Two-sample models with monotonic likelihood ratios for ordinal regression

Signal detection experiments with human observers frequently generate ordinal data which are evaluated using receiver operating characteristic (ROC) methods. These methods may include regressing a continuous two-distribution model to the data set. Because we assume that human observers will not systematically select observations absent the signal, this model should have a monotonic likelihood ratio between the distributions. This paper gives a general method for constructing pairs of distributions that have monotonic likelihood ratios and a possibly large number flexible parameters. It suggests two specific simple parametric forms of monotonic likelihood ratios, constructs new distributions with those likelihood ratios using other standard distributions, and performs ordinal regression with those new distributions to model some example data from the literature.