Solved – Reporting exponentiated coefficients in a logistic regression, t-value and confidence intervals

logisticodds-ratioreporting

I recently encountered a situation regarding the reporting of two predictor effects in a logistic regression, which I plan to report their exponentiated coefficients in the text with their SEs, t- & p-values, as well as provide a plot of their predicted effects with 95% confidence bands. I have no issues with computation of the logistic regression and exponentiated coefficients using the following in R

model <- glm(y ~ x1 + x2, family=binomial)
or <- exp(coef(model))

My issues concerns more the reporting as follows:

  1. Suppose the estimated coefficient of my x1, or β1 in this logistic regression is −1.49 (SE = 0.466). Computing the t-value (i.e. -1.49/0.466) on the basis of these values gives me t=-3.19, which is significant. However, if I were to generate the exponentiated coefficient i.e. exp(β1) = 0.225, and if I were to compute the SE using the delta method, I get SE = 0.154 (in R: deltamethod(~exp(x1), x1, x1se)) and the t-value is 1.465 which is non-significant. Is there something missing in my computation that is causing the discrepancy?

  2. A related issue is with regards to computing the 95% confidence intervals for exp(β1) which I initially planned as a prediction plot with different values of x1, however, given the issue in (1), I'm stuck as to how to proceed with this.

Best Answer

  1. In your second test you test the hypothesis that he Odds Ratio (exponentiated coefficient) is 0, which is impossible, so a useless test. Instead you probably wanted to test the hypothesis that the Odds Ratio is 1 (which is equivalent to the test that the log odds ratio is 0). Now you get a significant effect: (.225-1)/.154= -5.03.

  2. I don't understand what the problem is here. Could you clarrify?

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