AN IPSATIVE CLUSTERING MODEL FOR ANALYZING ATTITUDINAL DATA

This paper defines a model for analyzing the structure of attitude data, identifies valid methods for identifying distances (resemblances) when estimating groups of similar people, and shows in practical and theoretical terms when and why the model should be used. The model allows for respondents being in a particular social aggregate and for two individual (i.e., ipsative) effects: (1) of mean response level (an individual responding high or low compared to the group); and (2) of amplitude (narrow to wide response profile compared to the group). The appropriate resemblance measure for this model is based on the Pearson correlation, r(p), calculated between objects (e.g., people). Three alternative transformations of r(p) were examined: 1 - r(p), arccos (r(p)), and the cord of angle distance. The best distance measure for the model is arccos (r(p)) or arccos (r(p))(2), although the cord produces similar results. Simulation results show how some resemblance coefficients (e.g., Euclidean distance) can be inappropriate and yield invalid clusters. In using r(p) it is important to consider bimodality in ipsative factors because r(p), cannot detect clusters that collapse on each other under ipsative transformation. Finally, it is noted that for some types of attitudinal data (e.g., performance variables with an absolute zero point), alternative resemblance measures (e.g., cosine) should be considered.