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

 From Maarten Buis To statalist@hsphsun2.harvard.edu Subject Re: st: Calculating and interpreting effect size when DV is a proportion Date Mon, 14 Jan 2013 18:12:20 +0100

```They are both summaries of the same model, so I see no a priori reason
to prefer one over the other. Sometimes they appear to lead to
different conclusions, but that is only appearances. It is almost
always a consequence of the fact that AMEs quantify the effect in
terms of differences while relative proportion ratios do so in terms
of ratios. Finding the exact cause is usually quite a bit of work
involving staring at lots and lots of graphs of predicted proportions,
looking at graphs of the distribution of your explanatory variables,
and doing lots of hand calculations of differences and ratios at
typical values of the explanatory variables. It is however time well
spent. Afterwards you'll have a much deeper understanding of your data
and what your model is telling you, and you'll just know which one you
want to present (or maybe both, when there is an interesting story in
it).

-- Maarten

On Mon, Jan 14, 2013 at 5:55 PM, Michelle Dynes wrote:
> Thank you for providing your example Jeffrey! Is there a reasonable
> way to decide between generating Fractional Proportion Ratios with
> -eform- versus generating marginal effects using -margins- ? This
> seems like an important question given that I have done both and the
> two methods generate different results in terms of interpretation. The
> general direction and strength of the associations are the same for
> both strategies, but the percent change in my outcome variable is not
> the same. Insight?
> Thank you again to all who have contributed! I truly appreciate your
> time and consideration.
> Michelle
>
> On Mon, Jan 14, 2013 at 11:26 AM, Jeffrey Wooldridge
> <jmwooldridge60@gmail.com> wrote:
>> 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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>>> *   http://www.ats.ucla.edu/stat/stata/
>> *
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> *
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--
---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
---------------------------------
*
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```