Abstract
Singles indices of agreement or association from data in 2 × 2 tables may be unsatisfactory insofar as they cannot encapsulate all the information in the table. Recent dissatisfaction with the κ statistic arguably stems from this fact. The tetrachoric correlation model of Pearson (1900) posits three parameters which are 1-1 functions of the three pieces of independent information in a 2 × 2 table. Tallis (1962) exhibited full maximum likelihood estimation of the tetrachoric correlation model. The present paper extends Tallis' work by developing latent variable models for validity and reliability in 2 × 2 tables. Three latent trait models are developed, each with three interpretable parameters and full maximum likelihood estimation.
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