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

 From Tirthankar Chakravarty To statalist@hsphsun2.harvard.edu Subject Re: Re: Re: Re: st: 'margin' and marg. effects of second-order polynomials Date Thu, 30 Dec 2010 03:09:44 -0800

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.