SEMinR Lecture Series - Moderation Analysis

SEMinR Lecture Series - Moderation Analysis

SEMinR Lecture Series

This session is focused on how to perform moderation analysis using SEMinR in Cran R.

Moderation Analysis

  • 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 a model.
  • For example, research has shown that the relationship between Culture and Organizational Performance differs as a function of the Role Ambiguity.
  • Moderating relationships are hypothesized a priori by the researcher. 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 values of the moderator.

Modelling Moderating Effects

  • Figure illustrates the two-stage approach.
  • The main effect model in Stage 1 is run to obtain the latent variable scores for Y1, Y2, and M (i.e., LVS(Y1), LVS(Y2), and LVS(M)).
  • The latent variable scores of Y1 and M are then multiplied to form the single item used to measure the interaction term Y1 · M in Stage 2.
  • The latent variables Y1, Y2, and M are each measured with a single item of the latent variable scores from Stage 1.
  • It is important to note that the limitations identified when using single items do not apply in this case, since the single item represents the latent variable scores as obtained from a multi-item measurement in Stage 1.

Model Evaluation

  • For the interaction term, there is no requirement to assess its measurement model since it represents an auxiliary measurement that incorporates the interrelationships between the moderator and the exogenous construct in the path model.
  • This characteristic, however, renders any measurement model assessment of the interaction term meaningless. In addition, standard measurement model evaluation standards would not apply since the interaction term is measured with a single item.
  • Therefore, the interaction term does not necessarily have to be assessed in the measurement model evaluation step.
  • Finally, it is always important to consider the standard criteria for structural model assessment. In the context of moderation, particular attention should be paid to the f-Sq effect size of the interaction effect (Hair et al., 2022; Memon et al., 2018).
  • This criterion enables an assessment of the change in the R2 value when an exogenous construct is omitted from the model.
  • With regard to the interaction effect, the f2 effect size indicates how much the moderation contributes to the explanation of the endogenous construct. The effect size can be calculated as
  • where R-Sq included and R-Sq excluded are the R-Sq values of the endogenous construct when the interaction term of the moderator model is included in or excluded from the PLS path model.
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  • In this way, one can assess the relevance of the moderating effect.
  • General guidelines for assessing ƒ2 suggest values of 0.02, 0.15, and 0.35 represent small, medium, and large effect sizes, respectively (Cohen, 1988).
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  • However, Aguinis et al. (2005) have shown that the average effect size in tests of moderation is only 0.009.
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  • Against this background, Kenny (2018) proposes that 0.005, 0.01, and 0.025, respectively, constitute more realistic standards for small, medium, and large effect sizes of moderation but also points out that even these values are optimistic.
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Modelling Moderating Effects

  • Creating interaction terms by hand can be time-consuming and error prone. SEMinR provides functions for simply creating interactions between constructs. In doing so, SEMinR adjusts the standard errors of the construct scores in the generation of the interaction term (Henseler & Chin, 2010).
  • Interaction terms are described in the measurement model function constructs() using the following methods:
  • –two_stage implements the two-stage approach. It specifies the interaction term as the product of the scores of the exogenous construct and the moderator variable.
  • –product_indicator generates the interaction term by multiplying each indicator of the exogenous construct with each indicator of the moderator variable.
  • –orthogonal is an extension of the product indicator approach, which generates an interaction term whose indicators do not share any variance with the indicators of the exogenous construct and the moderator. The orthogonalizing approach is typically used to handle multicollinearity in the structural model.
  • Moderator variable is introduced through the interaction term in a PLS path model. But a fundamental question remains:
  • How should the interaction term be operationalized? Research has proposed three primary approaches for creating the interaction term: (1) the product indicator approach, (2) the orthogonalizing approach, and (3) the two-stage approach.
  • Simulation studies have shown that Chin, Marcolin, and Newsted’s (2003) two-stage approach excels in terms of parameter recovery and statistical power (e.g., Becker, Ringle, & Sarstedt, 2018; Henseler & Chin, 2010).
  • In addition, this approach offers much flexibility, as it is the only approach that is applicable when the exogenous construct (Y1) or the moderator (M) is specified formatively. We therefore recommend using the two-stage approach in most situations to create the interaction term.

