Probit Model : Joint significance of variables & Estimated Effect

[Mohsin Javed]

Suppose I estimate the following model:

probit y1 x1 x2 x3 x4

where y1 is binary variable, x1 is a proportion (ranging from 0 to 1), x2 and x3 are continuous variables and x4 is a dummy variable.

First, I want to see whether variable x2 and x3 are jointly significant or not. How should I proceed? Is there any command?
Is it correct to use the F-statistic? That is, comparing the R-squared of the full model and the restricted model.

Second, I want find the estimated probability of y1 if x1 increases from 0.2 to 0.5 with x2 and x3 at their average values and x4=1. I have solved such problems for OLS by writing down the equation with coefficients and then plugging the respective values to find the predicted value of the dependent variable. Not sure about Probit models.

[Clyde Schechter]

First, I want to see whether variable x2 and x3 are jointly significant or not. How should I proceed? Is there any command?

test x2 x3

It gives a chi square test rather than an F test.

The "R-squared" from a probit regression is not a real R-squared. It does not have the same sampling distribution as an R-squared from a linear regression, so calculating an F test based on it will be misleading.

Second, I want find the estimated probability of y1 if x1 increases from 0.2 to 0.5 with x2 and x3 at their average values and x4=1. I have solved such problems for OLS by writing down the equation with coefficients and then plugging the respective values to find the predicted value of the dependent variable. Not sure about Probit models.

I'm not sure what you mean by this. There is a probability at x1 = 0.2 (with x2 at their means and x4 = 1) and another probability when x1 = 0.5 (others the same). But there is no probability as x1 increases from 0.2 to 0.5 -- there is a difference in probability. To get the two separate probabilities:

margins, at(x1 = (0.2 0.5)  x4 = 1) atmeans

For the difference between those probabilities, just add the -pwcompare- option to that.

[Mohsin Javed]

Clyde Schechter: thanks a lot!