[R] Can I do regression by steps?

[John Sorkin]

Can you perform regression by steps, yes. Will results be the same as those you would obtain from a multiple variable regression? No not if the independent variables are non-orthogonal and you don't take into consideration the correlation of the independent variables. Should you take into consideration the correlation of the independent variables? Yes if you want to reproduce the results of a multivariable regression. Should you use regression by step? I can't answer this for you, I can only tell you the differences between multivariable regression and regression by steps. The fact that the method is being used to allow  for missing data makes things more complicated. I have no experience using regression by steps in this setting. Have you considered multiple imputation to fill in the missing data and then using standard regression techniques?

I am sorry I can't be more helpful.
John 

John David Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)

>>> rlearner309 <unixunix99 at gmail.com> 7/8/2008 6:25 PM >>>

Thanks for the reply.
I am awared of the difference, but can I do regression by steps at all?  I
am not feeling comfortable about it.



John Sorkin wrote:
> 
> Be very careful!
> When regression is performed by steps, you often will not get the same
> results as you would get from a single multivariable regression. The
> explanation for this is not simple, but a simplified explanation is that
> when you do your first regression,
> y=f(x1)
> all the total variance that can be accounted for is sucked up by x1
> leaving little varinace to be accounted for by your second regression,
> residuals=f(x2). In contrast when you perform a multivariable regression,
> y=f(x1,x2) the total variance is proportioned between x1 and x2.
> John
> 
> John David Sorkin M.D., Ph.D.
> Chief, Biostatistics and Informatics
> University of Maryland School of Medicine Division of Gerontology
> Baltimore VA Medical Center
> 10 North Greene Street
> GRECC (BT/18/GR)
> Baltimore, MD 21201-1524
> (Phone) 410-605-7119
> (Fax) 410-605-7913 (Please call phone number above prior to faxing)
> 
>>>> rlearner309 <unixunix99 at gmail.com> 7/8/2008 8:53 AM >>>
> 
> I saw this type of models in some of my company projects.  
> 
> To simplify:
> Y is regressed on X1 and X2.  But the regression is done by two steps: 
> First Y is regressed on X1 with intercept, and the residuals from the
> first
> step are used to regress on X2, without the constant.  The reason to do so
> is some observations have X1 data but do not have X2, so I guess the
> person
> wants to use as much information as he can to get the coef. for X1, and
> then
> use part of the residuals (that have X2 data) to catch what is left to be
> explained by X2.
> 
> But my concern is, should we consider the correlation between X1 and X2? 
> If
> residuals from the first step are used, then X1 effect has been removed. 
> Then what does it really mean by regressing residuals on X2, which has
> some
> X1 effect correlated with?? should X2 be adjusted by X1, too (regress X2
> on
> X1 and use the residuals)?  
> 
> What if both X1 and X2 are dummy variables?  Dummy variables can have a
> meaningful correlation, too, right?
> 
> Thanks a lot!
> -- 
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