# 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?

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