The Effects of Parcels and Latent Variable Scores on the Detection of Interactions in Structural Equation Modeling
Numerous theories in the behavioral and organizational sciences involve the regression of an outcome variable on component terms and their product to evaluate interaction effects. There are numerous statistical difficulties with this multiple regression approach. The most serious is measurement error, requiring the use of structural equation modeling. Jöreskog and Yang (1996) described a nonlinear structural equation modeling procedure that incorporates mean structures in the covariance analysis. They demonstrated that only one indicator for the product term is necessary for model identification. Unfortunately, the Jöreskog-Yang procedure leads to biased estimates of the product coefficient. In this dissertation, I propose that (1) the proper use of item parcels can reduce bias in estimates, and (2) that using a relatively new technique of analysis (creation of latent variable scores) can also be fruitful in removing measurement error and improving the estimation of product terms. Two studies investigated these proposals. In Study 1, archival data were analyzed using the proposed techniques. The interaction hypothesis tested by the various techniques is that a competitive climate influences perceptions of coworker support, and that this relationship is moderated by (interacts with) a person's level of trait competitiveness. Study 2 involved a Monte Carlo investigation of methods for estimating an interaction effect. The Monte Carlo research included design factors for (a) effect size, (b) parceling strategy, and (c) method of analysis. Study 1 demonstrated that method of analysis and parceling strategy affected the detection of the moderator effect of competition on two types of coworker support (instrumental and affective). Variability in the t-tests and effect size indices lend credibility for the need for the Monte-Carlo investigation. Study 2 demonstrated that (1) there is greater variability in the estimation of the interaction effect with the Jöreskog-Yang method than the latent variable scores method, (2) parceling strategy has the most influence on the interaction effect in the Jöreskog-Yang method, and this effect is dependent upon which strategy is used, and (3) the latent variable score method is superior to the Jöreskog-Yang method with respect to statistical decision making (i.e., fewer Type II errors). Practical implications and future research directions are considered.
Item parcels, Latent variable scores, Structural equation modeling, Industrial and Organizational Psychology, Quantitative Psychology, Social Psychology
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