Sufficiency and Conditional Estimation of Person Parameters in the Polytomous Rasch Model
Rasch models are characterised by sufficient statistics for all parameters. In the Rasch unidimensional model for two ordered categories, the parameterisation of the person and item is symmetrical and it is readily established that the total scores of a person and item are sufficient statistics for their respective parameters. In contrast, in the unidimensional polytomous Rasch model for more than two ordered categories, the parameterisation is not symmetrical. Specifically, each item has a vector of item parameters, one for each category, and each person only one person parameter. In addition, different items can have different numbers of categories and, therefore, different numbers of parameters. The sufficient statistic for the parameters of an item is itself a vector. In estimating the person parameters in presently available software, these sufficient statistics are not used to cond...
David Andrich (2010). Sufficiency and Conditional Estimation of Person Parameters in the Polytomous Rasch Model. Psychometrika, 75(2), 292-308. https://doi.org/10.1007/s11336-010-9154-8