- On 30 Sep 1997 at 11:04:55, "Bonate, Peter, HMR/US" (Peter.Bonate.-a-.hmrag.com) sent the message

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Does anyone have any references on what is the impact of collinearity

among predictor variables in a mixed effect model (either linear or

nonlinear)?

Thanks.

Peter L. Bonate, Ph.D.

Hoechst Marion Roussel

Clinical Pharmacokinetics

P.O. Box 9627 (F4-M3112)

Kansas City, MO 64134

fax: 816-966-6999

phone: 816-966-3723 - On 20 Oct 1997 at 12:25:52, "Steve Duffull" (sduffull.-a-.clear.net.nz) sent the message

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Peter

I think that this is a good question that I would also like to see further

discussion about. I have not read any literature specifically addressing

the effects of collinearity in nonlinear systems. For the linear system,

almost any good stats textbook will provide an adequate description.

For the linear model:

Multicollinearity

Where explanatory variables are highly correlated the following may occur:

1) Coefficients may have large standard errors, since large changes in one

coefficient can be compensated for by equally large changes in another.

Hence very different coefficient values may result in nearly the same sum

of sq.

2) May result in product moment correlation coefficients (r or r^2 values)

that are inappropriate (often constricted). For example regressing two

covariates, that have significant correlation with each other, against a

dependent variable, often results in higher r^2 values when each is

considered alone but the resultant model will often have a lower r^2 value

when both are considered together.

3) Significant rounding errors may be introduced into the system.

In terms of non linear models r^2 values are not usually considered and

hence point 2 will be will be seen in other ways. Obviously the

correlation between coefficients can be addressed prior to undertaking

non-linear regression.

I don't think the mixed effect model will alter the effect of

multicollinearity.

I do not see how accounting for random effects will change the influence of

multicollinearity (or

perhaps "multi-co-non-linearity"). However, it seems probable

that estimation of the random effect component will be in error if

there is significant correlation between the covariates. There will

obviously,

also be error in the coefficients that describe these covariates.

I hope these comments are useful. I look forward to the comments of others.

Cheers

Steve - On 21 Oct 1997 at 10:10:07, Carlos Ramos Mundo (cramos.aaa.cueyatl.uam.mx) sent the message

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Greeting from Mexico:

Steve / Peter:

Even when documented effect of collinearity in nonlinear models is quite a

few, there is a point of view that may help:

"Collinearity in nonlinear models could cause that parameters estimates in

iterative methods (like marquardt), present an "aparent" low ss, however

it is possible that ss surface is deformed by covariates, then predictors

could be far from real values. Maybe a procedure to try to avoid this

effect is to use partial correlation and other analytical procedure such

as cuadratical or transform covariates to get ride of collinearity"

As far as we concer, we try to several transformations to avoid

collinearity, but the final effect is a strong tendency in residuals, at

least in data that shows two- or one- compartment behaviour. The effect

is more evident when you try with flip-flop data.

Nowadays, we are trying with dud's method and it presents an error in

simulation aprox of 5 -12 % in final estimates. Hopefully we will try

this method with real data in next week.

It is important to point out that the main idea is to get a procedure to

reduce collinearity effects, even when is probably to derive in handling

experimental factors.

Hope this comments are useful

Carlos Ramos Mundo. M.S.

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