Difference between "fracreg" and "glm family(binomial) link(logit)"

[Pavel Satra]

Hello everyone,

I would be eager to know the difference between commands for fractional logistic regression. When I run "fracreg" or "glm family(binomial) link(logit)" in Stata 14.2, the coefficient size remains the same but several other values like number of observations or confidence intervals change.

You will find below the models and an example of the dependent variable data.

1)

2)

The dependent variable is called "dvfrac_year" and takes form of fractions (originally 0,1 values) and is weigted in the models [fweight=cnt_total_year].

* Example generated by -dataex-. To install: ssc install dataex
clear
input float dvfrac_year
         0
 .08333334
         1
       .75
       .75
         1
  .9333333
        .8
         0
 .14285715
       .25
 .16666667
         0
  .4285714
         0
         1
  .3333333
         0
        .5
      .375
  .9230769
  .8666667
         1
         1
      .125
         0
         0
  .4285714
         1
         0
        .2
  .8888889
         1
         1
        .2
         1
         1
         1
       .25
         1
       .05
 .44444445
  .2857143
         0
         0
         0
  .3333333
.071428575
         1
  .8888889
         1
        .8
      .875
  .8333333
         1
       .75
  .3333333
         0
         0
         1
  .6666667
         1
  .3636364
        .3
         0
         1
        .8
       .25
         0
         0
         0
   .968254
  .9565217
  .8333333
      .875
  .3214286
      .125
 .15384616
  .2857143
         0
 .06896552
       .25
  .6666667
  .8666667
         1
         1
         0
         0
         0
        .8
  .7692308
 .27272728
        .3
        .5
  .4285714
         1
         1
         1
  .6666667
         1
end

Thank you and have a good one!

[Scott Merryman]

Regarding the number of observation reported. The update February 20, 2019 reported:

    5.  fracreg with frequency weights reported the wrong number of observations.  This has been fixed.
         The reported coefficients, standard errors, test statistics, and confidence intervals were
         correct.

If you want the same standard errors and CI then you need to use the same estimate of the variance-covariance matrix. In particular, under glm use the vce(robust) option:

. webuse 401k,clear

. fracreg logit prate mrate [fw = age] , nolog


Fractional logistic regression                  Number of obs     =     33,360
                                                Wald chi2(1)      =    2009.30
                                                Prob > chi2       =     0.0000
Log pseudolikelihood = -11719.937               Pseudo R2         =     0.0221

------------------------------------------------------------------------------
             |               Robust
       prate |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       mrate |   1.005281   .0224267    44.83   0.000     .9613253    1.049236
       _cons |   1.535889   .0130905   117.33   0.000     1.510232    1.561546
------------------------------------------------------------------------------

. glm  prate mrate [fw = age], family(binomial) link(logit) vce(robust) nolog
note: prate has noninteger values

Generalized linear models                         No. of obs      =     33,360
Optimization     : ML                             Residual df     =     33,358
                                                  Scale parameter =          1
Deviance         =  6550.649419                   (1/df) Deviance =   .1963742
Pearson          =  6781.513586                   (1/df) Pearson  =    .203295

Variance function: V(u) = u*(1-u/1)               [Binomial]
Link function    : g(u) = ln(u/(1-u))             [Logit]

                                                  AIC             =    .546216
Log pseudolikelihood = -9108.883702               BIC             =  -340876.7

------------------------------------------------------------------------------
             |               Robust
       prate |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       mrate |   1.005281   .0224267    44.83   0.000     .9613253    1.049236
       _cons |   1.535889   .0130905   117.33   0.000     1.510232    1.561546
------------------------------------------------------------------------------

[Pavel Satra]

Dear Scott,

Thank you very much! When you reffer to an update from Feb. 20, do you mean an update of STATA or just the command which I could obtain by "ssc install"? Is there a web page to follow updates of specific commands or is "update query" the only way? Like setting a watchdog for a webpage would be more convenient than regulary checking "update query".

I forgot that fracreg computes robust standard errors by default. This shall be actually reported even in the short help info, not only in the PDF version.

Enjoy the day!

[Scott Merryman]

help whatsnew

will show the Stata updates you have on your machine. This fracreg update occurred under the current release Stata 15.

[Pavel Satra]

Well then, it is time for me to upgrade to Stata 15.