Here are some general areas of research and papers for methods with ordinal or rank data. This work has involved many fabulous students and colleagues.
Covariate-adjusted Spearman rank correlation and rank ICC
Li C, Shepherd BE. Test of association between two ordinal variables while adjusting for covariates. Journal of the American Statistical Association 2010; 105: 612-620. link
Liu Q, Li C, Wanga V, Shepherd BE. Covariate-adjusted Spearman’s rank correlation with probability-scale residuals. Biometrics 2018; 74: 595-605. PMCID: PMC5949238. link
Eden S, Li C, Shepherd BE. Non-parametric estimation of Spearman’s rank correlation with bivariate survival data. Biometrics 2022; 78: 421-434. link software
Tu S, Li C, Zeng D, Shepherd BE. Rank intraclass correlation for clustered data. Statistics in Medicine 2023; 42: 4333-4348. link software
Eden S, Li C, Shepherd BE. Spearman-like correlation measure adjusting for covariates in bivariate survival data. Biometrical Journal 2023; 65: 2200137. link
Tu S, Li C, Shepherd BE. Between- and within-cluster Spearman rank correlation. Statistics in Medicine 2025; 44: e10326. link software
Analyzing continuous data with ordinal models
Liu Q, Shepherd BE, Li C, Harrell FE. Modeling continuous response variables using ordinal regression. Statistics in Medicine 2017;36(27):4316-35. PMCID: PMC5675816. link software
Tian Y, Hothorn T, Li C, Harrell FE, Shepherd BE. An empirical comparison of two novel transformation models. Statistics in Medicine 2020; 39: 562-576. link
Li C, Tian Y, Zeng D, Shepherd BE. Asymptotic properties for cumulative probability models for continuous outcomes. Mathematics 2023; 11: 4896. link
Tian Y, Shepherd BE, Li C, Zeng D, Schildcrout JS. Analyzing clustered continuous response variables with ordinal regression models. Biometrics 2023; 79: 3764-3777. link software
Tian Y, Li C, Tu S, James NT, Harrell FE, Shepherd BE. Addressing multiple detection limits with semiparametric cumulative probability models. Journal of the American Statistical Association 2024; 119: 864-874. link software
Probability-scale residuals for ordinal (and general) outcomes
Li C, Shepherd BE. A new residual for ordinal outcomes. Biometrika. 2012;99(2):473-80. PMCID: PMC3635659. link
Shepherd BE, Li C, Liu Q. Probability-scale residuals for continuous, discrete, and censored data. Canadian Journal of Statistics 2016; 44: 463-479. link
Software
Liu Q, Shepherd BE, Li C. PResiduals: an R package for residual analysis using probability-scale residuals. Journal of Statistical Software 2020; 94: 12. link