Testing Process Factor Analysis Models Using the Parametric Bootstrap.

Process factor analysis (PFA) is a latent variable model for intensive longitudinal data. It combines P-technique factor analysis and time series analysis. The goodness-of-fit test in PFA is currently unavailable.

Multiple Local Solutions and Geomin Rotation.

In exploratory factor analysis, factor rotation is conducted to improve model interpretability. A promising and increasingly popular factor rotation method is geomin rotation. Geomin rotation, however, frequently encounters multiple local solutions.

Empirically Corrected Rescaled Statistics for SEM with Small N and Large p.

Survey data often contain many variables. Structural equation modeling (SEM) is commonly used in analyzing such data. With typical nonnormally distributed data in practice, a rescaled statistic T proposed by Satorra and Bentler was recommended in the literature of SEM.

Robust Methods for Moderation Analysis with a Two-Level Regression Model.

Moderation analysis has many applications in social sciences. Most widely used estimation methods for moderation analysis assume that errors are normally distributed and homoscedastic. When these assumptions are not met, the results from a classical moderation analysis can be misleading.

A Bayesian Power Analysis Procedure Considering Uncertainty in Effect Size Estimates from a Meta-analysis.

In conventional frequentist power analysis, one often uses an effect size estimate, treats it as if it were the true value, and ignores uncertainty in the effect size estimate for the analysis. The resulting sample sizes can vary dramatically depending on the chosen effect size value. To resolve the problem, we propose a hybrid Bayesian power analysis procedure that models uncertainty in the effect size estimates from a meta-analysis.

Estimating Standard Errors in Exploratory Factor Analysis.

The article describes 6 issues influencing standard errors in exploratory factor analysis and reviews 7 methods of computing standard errors for rotated factor loadings and factor correlations. These 7 methods are the augmented information method, the nonparametric bootstrap method, the infinitesimal jackknife method, the method using the asymptotic distributions of unrotated factor loadings, the sandwich method, the parametric bootstrap method, and the jackknife method. Standard error estimates are illustrated using a personality study with 537 men and an intelligence study with 145 children.

A Comparison of the Cross-Sectional and Sequential Designs when Assessing Longitudinal Mediation.

Mediational studies are often of interest in psychology because they explore the underlying relationship between 2 constructs. Previous research has shown that cross-sectional designs are prone to biased estimates of longitudinal mediation parameters. The sequential design has become a popular alternative to the cross-sectional design for assessing mediation.

Investigating Reliabilities of Intraindividual Variability Indicators.

Reliabilities of the two most widely used intraindividual variability indicators, ISD (2) and ISD, are derived analytically. Both are functions of the sizes of the first and second moments of true intraindividual variability, the size of the measurement error variance, and the number of assessments within a burst. For comparison, the reliability of the intraindividual mean, [Formula: see text], is also derived.

Diagnostics of Robust Growth Curve Modeling Using Student's t Distribution.

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 are proposed and evaluated. The methods include (a) distribution checking based on individual growth curve analysis; (b) distribution comparison based on Deviance Information Criterion, and (c) post hoc checking of degrees of freedom estimates for t distributions.

Ordinary Least Squares Estimation of Parameters in Exploratory Factor Analysis With Ordinal Data.

Exploratory factor analysis (EFA) is often conducted with ordinal data (e.g., items with 5-point responses) in the social and behavioral sciences.

Abstract: Sample Size Planning for Latent Curve Models.

When designing a study that uses structural equation modeling (SEM), an important task is to decide an appropriate sample size. Historically, this task is approached from the power analytic perspective, where the goal is to obtain sufficient power to reject a false null hypothesis. However, hypothesis testing only tells if a population effect is zero and fails to address the question about the population effect size.

Bias in Cross-Sectional Analyses of Longitudinal Mediation: Partial and Complete Mediation Under an Autoregressive Model.

Maxwell and Cole (2007) showed that cross-sectional approaches to mediation typically generate substantially biased estimates of longitudinal parameters in the special case of complete mediation. However, their results did not apply to the more typical case of partial mediation. We extend their previous work by showing that substantial bias can also occur with partial mediation.

Accuracy in Parameter Estimation for the Root Mean Square Error of Approximation: Sample Size Planning for Narrow Confidence Intervals.

The root mean square error of approximation (RMSEA) is one of the most widely reported measures of misfit/fit in applications of structural equation modeling. When the RMSEA is of interest, so too should be the accompanying confidence interval. A narrow confidence interval reveals that the plausible parameter values are confined to a relatively small range at the specified level of confidence.

Bootstrap Standard Error Estimates in Dynamic Factor Analysis.

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 interdependence of successive observations. Bootstrap methods can fill this need, however.

Bootstrap Confidence Intervals for Ordinary Least Squares Factor Loadings and Correlations in Exploratory Factor Analysis.

This article is concerned with using the bootstrap to assign confidence intervals for rotated factor loadings and factor correlations in ordinary least squares exploratory factor analysis. Coverage performances of SE-based intervals, percentile intervals, bias-corrected percentile intervals, bias-corrected accelerated percentile intervals, and hybrid intervals are explored using simulation studies involving different sample sizes, perfect and imperfect models, and normal and elliptical data. The bootstrap confidence intervals are also illustrated using a personality data set of 537 Chinese men.

Local Influence and Robust Procedures for Mediation Analysis.

Existing studies of mediation models have been limited to normal-theory maximum likelihood (ML). Because real data in the social and behavioral sciences are seldom normally distributed and often contain outliers, classical methods generally lead to inefficient or biased parameter estimates. Consequently, the conclusions from a mediation analysis can be misleading.

Abstract: Local Influence and Robust Methods for Mediation Models.

Mediation analysis investigates how certain variables mediate the effect of predictors on outcome variables. Existing studies of mediation models have been limited to normal theory maximum likelihood (ML) or least squares with normally distributed data. Because real data in the social and behavioral sciences are seldom normally distributed and often contain outliers, classical methods can result in biased and inefficient estimates, which lead to inaccurate or unreliable test of the meditated effect.

Abstract: A Comparison of the Factor Mixture Model and Taxometric Procedures.

Taxometric procedures and the Factor Mixture Model (FMM) have a complimentary set of strengths and weaknesses. Both approaches purport to detect evidence of a latent class structure. Taxometric procedures, popular in psychiatric and psychopathology literature, make no assumptions beyond those needed to compute means and covariances.