IDSORT: An individual differences multidimensional scaling program for sorting data

Abstract

IDSORT is an individual differences multidimensional scaling (MDS) program specifically designed for sorting data. It is a three-way extension ofthe MDSORT program (Takane, 1980, 1981). While the MDSORTprogram finds a single stimulus configuration from N sets of sorting data, IDSORT also obtains dimensional weights for subjects, which account for certain individual differences in sorting behavior. That is, IDSORT fits the INDSCAL (Carroll & Chang, 1970) type of the weighted euclidean distance model to sorting data. The stimulus sorting method, in which the subjects are asked to sort a set of stimuli into several groups (clusters) in terms of their similarity, has been very popular among social scientists because of its simplicity. Yet when the sorting data are analyzed by a nonmetric MDS procedure, such as ALSCAL (Takane, Young, & de Leeuw, 1977), there is some uncertainty as to how similarity measures should be defined based on the sorting information. IDSORT, on the other hand, simultaneously scales the sorting data (i.e., it derives a similarity measure from the sorting data) and represents them (i.e., it finds a stimulus representation from the derived similarity measure) based on a single common criterion. IDSORT is the first individual differences MDS method that directly applies to the sorting data. Description. IDSORT allows a user to directly input original sorting data. The program then derives similarity matrices (one for each subject) between the stimuli and finds a stimulus configuration and dimensional weights for the subjects. The stimulus configuration and the dimensional weights are determined in such a way that the sum of squared intercluster distances in the subject space (summed over the subjects) is maximized under suitable normalization restrictions. As in the MDSORT program, cluster centroids for the stimuli classified into certain clusters by each subject may optionally be calcu·lated. These provide information concerning another source of individual differences in sorting behavior. Unlike two-way MDS, lower dimensional solutions are not proper subsets of a higher dimensional solution. So, separate analyses have to be conducted to obtain solutions with different dimensionalities.