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of categories of item i, and mƒ°m1. Once the questionnaire is administered to N subjects, optimal scaling of the items can be defined as a procedure to assign weights to the m categories so as to maximize the between-subject variance relative to the total variance of the weighted linear composite scores. This is an eigenvalue problem of a matrix of order m, which can easily exceed the capacity of a computer program. For example, if each of eighty items has five categories, m=400, and a 400 400 matrix is perhaps too large to handle with the computer. This is what is referred to as a size problem. The practical problem of the a priori order of categories can be explained in the following way. Suppose that all the m categories have an a priori order such that the weight of category (j+ 1) is larger than that of category j, that is,

PARTIALLY OPTIMAL SCALING OF ITEMS WITH ORDERED CATEGORIES