On the Existence and Uniqueness of Maximum-Likelihood Estimates in the Rasch Model
- 1 March 1981
- journal article
- Published by Cambridge University Press (CUP) in Psychometrika
- Vol. 46 (1) , 59-77
- https://doi.org/10.1007/bf02293919
Abstract
Necessary and sufficient conditions for the existence and uniqueness of a solution of the so-called “unconditional” (UML) and the “conditional” (CML) maximum-likelihood estimation equations in the dichotomous Rasch model are given. The basic critical condition is essentially the same for UML and CML estimation. For complete data matrices A, it is formulated both as a structural property of A and in terms of the sufficient marginal sums. In case of incomplete data, the condition is equivalent to complete connectedness of a certain directed graph. It is shown how to apply the results in practical uses of the Rasch model.Keywords
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