Re: Collinearity, confidence intervals and sampling

On Wed, 14 May 2008 21:43:06 +0100, "reflex" <sdfs@xxxxxxxxx> wrote:

Ok I've been doing some more reseach on this whole collinearity thing and
read that if you have collinear variables, the best fitting plane of the
data points in a regression will be narrower and less achored (because the
predictors are highly correlated so the predictor values fall in a straight
line). Consequently, if response varied from sample to sample, the
coefficients could change substantially. Therefore the standard errors of
the coefficients are necessarily larger.

Does this mean that this is not a problem if you have population level data
(ie sample size doesn't matter because you have 'sampled' the entire
population you are interested)?

That's a slightly-true observation, with no real application.

With true Population level data, you might have "measurement
error" but you have no "statistical error." This is like the
results of taking a vote, as compared to taking an opinion poll.
("Recounts" are used to reduce "measurement error" in votes.)

With true population data, or data treated as such, you have no
role for inference or generalization or the direct application
of science; you have an administrative tool.

Basically - If you are hoping to say anything interesting to
almost anybody else, you are treating some "population" as
a sample. So, unless there is special reason, you never will
treat a population as a "population."

If you want more discussion, you might Google-groups and
look at threads found by
< groups:sci.stat.* "finite population" author:ulrich >


Are there are other effects of collinearity that do not matter if you have
population level data? What about other assumptions of regression e.g.
normal distribution of variables, homoskedasticity.

The website I've been looking at is
http://www.stat.psu.edu/~jglenn/stat501/12multicollinearity/04multico_corr.html
which is an excellent source on collinearity.

As always, any replies well appreciated.

--
Rich Ulrich

http://www.pitt.edu/~wpilib/index.html
.

Relevant Pages

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  • Collinearity, confidence intervals and sampling
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