"Ordered probit amounts to estimating (1.3) and (1.2) simultaneously, and with the constraint, that b in (1.3) equals b in (1.2). Ergo, ordered probit amounts to estimating the standard binary probit models
Pr(outcome==3) = Pr( X*b + (−/cut2) + u > 0) (1.3)
and
Pr(outcome>=2) = Pr( X*b + (−/cut1) + u > 0) (1.2)
with the constraint that the cofficients, but not the INTERCEPTS, are equal."
My question: Say we estimate two probits as above and test the constraint that the coefficients are equal. Can we interpret this test as a test of probit vs. ordered probit? That is, if the test fails to reject the null that the coefficients are different, would estimated an ordered probit be a logical next step?
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