# How to interpret GLM coefficients?

I am reproducing the results from COMPAS analysis done by propublica and I needed some help understanding how they handled interpretation of GLM coefficients. Score_factor is a variable indicating risk of recidivism and its regressed against variables like race, gender etc. The model is given below.

Call:
glm(formula = score_factor ~ gender_factor + age_factor + race_factor +
priors_count + crime_factor + two_year_recid, family = "binomial",
data = df)

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)                 -1.52554    0.07851 -19.430  < 2e-16 ***
gender_factorFemale          0.22127    0.07951   2.783 0.005388 **
age_factorGreater than 45   -1.35563    0.09908 -13.682  < 2e-16 ***
age_factorLess than 25       1.30839    0.07593  17.232  < 2e-16 ***
race_factorAfrican-American  0.47721    0.06935   6.881 5.93e-12 ***
race_factorAsian            -0.25441    0.47821  -0.532 0.594717
race_factorHispanic         -0.42839    0.12813  -3.344 0.000827 ***
race_factorNative American   1.39421    0.76612   1.820 0.068784 .
race_factorOther            -0.82635    0.16208  -5.098 3.43e-07 ***
priors_count                 0.26895    0.01110  24.221  < 2e-16 ***
crime_factorM               -0.31124    0.06655  -4.677 2.91e-06 ***
two_year_recid               0.68586    0.06402  10.713  < 2e-16 ***


From the model above, they concluded that "Black defendants are 45% more likely than white defendants to receive a higher score correcting for the seriousness of their crime, previous arrests, and future criminal behavior." (Note race_factorWhite is part of intercept) based on following calculation:

control <- exp(-1.52554) / (1 + exp(-1.52554))
exp(0.47721) / (1 - control + (control * exp(0.47721)))
[1] 1.452841


I am aware that we can get change in odds ratio of score_factor between white and black defendants by doing exp(0.47721). But I am not sure what the calculation with control and intercept is doing. Can someone please explain?

• @Rajesh In most cases you can estimate the relative risk directly with relative risk regression. Relative risk regression is a glm with binomial variance formula (var = mean * (1-mean)), but uses a log link. Attempt the analysis again with family=binomial(link=log) and you should get comparable results. I cannot advocate enough transforming ORs to RRs when possible. Commented Sep 8, 2016 at 19:58