Abstract

Mortgage lending decisions directly affect households’ access to housing and their ability to build wealth. This study adapts methods of symbolic data analysis (SDA) to visualize and predict loan acceptance rates for categories of mortgage applicants defined by demographic attributes such as sex, age, race and ethnicity. The aim is to identify potential biases in mortgage market activity.
The analysis uses data collected under the Home Mortgage Disclosure Act (HMDA), the most comprehensive publicly available source of information on mortgage market activity in the United States. The recorded attributes cover the characteristics of the application and the loan, the property, the applicant’s financial situation, the applicant’s demographic characteristics, and the outcome of the decision process
Rather than analysing individual records, applicants are aggregated into classes defined by their demographic attributes. Each class is described by symbolic data, which preserves the variability within the class. For visualization, we apply the measures of symbolic concordance (s-concordance) and symbolic discordance (s-discordance) introduced by Diday (2020, 2023). Measures of s-concordance and s-discordance measure similarity, and, respecively, dissimilarity between a class and a collection of classes for a given value x of a categorical variable X. These measures highlight categories of applicants whose lending outcomes differ markedly from those of the rest of the population.
Acceptance rates for demographic categories are predicted using linear regression for distributional symbolic variables based on the Wasserstein distance (Irpino & Verde, 2015).
The results provide insight into possible biases in mortgage market activity across classes of applicants defined by sex, age, race and ethnicity. The study shows how recently developed SDA tools (Verde et al., 2024) can be applied to large administrative datasets to produce interpretable, class-level evidence on fairness in lending, with potential uses in official statistics.

Diday, E. (2020). Explanatory tools for machine learning in the symbolic data analysis framework. In E. Diday, R. Guan, G. Saporta, & H. Wang (Eds.), Advances in data science: Symbolic, complex and network data (Vol. 4, pp. 3–30). ISTE Ltd & John Wiley & Sons.
Federal Financial Institutions Examination Council. (2025). HMDA data publication 2025. https://ffiec.cfpb.gov/data-publication/2025
Irpino, A., & Verde, R. (2015). Linear regression for numeric symbolic variables: A least squares approach based on Wasserstein distance. Advances in Data Analysis and Classification, 9(1), 81–106. https://doi.org/10.1007/s11634-015-0197-7
Verde, R., Batagelj, V., Brito, P., Duarte Silva, A. P., Korenjak-Černe, S., Dobša, J., & Diday, E. (2024). New skills in symbolic data analysis for official statistics. Statistical Journal of the IAOS, 40(3). https://doi.org/10.3233/SJI-240013