Source: Ramayah et al (2018)

Moderation Analysis Illustration

  • In this example the impact of Collaborative Culture on Organizational Performance is moderated by Role Ambiguity. Role Ambiguity negative affect the strength of relationship between Collaborative Culture and Organizational Performance..
  • Creating interaction terms by hand can be time-consuming and error prone. SEMinR provides functions for simply creating interactions between constructs. In doing so, SEMinR adjusts the standard errors of the construct scores in the generation of the interaction term (Henseler & Chin, 2010).
  • The SEMinR syntax uses an asterisk (“*”) as a naming convention for the interaction construct. Thus, when creating an interaction from the constructs Collaborative Culture and Role Ambiguity, the resulting interaction is called “Collaborative Culture*Role Ambiguity” in the structural model.
  • Therefore it is recommended to refrain from using an asterisk in the naming of noninteraction constructs.
  • In addition to including the moderator construct, we need to specify the interaction term composed of the independent variable Collaborative Culture and the moderator Role Ambiguity using the interaction_term() function.
  • The interaction_term() function takes the following arguments: iv specifies the independent variable (i.e., exogenous construct); moderator specifies the moderating variable; and method specifies the interaction calculation method (with values product_indicator, orthogonal, or two_stage).
  • We now need to choose the two-stage approach to create the interaction term. We specify the interaction term as follows: interaction_ term (iv = “Collaborative Culture”, moderator = “Role Ambiguity”, method = two_stage).
  • SEMinR automatically generates a name for the new interaction term by combining the exogenous construct’s and the moderator construct’s name separated by an asterisk (“*”), representing multiplication. Thus, the newly created interaction term will be called Collaborative Culture*Role Ambiguity. Note that SEMinR always standardizes the data when calculating the interaction term.
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Output

  • When the measurement model has been updated with the identification of the Moderator and Interaction term. We need to add the new structural paths.
  • There is a new path in the model: from Role Ambiguity to Organizational Performance
  • The Interaction Effect (Collaborative Culture* Role Ambiguity) to Organizational Performance
  • With the measurement and structural models now updated, the model can be estimated, bootstrapped, and summarized.

F-Sq Effect Size Calculation

  • R-Sq Excluded.
    • –In this example, RA is not a proper antecedent that affects Organizational Performance, and the objective is to assess the moderating role of RA. Hence, When calculating R-Sq excluded both the moderator and the moderating effect are removed from the model. Hence, the R-Sq excluded is comprised of the effect of Collaborative Culture on OP.
    • –Just in case, if RA was a proper antecedent of OP, then I would include it so that the f-sq just tells the effect size of the interaction. The f-sq term would then compare the R-sq of the additive terms plus interaction term versus just the additive main terms.
  • R-Sq Excluded = 0.324
  • R-Sq Included = 0.381
  • F-Sq = (0.381 – 0.324)/(1-0.381)
  • F-Sq = 0.057/0.619
  • F-Sq = 0.092
  • Based on Kenny (2018) proposition, that 0.005, 0.01, and 0.025, respectively, constitute small, medium, and large effect sizes of moderation. There is a large effect size.
  • As normal, the first step is to assess the measurement model. Assess and report the reliability and validity. As we have previously discussed in evaluating measurement model.
  • NOTE: When assessing the Measurement Model, there is no need to create the interaction effect. Create your interaction effect for structural model assessment.
  • The next concern is the size of the moderating effect. In order to evaluate the moderating effect, we need to inspect the bootstrapped_paths element within the summary_boot object, summary_boot$bootstrapped_paths.

Slope Analysis

  • As can be seen in the results, the interaction term (Collaborative Culture*Role Ambiguity) has a negative effect on Orgnaizaitonal Performance of −0.130, whereas the simple effect of Collaborative Culture on Organizational Performance is 0.514.
  • Jointly, these results suggest that the relationship between Collaborative Culture on Organizational Performance is 0.514 for an average level of Role Ambiguity.
  • For higher levels of Role Ambiguity (i.e., for every standard deviation unit increase of Role Ambiguity), the relationship between Collaborative Culture and Organizational Performance decreases by the size of the interaction term (i.e., 0.514 + (−0.130) = 0.384).
  • On the contrary, for lower levels of Role Ambiguity (i.e., for every standard deviation unit decrease of Role Ambiguity), the relationship between Collaborative Culture and Organizational Performance increases the size of the interaction term (i.e., 0.514 − (−0.130) = 0.644).
  • To better comprehend the results of the moderator analysis, we can use the slope_analysis() function to visualize the two-way interaction effect. This function takes the arguments shown in Table.

    We apply the slope_analysis() function to the simple_model, with Organizational Performance as the endogenous construct, Role Ambiguity as the moderator construct, and Collaborative Culture as the exogenous construct. Finally, we assign the legend to the bottom-right corner of the plot.

The Slops

Slope Analysis Arguments

 

Video Tutorial - Step 1

Complete Code

Reference

Hair Jr, J. F., Hult, G. T. M., Ringle, C. M., Sarstedt, M., Danks, N. P., & Ray, S. (2021). Partial Least Squares Structural Equation Modeling (PLS-SEM) Using R: A Workbook.

Partial Least Squares Structural Equation Modeling (PLS-SEM) Using R

The tutorials on SEMinR are based on the mentioned book. The book is open source and available for download under this link.

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Additional SEMinR Tutorials