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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.

Using a scale of test-taking motivation designed to have multiple factors, results are compared from a confirmatory factor analysis (CFA) using LISREL and a multidimensional Rasch partial credit model using ConQuest. Both types of analyses work with latent factors and allow the comparison of nested models. CFA models most typically model a linear relationship between observed and latent variables, while Rasch models specify a non-linear relationship between observed and latent variables. The CFA software provides many more measures of overall fit than ConQuest, which is focused more on the fit of individual items. Despite the conceptual differences in these techniques, the results were similar. The data fit a three-dimensional model better than the one-dimensional or two-dimensional models also hypothesized, although some misfit remained.