My question concerns management issues more than statistical theory. I am searching for a way to measure the relative importance/influence of categorical variables in a logistic regression model with continuous and categorical variables. Since the standard deviation of dummy variables is hard to interpret, I am searching for a robust method which doesn’t include the standard deviation. Usually I use the standardized coefficients to evaluate the influence of a variable.
Personally, I'm not a fan of using standardized coefficients for the purpose of estimating relative importance for the simple reason that variables are standardized prior to model building but the coefficients that are reported are conditional. Given that, the a priori standardization will be biased.
There are many other measures of relative importance. One quick and dirty heuristic that is strongly associated with more complex, multivariate variable decomposition approaches is simply to use the aggregate F- or chi-square statistics associated with each parameter, sum up their values, repercentage to 100% and rank order based on the magnitude of the resulting percentages.
I've found the relaimpo package in R to work well for categorical and continuous variables. I've always coded catagorical variables (-1,1) etc. The relaimpo package will compute the relative contribution of each factor to the overall variance explained by the model.