Re: st: ratio of marginal effects when using two -margins- commands

[Mirko <mirko.moro@gmail.com>]

Thank you.
Mirko

On 15 April 2010 23:04, Jeff Pitblado, StataCorp LP <jpitblado@stata.com> wrote:
> Mirko <mirko.moro@gmail.com> asks how to use -nlcom- with results from
> multiple calls to -margins-:
>
>> I am wondering whether is possible to obtain standard errors and
>> confidence intervals of ratio of marginal effects when they are
>> obtained by running two (or more) times the command -margins-.
>> -margins- makes life a lot easier especially after estimating models
>> with interaction terms or nonlinear models:
>>
>> * simple case
>> use http://www.stata-press.com/data/r11/margex
>> logistic outcome sex##group age
>> margins sex, post
>> nlcom (risk_ratio: _b[1.sex] / _b[0.sex])
>>
>>
>> However, there may be some cases in which one needs to compute two
>> separate -margins- commands to obtain the marginal effects of
>> interest. For example, after a model of Y on X, Z and the interaction
>> term XZ:
>>
>> Y = a + bX + bZ + bXZ + e,
>>
>> I'd like to obtain the statistical significance of the ratio of
>>
>> (marginal effects of variable X conditional on variable Z)/ (marginal
>> effects of variable Z conditional on X) =
>>
>> ME1/ME2
>>
>> ****begin example****
>> * -margins*
>>
>> sysuse auto, clear
>> set more off
>> qui regress mpg foreign i.rep78##c.weight headroom
>> * ME1
>> margins, dydx(rep78) atmeans
>> * ME2
>> margins, dydx(weight) over(rep78)
>>
>> ****end example****
>>
>> Is there an easy way to get standard errors and confidence intervals
>> of ratios of two -margins- ME1/ME2?
>>
>> Or do I need to use -nlcom- like below?
>>
>>
>> ****begin example****
>> * ratio of marginal effects with -nlcom-
>> sysuse auto, clear
>> set more off
>> qui tab rep78, gen(rep)
>> forval i=2/5{
>>       qui gen rep`i'Xweight = rep`i'*weight
>> }
>> regress mpg foreign rep2-rep5 rep2Xweight-rep5Xweight weight headroom
>> qui sum weight if e(sample)
>> local meanw = r(mean)
>> * ratio of ME1/ME2
>> nlcom (_b[rep2] + _b[rep2Xweight]*`meanw')/(_b[weight] + _b[rep2Xweight])
>> nlcom (_b[rep3] + _b[rep3Xweight]*`meanw')/(_b[weight] + _b[rep3Xweight])
>> nlcom (_b[rep4] + _b[rep4Xweight]*`meanw')/(_b[weight] + _b[rep4Xweight])
>> nlcom (_b[rep5] + _b[rep5Xweight]*`meanw')/(_b[weight] + _b[rep5Xweight])
>>
>> ****end example****
>
> The -margins- command specifically posts the Jacobian matrix in -r(Jacobian)-
> so that results from different -margins- calls on the same model fit can be
> combined.  Mirko just needs to be careful about equation names in the combined
> results before -ereturn post-ing them.
>
> We'll use Mirko's second example to illustrate how to combine the results
> from two separate calls to -margins-.
>
> First let's respecify the model using factor variables notation so that we can
> use -margins- to get the numerator and denominator marginal effects:
>
> . regress mpg for rep78##c.weight headroom
> (output omitted)
>
> The equivalent -nlcom- command to Mirko's is:
>
> ***** BEGIN:
> . nlcom (R2: (_b[2.r] + _b[2.r#w]*`meanw')/(_b[w] + _b[2.r#w])) ///
>>       (R3: (_b[3.r] + _b[3.r#w]*`meanw')/(_b[w] + _b[3.r#w])) ///
>>       (R4: (_b[4.r] + _b[4.r#w]*`meanw')/(_b[w] + _b[4.r#w])) ///
>>       (R5: (_b[5.r] + _b[5.r#w]*`meanw')/(_b[w] + _b[5.r#w]))
>
>          R2:  (_b[2.r] + _b[2.r#w]*3032)/(_b[w] + _b[2.r#w])
