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)?

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.

On Wed, 14 May 2008 21:43:06 +0100, "reflex" <sdfs at (no spam) sdfsd.com> 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

Say if you had a population sample of all hospitals in England, and you
wanted to say something interesting about all hospitals in England, then you
wouldn't need to generalise to a wider population because you know the whole
population. Surely that's a real application?

On Fri, 16 May 2008 09:54:15 +0100, "reflex" <sdfs at (no spam) sdfsd.com> wrote:


Say if you had a population sample of all hospitals in England, and you
wanted to say something interesting about all hospitals in England, then
you
wouldn't need to generalise to a wider population because you know the
whole
population. Surely that's a real application?

What can you say about "all the hospitals in England"
in the year 2007 that *remains interesting to people* , if
you are unable to extrapolate or infer something about
the hospitals in the year 2008?
- or any other hospitals in any time or place....

Come up with something *interesting*, and I think I
can show you that you are drawing inferences.


--
Rich Ulrich
http://www.pitt.edu/~wpilib/index.html

"Richard Ulrich" <Rich.Ulrich at (no spam) comcast.net> wrote in message
news:5o0s24p0al837j4esq82vm9bs0os8slj1m at (no spam) 4ax.com...
On Fri, 16 May 2008 09:54:15 +0100, "reflex" <sdfs at (no spam) sdfsd.com> wrote:


Say if you had a population sample of all hospitals in England, and you
wanted to say something interesting about all hospitals in England, then
you
wouldn't need to generalise to a wider population because you know the
whole
population. Surely that's a real application?

What can you say about "all the hospitals in England"
in the year 2007 that *remains interesting to people* , if
you are unable to extrapolate or infer something about
the hospitals in the year 2008?
- or any other hospitals in any time or place....

Come up with something *interesting*, and I think I
can show you that you are drawing inferences.



The population of interest is what you are trying to generalise to in the
first place though isn't it? So in taking a random sample from a set
population (hospitals in England) you can arguably generalise to all
hospitals (assuming you sample is good/representative enough). And if you
have data on the whole population, no generalising is needed, and hence this
is a good thing. You *are* inferring about all hospitals in the future of
course, but aren't you doing this with all research? You can't sample the
future, yet! So it is preferable to have population-level data and draw
inferences about the future than have a random sample of that population and
draw inferences about the future.

On Sat, 17 May 2008 13:04:35 +0100, "reflex" <sdfs at (no spam) sdfsd.com> wrote:


"Richard Ulrich" <Rich.Ulrich at (no spam) comcast.net> wrote in message
news:5o0s24p0al837j4esq82vm9bs0os8slj1m at (no spam) 4ax.com...
On Fri, 16 May 2008 09:54:15 +0100, "reflex" <sdfs at (no spam) sdfsd.com> wrote:


Say if you had a population sample of all hospitals in England, and
you
wanted to say something interesting about all hospitals in England,
then
you
wouldn't need to generalise to a wider population because you know the
whole
population. Surely that's a real application?

What can you say about "all the hospitals in England"
in the year 2007 that *remains interesting to people* , if
you are unable to extrapolate or infer something about
the hospitals in the year 2008?
- or any other hospitals in any time or place....

Come up with something *interesting*, and I think I
can show you that you are drawing inferences.



The population of interest is what you are trying to generalise to in the
first place though isn't it? So in taking a random sample from a set
population (hospitals in England) you can arguably generalise to all
hospitals (assuming you sample is good/representative enough). And if
you
have data on the whole population, no generalising is needed, and hence
this
is a good thing. You *are* inferring about all hospitals in the future
of
course, but aren't you doing this with all research? You can't sample
the
future, yet! So it is preferable to have population-level data and draw
inferences about the future than have a random sample of that population
and
draw inferences about the future.

You miss the point about drawing inferences.
Re-read some posts. Do some Googling-groups as I suggested
if it remains opaque.

