A proportional likelihood ratio model

Abstract

We propose a semiparametric proportional likelihood ratio model which is particularly suitable for modelling a nonlinear monotonic relationship between the outcome variable and a covariate. This model extends the generalized linear model by leaving the distribution unspecified, and has a strong connection with semiparametric models such as the selection bias model (Gilbert et al., 1999), the density ratio model (Qin, 1998; Fokianos & Kaimi, 2006), the single-index model (Ichimura, 1993) and the exponential tilt regression model (Rathouz & Gao, 2009). A maximum likelihood estimator is obtained for the new model and its asymptotic properties are derived. An example and simulation study illustrate the use of the model. Copyright 2012, Oxford University Press.