Conditional Rank-Rank Regression via Deep Conditional Transformation Models
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Conditional Rank-Rank Regression
Rank-rank regression is commonly employed in economic research as a way of capturing the relationship between two economic variables. It frequently features in studies of intergenerational mobility as the resulting coeff…
regressionDeep Neural Networks for Rank-Consistent Ordinal Regression Based On Conditional Probabilities
In recent times, deep neural networks achieved outstanding predictive performance on various classification and pattern recognition tasks. However, many real-world prediction problems have ordinal response variables, and…
regressionEfficient Regularized Least-Squares Algorithms for Conditional Ranking on Relational Data
In domains like bioinformatics, information retrieval and social network analysis, one can find learning tasks where the goal consists of inferring a ranking of objects, conditioned on a particular target object. We pres…
Computational EfficiencyInformation RetrievalregressionRetrievalDistributional conformal prediction
We propose a robust method for constructing conditionally valid prediction intervals based on models for conditional distributions such as quantile and distribution regression. Our approach can be applied to important pr…
Conformal PredictioncounterfactualPredictionPrediction Intervals+4Learning Bayesian Networks with Low Rank Conditional Probability Tables
In this paper, we provide a method to learn the directed structure of a Bayesian network using data. The data is accessed by making conditional probability queries to a black-box model. We introduce a notion of simplicit…