This paper deals with two-group classification when a unidimensional latent trait,ϑ, is appropriate for explaining the data,X. It is shown that ifX has monotone likelihood ratio then optimal allocation rules can be based on its magnitude when allocation must be made to one of two groups related toϑ. These groups may relate toϑ probabilistically via a non-decreasing functionp(ϑ), or may be defined by all subjects above or below a selected value onϑ.
In the case where the data arise from dichotomous items, then only the assumption that the items have nondecreasing item characteristic functions is enough to ensure that the unweighted sum of responses (the number-right score or raw score) possesses this fundamental monotone likelihood ratio property.
monotone likelihood ratio latent trait two-group classification number-right score