Background

The PLS-PM approach is a statistical method for modeling complex relationships between latent variables and manifest variables, belonging to the family of Structural Equation Models (SEM). It emphasizes a predictive dimension to estimate relationships and test causal hypotheses, while allowing theoretical knowledge to be incorporated through variants such as the hierarchical or confirmatory approaches.

 

Example dataset

250 customers of a mobile phone operator were surveyed to answer a large number of questions to model their loyalty to the operator. The PLS-PM model is based on the European Customer Satisfaction Index (ECSI).

 

Setup

• To create a new file, select the New project option. When you create a new project, its default name starts with PLSPMBook.

A raw XLSTAT-PLSPM project contains two sheets that cannot be removed:

D1: This sheet is empty. You will need to add all the input data that you want to use into that worksheet.

PLSPMGraph: This sheet is blank and is used to design the model. When you select this sheet, the "Path modeling" menu is displayed on the upper left part of the page.

• Save and label it by using the Save as command of the XLSTAT-PLSPM menu to save it in the folder dedicated to the PLSPM projects using the *.ppmx extension.

• As the PLS approach is a complex statistical method and as the developments in the PLS-PM module are highly developed, we have set up three types of menu display.

The first is called classic and includes the main functions associated with the PLS approach; the second is called expert and allows more advanced analysis; and the third is called marketing and includes specific options for the marketing field. To modify this option, click on the XLSTAT-PLPM options button on the XLSTAT-PLSPM toolbar.

• Copy the data from a standard Excel sheet to sheet D1.

• Build the model:

  • Go to the PLSPMGraph sheet. The command bar is at top left:

• • To create several latent variables in a row, double click on the circle button so that it stays pressed while you add variables:

• • Add arrows linking latent variables to each other. To add an arrow, simply click on the latent variable from which it starts and select the destination latent variable while holding down the Ctr+L button. Once both variables have been selected, use either the toolbar button shown in the following figure or the keyboard shortcut Ctrl+L.

• • Define the manifest variables associated with each latent variable. Click on the latent variable and use the MV button on the bar:

In the General tab:

• Select the quantitative data columns linked to the latent variable.

• Choose the reflective mode.

For example, for the latent variable Expectations, the dialog box will look like this:

The obtained model has the following form:

• Click on the icon to select calculation options.

In the General tab:

• Select the option to process standardized manifest variables, weights on standardized VM, and initialize weights by taking the values of the first eigenvector.

• Be sure to select the PLSPM method.

In the Options tab:

• Select the Centroid internal weight estimation scheme and select bootstrap calculation of confidence intervals.

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the results – part 1

The first important elements are the composite reliability indexes:

In this application, latent variables are reflective. The blocks must be one-dimensional. We can see that Dillon-Goldstein’s rho is higher than 0.7 and that the first eigenvalue is always far greater than the second one. Expectation and loyalty have bad values for the Cronbach’s alpha and a second dimension could be significant. In this tutorial, we will focus on the case of one dimension. Applying PLS path modelling gives the table with GoF indexes:

We can see the absolute GoF is 0.471, very close to the bootstrap estimate. This value is hard to interpret; it could be useful when comparing the global quality of two groups of observations or two different models. The relative GoF is very high and so are inner and outer models GoF.

Then, you should check the cross-loadings:

In the case of our dataset, loadings between manifest variables and their own latent variable are the highest. Then, outer weights and correlations are gathered in two large tables. If we study the correlations between manifest variables and latent variables, we can see that, for example, the manifest variables CUSA3 and CUSA2 have a greater effect on satisfaction than CUSA1. These tables allow you to see the impact of each manifest variable on its associated latent variable.

 

Interpreting the results – part 2

The results associated with the structural model are shown below. For each latent variable, information on the structural model is gathered. In the case of satisfaction, we have:

A R’² of 0.680 can be considered as a good result. We can see that perceived quality has the greatest effect on satisfaction and that the impact of expectation is not significant. The last table summarizes the results and shows that perceived quality contributes to 60% of the R² of satisfaction.

The next table shows different predictive quality indexes associated with both outer and inner models for each latent variable. Mean values of these indices give a global quality value. We see that the mean of all R² is 0.387 and the R² of satisfaction is the highest one. Communalities are always greater than redundancies because PLSPM favors the measurement model in its estimation procedure.

One of the greatest advantages of PLSPM is the latent variable scores. They are given and can be used for other statistical treatments with XLSTAT.

This study has shown how to use XLSTAT-PLSPM module in the case of real data. Once the model has been drawn, the procedure is simple. Once the model has been validated, interpretation of the result can be done by reading the tables with path coefficients and correlations.

 

Displaying results on the graph

You can display many types of results on the path model with XLSTAT-PLSPM. Choose between al the possible indexes obtained when clicking on the button “Choose the results to display”:

The results dialog box appears. It has three pages:

• The LV tab displays the indices linked to the latent variables in the graph.

• The Arrows (LV) tab displays indices and coefficients on the arrows between latent variables.

• The Arrows (MV) tab displays a number of indices and coefficients on the arrows between the manifest variables (MV) and their associated latent variable.

• Select the parameters of interest and click OK.

• Click on the Show results button, and the results will appear on the PLSPMGraph sheet.