I am making a table from results of an analysis using generalised linear model which involves detecting association of a categorical predictor variable over multiple outcome variables. Of those multiple outcome variables, few are binary where I display the odds ratio for each category of the predictor (as we do in logistic regression); while few are continuous outcome variables, in which case I can display the beta estimate for each category of the predictor. My question is will it be ok if exponentiate the beta value and express it as odds ratios. Can I do that?
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2 Answers
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There are two issues with that. First, you are assuming that a one-unit change in $x$ is meaningful. Second, you are restricting yourself to the case where $x$ is linear. In general think of odds ratios as anti-logs of differences in predicted logits ($X\hat{\beta}$). That way you can handle nonlinearities and meaningful ranges. The R rms package by default produces inter-quartile-range odds ratios for continuous predictors.
answered Nov 8, 2014 at 13:30
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The issue of single exposure / many outcomes is not unfamiliar. I would separate the analysis table into lines of continuous measures and their associations (labeled as mean differences) and lines of categorical measures and their associations (labeled as odds ratios or risk ratios).
The rationale for exponentiating a coefficient is usually when the outcome is on a log scale, either in a linear model or GLM. If you have not applied such a transformation, an exponentiated coefficient does not make sense.
There are also latent variable or mixed model methods to present a "grand" beta of association with all measures simultaneously. This suffers from having no meaningful interpretation.
