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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
Peter L. Bonate, Ph.D.
Hoechst Marion Roussel
P.O. Box 9627 (F4-M3112)
Kansas City, MO 64134
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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:
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
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
I don't think the mixed effect model will alter the effect of
I do not see how accounting for random effects will change the influence of
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
also be error in the coefficients that describe these covariates.
I hope these comments are useful. I look forward to the comments of others.
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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
Hope this comments are useful
Carlos Ramos Mundo. M.S.
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