John--
If you are interested in PREDICTION then the
way YOU use your information is up to
YOU. By Cross-validation, Resampling etc.
you can determine which prediction method
seems to be "best" for your
situation.
-- Joe
************************************************************************
* Joe Ward Health Careers High School *
* 167 East Arrowhead Dr 4646 Hamilton Wolfe *
* San Antonio, TX 78228-2402 San Antonio, TX 78229 *
* Phone: 210-433-6575 Phone: 210-617-5400 *
* Fax: 210-433-2828 Fax: 210-617-5423 *
* [EMAIL PROTECTED] *
* http://www.ijoa.org/joeward/wardindex.html *
************************************************************************
* Joe Ward Health Careers High School *
* 167 East Arrowhead Dr 4646 Hamilton Wolfe *
* San Antonio, TX 78228-2402 San Antonio, TX 78229 *
* Phone: 210-433-6575 Phone: 210-617-5400 *
* Fax: 210-433-2828 Fax: 210-617-5423 *
* [EMAIL PROTECTED] *
* http://www.ijoa.org/joeward/wardindex.html *
************************************************************************
----- Original Message -----
From: John Hendrickx <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Wednesday, March 15, 2000 1:22
AM
Subject: Re: When *must* use weighted
LS?
| [EMAIL PROTECTED] says...
| >
| > I think I made the formulation too wordy in previous
| > post.
| >
| > Let me try this simple question:
| >
| > When one wishes to do a (multi)linear regression on a set of
| > observed data, and one is in the (unusual) position of possessing
| > a set of sample standard deviations (of varying degrees of f.)
| > at each value of the "explanatory" variable, how does one
| > determine whether one ought or ought not to solve the weighted
| > least squares problem using those sample standard deviations?
| >
| > What is the usual decision test for "heterscedasticity" *before* one
| > solves the regression system? What do people do in practise?
| >
| Most social scientists don't worry very much about the assumptions of OLS
| regression, noting that OLS estimates are fairly robust and can give
| unbiased estimates even if those assumptions aren't fulfilled. Exceptions
| are multilevel models and time series data, data for which the assumption
| of uncorrelated error terms is violated. But these require special
| programs, not weighted least squares.
|
| There is also some debate on using weights for stratified sampling and/or
| to correct for sampling bias. Weighting leads to correct estimates but
| incorrect standard errors. One solution is to include the design
| variables in the model instead of weighting. Stata and Wesvar are two
| programs that can take weighting into account when calculating standard
| errors of estimates. But a quite common approach is to use weights for
| descriptive statistics, but not in multivariate models.
|
| Weights can also be used for certain dependent variables that will
| violate the assumption of heteroscedasticity, e.g. a dichotomous
| dependent. I recently did a weighted least squares analysis for a co-
| worker to replicate an analysis in another paper. The weight was
| groupn*pct*(1-pct), where groupn was the number of cases per group and
| pct was the proportion with a positive response within each group. But
| this basically amounts to a poor approximation of a logit model. Programs
| like GLIM that use iteratively reweighted least squares use pct*(1-pct)
| as the weight when estimating the model, but now pct is the predicted
| probability from the previous iteration.
|
| As for a test for heteroscedasticity, Stata has a "hettest", which
| performs a Cook-Weisberg test and produces a chi-square statistic. They
| wrote a book in 1982, "Residuals and influence in regression". I've never
| used it though.
|
| Hope this helps,
| John Hendrickx
|
|
| ===========================================================================
| 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/
| ===========================================================================
|
