Maximum Likelihood Regression of Rank-Censored Data

Abstract

Abstract Linear regression is a common method for analyzing continuous, cardinal data, but it is inappropriate when the dependent variable is an ordinal ranking. The model proposed for analyzing these data sets is the general linear model u = Xβ + e, where the rank of the dependent variable u is observed instead of its value. A description is given for a numerical algorithm to evaluate the likelihood function that is efficient enough to permit maximum likelihood estimation of normalized regression coefficients. This algorithm can be modified to evaluate the cumulative distribution function of any multivariate normal random vector with nonsingular tridiagonal covariance matrix. Large sample properties of the maximum likelihood estimator are provided in the Appendix. Finite sample properties of the estimator are examined in a Monte Carlo experiment, and the exact finite sample distribution in one particular case is analyzed. The model is applied to voter preference data from a Louis Harris poll.