Re: st: Relative Importance of predictors in regression

[Jorge Eduardo Pérez Pérez <jorge_perez@brown.edu>]

You are right about the MS. In my calculations I used the partial SS
themselves. These should add up to the R squared.

I don't really have much on the way of interpretation of the shared
variance, in fact I found that it is hard to interpret it here:

http://www.education.umd.edu/EDMS/fac/Harring/Past-Classes/EDMS651/Notes/MRA-MS.pdf

--------------------------------------------
Jorge Eduardo Pérez Pérez
Graduate Student
Department of Economics
Brown University


On Tue, Nov 5, 2013 at 11:58 AM, David Hoaglin <dchoaglin@gmail.com> wrote:
> Dear Jorge,
>
> Thank you for the clarification.  Being able to get all the necessary
> partial sums of squares from a single command is a big help.
>
> If we look at the regression coefficients, the step
> reg lhs rhs
> nicely illustrates the point that I have been making about interpretation.
>
> reg lhs rhs will give the partial SS for mpg, but the MS from that
> command may not have the correct degrees of freedom, because -reg-
> does not know about the degrees of freedom that have been partialled
> out of price.
>
> In deriving the part of R-squared attributed to a variable, you need
> to use the same denominator as R-squared itself uses.
>
> Setting aside the example and the calculations for a moment, what is
> the definition of "the shared variance of the [in]dependent
> variables"?
>
> Regards,
>
> David Hoaglin
>
> On Tue, Nov 5, 2013 at 11:00 AM, Jorge Eduardo Pérez Pérez
> <jorge_perez@brown.edu> wrote:
>> I should have been more specific, sorry, Ignore the SJ paper.
>>
>> Analysis of variance with continuous covariates and regression are
>> general linear models. All these models are equivalent:
>>
>> sysuse auto, clear
>> reg price mpg trunk
>> anova price c.mpg c.trunk
>> glm price mpg trunk, family(gaussian) link(identity)
>>
>>
>> The anova view of the model will yield the partial sums of squares
>> attributed to each regressor. In regression vocabulary, this would be
>> the model sum of squares of regressing the dependent variable on each
>> one of the independent variables, after partialling out the remaining
>> variables. For example, the MS attributed to mpg in the previous
>> regression could be obtained as follows, by first removing the
>> influence of trunk from both variables:
>>
>> reg price trunk
>> predict lhs, resid
>> reg mpg trunk
>> predict rhs, resid
>> reg lhs rhs
>>
>> From the anova view, dividing the partial SS of each variable over the
>> sum of the partial SS of the variable and the residual will give you
>> the part of the R squared attributed to that variable. It will be the
>> same as the R squared of the "partialled out" regression I showed
>> before.
>> The remainder will be the part attributed to the shared variance of
>> the dependent variables.
>>
>> * Part attributed to mpg
>> di e(ss_1)/(e(ss_1)+e(rss))
>> * Part attributed to trunk
>> . di e(ss_2)/(e(ss_2)+e(rss))
>> * Remainder (shared variance)
>> di e(r2) -  e(ss_1)/(e(ss_1)+e(rss)) - e(ss_2)/(e(ss_2)+e(rss))
>>
>> My suggestion from the anova paper is that the anova view calculates
>> all of the sums of squares at once, instead of having to calculate of
>> the partial regression sums of squares one by one.
>>
>> -----------------------------------------
>> Jorge Eduardo Pérez Pérez
>> Graduate Student
>> Department of Economics
>> Brown University
>
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