A Prediction-Oriented Specification Search Algorithm for Generalized Structured Component Analysis

Generalized structured component analysis (GSCA) is used for specifying and testing the relationships between observed variables and components. GSCA can perform model selection by comparing theoretically established models. In practice, however, theories may not always completely and unambiguously specify the relationships between variables in the model. In such situations, a specification search strategy allows for exploring potential relationships between variables in a data-driven manner. A specification search based on prediction of unseen observations is attractive as it does not require the provision of theoretically plausible models. To date, GSCA has not been equipped with such a specification search strategy. Addressing this limitation, we propose a prediction-oriented specification search algorithm for GSCA, which reveals the best combination of predictors that minimizes each target variable’s prediction error. We conduct a simulation study to examine the new algorithm’s performance and apply it to real data to further investigate and demonstrate its practical usefulness.