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From |
Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: Re: Re: Re: st: 'margin' and marg. effects of second-order polynomials |

Date |
Thu, 30 Dec 2010 03:13:30 -0800 |

standard normal density. T On Thu, Dec 30, 2010 at 3:09 AM, Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com> wrote: > Justina, > > While the following sentence at <http://www.stata.com/stata11/margins.html>: > > "[...] Because of Stata 11’s new factor-variable features, we can get > average partial and marginal effects for age even when age enters as a > polynomial:" > > confirms what I have said above, it is sometimes a good exercise to > check these yourself. I show below how you might do this for a probit > model with higher-order terms (in principle, the extension to ordered > probit is the same because of the parallel lines assumption). Recall > that the formula for the change in probability of success is (_not_ as > you write): > > d(P(y=1))/dx = \phi(x'b)(b_1+2*b_{12}*x_1) > > where x is the entire vector of covariates, and x_1 is the covariate > of interest (for which the second-order term is also included in the > linear index, hence the form of the marginal effect), b_1 is the > coefficient on the main term and b_{12} is the coefficient on the > polynomial term. Note that this is for each individual observation. > From these, computing the so-called average marginal effects is easy. > Here is the code: > > ************************************************ > clear* > clear mata > sysuse auto, clear > g mpgsq = mpg^2 > > mata > // probit log-likelihood > void fnProbitLL(todo,b,crit,g,H) > { > external vY,mX > crit= vY'*log(normal(mX*b'))+(1:-vY)'*log(1:-normal(mX*b')) > } > > // create data > vY = st_data(., ("foreign")) > cons=J(rows(vY),1,1) > mX = st_data(., ("mpg", "price", "mpgsq")), cons > stata("qui: logit foreign mpg price mpgsq ") > init = st_matrix("e(b)") > > // optimize > S=optimize_init() > optimize_init_valueid(S, "log-likelihood") > optimize_init_which(S, "max") > optimize_init_evaluatortype(S,"d0") > optimize_init_evaluator(S, &fnProbitLL()) > optimize_init_params(S, init) > optimize_init_technique(S, "nr") > optimize_init_trace_value(S, "on") > optimize_init_trace_params(S, "on") > optimize(S) > > // retrieve results > vB = optimize_result_params(S) > mVarCovar = optimize_result_V_oim(S) > > // construct marginal effects (Ai & Norton, EL, 2003) > dB12 = vB[1, 3] // coeff. on 2nd-order term > dB1 = vB[1, 1] // coeff. on main term > // vector of individual marginal effects > vPE = normalden(mX*vB'):*(dB1:+2*dB12:*mX[.,1]) > // average partial effect > printf("The average marginal effect of age= %g.\n", colsum(vPE)/rows(vPE)) > end > > // probit foreign c.mpg##c.mpg price > probit foreign mpg c.mpg#c.mpg price > margins, dydx(mpg) > ************************************************ > > And you see that the marginal effects computed directly from the > formula coincides exactly with what Stata gives you using -margins-. > > The standard reference for this sort of thing is Ai & Norton, > "Interaction terms in logit and probit models", Economics Letters, > 80(1), 2003, and the accompanying Stata Journal article, which can be > found here: > http://www.stata-journal.com/article.html?article=st0063 > > T > > > > On Thu, Dec 30, 2010 at 1:08 AM, Justina Fischer <JFischer@diw.de> wrote: >> thanks for these insights ans sorry for bothering you a last time: >> >> estimating >> >> logistic outcome treatment##group c.age##c.age >> >> what marginal effect does >> >> margins, dydx(age) >> >> estimate ? is it dy/dx = a + 2bx ? >> >> Justina > > > > -- > To every ω-consistent recursive class κ of formulae there correspond > recursive class signs r, such that neither v Gen r nor Neg(v Gen r) > belongs to Flg(κ) (where v is the free variable of r). > -- To every ω-consistent recursive class κ of formulae there correspond recursive class signs r, such that neither v Gen r nor Neg(v Gen r) belongs to Flg(κ) (where v is the free variable of r). * * 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/

**References**:**st: 'margin' and marg. effects of second-order polynomials***From:*Justina Fischer <JFischer@diw.de>

**Re: st: 'margin' and marg. effects of second-order polynomials***From:*Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>

**Antwort: Re: st: 'margin' and marg. effects of second-order polynomials***From:*Justina Fischer <JFischer@diw.de>

**Re: Re: st: 'margin' and marg. effects of second-order polynomials***From:*Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>

**Antwort: Re: Re: st: 'margin' and marg. effects of second-order polynomials***From:*Justina Fischer <JFischer@diw.de>

**Re: Re: Re: st: 'margin' and marg. effects of second-order polynomials***From:*Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>

**Antwort: Re: Re: Re: st: 'margin' and marg. effects of second-order polynomials***From:*Justina Fischer <JFischer@diw.de>

**Re: Re: Re: Re: st: 'margin' and marg. effects of second-order polynomials***From:*Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>

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