Interpretable Symbolic Regression for Psychological Questionnaire Data: Prediction, Descriptor Discovery, and Nonlinear Interaction Analysis

<p>Psychological researchers increasingly use machine-learning methods to improve prediction, yet many high-performing models require post-hoc explanation and provide limited insight into how predictors combine to shape outcomes. We present an application-oriented workflow for GoodRegressor, a hierarchical, depth-controlled symbolic-regression framework, using psychological questionnaire data. The workflow was demonstrated with independent datasets of middle-aged wives from Japan (n = 201) and South Korea (n = 220), with marital satisfaction predicted from demographic variables, family viewpoints, conflict-resolution strategies, and derived descriptors. The datasets were analyzed separately because the family-viewpoint measure was not sufficiently invariant across countries. Nine regression methods were evaluated using identical deterministic five-fold test partitions. In five-fold held-out testing, GoodRegressor showed the strongest predictive performance in Japan (5 = .441, 5 = 0.220, 5 = .178). In South Korea, GoodRegressor remained competitive (5 = .338, 5 = 0.199, 5 = .155), although Elastic Net, Ridge, and Random Forest performed somewhat better overall. Among equation-oriented methods, GoodRegressor substantially outperformed PhySO and EQL. Full-data GoodRegressor ensembles identified husband’s age, assertion, and age-difference-by-assertion structure in Japan, and avoidance, husband’s age, and family-priority-by-avoidance structure in South Korea. These findings support symbolic regression as a practical approach for combining competitive prediction with directly inspectable nonlinear and interaction structure, facilitating interpretable hypothesis generation in psychological research.</p>