Graphical Ising Models for Missing Data Patterns Detection in Sustainability Surveys

Ensuring sustainability in the agri-food sector requires comprehensive data analysis. This study examines missing data patterns in a large-scale survey of Italian agri-food companies within the Italian National Research Center for Technology in Agriculture (Agritech), focusing on sustainability variables. The underlying idea is that failure to report a value for these variables indicates low attention to sustainability. We employ graphical Ising models to infer the conditional independence structure among missingness indicators and fully observed farm characteristics, which are modeled as binary variables. The graph structure is selected through node-wise logistic regressions with variable selection based on a backward stepwise procedure guided by the Bayesian Information Criterion (BIC). This approach enables the recovery of sparse and interpretable graphs while controlling for model complexity. We are not interested in causal relationships between missingness indicators and fully observed variables; rather, our focus is on the dependence structure among these variables. The method is applied to the Agritech data, yielding both a national graph and macro-regional graphs, as well as differential networks that highlight structural differences between each macro-region and the national graph. These results provide new insights into systematic patterns of missing data, offering a rigorous framework for improving data quality in terms of completeness and reliability.