# Interpretation of logistic regression coefficients when there are multiple levels

Suppose that the model had the following output:

                        Estimate Std. Error z value Pr(>|z|)
(Intercept)              0.07       0.33      0.21   0.829
x0_low                   0.44       0.22      1.96   0.049   *
x1_m                    -0.51       0.25     -1.98   0.047   *
x1_l                    -0.05       0.22     -0.24   0.809
x2_no                    0.51       0.26      1.94   0.051   .


where

• x0 has levels hi, low
• x1 has levels s, m, l
• x2 has levels yes, no

I'm wondering what an interpretation for the coefficient x1_m would be.

It seems as though it could be:

x1_m reduces the log(odds) by roughly 40% having adjusted for x0 and x2

But what I'm a bit confused about is whether this is actually what it's saying, because x1_m is simply a level within the factor x1, so does that change its meaning?

x0, x1 and x2 are factors. So, so called 'reference levels' are chosen for them (by default these wolud be their first levels: hi, s and yes respectively).
So, in you case, x1=m reduces the log(odds) by roughly 0.51, as comapred to x1=s and having adjusted for x0 and x2.