Comparing Causes of Dependency: Shared Latent Trait or Dependence on Observed Response

Accurate parameter estimation in the Rasch model involves the assumption of conditional independence, also termed local independence. Conditional on ability, the responses to items A and B should be independent. Two types of conditional dependence are detailed in this pedagogical piece: trait dependency and response dependency. The bias in difficulty and reliability and the estimates of fit and correlated residuals resulting from these dependencies are compared and contrasted to results from using models that account for the dependency. Contrasts with results from a 2-parameter item response theory model are also briefly noted.