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From |
May Boggess <mboggess@stata.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: marginal effects and interactions |

Date |
01 Apr 2004 19:35:33 -0600 |

On Thursday, Scott Merryman wrote: > one can easily obtain the marginal effects and standard errors for linear models > using -lincom- > > For example: > > . sysuse auto > (1978 Automobile Data) > > . gen mpgXprice = mpg*price > > . gen mpgXgear = mpg*gear > > . qui reg weight mpg price gear mpgX* > > . qui sum price if e(sample) > > . local mean1 = r(mean) > > . qui sum gear if e(sample) > > . local mean2 = r(mean) > > . lincom mpg + mpgXp*`mean1' + mpgXg*`mean2' > > ( 1) mpg + 6165.257 mpgXprice + 3.014865 mpgXgear = 0 > > ------------------------------------------------------------------------------ > weight | Coef. Std. Err. t P>|t| [95% Conf. Interval] > -------------+---------------------------------------------------------------- > (1) | -73.55893 10.69451 -6.88 0.000 -94.89949 -52.21836 > ------------------------------------------------------------------------------ > > We can use this for any function of the covariates and coefficients, after an estimation, as long as we can differentiate the function by hand, as was done in the example above. Let's go over the example above in more detail. Here the function of the covariates and coefficients was f = b0 + b1*mpg + b2*price + b3*gear + b4* mpg*price + b5 * mpg*gear If we differentiate this with respect to mpg we obtain df/dx = b1 + 0 + 0 + b4*price + b5*gear. In the example, this derivative (ie. marginal effect) is evaluated at average price and average gear. They were called mean1 nad mean2. This is the function that was evaluated by -lincom-. The extra milage that -lincom- gets us is the standard error of this marginal effect. You can use -predictnl- in the same way, since it is also designed to use the delta method to obtain standard errors: clear sysuse auto gen mpgXprice = mpg*price gen mpgXgear = mpg*gear reg weight mpg price gear mpgX* qui sum price if e(sample) local mean1 = r(mean) qui sum gear if e(sample) local mean2 = r(mean) di _b[mpg] + _b[mpgXp]*`mean1' + _b[mpgXg]*`mean2' lincom mpg + mpgXp*`mean1' + mpgXg*`mean2' predictnl dfdx =_b[mpg] + _b[mpgXp]*`mean1' + _b[mpgXg]*`mean2' in 1, se(se) list dfdx se in 1 Here is one more example, using -probit-, as requested by Javier. I haven't used an interaction in this example, because I want to be able to check my answer: clear sysuse auto probit for price gear qui sum price if e(sample) local mean1 = r(mean) qui sum gear if e(sample) local mean2 = r(mean) predict xb,xb predict p,p gen myxb = _b[price]* price + _b[gear]*gear + _b[_cons] gen myp = norm(myxb) sum myp p xb myxb di normd(_b[price]* `mean1' + _b[gear]*`mean2' + _b[_cons])*_b[price] *lincom lincom normd(_b[price]* `mean1' + _b[gear]*`mean2' + _b[_cons])*_b[price] predictnl dfdp = normd(_b[price]* `mean1' + _b[gear]*`mean2' + _b[_cons])*_b[price] in 1, se(sep) list dfdp sep in 1 predictnl dfdg = normd(_b[price]* `mean1' + _b[gear]*`mean2' + _b[_cons])*_b[gear] in 1, se(seg) list dfdg seg in 1 mfx, predict(p) After I run the model, I check that I understand the function for which I want the marginal effects. In this example I am interested in p, the probability of success. So, I check I know how to compute it as Stata would. Then I have done the derivative by hand using the chain rule. Note that the derivative of the cumulative distribution fuction -norm- is the density function -normd-. I have commented out -lincom- because, as you will see, it's equation parser isn't quite as clever as -predictnl-'s (either that or I haven't found the correct way to enter it into -lincom-). However, -predictnl- handles it well. I do it twice, to get both marginal effects. I confirm my answer using -mfx-. -- May mmb@stata.com * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: marginal effects and interactions***From:*"Scott Merryman" <smerryman@kc.rr.com>

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