Any comparison test of the standardized beta coefficients in the same model?

[Namkyung Lee]

Hi, I ran a multiple regression and want to compare the effect of several predictors on the response variable.

Do I simply get the standardized beta coefficient and compare the absolute value of the coefficient?

Or is there any test for that?

[Marcos Almeida]

Welcome to the Stata Forum / Statalist,

I assume by "multiple regression" you mean - regress - command.

Depending on your study question, you have - test - as well as - testparm - commands.

[Richard Williams]

I am not a fan of standardization, and even less of a fan of doing equality tests of standardized coefficients. Once you standardize, differences in exogenous variances, residual variances, and unstandardized coefficients can all get confounded, and you can't really what is causing standardized coefficients to differ. For a discussion, see

https://www3.nd.edu/~rwilliam/stats2/l71.pdf

https://www3.nd.edu/~rwilliam/stats2/l72.pdf

But, if you really really really want to do it anyway, x standardization is probably sufficient. That was discussed yesterday in

https://www.statalist.org/forums/for...ed-coefficient

Extending the example presented there,

. webuse nhanes2f, clear

. logit diabetes weight height, nolog

Logistic regression                             Number of obs     =     10,335
                                                LR chi2(2)        =     130.28
                                                Prob > chi2       =     0.0000
Log likelihood = -1933.9288                     Pseudo R2         =     0.0326

------------------------------------------------------------------------------
    diabetes |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |   .0301604   .0028288    10.66   0.000     .0246161    .0357048
      height |  -.0473011   .0052236    -9.06   0.000    -.0575391   -.0370631
       _cons |   2.671749   .8062233     3.31   0.001      1.09158    4.251917
------------------------------------------------------------------------------

. egen xweight = std(weight) if e(sample)
(2 missing values generated)

. egen xheight = std(height) if e(sample)
(2 missing values generated)

. logit diabetes xweight xheight,nolog

Logistic regression                             Number of obs     =     10,335
                                                LR chi2(2)        =     130.28
                                                Prob > chi2       =     0.0000
Log likelihood = -1933.9288                     Pseudo R2         =     0.0326

------------------------------------------------------------------------------
    diabetes |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     xweight |   .4631369   .0434386    10.66   0.000     .3779987    .5482751
     xheight |  -.4569181   .0504586    -9.06   0.000    -.5558151   -.3580211
       _cons |  -3.089788   .0499536   -61.85   0.000    -3.187695   -2.991881
------------------------------------------------------------------------------

. test xweight = -xheight

 ( 1)  [diabetes]xweight + [diabetes]xheight = 0

           chi2(  1) =    0.01
         Prob > chi2 =    0.9048

Notice that I tested whether one coefficient equaled the negative of the other. Thus, in this example, we would not reject the hypothesis that the standardized coefficients were opposite in sign but equal in magnitude.