Donald Burrill wrote:
>
> On Sat, 17 Jun 2000, Cecil Chan wrote:
>
> > If the dependent variable of the equation to be estimated using OLS
> > method is a proportion (i.e. it varies between 0 and 1), while the
> > explanatory variable is unbounded, will the estimated coefficients
> > still maintain the Best Linear Unbiased Estimator (BLUE) properties?
>
> Why wouldn't they? All you've postulated is that the true relationship
> between the variables is not linear over the entire real line (although
> it may be approximately linear, and to a pretty good approximation, over
> a bounded region of the explanatory variable). If this nonlinearity is
> important for your purposes, you should be modelling it explicitly, and
> you would then not be interested in a BLUE (except, perhaps, a BLUE for
> estimating f(Y) from X where f(Y) is a suitable nonlinear function of Y).
> If the nonlinearity is not important, the actual (as distinct
> from theoretical) range of the explanatory variable must be bounded, a
> linear estimator is satisfactory, and among the set of linear estimators
> OLS should still be BLUE, shouldn't it?
> -- DFB.
> ------------------------------------------------------------------------
> Donald F. Burrill [EMAIL PROTECTED]
> 348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
> MSC #29, Plymouth, NH 03264 603-535-2597
> 184 Nashua Road, Bedford, NH 03110 603-471-7128
> ===========================================================================
My first remark is:
When one use the proportion as a dependent variable, it is important to take
into
account the size of the sample on which each proportion was calculated, because
the points are not the same importance: deux proportions of .5 are not the same
importance if the first is calculted on 10 subjects and the second on 100 !!!
and this might infuence considerably the coefficients of regression and their
significant.
My second remark is:
Why don't use the logistic regression on the binary data before calculating the
proportions ?
My third remark is:
it seems to me that is preferable to use the tendency test (rather than the OLS
regression)
on the proportion if the tendency is really linear. The tendency test has the
merit to take
into account all available informations.
Hassane ABIDI.
|=======================================================|
| Hassane ABIDI (PhD) |
| Unite d'Epidemiologie; Centre Hospitalier Lyon-Sud |
| Pavillon 1.M, 69495 Pierre Benite Cedex, France |
| Tel: (33) 04 78 86 56 87 ; Fax: (33) 04 78 86 33 31 |
| E. mail: [EMAIL PROTECTED] |
|=======================================================|
===========================================================================
This list is open to everyone. Occasionally, less thoughtful
people send inappropriate messages. Please DO NOT COMPLAIN TO
THE POSTMASTER about these messages because the postmaster has no
way of controlling them, and excessive complaints will result in
termination of the list.
For information about this list, including information about the
problem of inappropriate messages and information about how to
unsubscribe, please see the web page at
http://jse.stat.ncsu.edu/
===========================================================================
