No abstract

Because of the importance of mediation studies, researchers have been continuously searching for the best statistical test for mediation effect. The approaches that have been most commonly employed include those that use zero-order and partial correlation, hierarchical regression models, and structural equation modeling (SEM). This study extends MacKinnon and colleagues (MacKinnon, Lockwood, Hoffmann, West, & Sheets, 2002; MacKinnon, Lockwood, & Williams, 2004, MacKinnon, Warsi, & Dwyer, 1995) works by conducting a simulation that examines the distribution of mediation and suppression effects of latent variables with SEM, and the properties of confidence intervals developed from eight different methods. Results show that SEM provides unbiased estimates of mediation and suppression effects, and that the bias-corrected bootstrap confidence intervals perform best in testing for mediation and suppression effects. Steps to implement the recommended procedures with Amos are presented.

Extreme response styles (ERS) and acquiescence response styles (ARS) may constitute important sources of cross-cultural differences on survey-type instruments. Differences in ERS and ARS, if undetected, may give rise to spurious results that do not reflect genuine differences in attitudes or perceptions. Multiple-group confirmatory factor analysis is recommended as the most effective method of testing for ERS and ARS and determining whether cultural groups can be meaningfully compared on the basis of factor (latent) means. A detailed numerical example is provided.

Many cross-cultural researchers are concerned with factorial invariance; that is, with whether or not members of different cultures associate survey items, or similar measures, with similar constructs. Researchers usually test items for factorial invariance using confirmatory factor analysis (CFA). CFA, however, poses certain problems that must be dealt with. Primary among them is standardization, the process that assigns units of measurement to the constructs (latent variables). Two standardization procedures and several minor variants have been reported in the literature, but using these procedures when testing for factorial invariance can lead to inaccurate results. In this paper we review basic theory, and propose an extension of Byrne, Shavelson, and Muthgn’s (1989) procedure for identifying non-invariant items. The extended procedure solves the standardization problem by performing a systematic comparison of all pairs of factor loadings across groups. A numerical example based upon a large published data set is presented to illustrate the utility of the new procedure, particularly with regard to partial factorial invariance.

This teaching note starts with a demonstration of a straightforward procedure using Mplus Version 6 to produce a bias-corrected (BC) bootstrap confidence interval for testing a specific mediation effect in a complex latent variable model. The procedure is extended to constructing a BC bootstrap confidence interval for the difference between two specific mediation effects. The extended procedure not only tells whether the strengths of any direct and mediation effects or any two specific mediation effects in a latent variable model are significantly different but also provides an estimate and a confidence interval for the difference. However, the Mplus procedures do not allow the estimation of a BC bootstrap confidence interval for the difference between two standardized mediation effects. This teaching note thus demonstrates the LISREL procedures for constructing BC confidence intervals for specific standardized mediation effects and for comparing two standardized mediation effects. Finally, procedures combining Mplus and PRELIS are demonstrated for constructing BC bootstrap confidence intervals for the difference between the between-part and within-part path coefficients in multilevel models and for examining models with interactions of latent variables.