, no significant differences were found in response rates, demographics, or patronage frequency of three stores between numerical (n=453) and graphic…