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From |
jpitblado@stata.com (Jeff Pitblado, StataCorp LP) |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Thu, 15 Apr 2010 17:04:33 -0500 |

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 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: ratio of marginal effects when using two -margins- commands***From:*Mirko <mirko.moro@gmail.com>

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