# PharmPK Discussion - Collinearity and mixed effect models

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• On 30 Sep 1997 at 11:04:55, "Bonate, Peter, HMR/US" (Peter.Bonate.-a-.hmrag.com) sent the message
`Does anyone have any references on what is the impact of collinearityamong predictor variables in a mixed effect model (either linear ornonlinear)?Thanks.Peter L. Bonate, Ph.D.Hoechst Marion RousselClinical PharmacokineticsP.O. Box 9627  (F4-M3112)Kansas City, MO  64134fax:  816-966-6999phone:  816-966-3723`
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• On 20 Oct 1997 at 12:25:52, "Steve Duffull" (sduffull.-a-.clear.net.nz) sent the message
`PeterI think that this is a good question that I would also like to see furtherdiscussion about.  I have not read any literature specifically addressingthe effects of collinearity in nonlinear systems.  For the linear system,almost any good stats textbook will provide an adequate description.For the linear model:MulticollinearityWhere explanatory variables are highly correlated the following may occur:1) Coefficients may have large standard errors, since large changes in onecoefficient can be compensated for by equally large changes in another.Hence very different coefficient values may result in nearly the same sumof sq.2) May result in product moment correlation coefficients (r or r^2 values)that are inappropriate (often constricted).  For example regressing twocovariates, that have significant correlation with each other, against adependent variable, often results in higher r^2 values when each isconsidered alone but the resultant model will often have a lower r^2 valuewhen 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 andhence point 2 will be will be seen in other ways.  Obviously thecorrelation between coefficients can be addressed prior to undertakingnon-linear regression.I don't think the mixed effect model will alter the effect ofmulticollinearity.I do not see how accounting for random effects will change the influence ofmulticollinearity (orperhaps "multi-co-non-linearity").  However, it seems probablethat estimation of the random effect component will be in error ifthere is significant correlation between the covariates.  There willobviously,also be error in the coefficients that describe these covariates.I hope these comments are useful.  I look forward to the comments of others.CheersSteve`
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• On 21 Oct 1997 at 10:10:07, Carlos Ramos Mundo (cramos.aaa.cueyatl.uam.mx) sent the message
` Greeting from Mexico: Steve / Peter:Even when documented effect of collinearity in nonlinear models is quite afew, there is a point of view that may help:"Collinearity in nonlinear models could cause that parameters estimates initerative methods (like marquardt), present an "aparent" low ss, howeverit is possible that ss surface is deformed by covariates, then predictorscould be far from real values.   Maybe a procedure to try to avoid thiseffect is to use partial correlation and other analytical procedure suchas cuadratical or transform covariates to get ride of collinearity"As far as we concer, we try to several transformations to avoidcollinearity, but the final effect is a strong tendency in residuals, atleast in data that shows two- or one- compartment behaviour.   The effectis more evident when you try with flip-flop data.Nowadays, we are trying with dud's method and it presents an error insimulation aprox of 5 -12 % in final estimates.  Hopefully we will trythis method with real data in next week.It is important to point out that the main idea is to get a procedure toreduce collinearity effects, even when is probably to derive in handlingexperimental factors.Hope this comments are usefulCarlos Ramos Mundo. M.S.`
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