Postestimation tests for fractional probit model

[Muhammad Abid Shahzad]

Hello,
I have used fractional probit model in my study. I want to run goodness of fit test on the regression.
Can anybody please guide on what tests can be conducted check the goodness of fit and what commands to be used?

Thanks

[Jeff Wooldridge]

The fractional probit is only intended to model the conditional mean, so any goodness-of-fit test should be in that spirit. In my 1996 paper with Papke, we proposed computing an R-squared as the squared correlation coef between the outcome and fitted values. An R^2 based on sum of squared residuals is also easy to compute. This can be compared with the linear model R-squared.

If you want a functional form test, you might try the extension of RESET we propose:

fracreg probit y x1 ... xK
predict yh
gen yhsq = yh^2
gen yhcu = yh^3
fracreg probit y x1 ... xK yhsq yhcu
test yhsq yhcu

A rejection may be mostly a statistical rejection, though. You can try adding squares and interactions of key variables if the test rejects.

[John Mullahy]

In addition to Jeff's suggestions, which pertain to in-sample fit, if you are interested in out-of-sample performance you might consider cross-validation assessments. Stata's splitsample command can be helpful in conducting such exercises.