Scaling Binary Data Using a Factor Model

SUMMARY A simple method for scaling a set of binary responses is proposed using the logit factor model of Bartholomew (1980). It is shown that individuals may be ranked on the basis of a linear combination, ∑αi x i of the responses (xi = 0 or 1) where the αi's are the appropriate factor loadings. This completely avoids the need to calculate the y-scores suggested in Bartholomew (1980) and hence the heavy numerical integration which that method involves.