# Comparing the marginal effect of a GLM to the OLS estimates

My question is, whether there is any way to (somewhat) compare the marginal effect of a GLM estimate to an OLS estimate. As in, "since the OLS and GLM results are very similar, I will favour OLS because of ease of interpretation"

If the answer is a hard no, I would still be very interested in why this is a no.

In my example Crime is a dummy variable (I have recoded it as such).

My example output is as follows:

lm_1st <- glm(lm_form_1st, ,data=full)

Estimate Std. Error t value             Pr(>|t|)
(Intercept)                    0.7896258  0.0792442   9.964 < 0.0000000000000002 ***
Crime                          0.3824961  0.0214503  17.832 < 0.0000000000000002 ***

glm_1st <- glm(glm_form_1st, family="quasipoisson", data=full); summary(glm_1st)
summary(margins(glm_1st, variables = "Crime"))

Estimate Std. Error t value             Pr(>|t|)
(Intercept)                   -0.2140713  0.0875054  -2.446             0.014438 *
Crime                          0.3524041  0.0221681  15.897 < 0.0000000000000002 **

factor    AME     SE       z      p  lower  upper
Crime 0.3302 0.0209 15.7771 0.0000 0.2892 0.3712   # Marginal effect of the GLM


# Related questions:

How does OLS regression relate to generalised linear modelling

How to determine if GLS improves on OLS?

The interpretation of a positive glm coefficient, with a negative marginal effect

• What are the values of crime? Apr 17, 2021 at 9:34
• @SextusEmpiricus In this case Crime is a dummy variable. Sorry, I realise that I should have added that. I'll add it with my question about marginal effects as well.
– Tom
Apr 17, 2021 at 9:44
• *question = other questions
– Tom
Apr 17, 2021 at 9:50