A Technique for Comparing Path Models Between Subgroups

A standardization procedure is presented which facilitates comparisons of path coefficients or regression coefficients simultaneously between subgroups and between independent variables. It is noted that standardized path coefficients are generally appropriate when comparisons of the magnitude of effects of different independent variables within a subgroup are desired, and unstandardized path-regression coefficients are appropriate for comparisons between subgroups for a given independent variable. If both types of comparisons are desired simultaneously, however, neither type of path coefficients is satisfactory. To remedy this problem, it is suggested that data be converted to standard scores over all subgroups and that subgroup specific unstandardized coefficients be calculated on the transformed scores. The resulting coefficients are called standardized path-regression coefficients. Convenient calculating formulas which do not depend on actual manipulation of the data matrix are presented. It is shown that the new coefficients are consistent estimators and that usual hypothesis tests can be applied.