With any set of polytomous items, where all response categories are logically possible for each item, it will sometimes happen that certain categories are unused in the immediate sample of data. This sample characteristic can not be allowed to interfere with a response framework which is a characteristic of the research design. The distinction between a logically null category and a category that is observed to be null in some sample is analogous to the distinction between a structural zero and a sampling zero in contingency table analysis (Fienberg 1985). When a category is not used for a particular item, we would not recommend omitting reference to that category by down-coding the categories above it, such as is the default in many Rasch analysis programs. This kind of down-coding can alter a person's ranking on a test. Of course, when a sampling zero occurs repeatedly for a particular item, it is wise to examine the item for an explanation.
A simple modification of the Partial Credit model retains all categories so that none are "collapsed" out (Wilson & Masters 1991). This reformulation has been incorporated into several Rasch programs. If z is the category corresponding to a sampling zero and categories z-1 and z+1 are present in the data, then, in the notation of Wright & Masters (1982),
Pnix = exp (sum j=0 to x (except z) (Bn - Dij) / sum k=0 to mi (except z) (exp (sum j=0 to k (except z) (Bn - Dij) )
with Pniz locally zero. Diz+1 is twice the calibration of the intersection of the probability curves for categories z-1 and z+1.
Unobserved or Null Categories, M Wilson … Rasch Measurement Transactions, 1991, 5:1 p. 128
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