Decomposing Area of Residence Differences in Multiple Regression Studies: The Relative Contributions of Independent Variables and Model Coefficients

When rural/urban differences are found in health status or health care use, it is often desirable to identify those factors (such as age, social structure, income, etc.) that influence such differences. To this end, researchers often test rural/urban differences in age, social structure, income, etc., for statistical significance. Also, researchers commonly perform multivariate analyses (such as multiple regressions) to examine rural-urban differences in the influence of various independent variables on the dependent variable of interest. Frequently, researchers discover: (1) statistically significant rural/urban differences in the independent variables (such as age, social structure, income, etc.) and (2) statistically significant rural/urban differences in the effects of these independent variables (i.e., statistically significant rural/urban differences in regression coefficients). The analysis typically stops here, without addressing the relative contributions of (1) and (2) to the rural/urban differences in the dependent variable. This paper argues that the relative contributions of (1) and (2) have important implications for the way policy-makers address rural health problems. This paper presents a method for assessing the relative contributions of differences in the independent variables and differences in regression coefficients to observed differences in the dependent variable, and illustrates the application of the method by analyzing rural/urban differences in the risk of institutionalization.