# Interpretation of Multiple Logistic Regression with Categorical Variable

I'm currently trying to interpret multiple logistic regression with a categorical variable.

Description of variables:

• region = the beneficiary’s residential area in the US; a factor with levels northeast, southeast, southwest, northwest.

• charges_cat = which takes the value 0 (low) when charges are less than 10000 dollars and the value 1 (high) in all other cases.

• bmi = body mass index of primary beneficiary in Kg/m2.

> logm2<-glm(charges_cat~bmi+region, family=binomial)

Coefficients:
Estimate
(Intercept)     -0.754605
bmi              0.026294
regionnorthwest -0.180464
regionsoutheast -0.244276
regionsouthwest -0.292365


My interpretation for b2 = regionnorthwest is:

> exp(-0.180464)
[1] 0.8348827


Given that southeast and southwest regions (dummy variables) and also bmi is fixed, the odds of charges being more than 10000 dollars is 16.51% lower than the odds of charges being more than 10000 dollars for a beneficiary who lives in the northeast region of the US.

My question is: in multiple logistic regression should I state the factor levels of the region are fixed, such as “southeast and southwest regions are fixed.” or there is no need to state the dummy variables of the region fixed?

Also, any other way to interpret b2?

The correct and complete interpretation for b2 is as follows:

Among US beneficiaries with the same body mass index (bmi), those who live in the northwest region of the US have 16.51% lower odds of incurring charges of 10000 dollars or more than those who live in the northeast region of the US.

Notice the use of plural for odds and also the fact that we are controlling for bmi when making the comparison of odds among the two regions. It would be good practice to also report the 95% confidence interval not just the point estimate for the percent reduction in odds.

The interpretations of b3 and b4 would be similar. That is all you would need to report - no other statements are necessary. The above interpretation assumes that your response variable is set to 1 for charges of 10000 dollars or more and 0 for charges strictly less than 10000 dollars. It also assumes that your data are valid and your model is appropriate for these data.

• Thank you for accepting my answer. See also this thread I wrote on Twitter after reading your question: twitter.com/IsabellaGhement/status/1314606940115226624. It provides an overview for interpreting a binary logistic regression model with a single, continuous predictor on 3 different scales: 1. log-odds ratio scale, 2. odds scale and 3. probability scale. Oct 9 '20 at 19:05