SEM-Based Out-of-Sample Predictions

• Published in: Structural equation modeling 2023-01, Vol.30 (1), p.132-148
• Main Authors: de Rooij, Mark, Karch, Julian D., Fokkema, Marjolein, Bakk, Zsuzsa, Pratiwi, Bunga Citra, Kelderman, Henk
• Format: Article
• Language: English
• Subjects: Cross-validation; machine learning; prediction rule; regression; Structural equation modeling
• ISSN: 1070-5511; 1532-8007
• DOI: 10.1080/10705511.2022.2061494

Predictive modeling is becoming more popular in psychological science. Machine learning techniques have been used to develop prediction rules based on items of psychological tests. However, this approach does not take into account that these items are noisy indicators of the constructs they intend to measure. Structural equation modeling does take this into account. Several authors have concluded that it is impossible to make out-of-sample predictions based on a reflective structural equation model. We show that it is possible to make such predictions and we develop R-code to do so. With two empirical examples, we show that SEM-based prediction can outperform prediction based on linear regression models. With three simulation studies, we further investigate the SEM-based prediction rule and its robustness in comparison with predictions using regularized linear regression. We conclude that the new SEM-based prediction rule is robust against violation of the normality assumption but sensitive to model misspecification.