The General Linear Model and Direct Standardization

Abstract

A formal comparison is made between direct standardization and three cross- classified data structures: tables of means which are linear additive; tables of means which are log-linear additive; and tables of frequencies which are log-linear addi tive and can be converted to tables of proportions which are logit-linear additive. Standardization is an appropriate method of summarizing the data if the differ ences between standardized means and so on are not affected by the choice of standard distribution. This condition occurs when there is no interaction between the predictor and control variables in their impact on the dependent variable. It is shown that the condition may also be expressed in the form of the general linear model with the corresponding interaction terms absent. Then, when standardiza tion is appropriate, differences between standardized quantities are estimates of differences between parameters in linear models. In some circumstances, e.g. when the cell sizes are small, if the specified interactions are believed absent then the cell entries may be fitted using the general linear model; standardization of the fitted entries would then be preferable to standardization of the observed entries.