RE: st: Generalised interval regression

[Richard Williams <Richard.A.Williams.5@ND.edu>]

At 08:05 AM 12/4/2006, Mentzakis, Emmanouil wrote:
> Dear Richard,
>
> Thank you very much. What I meant in my question was, if there is a way
> to relax the parallel line assumption when using intreval regression and
> I think what you prospose does exactly that.
>
> However, I d like to ask how could I specify these inetrvals?
>
> If I had these inetervals: 0-20, 21-60 and 61-100
>
> Would it be correct to write:
>
> constraint 1 depvar>0 & depvar<20 if depvar==1
> constraint 2 depvar>20 & depvar<60 if depvar==2
> constraint 3 depvar>60 & depvar<100 if depvar==3
>
> And then
>
> oglogit2 depvar indepvar, npl() constraints(1-3)
I'm not sure how you would do it - or even if it can be done! - but 
it wouldn't be done like that.  Again, if there is a paper out there 
that has actually done this, it would help to look at it.  If there 
isn't one, I'd be leery of trying to invent a new technique without 
spending some time working through all the math behind it.

My guess is that a correct procedure would look something like this:

. use "http://www.indiana.edu/~jslsoc/stata/spex_data/ordwarm2.dta";, clear
(77 & 89 General Social Survey)

. constraint 1[eq1]_cons = 1.0
. constraint 2 [eq2]_cons = .5
. constraint 3 [eq3]_cons = -.6
. gologit2  warm yr89 male white age ed prst, link(p) npl nolabel c(1-3)

Generalized Ordered Probit Estimates              Number of obs   =       2293
                                                  Wald chi2(18)   =     616.50
                                                  Prob > chi2     =     0.0000
Log likelihood = -2820.7554                       Pseudo R2       =     0.0584

 ( 1)  [eq1]_cons = 1
 ( 2)  [eq2]_cons = .5
 ( 3)  [eq3]_cons = -.6

[rest of output omitted]

Now, what I am not sure of, is how you would determine the values of 
the constraints?  Since the errors in probit are normal(0, 1) you 
would have to figure out some way to convert your intervals into 
appropriate values, i.e. you couldn't just use 20, 60 and 100.

Again, though, I stress that this is a wild guess.  I wouldn't trust 
it too much unless, say, there is a published paper using the method 
and I could replicate its results.




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Richard Williams, Notre Dame Dept of Sociology
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