>          R3:  (_b[3.r] + _b[3.r#w]*3032)/(_b[w] + _b[3.r#w])
>          R4:  (_b[4.r] + _b[4.r#w]*3032)/(_b[w] + _b[4.r#w])
>          R5:  (_b[5.r] + _b[5.r#w]*3032)/(_b[w] + _b[5.r#w])
>
> ------------------------------------------------------------------------------
>         mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>          R2 |  -33.06524   311.6278    -0.11   0.916    -657.0891    590.9586
>          R3 |   166.0963   502.9187     0.33   0.742     -840.981    1173.174
>          R4 |   76.42387   460.7441     0.17   0.869    -846.2003     999.048
>          R5 |   363.8427   148.9601     2.44   0.018     65.55527    662.1302
> ------------------------------------------------------------------------------
> ***** END:
>
> Now that we have the -regress- model using factor variables notation, we can
> get the two sets of marginal effects results.  We'll need to grab the point
> estimates from -r(b)- and corresponding Jacobian matrix from -r(Jacobian)-.
> We can use the Jacobian matrix to reproduce the variance estimates by the
> following matrix product
>
>        r(V) = r(Jacobian)*e(V)*r(Jacobian)'
>
> ***** BEGIN:
> . * reference contrasts on the margins of rep78, i.e. effects of factor rep78
> . margins, dydx(rep78)
> (output omitted)
> . matrix b_num = r(b)
> . matrix colna b_num = num:
> . matrix J_num = r(Jacobian)
> . matrix rowna J_num = num:
>
> . * marginal effects of weight for each level of rep78
> . margins, dydx(weight) over(rep78)
> (output omitted)
> . matrix b_den = r(b)
> . matrix colna b_den = den:
> . matrix J_den = r(Jacobian)
> . matrix rowna J_den = den:
> ***** END:
>
> Notice that we added our own equation name to each set of results we pulled
> from -margins-.  We used 'num' for the numerator results, and 'den' for the
> denominator.
>
> All we need to do now is post the combined results, then use -nlcom-:
>
> ***** BEGIN:
> . * combine the results
> . matrix b = b_num, b_den
> . matrix J = J_num \ J_den
> . matrix V = J*e(V)*J'
> . ereturn post b V
> . * check that the combined results match those from the original
> . ereturn display
> (output omitted)
> ***** END:
>
> ***** BEGIN:
> . nlcom   (R2: [num]_b[2.r]/[den]_b[2.r]) ///
>>         (R3: [num]_b[3.r]/[den]_b[3.r]) ///
>>         (R4: [num]_b[4.r]/[den]_b[4.r]) ///
>>         (R5: [num]_b[5.r]/[den]_b[5.r])
>
>          R2:  [num]_b[2.r]/[den]_b[2.r]
>          R3:  [num]_b[3.r]/[den]_b[3.r]
>          R4:  [num]_b[4.r]/[den]_b[4.r]
>          R5:  [num]_b[5.r]/[den]_b[5.r]
>
> ------------------------------------------------------------------------------
>             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>          R2 |  -33.06645   311.6233    -0.11   0.915    -643.8368    577.7039
>          R3 |   166.0723   502.9125     0.33   0.741     -819.618    1151.763
>          R4 |   76.40598   460.7396     0.17   0.868    -826.6271     979.439
>          R5 |   363.8585   148.9596     2.44   0.015     71.90304     655.814
> ------------------------------------------------------------------------------
> ***** END:
>
> Note that -nlcom- after -regress- reports 't' statistics, p-values, and CIs;
> but -margins- and our combined results report 'z' statistics.  This is because
> we didn't post the -e(df_r)- from the -regress- results in our combined
> results.
>
> --Jeff
> jpitblado@stata.com
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