st: Interpretation of Cut Points in Ordered Probit (Logit) Model

["Auh, Jun Kyung" <jauh14@gsb.columbia.edu>]

Hi All-

I am having a hard time to give an interpretation on the cut off points in ordered probit regression.
Suppose that I have the following structure:

The latent variable Z is linear in observable variable X:

Z = b*X + u , u~N(0,1)

The resulting (observable) variable takes 3 values:

Y = 3 if Z > cut1
Y = 2 if cut2<Z<cut1
Y = 1 if cut2>Z

X variable has non-zero value and Y is distributed in normal way in the data (say Y = 1 is 20%,  Y = 2 is 60% and Y =3 is 20%)

The regression results show that I have negative value for cut2.
If cut2 < 0, wouldn't the model predict that there is zero observation with Y = 1?
Or, is the cut points are de-meaned? i.e, do I have to add back the mean of X to have correct interpretation?

Any help would be greatly appreciated!


Best,
JK


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