Factor analysis models with ordinal indicators are often estimated using a 3-stage procedure where the last stage involves obtaining parameter estimates by least squares from the sample polychoric correlations. A simulation study involving 324 conditions (1,000 replications per condition) was performed to compare the performance of diagonally…

This study is a methodological-substantive synergy, demonstrating the power and flexibility of exploratory structural equation modeling (ESEM) methods that integrate confirmatory and exploratory factor analyses (CFA and EFA), as applied to substantively important questions based on multidimentional students' evaluations of university teaching…

We evaluated the statistical power of single-indicator latent growth curve models to detect individual differences in change (variances of latent slopes) as a function of sample size, number of longitudinal measurement occasions, and growth curve reliability. We recommend the 2 degree-of-freedom generalized test assessing loss of fit when both…

This study examined the efficacy of 4 different parceling methods for modeling categorical data with 2, 3, and 4 categories and with normal, moderately nonnormal, and severely nonnormal distributions. The parceling methods investigated were isolated parceling in which items were parceled with other items sharing the same source of variance, and…

Some authors have suggested that sample size in covariance structure modeling should be considered in the context of how many parameters are to be estimated (e.g., Kline, 2005). Previous research has examined the effect of varying sample size relative to the number of parameters being estimated (N:q). Although some support has been found for this…

Univariate latent growth modeling (LGM) of composites of multiple items (e.g., item means or sums) has been frequently used to analyze the growth of latent constructs. This study evaluated whether LGM of composites yields unbiased parameter estimates, standard errors, chi-square statistics, and adequate fit indexes. Furthermore, LGM was compared…

This article considers models involving a single structural equation with latent explanatory and/or latent dependent variables where discrete items are used to measure the latent variables. Our primary focus is the use of scores as proxies for the latent variables and carrying out ordinary least squares (OLS) regression on such scores to estimate…

A covariance structure modeling method to test equality in proportions explained variance in studied unobserved dimensions by means of latent predictors is outlined. The procedure is applicable with multiple-indicator, structural equation models where of interest is to compare the predictive power of sets of latent independent variables for given…

This study examined the extent of measurement invariance of the Basic Psychological Needs in Exercise Scale responses (BPNES; Vlachopoulos & Michailidou, 2006) across male (n = 716) and female (n = 1,147) exercise participants. BPNES responses from exercise participants attending private fitness centers (n = 1,012) and community exercise programs…

Confirmatory factor analytic (CFA) procedures can be used to provide evidence of measurement invariance. However, empirical evaluation has not focused on the accuracy of common CFA steps used to detect a lack of invariance across groups. This investigation examined procedures for detection of test structure differences across groups under several…

Structural equation modeling allows several methods of estimating the disattenuated association between 2 or more latent variables (i.e., the measurement model). In one common approach, measurement models are specified using item parcels as indicators of latent constructs. Item parcels versus original items are often used as indicators in these…

The goals of this article are twofold: (a) briefly highlight the merits of residual centering for representing interaction and powered terms in standard regression contexts (e.g., Lance, 1988), and (b) extend the residual centering procedure to represent latent variable interactions. The proposed method for representing latent variable…

This simulation study investigated the robustness of structural equation modeling to different degrees of nonnormality under 2 estimation methods, generalized least squares and maximum likelihood, and 4 sample sizes, 100, 250, 500, and 1,000. Each of the slight and severe nonnormality degrees was comprised of pure skewness, pure kurtosis, and both…

A simulation study was conducted to examine the effect of item parceling on confirmatory factor analysis parameter estimates and their standard errors at different levels of sample size, number of indicators per factor, size of factor structure/pattern coefficients, magnitude of interfactor correlations, and variations in item-level data…

Structural equation models are widely appreciated in social-psychological research and other behavioral research to model relations between latent constructs and manifest variables and to control for measurement error. Most applications of SEMs are based on fully observed continuous normal data and models with a linear structural equation.…