Conditional Rank-Rank Regression via Deep Conditional Transformation Models

• URL: http://arxiv.org/abs/2603.07230v1
• Date: Sat, 07 Mar 2026 14:27:09 GMT
• Title: Conditional Rank-Rank Regression via Deep Conditional Transformation Models
• Abstract summary: Intergenerational mobility quantifies the transmission of socio-economic outcomes from parents to children.<n> Conditional rank-rank regression (CRRR) measures within-group mobility using conditional ranks.<n>We extend CRRR to discrete outcomes via an $$-indexed conditional-rank definition and study sensitivity to $$.<n>For continuous outcomes, we establish a theory for the proposed estimators and verify the validity of exchangeable inference.
• Score: 8.100828624916574
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Intergenerational mobility quantifies the transmission of socio-economic outcomes from parents to children. While rank-rank regression (RRR) is standard, adding covariates directly (RRRX) often yields parameters with unclear interpretation. Conditional rank-rank regression (CRRR) resolves this by using covariate-adjusted (conditional) ranks to measure within-group mobility. We improve and extend CRRR by estimating conditional ranks with a deep conditional transformation model (DCTM) and cross-fitting, enabling end-to-end conditional distribution learning with structural constraints and strong performance under nonlinearity, high-order interactions, and discrete ordered outcomes where the distributional regression used in traditional CRRR may be cumbersome or prone to misconfiguration. We further extend CRRR to discrete outcomes via an $ω$-indexed conditional-rank definition and study sensitivity to $ω$. For continuous outcomes, we establish an asymptotic theory for the proposed estimators and verify the validity of exchangeable bootstrap inference. Simulations across simple/complex continuous and discrete ordered designs show clear accuracy gains in challenging settings. Finally, we apply our method to two empirical studies, revealing substantial within-group persistence in U.S. income and pronounced gender differences in educational mobility in India.

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