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I want to do a stepwise "regression" but not with an OLS but with an ordered probit problem. As far as I can see, the stepwise regression implemented in EVIEWS is for linear regressions exclusively?

Is there a command which gives out the p-values (which I want to use as stop criterion) or is it necessary to compute them with the values of the t-statistics?

You are correct that the in-built stepwise routine only handles linear models.

You are also correct that the best way to get the p-values is to compute them using the t-statistics.

You should note though, that if you are only interested in the p-values as selection criteria for the stepwise routine, you don't really need to calculate the p-values at all, simply convert the p-value criteria into a t-statistic criteria, and then use the t-stats themselves.