# How to explain the coefficients in the marginal effects of Logit regression?

I am asked to interpret the coefficients of the specification showed the marginal effects of Logit regression.

I am wondering if there is any reference for this work. I am finding a link that is quite useful in interpreting the coefficients in the Logit model but not sure if it is different from the "marginal effects of Logit regression".

Coefficients from logit have essentially no practical interpretation.

$$Pr(y = 1 |X) = \frac{e^{\beta_0 +\beta_1 x_{1i}+...+\beta_k x_{ki}}}{1+e^{\beta_0 +\beta_1 x_{1i}+...+\beta_k x_{ki}}}$$

It's really not obvious how to interpret $$\beta_j$$ for any $$j$$.

The marginal effect is: $$\frac{\partial Pr(y=1|X)}{\partial Xj}= \beta_j \frac{e^{\beta_0 +\beta_1 x_{1i}+...+\beta_k x_{ki}}}{(1+e^{\beta_0 +\beta_1 x_{1i}+...+\beta_k x_{ki}})^2}$$

The marginal effect is the derivative of $$Y$$ with respect to $$X$$, this is easier to interpret. Marginal effects can be evaluated (1) for a specific individual, plugging that individual's X values, (2) for the mean individual, plugging in the average of X for all individuals, or (3) for all individuals, then averaged.

The third option is "average marginal effects", and typically considered "best".

My slides on this are here. Logit starts around slide 20 and I talk about marginal effects around slide 30.