Factor comparison: An examination of three methods

Three coefficients of factor similarity were examined with regard to their behaviour within four sets of data. Two simple methods using Pearson r correlations and Tucker Congruence coefficients were compared with a more complex method given by Kaiser, Hunka and Bianchini (1971). Three of the data sets involved the use of 100 random data matrices, the fourth was that provided by the Eysencks' work on cross-cultural differences in personality using the EPQ. Drawbacks with each other coefficient were apparent from the results, with the Kaiser et al. coefficient being capable of the most misleading results overall. However, use of the mean solution cosine in addition to the variable pair cosines was suggested as a method of validating the Kaiser et al. coefficient. It was concluded that using the three coefficients simultaneously as a multiple indicator yielded the best solution to the problem. In addition, it was suggested that other psychometric indicators should be employed to increase the degree of certainty of factor similarity.