Calculating standard deviations from wtp command

[Hannah Sack]

Hi all

I am needing to calculate the standard deviations from my wtp estimates. I have used the wtp, krinsky command and get wtp estimates and confidence levels. Is there a formula or code which will give me the standard error?

Regards

[Andrew Musau]

So, you need to know whether you have confidence intervals with a z-distribution or t-distribution. Once you know this, backing out the standard error is straightforward. You have

$$\text{CI} = \hat{y} \pm \text{t/z crit.}\cdot \text{s.e.}$$

This implies

$$\text{s.e.}= \text{abs}\left(\frac{CI-\hat{y}}{\text{t/z crit.}}\right).$$

In Stata, you calculate the 95% t crit. value as

 di invt(df, 0.975)

where -df- is the degrees of freedom. Critical values for the normal distribution do not depend on the degrees of freedom, and therefore for the 95% z crit. value, you simply need

 di invnormal(0.975)

Below, l back out the standard error in the regression outputting t-statistics from the lower limit CI and for the regression outputting z-statistics from the upper level CI.

. sysuse auto, clear
(1978 Automobile Data)

. regress foreign mpg

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(1, 72)        =     13.18
       Model |  2.39252954         1  2.39252954   Prob > F        =    0.0005
    Residual |  13.0669299        72  .181485138   R-squared       =    0.1548
-------------+----------------------------------   Adj R-squared   =    0.1430
       Total |  15.4594595        73  .211773417   Root MSE        =    .42601

------------------------------------------------------------------------------
     foreign |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |   .0312915   .0086182     3.63   0.001     .0141114    .0484716
       _cons |  -.3691266   .1901085    -1.94   0.056    -.7481011    .0098478
------------------------------------------------------------------------------

. mat r= r(table)

. mat list r

r[9,2]
               mpg       _cons
     b   .03129148  -.36912663
    se   .00861823   .19010853
     t   3.6308484  -1.9416626
pvalue   .00052542   .05609126
    ll   .01411136  -.74810105
    ul    .0484716    .0098478
    df          72          72
  crit   1.9934636   1.9934636
 eform           0           0

. di abs(r[5,1] - _b[mpg])/invt(e(df_r), 0.975)
.00861823

. logit foreign mpg

Iteration 0:   log likelihood =  -45.03321  
Iteration 1:   log likelihood = -39.380959  
Iteration 2:   log likelihood = -39.288802  
Iteration 3:   log likelihood =  -39.28864  
Iteration 4:   log likelihood =  -39.28864  

Logistic regression                             Number of obs     =         74
                                                LR chi2(1)        =      11.49
                                                Prob > chi2       =     0.0007
Log likelihood =  -39.28864                     Pseudo R2         =     0.1276

------------------------------------------------------------------------------
     foreign |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |   .1597621   .0525876     3.04   0.002     .0566922     .262832
       _cons |  -4.378866   1.211295    -3.62   0.000    -6.752961   -2.004771
------------------------------------------------------------------------------

. mat r2= r(table)

. mat list r2

r2[9,2]
           foreign:    foreign:
               mpg       _cons
     b   .15976213   -4.378866
    se   .05258764   1.2112952
     z   3.0380166   -3.615028
pvalue   .00238141   .00030032
    ll   .05669225  -6.7529609
    ul   .26283202   -2.004771
    df           .           .
  crit    1.959964    1.959964
 eform           0           0

. di abs(r2[6,1] - _b[mpg])/invnormal(0.975)
.05258764