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We consider two recent approaches to characterizing the manifest probabilities ofa strictly unidimensional latent variable representation (one satisfying local independenceand response curve monotonicity with respect to a unidimensional latent variable)for binary response variables, such as those arising from the dichotomous scoringof items on standardized achievement and aptitude tests. Holland and Rosenbaum(1986) show that conditional association is a necessary condition for strict...

Conditional Association, Essential Independence and Monotone Unidimensional Item Response Models