When moderation is present, the strength or even the direction of a relationship between two constructs depends on a third variable. In other words, the nature of the relationship differs depending on the values of the third variable. As an example, the relationship between two constructs is not the same for all customers, but differs depending on their income. As such, moderation can (and should) be seen as a means to account for heterogeneity in the data.
Moderation describes a situation in which the relationship between two constructs is not constant but depends on the values of a third variable, referred to as a moderator variable. The moderator variable (or construct) changes the strength or even the direction of a relationship between two constructs in the model. For example, prior research has shown that the relationship between customer satisfaction and customer loyalty differs as a function of the customers’ switching barriers. More precisely, switching barriers have a pronounced negative effect on the satisfaction-loyalty relationship: the higher the switching barriers, the weaker the relationship between satisfaction and loyalty. In other words, switching barriers serve as a moderator variable that accounts for heterogeneity in the satisfaction-loyalty link. Thus, this relationship is not the same for all customers, but instead differs depending on their switching barriers. As such, moderation can (and should) be seen as a means to account for heterogeneity in the data.
Moderating relationships are hypothesized a priori by the researcher and specifically tested. The testing of the moderating relationship depends on whether the researcher hypothesizes whether one specific model relationship or whether all model relationships depend on the scores of the moderator. In the prior example, we hypothesized that only the satisfaction-loyalty link is significantly influenced by income. These considerations also apply for the relationship between CUSA and CUSL in the corporate reputation model example. In such a setting, we would examine if and how the respondents’ switching barriers influences the relationship. The following figure shows the conceptual model of such a moderating relationship, which only focuses on the satisfaction-loyalty link in the corporate reputation model.
A typical moderator analysis results representation use simple slope plots, as provided by SmartPLS.
Hair et al. (2017) describe PLS-SEM moderator analysis in more detail.
Moderation Settings in SmartPLS
The selected dependent variable for which a moderating effect will be estimated.
Field to define the predictor variable for which a moderating effect will be estimated.
Field to define the moderator variable for which a moderating effect will be estimated.
Selects the method of interaction term construct in PLS path modeling. There are three options:
(1) Product Indicator
This approach uses all possible pair combinations of the indicators of the latent predictor and the latent moderator variable. These product terms serve as indicators ("product indicators") of the interaction term in the structural model.
(2) Two-stage (default)
This approach uses the latent variable scores of the latent predictor and latent moderator variable from the main effects model (without the interaction term). These latent variable scores are saved and used to calculate the product indicator for the second stage analysis that involves the interaction term in addition to the predictor and moderator variable.
This approach uses residuals that are calculated by regressing all possible pairwise product terms of the indicators of the latent predictor and the latent moderator variable (i.e., product indicators) on all indicators of the latent predictor and the latent moderator variable. These residuals serve as indicators of the interaction term in the structural model.
The residuals will be orthogonal to all indicators of the predictor and moderator variable to ensure that the indicators of the interaction term do not share any variance with any of the indicators of the predictor or moderator variable.
Product Term Generation
Defines how product terms for the interaction effect will be calculated. There are three options:
Unstandardized data are used for the calculation of the product terms of the interaction effect.
Mean-centered data are used for the calculation of the product terms of the interaction effect.
(3) Standardized (default)
Standardized data are used for the calculation of the product terms of the interaction effect.
Note: If the Two-stage approach is used as calculation method, all options should lead to the same results, because the components for the product term calculation (i.e., latent variable scores) are always standardized.
For the Product Indicator and Orthogonalization approach the default option should be standardized.
Interaction Effect Term and Regression Handling
The interaction term (latent variable) is left as it is when entering the final regression of the moderator model (i.e., independent and moderator variables as well as interaction term on the selected dependent variable). Hence, it is not standardized which would bias the results.
Chin, W. W., Marcolin, B. L., and Newsted, P. R. 2003. A Partial Least Squares Latent Variable Modeling Approach for Measuring Interaction Effects: Results from a Monte Carlo Simulation Study and an Electronic-Mail Emotion/Adoption Study. Information Systems Research, 14(2): 189-217.
Hair, J. F., Hult, G. T. M., Ringle, C. M., and Sarstedt, M. 2017. A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM), 2nd Ed., Sage: Thousand Oaks. Link to Book
Henseler, J., and Chin, W. W. 2010. A Comparison of Approaches for the Analysis of Interaction Effects Between Latent Variables Using Partial Least Squares Path Modeling. Structural Equation Modeling: A Multidisciplinary Journal, 17(1): 82-109.
Henseler, J., Fassott, G., Dijkstra, T., and Wilson, B. 2012. Analysing Quadratic Effects of Formative Constructs by Means of Variance-Based Structural Equation Modelling. European Journal of Information Systems, 21(1): 99-112.
- Rigdon, E. E., Ringle, C. M., and Sarstedt, M. 2010. Structural Modeling of Heterogeneous Data with Partial Least Squares, in Review of Marketing Research, N. K. Malhotra (ed.), Sharpe: Armonk, 255-296. Link to Article