SMALL-SAMPLE AND IMBALANCED DATA MODELING OF FAMILY QUALITY INDEX: A FIRTH LOGISTIC REGRESSION STUDY

Abstract

The Family Quality Index (FQI) in Indonesia is not published annually, limiting the availability of timely information for monitoring and evaluating family development policies. This study addresses this issue by identifying determinants of provincial FQI categories and developing a classification model that can be applied when official FQI measurements are unavailable. Secondary data from 34 provinces in Indonesia for 2023 were analyzed using Firth logistic regression, a method designed to reduce bias in small samples and imbalanced datasets.  The response variable was the FQI category, classified into moderately responsive and responsive groups. Explanatory variables included mean years of schooling, open unemployment rate, poverty rate, and population density. The results show that poverty rate is the only predictor that remains statistically significant after bias correction, with higher poverty levels associated with a lower probability of a province being classified as responsive. The other variables were not statistically significant.  Model performance was evaluated using Leave-One-Out Cross-Validation (LOOCV). Compared with conventional logistic regression estimated by maximum likelihood, the Firth model achieved higher accuracy (88.24% vs. 85.29%), Kappa (0.531 vs. 0.459), and sensitivity (0.931 vs. 0.897), while maintaining the same specificity. Additional sensitivity analyses using a reduced model produced similar results, indicating that the effect of poverty was stable across model specifications.  These findings suggest that annually available socio-economic indicators may be used to provide provisional estimates of provincial FQI categories when official FQI data are unavailable, thereby supporting evidence-based family development policy evaluation.