Drawing "inferences" says that whatever is on hand is being
treated as a "sample". So, even if it is a full set of the hospitals
of England, you use the confidence limits as if it were any
other tiny sample.

If you do just want to describe a fixed set of hospitals, it is
like reporting any vote, that is, the only error is in counting.
If it is supposed to generalize or have another meaning, then
it is a sample. From a population on hand, you know how
many meals to order, etc. Or how many were eaten for the
term. You don't know about next year.

--
Rich Ulrich

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

I'm really busy with revision atm (not related to populations) so I don't
have time to search the groups but I will do in the future as I'm quite
confused over this issue. For example I have an assignment soon that we
have been given a population-level dataset for which says that all tests of
significance are irrelevant so don't talk about them in the analysis.

What I would say is that the ordering meals example is very specific and
therefore it's harder to generalise to next year. But you can still get an
idea.

If however your analysis demonstrated something much more general,
say that patient satisfaction is determined by the socio-economic
characteristics of the local area and not management organisation (I can't
think of a better example but you get the idea) then commonsense tells you
this is likely to apply to next year.

Say if you had a population sample of all hospitals in England, and you
wanted to say something interesting about all hospitals in England, then you
wouldn't need to generalise to a wider population because you know the whole
population. Surely that's a real application?

reflex <sdfs at (no spam) sdfsd.com> wrote:

Say if you had a population sample of all hospitals in England, and you
wanted to say something interesting about all hospitals in England, then
you
wouldn't need to generalise to a wider population because you know the
whole
population. Surely that's a real application?

There are various ways of looking at how the hospitals in England got
there!

Your are in the "They are there, so what more is to be said" camp.
Which is the least imaginative point of view of all, but the way in
which the majority of people think. So, life being what it is, a
proportion of professional statisticians think exactly like that, and
get very cross if asked to think in any other way. As similarly do a
proportion of academic/teaching statisticians.

[Remark: One view of the origins of crossness in the human mind is that
it results from the person who is cross not having any relevant concept
in his/her head to deal with the situation. The crossness emerges in
bluster, posturing, contempt ... but only rarely calms into humility!]

Another, far-richer but far-more-complex, point of view is that the
hospitals that are actually there are there as the outcome of some
hidden (partly probabilistic) process, which in re-runs of life starting
from the same point, say 50 years ago, could have turned out in a whole
variety of ways.

It would be useful to establish things about that process
- to foresee how it might develop,
- to intervene at well-judged points to change the likely outcomes.
- and just to understand how things happen.

So the intellectual challenge is to model how the hospitals got into
their present state, and to do so in ways which leaves you with a useful
model for exploring policy issues for the future.

In that sense, the current set of hospitals is simply a sample of the
"might-have-been"s to give you a clue about the future set of
"could-be"s.

I'm in the camp that thinks that if you aren't at least trying to think
in those terms you haven't begun to be potentially useful. Facts are
useless without an interpretive context.

--
Hylton

So the intellectual challenge is to model how the hospitals got into
their present state, and to do so in ways which leaves you with a useful
model for exploring policy issues for the future.

In that sense, the current set of hospitals is simply a sample of the
"might-have-been"s to give you a clue about the future set of
"could-be"s.

On Sun, 18 May 2008 10:50:18 +0100, "reflex" <sdfs at (no spam) sdfsd.com> wrote:

[snip, previous comments. On Finite Populations.

I'm really busy with revision atm (not related to populations) so I don't
have time to search the groups but I will do in the future as I'm quite
confused over this issue. For example I have an assignment soon that we
have been given a population-level dataset for which says that all tests
of
significance are irrelevant so don't talk about them in the analysis.

"All tests are irrelevant" is an acceptable mandate
when the sample is very large, which is what "populations"
frequently are. The New England Journal of Medicine, many
years ago, told authors to omit tests when reporting huge
health surveys. Especially when everything trivial comes out
as nominally "significant", the proper approach is to describe
effect sizes.
- Either your population is *large* (and not just a "population")
and you have elided the instructions, or (a) you are dealing with
an odd question, or (b) you have a questionable textbook or
instructor. Is this assignment from a text that can be named?

