Predictive Power Assessment using PLSPredict in SmartPLS3

Learn to assess Predictive Power in PLS-SEM

The Concept and Process of Predictive Power Assessment using PLSPredict in SmartPLS3

What is Predictive Power?

Many researchers interpret the R-Sq statistic as a measure of their model’s predictive power (Sarstedt & Danks, 2021; Shmueli & Koppius, 2011). This interpretation is not entirely correct, however, since the R-Sq only indicates the model’s in-sample explanatory power.
“In sample” refers to the data that you have, and “out of sample” to the data you don’t have but want to forecast or estimate.
It says nothing about the model’s predictive power (Chin et al., 2020; Hair & Sarstedt, 2021), also referred to as out-of-sample predictive power, which indicates a model’s ability to predict new or future observations.
Does the model has good predictive quality?
Addressing this concern, Shmueli, Ray, Estrada, and Chatla (2016) introduced PLSpredict, a procedure for out-of-sample prediction.
Execution of PLSpredict involves estimating the model on a training sample and evaluating its predictive performance on a holdout sample (Shmueli et al., 2019).
Note that the holdout sample is separated from the total sample before executing the initial analysis on the training sample data, so it includes data that were not used in the model estimation.
Researchers need to make sure that the training sample for each fold meets minimum sample size guidelines (e.g., by following the inverse square root method).

How to Assess Predictive Power?

To assess a model’s predictive power, researchers can draw on several prediction statistics that quantify the amount of prediction error in the indicators of a particular endogenous construct.
Error is not an error (as in a mistake). It is a residual, the lower the better, this is the difference between actual values and the predicted values.
The most popular metric to quantify the degree of prediction error is the root-mean-square error (RMSE).
Another popular metric is the mean absolute error (MAE).
In most instances, researchers should use the RMSE to examine a model’s predictive power.
But if the prediction error distribution is highly nonsymmetric, as evidenced in a long left or right tail in the distribution of prediction errors (Danks & Ray, 2018), the MAE is the more appropriate prediction statistic (Shmueli et al., 2019).
To assess the degree of prediction error, use the RMSE unless the prediction error distribution is highly non-symmetric. In this case, the MAE is the more appropriate prediction statistic
To interpret these metrics, researchers need to compare each indicator’s RMSE (or MAE) values with a naïve linear regression model (LM) benchmark.
The LM benchmark values are obtained by running a linear regression of each of the dependent construct’s indicators on the indicators of the exogenous constructs in the PLS path model (Danks & Ray, 2018). In comparing the RMSE (or MAE) values with the LM values, the following guidelines apply (Shmueli et al., 2019):
- If all indicators in the PLS-SEM analysis have lower RMSE (or MAE) value compared to the naïve LM benchmark, the model has high predictive power.
- If the majority (or the same number) of indicators in the PLS-SEM analysis yields smaller prediction errors compared to the LM, this indicates a medium predictive power.
- If a minority of the dependent construct’s indicators produce lower PLS-SEM prediction errors compared to the naïve LM benchmark, this indicates the model has low predictive power.
- If the PLS-SEM analysis (compared to the LM) yields lower prediction errors in terms of the RMSE (or the MAE) for none of the indicators, this indicates the model lacks predictive power.

In comparing the RMSE (or MAE) values with the LM values, the following guidelines apply

All Indicators

If all indicators in the PLS-SEM analysis have lower RMSE (or MAE) value compared to the naïve LM benchmark, the model has high predictive power.

Majority

If the majority (or the same number) of indicators in the PLS-SEM analysis yields smaller prediction errors compared to the LM, this indicates a medium predictive power.

Minority

If a minority of the dependent construct’s indicators produce lower PLS-SEM prediction errors compared to the naïve LM benchmark, this indicates the model has low predictive power.

None

If the PLS-SEM analysis (compared to the LM) yields lower prediction errors in terms of the RMSE (or the MAE) for none of the indicators, this indicates the model lacks predictive power.

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