Measuring Women's Autonomy and Violence Vulnerability: An Integrated Framework Combining Causal Inference and Explainable Machine Learning

Women's autonomy has been increasingly recognized as a key dimension of gender inequality and women's empowerment. However, quantitative approaches capable of operationalizing women's autonomy as a multidimensional construct and assessing its relationship with gender-based violence remain limited. This study proposes and applies an integrated methodological framework combining multidimensional measurement, causal inference, and explainable machine learning to investigate the association between women's autonomy and violence against women in Brazil. Using nationally representative microdata from the 2023 National Survey on Violence Against Women (Pesquisa Nacional de Violência contra a Mulher – PNVCM), conducted by the DataSenado Institute in partnership with the Observatory for Women Against Violence of the Brazilian Federal Senate (DataSenado & Observatory for Women Against Violence, 2023), a Composite Women's Autonomy Index (CWAI) was constructed from three dimensions: Institutional Autonomy, Service Access, and Economic Autonomy. Associations were estimated using weighted logistic regression and Double Machine Learning (DML), while predictive performance was evaluated through XGBoost models interpreted with SHAP values. The weighted prevalence of violence was 30.48% among Brazilian women. Logistic regression indicated a significant negative association between CWAI and violence (OR = 0.909; 95% CI: 0.865–0.956), although this relationship was not robust in the DML specification. Among the CWAI dimensions, Service Access emerged as the most consistent protective factor, remaining statistically significant across both inferential approaches. Institutional Autonomy was positively associated with violence, whereas Economic Autonomy was not statistically significant. The predictive model achieved modest performance (AUC = 0.574), with CWAI identified as the most influential predictor according to SHAP values. The findings demonstrate that different dimensions of women's autonomy exhibit distinct relationships with violence and highlight the value of integrating measurement, causal inference, and explainable machine learning in the analysis of complex social phenomena using observational data.