sem or 95%CI for X-standardized coefficient?

[Sharon Kidd]

Hello,

I am using Stata v 15.1
After running a logistic regression
. logit y x
I used the syntax:
. listcoef, std help

it returns output for full, X, and Y standardized estimates with the definition of "bStdX = x-standardized coefficient". In a Stata example, this was 1.319. However, there is no info about how to obtain the standard error or 95% confidence intervals. I tried something from a Nov 2015 thread
. stdbeta,se
but this returns a comment that stdbeta is an "unrecognized command"
Dos anyone have syntax to get the sem or 95% CI for an X-standardized coefficient?

Thank you,
Sharon

[Richard Williams]

For those who don't know, listcoef is part of spost13_ado (findit spost13_ado).

The simplest way may be to do the X standardization yourself.

. 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
------------------------------------------------------------------------------

Harder ways (which I might skip if I hadn't done them first!). To get stdbeta,

findit stdbeta   (install the program)

Then,

. 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
------------------------------------------------------------------------------

. listcoef, std

logit (N=10335): Unstandardized and standardized estimates

  Observed SD:  0.2144
    Latent SD:  1.8738

-------------------------------------------------------------------------------
             |         b        z    P>|z|    bStdX    bStdY   bStdXY     SDofX
-------------+-----------------------------------------------------------------
      weight |    0.0302   10.662    0.000    0.463    0.016    0.247    15.356
      height |   -0.0473   -9.055    0.000   -0.457   -0.025   -0.244     9.660
    constant |    2.6717    3.314    0.001        .        .        .         .
-------------------------------------------------------------------------------

. stdBeta, nodepvar se
generate:

-----------------------------------------------------------
    Variable |   Original       Centered     Standardized  
-------------+---------------------------------------------
      weight |    .03016043      .03016043      .46313689  
             |    .00282881      .00282881      .04343864  
      height |   -.04730107     -.04730107      -.4569181  
             |    .00522357      .00522357      .05045859  
       _cons |    2.6717487     -3.0897879     -3.0897879  
             |    .80622326       .0499536       .0499536  
-----------------------------------------------------------
                                               legend: b/se

.

That gives you the standard errors. You can hand calculate the CIs easily enough. Just multiply the CI's by the Standard deviation of X.

Hopefully, all the results are internally consistent.

EDIT: The egen do it yourself approach, listcoef, and stdBeta all give the same values for the X-standardized coefficients. stdBeta and egen both give the same X-standardized standard errors. The egen approach also gives you the CIs so you don't have to calculate them yourself. With the egen approach you could pick and choose which variables got X-standardized, e.g. you could not standardize dummy variables. There may be an even easier approach but I don't know what it is.

[Sharon Kidd]

Perfect! Thank you!