A simulation study compared the performance of robust normal theory maximum likelihood (ML) and robust categorical least squares (cat-LS) methodology for estimating confirmatory factor analysis models with ordinal variables. Data were generated from 2 models with 2-7 categories, 4 sample sizes, 2 latent distributions, and 5 patterns of category…

Re-parameterized regression models may enable tests of crucial theoretical predictions involving interactive effects of predictors that cannot be tested directly using standard approaches. First, we present a re-parameterized regression model for the Linear x Linear interaction of 2 quantitative predictors that yields point and interval estimates…

In multilevel modeling, one often distinguishes between macro-micro and micro-macro situations. In a macro-micro multilevel situation, a dependent variable measured at the lower level is predicted or explained by variables measured at that lower or a higher level. In a micro-macro multilevel situation, a dependent variable defined at the higher…

In a well-designed experiment, random assignment of participants to treatments makes causal inference straightforward. However, if participants are not randomized (as in observational study, quasi-experiment, or nonequivalent control-group designs), group comparisons may be biased by confounders that influence both the outcome and the alleged…

Researchers often have one or more theories or expectations with respect to the outcome of their empirical research. When researchers talk about the expected relations between variables if a certain theory is correct, their statements are often in terms of one or more parameters expected to be larger or smaller than one or more other parameters.…

Uncorrectable skew and heteroscedasticity are among the "lemons" of psychological data, yet many important variables naturally exhibit these properties. For scales with a lower and upper bound, a suitable candidate for models is the beta distribution, which is very flexible and models skew quite well. The authors present…

It is well-known that for normally distributed errors parametric tests are optimal statistically, but perhaps less well-known is that when normality does not hold, nonparametric tests frequently possess greater statistical power than parametric tests, while controlling Type I error rate. However, the use of nonparametric procedures has been…

Often quantitative data in the social sciences have only ordinal justification. Problems of interpretation can arise when least squares multiple regression (LSMR) is used with ordinal data. Two ordinal alternatives are discussed, dominance-based ordinal multiple regression (DOMR) and proportional odds multiple regression. The Q[superscript 2]…