This tutorial will show you how to investigate moderating effects in a Partial Least Squares Path Modeling (PLS-PM) context in XLSTAT.

## Moderating effects in PLS path modelling

In this tutorial, we present an application of the study of moderating effects. If you are not familiar with PLS Path Modeling, please refer to the tutorial: “Creating and running a basic PLSPM project” More detailed explanations are available in the help of XLSTAT.

With XLSTAT, you can analyse moderating effects within a PLS model.

Two main approaches are used to identify and measure moderating effects in PLS Path Modeling:

- The direct approach which is automatic in XLSTAT-PLSPM.
- The two-step approach which need a two-step process in XLSTAT-PLSPM.

Moderating effects are very important in PLS Path Modeling. “In general terms, a moderator can be a qualitative (e.g., sex, race, class) or quantitative (e.g., level of reward) variable that affects the direction and/or strength of the relation between an independent or predictor variable and a dependent or criterion variable” (Baron/Kenny 1986 p 1174)

The effect of a moderator variable on the relation between two variables is called a “moderating effect” or an “interaction effect”. In the case of a qualitative moderating variable, the group comparison approach can be used (see tutorial on group comparison with XLSTAT-PLSPM). When the moderating variable is quantitative, an interaction latent variable is used.

Let A, B and C be three latent variables, we want to understand the moderating effect of B on the relation between A and C. We will have the following model:

The latent variables are A, B, C and A*B which is the interaction term. It is used to understand the strength of the moderating effect.

There are two methods for building the interaction latent variable:

**The Product‐Indicator Approach:**- Based on Kenny/Judd (1984) and Chin/Marcolin/ Newsted (1996, 2003).
- Mode A (arrows outwards) has to be used.
- Procedure:
- Each of the g indicators of the exogenous variable is elementwise multiplied with each of the h indicators of the moderator variable, resulting in g*h product indicators.
- These product indicators serve as indicators of the interaction term.

**Two‐Stage Approach:**- Chin/Marcolin/ Newsted (2003, online appendix).
- Feasible for every Mode (Mode A, Mode B, Mode MIMIC, Mode PLS, Mode PCA).
- Procedure:
- Run the main effect model.
- Extract the latent variable scores.
- Use these latent variable scores as indicators of the exogenous and endogenous variables.
- The elementwise product of the latent variable scores of the exogenous variable and the moderator variable serves as the indicator of the interaction term.

These two approaches can be used in XLSTAT-PLSPM, we will detail the application of each one.

## Dataset to study moderating effects

We will use a part of the data used in the general tutorial on how to use XLSTAT-PLSPM. It is based on the ECSI model with a sample of 250 observations. The new file can be downloaded here. Note that this tutorial is **only available for users of Excel 2007 and Excel 2010**.

We want to study the moderating effect of the image of a mobile phone provider on the relation between satisfaction and loyalty of the customers.

## Setting up the moderating effects for PLS path modelling

First of all, you have to switch to the expert display. In the **XLSTAT-PLSPM** menu, click on **XLSTAT-PLSPM** options.

This dialog box appears:

Select the expert display and save your settings. As in the general tutorial, we build a special model only including Image, Satisfaction and loyalty using the PLSPMGraph sheet and the “Path Modeling” toolbar.

Once the model has been drawn, two approaches are available to study moderating effects.

## The product indicator approach

This approach can be automatically applied in XLSTAT-PLSPM. First, add a latent variable to the model and click on the toolbar button to define the latent variable. The following dialog box appears.

Instead of selecting data, click on the interaction button. A new tab is reachable in the dialog box. In the interaction tab, select the two exogenous variables which are image and satisfaction. We decide to standardize the manifest variables.

Then, click on the "Ok" button. A new latent variable appears on the diagram with 6 manifest variables being the products of the manifest variables associated to satisfaction and image.

You can now click on the run button of the XLSTAT-PLSPM bar located on the PLSPMGraph sheet. The run dialog box appears. In this tutorial, we will choose to standardize the manifest variables in the general tab.

In the options tab, we use the centroid scheme with OLS regression with no bootstrap. In the outputs tab, we ask for Standardized latent variables score.

Once you click on the "Ok" button, the computation starts.

The results are displayed on the PLSPM sheet of the workbook and can be seen on the diagram.

The most important result can be found in the path coefficients table.

We see that image and satisfaction have a positive effect on loyalty and that the interaction term has a significant negative effect. That means that the moderating effect of image on the relation between satisfaction and loyalty is significant.

## The two-stage approach

If you already have applied the product indicator approach, first delete the interaction latent variable and launch XLSTAT-PLSPM using the run button of the toolbar located on the PLSPMGraph sheet.

The Run dialog box appears. We choose to standardize the manifest variables in the general tab.

In the options tab, we use the centroid scheme with OLS regression and no bootstrap. In the outputs tab, we ask for Standardized latent variables score.

Once you click on the "Ok" button, the computation starts.

The results are displayed on the PLSPM1 sheet of the workbook and can be seen on the diagram.

We are only interested in the latent variables scores for the simple model. In the PLSPM1 sheet, we compute the product of the latent variables Satisfaction and Image using Excel formulas next to the latent variable scores table.

Then, we change the definition of the latent variable, replacing the manifest variables by the latent variable scores that can be selected in the PLSPM1 sheet. We add a latent variable with only one manifest variable being the new column. The new model has the following form:

You can now run the model with the same parameters as before and study the results. The path coefficients are the most important results.

We see that image and satisfaction have a positive effect on loyalty and that the interaction term has a non significant negative effect. That means that the moderating effect of image on the relation between satisfaction and loyalty is not significant.