Dear Ayyappa,
A nice discussion!
It may be worthwhile to inspect further collinearity statistics, see
e.g.
https://cran.r-project.org/web/packages/olsrr/vignettes/regression_diagnostics.html
, with for example VIF and CI being sometimes useful to detect
problematic parameters in my experience.
As is already clear from the preceding discussion, indeed please do not
rely on just applying "rules" but try to think through what these
properties mean for your model.
Hope this helps,
Jeroen
http://pd-value.com
jer...@pd-value.com
@PD_value
+31 6 23118438
-- More value out of your data!
On 29-11-2022 17:25, Ayyappa Chaturvedula wrote:
Hi Ken,
You are correct, the 10^n rule is in the context of individual level
modeling.
Thank you Pete for chiming in, I learned the difference you mention
from your book too.
Regards,
Ayyappa
On Tue, Nov 29, 2022 at 10:19 AM Ken Kowalski <kgkowalsk...@gmail.com>
wrote:
I have seen models with a successful COV step and CN > 10^5 but I
certainly have not seen COV steps run with a CN > 10^20. Thus,
the CN > 10^n has got to break down when n is large. Does
Gabrielsson and Weiner discuss this rule in the context of simple
nonlinear regression of individual subject (or animal) curves or
do they also propose this rule in the context of population models
with nonlinear mixed effects. I suspect it was only proposed for
the former.
Not to rehash old ground, but a successful COV step does not imply
that a model is stable even if none of the pairwise correlations
are extreme if CN is very large.
*From:*Ayyappa Chaturvedula [mailto:ayyapp...@gmail.com]
*Sent:* Tuesday, November 29, 2022 11:07 AM
*To:* Ken Kowalski <kgkowalsk...@gmail.com>
*Cc:* nmusers@globomaxnm.com
*Subject:* Re: [NMusers] Condition number
Hi Ken,
Thank you again. But, I have seen models with 10^5 and above
with no issues with covariance step and correlations not reaching
0.95 but some with moderate levels. It will be interesting to
know other experiences.
The 10^n rule is from the PK-PD Data analysis, Gabrielsson and
Weiner, Edition 3, page 313. I read this book most of my grad
school days.
Regards,
Ayyappa
On Tue, Nov 29, 2022 at 9:35 AM Ken Kowalski
<kgkowalsk...@gmail.com> wrote:
Hi Ayyappa,
I have not seen this rule but it strikes me as being too
liberal to apply in pharmacometrics where n can be very large
for the models we fit. If we have a structural model with say
n=4 or 5 parameters and then also investigate covariate
effects on these parameters it would not be unusual to have a
covariate model with n=20+ fixed effects parameters. I doubt
we can get the COV step to run such that we can observe a CN
>10^20.
I have not seen CN criteria indexed by n. The classifications
of collinearity that I've seen based on CN are:
Moderate: 100 <= CN < 1000
High: 1000 <= CN < 10,000
Extreme: CN >= 10,000
Ken
-----Original Message-----
From: Ayyappa Chaturvedula [mailto:ayyapp...@gmail.com]
Sent: Tuesday, November 29, 2022 10:20 AM
To: Ken Kowalski <kgkowalsk...@gmail.com>
Cc: nmusers@globomaxnm.com
Subject: Re: [NMusers] Condition number
Thank you, Ken. It is very reassuring.
I have also seen a discussion on other forums that Condition
number as a function of dimension of problem (n). I am seeing
contradiction between 10^n and a static >1000 approach. I am
curious if someone can also comment on this and 10^n rule?
Regards,
Ayyappa
> On Nov 29, 2022, at 9:04 AM, Ken Kowalski
<kgkowalsk...@gmail.com> wrote:
>
> Hi Ayyappa,
>
> I think the condition number was first proposed as a
statistic to
> diagnose multicollinearity in multiple linear regression
analyses
> based on an eigenvalue analysis of the X'X matrix. You can
probably
> search the statistical literature and multiple linear
regression
> textbooks to find various rules for the condition number as
well as
> other statistics related to the eigenvalue analysis. For
the CN<1000
> rule I typically reference the following textbook:
>
> Montgomery and Peck (1982). Introduction to Linear
Regression Analysis.
> Wiley, NY (pp. 301-302).
>
> The condition number is good at detecting model instability
but it is
> not very good for identifying the source. Inspecting the
correlation
> matrix for extreme pairwise correlations is better suited
for identifying the source of
> the instability when it only involves a couple of
parameters. It becomes
> more challenging to identify the source of the instability
> (multicollinearity) when the CN>1000 but none of the pairwise
> correlations are extreme |corr|>0.95. Although when CN>1000
often we
> will find several pairwise correlations that are moderately
high
> |corr|>0.7 but it may be hard to uncover a pattern or source
of the
> instability without trying alternative models that may
eliminate one
> or more of the parameters associated with these moderate to
high correlations.
>
> Best,
>
> Ken
>
> Kenneth G. Kowalski
> Kowalski PMetrics Consulting, LLC
> Email: kgkowalsk...@gmail.com
> Cell: 248-207-5082
>
>
>
> -----Original Message-----
> From: owner-nmus...@globomaxnm.com
> [mailto:owner-nmus...@globomaxnm.com] On Behalf Of Ayyappa
> Chaturvedula
> Sent: Tuesday, November 29, 2022 8:52 AM
> To: nmusers@globomaxnm.com
> Subject: [NMusers] Condition number
>
> Dear all,
> I am wondering if someone can provide references for the
condition
> number thresholds we are seeing (<1000) etc. Also, the other
way I
> have seen when I was in graduate school that condition
number <10^n
> (n- number of parameters) is OK. Personally, I am depending on
> correlation matrix rather than condition number and have
seen cases
> where condition number is large (according to 1000 rule but
less than
> 10^n rule) but correlation matrix is fine.
>
> I want to provide these for my teaching purposes and any
help is
> greatly appreciated.
>
> Regards,
> Ayyappa
>
>
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