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Re: st: Cutoff estimation by MLE
At 09:22 AM 12/4/2007, Bradley Chen wrote:
Dear Statlisters,
I have a problem with estimating the ordered probit cutoff, and I
realized that there is probably no precoded command in STATA doing
what I want so I need to do the maximum likelihood estimation
This is what I want to estimate:
I have a dependent variable, which is a four category ordered
response Yi={1,2,3,4}, whose value depends on a latent variable Y*=Xb+e
The observed Yi=j if C(j-1)<Y*<Cj with C0=minus infinity. And the
most important part for me is that the cutoff level C is also a
function of the observed characteristics: Cj=X*b'
So the the log likelihood equation I want to maximize is
L={Yi=1}*log(cnorm(-C1))+{Yi=2}*log(cnorm(C2-C1)-cnorm(-C1))++{Yi=3}
*log(cnorm(C3-C1)-cnorm(-21))+{Yi=4}*log(cnorm(C1-C3)),
to attain the coefficients b' in the cutoff equation
Could someone kindly teach me how to write the STATA command?
I am wondering now if this is a problem gologit2 can handle. Suppose
you have gender as an indpendent var. The coefficient for gender
might reflect (a) a real effect of gender on the underlying latent
variable, or (b) differences in the cutpoints for men and women, e.g.
two men and women could have the same underlying value but their
observed responses are different because women use different
cutpoints than men. So, instead of using the effect of gender to
compute y*, you use it to come up with the cutpoints for women as
opposed to men. I think you have to choose (a) or (b) though; there
is no way to estimate both effects, although I suppose you could have
some kind of theory that would let you say there is a 50-50 split or
something like that.
The terminology cut-point shift and index shift are sometimes
used. If the difference in cutpoints between men and women is always
the same (index shift), then oprobit is fine. If the difference
varies (e.g. first 2 cutpoints are the same but the third differs)
then you have cut-point shift and use gologit2 with link probit.
Put another way, you might estimate something like
oprobit y x1 x2 x3 male
You could then view the effect of male as the difference in cut
points for men and women; and in this case you would be saying the
difference was the same for every cutpoint. Or, if you did
gologit2 y x1 x2 x3 male, npl(male) link(probit)
you could again be saying the cut points for men and women differ,
but the difference need not be the same at each cut point.
Just speculation here; maybe you have something very different in mind.
-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
HOME: (574)289-5227
EMAIL: [email protected]
WWW: http://www.nd.edu/~rwilliam
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