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Re: st: oprobit with cutpoints as function of covariates
At 08:40 PM 4/11/2007, [email protected] wrote:
Dear All,
Thanks for your replies. I apologise for my lack of clarity in setting my
initial query. I will explain it in more detail now.
Basically, I have an ordered categorical model (ordered probit) where,
theoretically, people tend to overstate the values of the dependent variable
for higher values. That is, y can take for values 1, 2, 3 or 4 and my
assumption is that certain people in my sample (i.e., with some particular
values of covariates) tend to answer most often say, 3 or 4; so I am facing a
measurement error problem in the dependent variable, and by modelling the
cut-points as function of those covariates I would be able to take this into
account. However, as mentioned by Stat Kolenikov�s reply, I would face an
identification problem if the covariates I use to measure these errors in the
cut points are not different from the one in the main equation. The references
I found so far � not too many though- are:
This is starting to sound familiar; see slides 14-20 of
http://www.nd.edu/~rwilliam/gologit2/RWNASUG2006.pdf
So, if I understand you correctly, suppose gender
(coded 1 = female, 0 = male) has a significant
positive effect. This might be because (a) women
really do score higher on the underlying latent
variable, and/or (b) women apply different
standards when answering the question, e.g. what
a man would call "average" a woman would call
"above average". If the latter, then apparent
differences between men and women would just be
measurement artifacts caused by men and women
coding their responses differently.
Now, if you think it could be both (a) and (b),
then as far as I know Stas is right. You have an
identification problem. I don't know how you
would decompose the gender differences into the
"real" versus "artifactual" components. If, on
the other hand, your theory is strong enough to
rule out (a), i.e. gender does not have a "real"
effect, then any observed effect could be
attributed to measurement differences. This
might be reasonable if, say, your theory
convincingly argue that any effect of gender on Y
must be indirect and you control for the vars
that gender affects which then affect Y.
In general, I think this is the kind of issue
that could make you want to give up quantitative
research altogether. :) You are counting on
respondents to code themselves as "above
average", "average", "below average" or
whatever. Who's to say that all respondents do
this coding the same? If we see differences by
gender, how do we know whether these differences
are real as opposed to just being differences due
to the fact that different people use different standards when coding?
In short, if I understand you correctly, the only
way I know of how to deal with this is to have a
great theory that lets you go with either (a) or
(b). If you want both (a) and (b), I don't know
how you accomplish the split (but I would be interested in any ideas).
-------------------------------------------
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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