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st: RE: logit and collinearity

From   "Maarten Buis" <>
To   <>
Subject   st: RE: logit and collinearity
Date   Tue, 29 Aug 2006 12:05:45 +0200

---Sami wrote:
> I want to model the association a binary variable Y and three independent
> variables X1, X2 continuous and X3 dichotomious
> There is a signficant association between X1 and X3
> Can I  consider in the same model both the three variables

Yes, we add multiple explanatory variables at the same time just because they 
are correlated. We think that both x1 and x3 influence y and that x1 and x3
are associated. If we don't add x3, than the b of x1 is the direct effect of x1 on
y plus the indirect effect of x1 on y through x3. And if you don't add x1, the b 
of x3 will be the direct effect of x3 on y plus the indirect effect through x1.
So leaving one variable out will contaminate the parameters with the indirect 
effects through the omitted variable. (In logistic regression and other non-linear
models the omitted variable bias is actually more complicated than that: omitting
a variable will cause bias even if it is uncorrelated with all other explanatory

However, if the variables become too correlated we can no longer separate the  
two variables, and it becomes difficult to estimate the model. If the correlation
is perfect estimation becomes impossible. 


Maarten L. Buis
Department of Social Research Methodology 
Vrije Universiteit Amsterdam 
Boelelaan 1081 
1081 HV Amsterdam 
The Netherlands

visiting adress:
Buitenveldertselaan 3 (Metropolitan), room Z434 

+31 20 5986715

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