Comparing probabilities of Linear Probability Model and Probit Model using a graph

[Deepak Agarwal]

I have a model in which there are a lot of variables. I need to estimate the probit and the LPM estimated probabilities and compare them using a graph with educational attainment as X-axis and Y-axis as the predicted probabilities. How can I do this?

[Clyde Schechter]

Something like this:

probit outcome predictors
predict probit_predict, pr
regress outcome predictors
predict linear_predict, xb
graph twoway line *_predict educational_attainment, sort

[Phil Bromiley]

You might also consider using margins. Clyde's approach does the actual predictions which include the variation in all variables at once. An alternative is to only vary one variable while leaving all others at their means (which is the default in many margins specifications). I don't know an elegant way to do this - I would probably run margins on the probit results for multiple values of educational attainment, write those values into a new variable, run margins with the other model and save those, and then do a twoway graph. In theory, you could also just use the parameters and functional forms from the two estimates (Stata will also graph functions).

[Deepak Agarwal]

Thanks Sir Clyde Schechter and Phil Bromiley