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?
I make three elementary comments.
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
Tim Wade
> 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
> -------------+------------------------------ Adj
> 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
> -------------+------------------------------ Adj
> 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 headroom=-385.90483
> 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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