n Management Dynamics : Journal of the Southern African Institute for Management Scientists - Testing main and interaction effects in structural equation models with a categorical moderator variable
|Article Title||Testing main and interaction effects in structural equation models with a categorical moderator variable|
|© Publisher:||Southern African Institute for Management Scientists (SAIMS)|
|Journal||Management Dynamics : Journal of the Southern African Institute for Management Scientists|
|Affiliations||1 University of Pretoria|
|Publication Date||Dec 2014|
|Pages||31 - 68|
Moderation and mediation analyses are useful approaches to understand how third variables influence the relationships between two variables, X and Y. Moderation is present when a third variable changes the relationship between X and Y. On the other hand, mediation has an explanatory role: it explains why there is a correlational relationship between X and Y. Mediation therefore explicates or expresses the mechanism for the structural relationship that produces the correlation between X and Y, and thereby provides the rationale for the underlying correlation. On the other hand, moderation is often modelled as an interaction term in regression modelling. The analytical method that was traditionally used for mediation and moderation is multiple regression; but the specific steps differ substantially between a moderation and mediation analysis. However, Structural Equation Modelling (SEM) offers advantages over multiple regression methods. The main disadvantage of using multiple regression methods when latent variables are involved is that multiple regression does not account for measurement error, which is a major problem in social research. Ignoring measurement error in research could threaten the validity of statistical conclusions derived from the study. SEM accommodates measurement error, and this makes SEM approaches for mediation and moderation superior to others. In addition, it is possible within the SEM framework to make use of Means and Covariance Structure Analysis (MACS) over multiple groups, which is very useful for investigating moderation when the moderation variable is a grouping variable. An additional advantage of the MACS approach is that, if measurement invariance is tenable in the measurement model, moderation in the structural part of the model can be easily tested on a more fundamental premise of measurement equivalence across groups. This study proposes a detailed stepwise approach to evaluate moderating effects when the moderation variable is a discrete contextual or grouping variable. The suggested method includes the main effects of the grouping variable on the exogenous and the endogenous variables, a specific matter that has largely been ignored in current literature. The advantage of including the main effects in the testing of moderation is that it offers a more complete assessment of the role of the moderating variable on the outcome or endogenous variable as well as on the exogenous or independent predictor variable. Thus it offers a more rigorous understanding of the effect of the contextual variable on the exogenous and the endogenous, and of the relationship between the exogenous and endogenous variables. Model fit approaches in multiple group contexts, as discussed in the literature, are presented and summarised, and an example is provided to demonstrate the proposed approach.
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