Residual Scaling: An Alternative to Correspondence Analysis for the Graphical Representation of Residuals from...

The method of correspondence analysis, applied to a contingency table, provides a graphical representation of departures from the independence model. Generalized correspondence analysis has been proposed as a way of graphically representing departures from models other than independence. However, generalized correspondence analysis does not necessarily decompose a chi-square statistic for departures from non-independence models. We propose a method, called residual scaling (RESCAL), that does decompose chi-square and can also be used for decomposing the difference between any two log-linear models. The decomposition is represented graphically for ease of interpretation. RESCAL analysis results differ in interpretation from correspondence analysis results, although the differences have some advantages over correspondence analysis. RESCAL is demonstrated empirically with data concerning earned doctorates conferred in the United States from 1960 through 1982.