Growth curve models with different types of distributions of random effects and of intraindividual measurement errors for robust analysis are compared. After demonstrating the influence of distribution specification on parameter estimation, 3 methods for diagnosing the distributions for both random effects and intraindividual measurement errors…

Goodness-of-fit testing in factor analysis is based on the assumption that the test statistic is asymptotically chi-square, but this property may not hold in small samples even when the factors and errors are normally distributed in the population. Robust methods such as Browne's (1984) asymptotically distribution-free method and Satorra Bentler's…

This article addresses modeling oscillation in continuous time. It criticizes Steele and Ferrer's article "Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes" (2011), particularly the approximate estimation procedure applied. This procedure is the latent version of the local linear approximation procedure…

A common finding in studies of differential prediction across groups is that although regression slopes are the same or similar across groups, group differences exist in regression intercepts. Building on earlier work by Birnbaum (1979), Millsap (1998) presented an invariant factor model that would explain such intercept differences as arising due…

Researchers are increasingly using observational or nonrandomized data to estimate causal treatment effects. Essential to the production of high-quality evidence is the ability to reduce or minimize the confounding that frequently occurs in observational studies. When using the potential outcome framework to define causal treatment effects, one…

Previous studies of different methods of testing mediation models have consistently found two anomalous results. The first result is elevated Type I error rates for the bias-corrected and accelerated bias-corrected bootstrap tests not found in nonresampling tests or in resampling tests that did not include a bias correction. This is of special…

This article presents our response to Oud and Folmer's "Modeling Oscillation, Approximately or Exactly?" (2011), which criticizes aspects of our article, "Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes" (2011). In this response, we present a conceptual explanation of the derivative-based estimation…

Exploratory factor analysis (EFA) is often conducted with ordinal data (e.g., items with 5-point responses) in the social and behavioral sciences. These ordinal variables are often treated as if they were continuous in practice. An alternative strategy is to assume that a normally distributed continuous variable underlies each ordinal variable.…

We examine emotion self-regulation and coregulation in romantic couples using daily self-reports of positive and negative affect. We fit these data using a damped linear oscillator model specified as a latent differential equation to investigate affect dynamics at the individual level and coupled influences for the 2 partners in each couple.…

A method for selecting between K-dimensional linear factor models and (K + 1)-class latent profile models is proposed. In particular, it is shown that the conditional covariances of observed variables are constant under factor models but nonlinear functions of the conditioning variable under latent profile models. The performance of a convenient…

Theoretical models specifying indirect or mediated effects are common in the social sciences. An indirect effect exists when an independent variable's influence on the dependent variable is mediated through an intervening variable. Classic approaches to assessing such mediational hypotheses (Baron & Kenny, 1986; Sobel, 1982) have in recent years…

Dynamic factor analysis summarizes changes in scores on a battery of manifest variables over repeated measurements in terms of a time series in a substantially smaller number of latent factors. Algebraic formulae for standard errors of parameter estimates are more difficult to obtain than in the usual intersubject factor analysis because of the…

This article uses meta-analyses published in "Psychological Bulletin" from 1995 to 2005 to describe meta-analyses in psychology, including examination of statistical power, Type I errors resulting from multiple comparisons, and model choice. Retrospective power estimates indicated that univariate categorical and continuous moderators, individual…

Maxwell, Cole, and Mitchell (2011) demonstrated that simple structural equation models, when used with cross-sectional data, generally produce biased estimates of meditated effects. I extend those results by showing how simple structural equation models can produce biased estimates of meditated effects when used even with longitudinal data. Even…

The comparative format used in ranking and paired comparisons tasks can significantly reduce the impact of uniform response biases typically associated with rating scales. Thurstone's (1927, 1931) model provides a powerful framework for modeling comparative data such as paired comparisons and rankings. Although Thurstonian models are generally…