How to interpret the marginal effect of a log transformed independent variable in proc qlim?

[PJP]

In a logistic regression using SAS PROC QLIM, I have an independent variable, the natural log of annual earnings.

 
The average marginal effect on the dependent variable of this independent variable = -0.0204.

EXP(-.0204) = 0.9798 AND (1-0.9798) = 0.0202.
 
Does this mean that a 1.0 percent increase in log earnings reduces the probability of the event by 2.02 percent?

Or is the marginal effect interpreted differently?
 
Thanks.

[gunce_sas · Accepted solution]

Hello,

 For a logit model, the marginal effect of change in a regressor, say jth regressor for observation i, on the conditional probability that y_i=1 is

G(x_i'b)[1 - G(x_i'b)]b_j

where, G(x’b) = exp(x’b)/[1+exp(x’b)].

You can request these marginal effects for each regressor from PROC QLIM by specifying the OUTPUT statement and its MARGINAL option. For example,  

OUTPUT OUT=myoutputdata MARGINAL; 

The average marginal effect is the sample average of these marginal effects. For a logit model, this is 

(1/N)*SUMOVER_i{ G(x_i'b)[1 - G(x_i'b)] }b_j 

You can obtain this by averaging the column for the marginal effect of the log of annual earnings over the observations in the data set you specify with the OUT option (myoutputdata in the example above).

If you calculated the average marginal effect of the log of annual earnings as described above and obtained the value -0.0204, then the interpretation of this is that on average a 1 percent increase in log earnings reduces the probability of the event occurring by 2.04 percent.

I hope this helps,

Gunce

[PJP]

Very clear answer. Thank you.