Cut-points of Ordered Probit Model

[Ehsan Latif]

Dear Stata Forum Members,

I have following latent regression representation of the ordered probit model:
HAPit=1 if HAPit* ≤ μ₁
HAPit=2 if μ₁ < HAPit* ≤ μ₂
HAPit=3 if μ₂ < HAPit* ≤ μ₃
HAPit=4 if μ₃ < HAPit* ≤ μ₄
HAPit=5 if HAPit* > μ<sub>4
I estimated the model and found that all the threshold values have negative signs. I have following questions:
1. Is the latent representation in conformity with the negative cut-points? Or does the latent representation implicitly assume positive threshold values?
2. Is there any problem if all the cut-points have negative signs?

I will appreciate your kind response. Thanks.

Ehsan</sub>

[Maarten Buis]

The thresholds can be positive and/or negative, so all negative thresholds is in principle not a problem. It does indicate that when all your explanatory variables are zero the probability of falling in category HAPit=5 is larger than 50%. Depending on what kind of variables you added in the model and how they are scaled it could indicate that you have some sparse categories.

[Ehsan Latif]

Thanks Maarten for your response. The issue is clear to me, but wonder whether there is any literature/ paper that I can cite for this.

[Maarten Buis]

It follows directly from the definition of an ordered probit/logit model, so I don't think there is anything explicitly written about this "issue", since there is no "issue" worth talking about. However, since it follows directly from the definiton of the model you can ofcourse cite any text introducing the model, e.g. Chapter 5 of J. Scott Long (1997) Regression Models for Categorical and Limited Dependent Variables. Thousand Oaks: Sage. (That book happened to be on my desk as I am writing this answer)

[Ehsan Latif]

Thanks Dr. Buis for your response. As I am dealing with a comment from a reviewer on my paper, I thought that a reference would help.