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# Re: st: Calculating and interpreting effect size when DV is a proportion

 From Jeffrey Wooldridge To statalist@hsphsun2.harvard.edu Subject Re: st: Calculating and interpreting effect size when DV is a proportion Date Mon, 14 Jan 2013 11:26:57 -0500

```Here is an example I generated from data that comes with my MIT Press book:

. glm prate mrate c.mrate#c.mrate age c.age#c.age ltotemp i.sole,
note: prate has noninteger values

Iteration 0:   log pseudolikelihood = -1315.4966
Iteration 1:   log pseudolikelihood = -1288.1302
Iteration 2:   log pseudolikelihood = -1287.6149
Iteration 3:   log pseudolikelihood = -1287.6145
Iteration 4:   log pseudolikelihood = -1287.6145

Generalized linear models                          No. of obs      =      4075
Optimization     : ML                              Residual df     =      4068
Scale parameter =         1
Deviance         =  882.4410467                    (1/df) Deviance =  .2169226
Pearson          =  858.6841333                    (1/df) Pearson  =  .2110826

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

AIC             =  .6353936
Log pseudolikelihood = -1287.614502                BIC             = -32933.32

---------------------------------------------------------------------------------
|               Robust
prate |      Coef.   Std. Err.      z    P>|z|     [95%
Conf. Interval]
----------------+----------------------------------------------------------------
mrate |   1.377793   .1671457     8.24   0.000     1.050194
1.705393
|
c.mrate#c.mrate |  -.1943269   .1282904    -1.51   0.130    -.4457715
.0571177
|
age |   .0474067    .006151     7.71   0.000      .035351
.0594625
|
c.age#c.age |  -.0004339   .0001756    -2.47   0.013     -.000778
-.0000898
|
ltotemp |  -.2087835   .0141589   -14.75   0.000    -.2365345
-.1810325
1.sole |   .1675674   .0507829     3.30   0.001     .0680348
.2671
_cons |   2.330817   .1089061    21.40   0.000     2.117365
2.544269
---------------------------------------------------------------------------------

. margins, dydx(*)

Average marginal effects                          Number of obs   =       4075
Model VCE    : Robust

Expression   : Predicted mean prate, predict()
dy/dx w.r.t. : mrate age ltotemp 1.sole

------------------------------------------------------------------------------
|            Delta-method
|      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
mrate |   .1586229   .0125717    12.62   0.000     .1339829    .1832629
age |   .0053308   .0005544     9.61   0.000     .0042441    .0064174
ltotemp |  -.0265256    .001827   -14.52   0.000    -.0301065   -.0229447
1.sole |     .02093   .0062078     3.37   0.001     .0087628    .0330971
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

The AME for mrate means that if mrate (the match rate) increases by
.10 (ten cents on the dollar) then, on average, the prate
(participation rate) increases by about .016, or 1.6 percentage
points.

On Mon, Jan 14, 2013 at 11:06 AM, Michelle Dynes
<dynes.michelle@gmail.com> wrote:
> Thank you Maarten and Jeffrey for your prompt replies! I have gone
> ahead and followed the example Maarten provided by centering my
> continuous variables in the fractional logit model along with the
> -eform- command. Maarten, for further clarification, is it ok to refer
> to the ORs, produced using the -eform- command per your example, as
> Relative Proportion Ratios even though Stata reports them as ORs? This
> makes sense to me given the outcome variable is a proportion, but I
> thought I would double check. Many thanks!
> *
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```