How to interpret categorical variable in logistic regression with contrast coding I'm currently having the following regression that I found a bit tricky to explain:
# glm(formula = mask_got_20 ~ Sex + Amount + mask_wearing, family = "binomial", 
#    data = clean_data_third)

# Coefficients:
#               Estimate Std. Error z value Pr(>|z|)    
# (Intercept)    1.50966    0.27831   5.424 5.82e-08 ***
# Sex1           0.13040    0.17904   0.728 0.466395    
# Amount1        0.07623    0.17914   0.426 0.670433    
# mask_wearing1  1.02371    0.27780   3.685 0.000229 ***
#  ---
#  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

exp(coef(r5))
# (Intercept)          Sex1       Amount1 mask_wearing1 
#   4.525197      1.139287      1.079214      2.783507 

In this regression, I would like to explain the last variable -- mask_wearing, which is a categorical variable recording whether my participants are still wearing a facemask. The DV in this regression is whether the masked confederate receives £20 (1 = yes, 0 = no).
Since my main interest is the intercept, I used contrast coding where the intercept represents the mean of group means, and the parameter represents the difference from the intercept.
How should I compare if I would like to interpret the last variable as: "participants who reported they still wear a facemask regularly are about X times more likely to offer £20 to the masked confederate than participants who no longer wear facemasks."
Should I use the difference of intercept estimate +- the estimate of mask_wearing and then exponentiate it?
Thank you for your help.

It's best to choose variable coding on arbitrary convenience, then to get any contrast of interest by subtracting predicted log odds (and possibly anti-logging the difference to get an odds ratio).  This readily generalizes to more complex cases where the categorical predictor interacts with a complex function of another predictor such as a spline function to allow nonlinearity.  In the R rms package contrast function you'd do something like this:
f <- lrm(y ~ sex + mask + x, data=d)
contrast(f, list(mask = 'y'), list(mask = 'n'))

Since in this model mask doesn't interact with anything, it doesn't matter what values are assigned to sex and x.  rms sets them to the mode and median, respectively.
