# Re: st: Calculating Percent Change In Regression Coeffecients

 From "Tim Wade" To statalist@hsphsun2.harvard.edu Subject Re: st: Calculating Percent Change In Regression Coeffecients Date Tue, 30 May 2006 16:06:13 -0400

Nick,
One use for this type of metric could be used in a "backward deletion"
or "change in estimate" procedure for selecting important covariates
in a regression model. In this process a full model with an exposure
of interest and all other potentially important covariates is fit,
then the relative importance of each covariate is judged by how much
of an effect its removal has on the coefficient of the exposure of
interest. Variables that, when removed from the model, have little
effect on the exposure coefficient are rdeleted from the final model.
The result is a model where the effect of the exposure has been
adjusted  for confounding but with unimportant variables removed. It
is sometimes advocated as an alternative to stepwise methods that rely
on statistical significance.

Tim

On 5/30/06, Nick Cox <n.j.cox@durham.ac.uk> wrote:
On a different note, why this interest in percent
change in coefficient as a metric?

1. The behaviour of ratios can be complicated
already. This measure is a ratio calculated from
ratios.

2. Specifically, is the behaviour as the denominator
goes from small positive through zero to small
negative regarded as a feature?

3. There is a lack of symmetry in the calculation.

I can imagine a practical argument that (1) and
(2) do not matter for the application, and (3)
might be irrelevant given a time order, but I wouldn't
put much weight on this measure.

Nick
n.j.cox@durham.ac.uk

> Hi Raphael, I don't know how to do this in Mata, but here is a brute
> force solution using macros and for loops:
>
>
> . regress price headroom rep78 gear_ratio
>
>       Source |       SS       df       MS              Number
> of obs =      69
> -------------+------------------------------           F(  3,
>    65) =    4.68
>        Model |   102521828     3  34173942.7           Prob >
> F      =  0.0051
>     Residual |   474275131    65  7296540.47
> R-squared     =  0.1777
> R-squared =  0.1398
>        Total |   576796959    68  8482308.22           Root
> MSE      =  2701.2
>
> --------------------------------------------------------------
> ----------------
>        price |      Coef.   Std. Err.      t    P>|t|
> [95% Conf. Interval]
> -------------+------------------------------------------------
> ----------------
>     headroom |  -136.9778   414.9107    -0.33   0.742
> -965.6117    691.6561
>        rep78 |   576.2363   362.8717     1.59   0.117
> -148.4686    1300.941
>   gear_ratio |  -2995.126   829.7523    -3.61   0.001
> -4652.256   -1337.996
>        _cons |   13577.64   3025.567     4.49   0.000
> 7535.166    19620.12
> --------------------------------------------------------------
> ----------------
>
> /*only include coefficients you want to compare*/
>
> . foreach var of varlist headroom rep78 {
>   2. local `var'1=_b[`var']
>   3. }
>
> . regress price headroom rep78
>
>       Source |       SS       df       MS              Number
> of obs =      69
> -------------+------------------------------           F(  2,
>    66) =    0.43
>        Model |  7450346.06     2  3725173.03           Prob >
> F      =  0.6511
>     Residual |   569346613    66  8626463.83
> R-squared     =  0.0129
> R-squared = -0.0170
>        Total |   576796959    68  8482308.22           Root
> MSE      =  2937.1
>
> --------------------------------------------------------------
> ----------------
>        price |      Coef.   Std. Err.      t    P>|t|
> [95% Conf. Interval]
> -------------+------------------------------------------------
> ----------------
>     headroom |   391.6261   422.1074     0.93   0.357
> -451.1385    1234.391
>        rep78 |   69.23416   363.8024     0.19   0.850
> -657.1208    795.5892
>        _cons |   4735.368   1930.863     2.45   0.017
> 880.276    8590.459
> --------------------------------------------------------------
> ----------------
>
> . foreach var of varlist headroom rep78 {
>   2. local `var'2=_b[`var']
>   3. }
>
> . foreach var of varlist headroom rep78 {
>   2. di as result "percent change for
> `var'="((``var'2'-``var'1')/``var'1')*100
>   3. }
> percent change for rep78=-87.985109

Raphael Fraser

> > I would like to calculate the percentage change in the regression
> > coeffecients of model 1 and model 2. Can any one help? I tried using
> > Mata but I did not know how to divide each element in a matrix with
> > different scalars.
> >
> > sysuse auto, clear
> > stset mpg, failure(foreign)
> > stcox mpg price weight rep78, nohr nolog /*Model 1*/
> > stcox mpg weight rep78, nohr nolog /*Model 2*/
> >
> > For example % change = (rep78_m2 - rep78_m1) / rep78_m1

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