1988/09/01 by David Grayson · 123 citations
Social Sciences · Decision Sciences · Agricultural and Biological Sciences · Mathematics · #Qualitative Comparative Analysis Research #Psychometric Methodologies and Testing #Sensory Analysis and Statistical Methods #Mathematics #Monotone polygon #Trait #Statistics #Group (periodic table) #Raw score #Polytomous Rasch model #Item response theory #Econometrics #Property (philosophy) #Raw data #Psychometrics #Computer science
paper · doi:10.1007/bf02294219
published in Psychometrika 53(3), 383-392 (Springer Science+Business Media)
openalex publication_date 1988/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23
This paper deals with two-group classification when a unidimensional latent trait, θ , is appropriate for explaining the data, X . It is shown that if X 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 to θ . These groups may relate to θ probabilistically via a non-decreasing function p ( θ ), or may be defined by all subjects above or below a selected value on θ . 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.