Maximum likelihood methodology for diff fit measures for quasi orders
- Three inductive item tree analysis algorithms have been proposed for deriving quasi orders from dichotomous data. These procedures have been treated descriptively, without examining theory. In this paper, we introduce maximum likelihood methodology for the inductive item tree analysis methods. The diff fit measures of these methods can be interpreted as maximum likelihood estimators. We show that the estimators are asymptotically efficient, and hence they are asymptotically normal, asymptotically unbiased, and consistent. In simulation studies, the algorithms are compared regarding finite sample consistency, population ranks, and population symmetric differences. The approach to fit measures presented in this paper can be applied to any, sufficiently smooth, coefficient for multinomial count data. In particular, it allows introducing maximum likelihood methodology for measures assessing the fit of general knowledge structures.
