Accounting for Local Dependence with the Rasch Model: The Paradox of Information Increase

Test theories imply statistical, local independence. Where local independence is violated, models of modern test theory that account for it have been proposed. One violation of local independence occurs when the response to one item governs the response to a subsequent item. Expanding on a formulation of this kind of violation between two items in the dichotomous Rasch model, this paper derives three related implications. First, it formalises how the polytomous Rasch model for an item constituted by summing the scores of the dependent items absorbs the dependence in its threshold structure. Second, it shows that as a consequence the unit when the dependence is accounted for is not the same as if the items had no response dependence. Third, it explains the paradox, known, but not explained in the literature, that the greater the dependence of the constituent items the greater the apparent information in the constituted polytomous item when it should provide less information.