Overcoming the Reference Category Problem in the Presentation of Statistical Models

Effects of categorical variables in statistical models typically are reported in terms of comparison either with a reference category or with a suitably defined “mean effect,” for reasons of parameter identification. A conventional presentation of estimates and standard errors, but without the full variance-covariance matrix, does not allow subsequent readers either to make inference on a comparison of interest that is not presented or to compare or combine results from different studies where the same variables but different reference levels are used. It is shown how an alternative presentation, in terms of “quasi standard errors,” overcomes this problem in an economical and intuitive way. A primary application is the reporting of effects of categorical predictors, often called factors, in linear and generalized linear models, hazard models, multinomial-response models, generalized additive models, etc. Other applications include the comparison of coefficients between related regression equations—for example, log-odds ratios in a multinomial logit model—and the presentation of multipliers or “scores” in models with multiplicative interaction structure.