# Interpreting Marginal Effects

I am running a probit glmer, with a binary response varaible and a categorical explanatory variable with three dummy levels and have tried to calculate the marginal effect using the following code:

    ProbitScalar<- mean(dnorm(predict(m1,type = "link")))


The ProbitScalar value is then multiplied by the coefficient estimates from the regression output.

I get the following values:

-0.2946806 (referring to the intercept and reference level) -0.1527443 -0.07252501

I am slightly confused how to interpret them as they seem quite low compared to what I would expect from the raw data.

Is it correct that the second variable has a 15% lower chance of achieving success (the binary response variable) than the reference group and the final variable has a 7% less chance of achieving success than the reference group?

## 1 Answer

Yes, it is correct but make sure you followed the correct procedure to calculate the decrease.

Let’s say that your categorical variable has 3 levels A,B and C and that A is the reference. Then your model is :

Log(odds) = -0.29 -0.153*I(level=B) -0.0.73*I(level=C), or
odds = exp{ -0.29 -0.153*I(level=B) -0.0.73*I(level=C) }.


The coefficient -0.153 can be interpreted as follows:

odds(A)/odds(B) = exp{-0.29 }/exp{-0.29 -0.153} = exp{0.153} = 1.17, or
odds(A) = (1+17%)*odds(B) {A 17% more likely than B}, or
odds(B) = odds(A)/1.17 = 0.85 * odds(A) = (1-15%) * odds(A) {B 15% less likely than A}.


Similarly you can interpret the coefficient -0.073. Note that it is very likely to miss a little bit (%) increase or decrease when you round the coefficients (like I've done).

• Thanks - I am a bit confused how A can be 17% more likely than B but B can only be 15% less likely than A ? (Is this what you meant by rounding the coefficients) – Lola2000 Aug 19 '15 at 13:51