In the ''pick any/n'' method, subjects are asked to choose any number
of items from a list of n items according to some criterion. This kind
of data can be analyzed as a special case of either multiple-choice d
ata or successive categories data where the number of response categor
ies is limited to two. An item response model was proposed for the lat
ter case, which is a combination of an unfolding model and a choice mo
del. The marginal maximum-likelihood estimation method was developed f
or parameter estimation to avoid incidental parameters, and an expecta
tion-maximization algorithm used for numerical optimization. Two examp
les of analysis are given to illustrate the proposed method, which we
call MAXSC.