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Re: st: Dependent continuous variable with bounded range


From   "Pavlos C. Symeou" <p.symeou@jbs.cam.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Dependent continuous variable with bounded range
Date   Thu, 17 Apr 2008 01:26:54 +0100

Dear Anders,

"Are we talking about a fractional response on unbalanced panel data?
In that case, how about using using -glm ..., family(binomial)
link(logit) robust- but separately for each panel? That (or with the
probit link) seems to be what Jeffrey Wooldridge suggests at the end
of this paper:
http://www.msu.edu/~ec/faculty/wooldridge/current%20research/clus1aea.pdf
I'm sure he would be happy to clarify this at 2008 SNASUG, if needed :-)

Anders Alexandersson"

we are talking about balanced panel data...I am not sure what you mean by fractional responses...As i explained in correspondence the variable in question, "reputation", results from the addition of the values of three other variables which take discrete values ranging from 0 to 10 and thereafter tiehr sum is divided by 3. Therefore, "reputation" as expected, has upper and lower bounds the values 10 and 0, respectively. In particular, my sample's values range from 2.95 to 8.45.

Reading through everyone's invaluable responses, which I need to admit have given me substantial food for thought, I have construed that the OLS model might not be that inappropriate to fit the data after all. That is based on that the "reputation" variable manifests a normal distribution; its values are quite distant from the bounds; the coefficients of the explanation variables appear to support the theoretical arguments; the idiosyncratic errors from the - xtreg, fe (or re) - regression model approach a normal distribution; the logit transformation of the "reputation" variable does not seem to improve the model; either the -xtgee- or the -glm- commands do not yield any satisfactory results.


Anders Alexandersson wrote:

Pavlos C. Symeou <p.symeou@jbs.cam.ac.uk> wrote originally:

I have panel data for 100 firms for five years and I want to examine the
effects of various variables on "reputation". My variable "reputation"
takes continuous values in the range of 0-10. Namely, it can take
values of 1,2,3 but also of 2.5, 9.6, etc. The values that the variable
"reputation" takes in my sample range between 2.6 - 8.3. Can you please
advise if I can still use panel OLS estimation for panel data or should
I use a different model? In essence, my main concern is the limitations
of the bounded range of my variable.
There were several responses and clarifications. Nick Cox suggested

gen repute = reputation / 10
xtgee repute ..., link(logit) family(<continuous>)
Unfortunately this is not allowed, Nick confirmed to Pavlos:

You are correct in that -xtgee- (Stata 8) does not support -f(gamma)
link(logit)- or -f(normal) link(logit)-. I was guessing by analogy with
-glm- which does support those combinations. I am away from base at
present and unable to check Stata 10. (I assume from your reference to
Stata 8 manuals that you are using Stata 8. If that is true, it is
prudent to flag the fact in your postings.)

I don't know of any reason why those combinations are not supported by
-xtgee- when they are by -glm-. As a programmer, I am sympathetic to any
explanation of the form "Just didn't think of that" or "Not got round to
that yet".

The other link functions are in principle unsuitable, as they pay no
heed to the range restriction, but you could try
-link(identity)- and -f(gamma)- or -f(normal)-.
Are we talking about a fractional response on unbalanced panel data?
In that case, how about using using -glm ..., family(binomial)
link(logit) robust- but separately for each panel? That (or with the
probit link) seems to be what Jeffrey Wooldridge suggests at the end
of this paper:
http://www.msu.edu/~ec/faculty/wooldridge/current%20research/clus1aea.pdf
I'm sure he would be happy to clarify this at 2008 SNASUG, if needed :-)

Anders Alexandersson
andersalex@gmail.com
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