Interpreting Logit Interaction Term Coefficients (continuous * categorical)

Question

I have the following output from a logistic regression model.

Coefficients:
                             Estimate Std. Error z value Pr(>|z|)    
(Intercept)                -2.6023448  0.0694696 -37.460  < 2e-16 ***
our_bid                     0.0039520  0.0007646   5.169 2.35e-07 ***
our_bid:zipcode10000:14849  0.0019334  0.0009006   2.147 0.031807 *  
our_bid:zipcode14850:19699  0.0022905  0.0009514   2.407 0.016064 *  
our_bid:zipcode19700:29999 -0.0009483  0.0008583  -1.105 0.269231    
our_bid:zipcode30000:31999 -0.0016309  0.0011028  -1.479 0.139161    
our_bid:zipcode32000:34999  0.0016241  0.0007856   2.067 0.038688 *  
our_bid:zipcode35000:42999  0.0023549  0.0008541   2.757 0.005831 ** 
our_bid:zipcode43000:49999  0.0007096  0.0008104   0.876 0.381286    
our_bid:zipcode50000:59999  0.0006533  0.0009269   0.705 0.480942    
our_bid:zipcode60000:69999  0.0030564  0.0008169   3.742 0.000183 ***
our_bid:zipcode7000:9999   -0.0027419  0.0012699  -2.159 0.030847 *  
our_bid:zipcode70000:79999  0.0013243  0.0007809   1.696 0.089921 .  
our_bid:zipcode80000:89999  0.0038726  0.0008006   4.837 1.32e-06 ***
our_bid:zipcode90000:96999  0.0038746  0.0007817   4.957 7.18e-07 ***
our_bid:zipcode97000:99820  0.0009085  0.0010044   0.905 0.365726    
---

I am using these coefficients to draw the predicted probabilities such that.

$$\text{Prob} = \frac{1}{1 + e^{-z}}$$

where

$$z = B_0 + B_1X_1 + \dots + B_nX_n.$$

I realize that interpreting these interaction terms can be challenging. However, I generate the main regression equation and use that to formulate the probability curve. However, I'm not sure how to make sense of any of the "our_bid:zipcode" variables?

What about if my model output was: (instead saving zipcode as a factor, I make it a continuous variable)

Coefficients:
                             Estimate Std. Error z value Pr(>|z|)    
(Intercept)                -2.6023448  0.0694696 -37.460  < 2e-16 ***
our_bid                     0.0039520  0.0007646   5.169 2.35e-07 ***
our_bid:zipcode             0.0019334  0.0009006   2.147 0.031807 *  

Would interpretation being easier with this approach? Keeping with the log-odds, how can I make sense of the log-odds effect that this model expresses for the interaction term?

Answer 1

Just a comment on your last suggestion, I would never consider putting ZIP code in as continuous, they're not continuous! they're distinct places. Your initial model is better. It might be more helpful to z-score your continuous predictor, that way a 1 unit change is more interpretable, especially for your interaction terms. R will pick the first alphanumeric zip code as the reference group if you're using standard contrasts, so for example, the log odds of what ever your outcome is are .1% higher (exp(.0019)-1) in if our_bid is increased by 1 in zipcode10000:14849 compared to the reference zip code. If you center your our_bid, the coeficients are a bit more interpretable, but since I have no idea what our_bid is ,I can't really comment beyond that