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Re: st: ratio of marginal effects when using two -margins- commands
From
Mirko <[email protected]>
To
[email protected]
Subject
Re: st: ratio of marginal effects when using two -margins- commands
Date
Sun, 18 Apr 2010 20:14:40 +0100
Thank you.
Mirko
On 15 April 2010 23:04, Jeff Pitblado, StataCorp LP <[email protected]> wrote:
> Mirko <[email protected]> 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
> [email protected]
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