R help - Apr 2008 - Regression inclusion of variable, effect on coefficients

Hello dear R users!

I know this question is not strictly R-help, yet, maybe some of the guru's
in statistics can help me out.

 

I have a sample of data all from the same "population". Say my
regression
equation is now this:

 

m1 <- lm(y ~ x1 + x2 + x3) 

 

I also regress on

 

m2 <- lm(y ~ x1 + x2 + x3 + x4)

 

The thing is, that I want to study the effect of "information" x4.

 

I would hypothesize, that the coefficient estimate for x1 goes down as I
introduce x4, as x4 conveys some of the information conveyed by x1 (but not
only). Of course x1 and x4 are correlated, however multicollinearity does
not appear to be a problem, the variance inflation factors are rather low
(around 1.5 or so).

 

I want to basically study, how the interplay between x1 and x4 is, when
introducing x4 into the regression equation and whether my hypothesis is
correct; i.e. that given I consider the information x4, not so much of the
variation is explained via x1 anymore.

 

I observe that introducing x4 into the regression, the coefficient estimate
for x1 goes down; also the associated p-value becomes bigger; i.e. x1
becomes comparatively less significant. However, x4 is not significant. Yet,
the observation is in line with my theoretical argument.

 

The question is now simple: how can I work this out?

 

I know this is likely a dumb question, but I would really appreciate some
links or help.


Regards

Thiemo


	[[alternative HTML version deleted]]

This is not a dump question. This is a serious problem and it depends on 
what you know or assume about the relastionship between x1 and x4. If 
you assume linear interaction, you might want to introduce some 
interaction term to the model for example.

Uwe Ligges


Thiemo Fetzer wrote:
> Hello dear R users!
> 
> I know this question is not strictly R-help, yet, maybe some of the
guru's
> in statistics can help me out.
> 
>  
> 
> I have a sample of data all from the same "population". Say my
regression
> equation is now this:
> 
>  
> 
> m1 <- lm(y ~ x1 + x2 + x3) 
> 
>  
> 
> I also regress on
> 
>  
> 
> m2 <- lm(y ~ x1 + x2 + x3 + x4)
> 
>  
> 
> The thing is, that I want to study the effect of "information"
x4.
> 
>  
> 
> I would hypothesize, that the coefficient estimate for x1 goes down as I
> introduce x4, as x4 conveys some of the information conveyed by x1 (but not
> only). Of course x1 and x4 are correlated, however multicollinearity does
> not appear to be a problem, the variance inflation factors are rather low
> (around 1.5 or so).
> 
>  
> 
> I want to basically study, how the interplay between x1 and x4 is, when
> introducing x4 into the regression equation and whether my hypothesis is
> correct; i.e. that given I consider the information x4, not so much of the
> variation is explained via x1 anymore.
> 
>  
> 
> I observe that introducing x4 into the regression, the coefficient estimate
> for x1 goes down; also the associated p-value becomes bigger; i.e. x1
> becomes comparatively less significant. However, x4 is not significant.
Yet,
> the observation is in line with my theoretical argument.
> 
>  
> 
> The question is now simple: how can I work this out?
> 
>  
> 
> I know this is likely a dumb question, but I would really appreciate some
> links or help.
> 
> 
> Regards
> 
> Thiemo
> 
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.