What I would say is that the ordering meals example is very specific and
therefore it's harder to generalise to next year. But you can still get
an
idea.

Finite: You use the numbers to pay for last year's meals.
For next year: You are "generalizing" from one year's data as
a "sample", to the next year's data. No longer a Finite population.

If however your analysis demonstrated something much more general,
say that patient satisfaction is determined by the socio-economic
characteristics of the local area and not management organisation (I
can't
think of a better example but you get the idea) then commonsense tells
you
this is likely to apply to next year.

Again - if you are applying inference to the next year, you
are treating the Population as a sample. Year-to-year correlation
might be estimated and applied in some fashion in order to
reduce the standard deviations, but SDs on the estimates are
still appropriate.

--
Rich Ulrich

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

"Hylton Boothroyd" <hylton.boothroyd at (no spam) null.c0m
There are various ways of looking at how the hospitals in England got
there!

Your are in the "They are there, so what more is to be said" camp.
Which is the least imaginative point of view of all, but the way in
which the majority of people think. So, life being what it is, a
proportion of professional statisticians think exactly like that, and
get very cross if asked to think in any other way. As similarly do a
proportion of academic/teaching statisticians.

Whoa there! I'm not cross!

Another, far-richer but far-more-complex, point of view is that the
hospitals that are actually there are there as the outcome of some
hidden (partly probabilistic) process, which in re-runs of life
starting from the same point, say 50 years ago, could have turned
out in a whole variety of ways.

In that sense, the current set of hospitals is simply a sample of the
"might-have-been"s to give you a clue about the future set of
"could-be"s.

My point was simply regarding the statistical side of
things, in that if you have population-level data,
as I've been taught, you don't need to worry about the
quality of your sample and the associated tests of significance.
Hence why I was asking whether or not collinearity
and confidence intervals are relevant if you have
population-level data.

So the intellectual challenge is to model how the hospitals got into
their present state, and to do so in ways which leaves you with a
useful model for exploring policy issues for the future.

In that sense, the current set of hospitals is simply a sample
of the "might-have-been"s to give you a clue about the future
set of "could-be"s.

Do you examples of any such research?

Could policy decisions not arise simply
from how things are now?

And does this mean tests of significance are still relevant?

"Richard Ulrich" <Rich.Ulrich at (no spam) comcast.net> wrote in message
news:mo3434hkic2s93942og5mf8r19s7p4s25p at (no spam) 4ax.com...
On Sun, 18 May 2008 10:50:18 +0100, "reflex" <sdfs at (no spam) sdfsd.com> wrote:

[snip, previous comments. On Finite Populations.
[snip. Again]

Finite: You use the numbers to pay for last year's meals.
For next year: You are "generalizing" from one year's data as
a "sample", to the next year's data. No longer a Finite population.
reflex
I see what you're saying here - your population of interest changes the
moment you draw inferences beyond it, right?

But it is ok to do this,
right? And what statistical tests would justify doing this or be
appropriate in doing this, if any?

If however your analysis demonstrated something much more general,
say that patient satisfaction is determined by the socio-economic
characteristics of the local area and not management organisation (I
can't
think of a better example but you get the idea) then commonsense tells
you
this is likely to apply to next year.
me
Again - if you are applying inference to the next year, you
are treating the Population as a sample. Year-to-year correlation
might be estimated and applied in some fashion in order to
reduce the standard deviations, but SDs on the estimates are
still appropriate.
reflex
So the 'specifity' of your inference makes no difference to whether it's
justified or not?

(As in, if I was to infer that next years all hospitals
would require X meals, this estimate would likely be out due to many
factors,

but if I was to infer that next year patient satisfaction will be
determined by the socio-economic characteristics of the local area as they
are this year, then commonsense says such things hold year on year).