The problems of hypothesis testing and interval estimation of the squared multiple correlation coefficient of a multivariate normal distribution are considered. It is shown that available one-sided tests are uniformly most powerful, and the one-sided confidence intervals are uniformly most accurate. An exact method of calculating sample size to…

Describes the implementation of a standard Pearson chi-square statistic to test the null hypothesis of bivariate normality for latent variables in the Type I censored model. Assesses the behavior of the statistic through simulation and illustrates the statistic through an empirical example. Discusses limitations of the test. (Author/SLD)

A Monte Carlo study extended the research of MacKinnon, Lockwood, Hoffman, West, and Sheets (2002) for single-level designs by examining the statistical performance of four methods to test for mediation in a multilevel experimental design. The design studied was a two-group experiment that was replicated across several sites, included a single…

In multigroup covariance structure analysis with structured means, the traditional latent selection model is formulated as a special case of phenotypic selection. Illustrations with real and simulated data demonstrate how one can test specific hypotheses concerning selection on latent variables. (SLD)

Criteria for factor identification in factor analysis according to J. Algina (1980) are summarized, and a procedure is presented to determine rotationally underidentified factors by adding restrictors and to carry out the rotation for old and new restrictions and in latent path analysis. Two illustrations are presented. (SLD)

How log-linear models for multiwave longitudinal data can be used to test hypotheses relating to stagelike relationships between variables is demonstrated using data from research on adolescent cigarette and marijuana experimentation. Results with 2,658 adolescents show that the multiwave analyses allow the testing of several hypotheses. (SLD)

This article presents a didactic discussion on the role of asymptotically independent test statistics and separable hypotheses as they pertain to issues of specification error, power, and model misspecification in the covariance structure modeling framework. A small population study supports the major findings. (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.…

MAXCOV-HITMAX was invented by Paul Meehl as a tool for the detection of latent taxonic structures (i.e., structures in which the latent variable, u, is not continuously, but rather Bernoulli, distributed). It involves the examination of the shape of a certain conditional covariance function and is based on Meehl's claims that (R1) Taxonic…

A strategy for evaluating/modifying covariance structure models (CSMs) is presented. The approach uses recent developments in estimation under nonstandard conditions and unified asymptotic theory related to hypothesis testing, and it determines the extent of sample size sensitivity and specification error effects by relying on existing statistical…

The empirical performance under null/alternative hypotheses of the likelihood ratio difference test (LRDT); Lagrange Multiplier test (evaluating the impact of model modification with a specific model); and Wald test (using a general model) were compared. The new tests for covariance structure analysis performed as well as did the LRDT. (RLC)

Alternative tests are presented for the between-by-within interaction null hypothesis and for two within-subjects main effects null hypothesis in a split plot design. Estimated Type I error rates for the interaction tests and for several tests of the second null hypothesis are reported. (SLD)

Multivariate permutation tests are described, and some are suggested as substitutions for Hotelling's one-sample T2 test in common situations in behavioral science research. A Monte Carlo study shows advantages of these tests when the T2 test fails or is suspect. (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)

Many important research hypotheses concern conditional relations in which the effect of one predictor varies with the value of another. Such relations are commonly evaluated as multiplicative interactions and can be tested in both fixed-and random-effects regression. Often, these interactive effects must be further probed to fully explicate the…