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From |
Misha Spisok <misha.spisok@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: Marginal effects with natural log of independent variable |

Date |
Thu, 4 Mar 2010 22:43:11 -0800 |

Hello, Statalist! I'm still trying to conquer the basic model (i.e., conditional logit) in ml, but I've been thinking about subsequent problems (er, challenges...) down the line. Foremost on my mind are marginal effects. Note that "_ij" is "subscript i,j." The basic issue is marginal effects when the independent variable is x vs. ln(x) (i.e., untransformed vs. transformed). If my model is p_ij = e^b*x_ij/[sum e^b*x_ik] (1) then the marginal effect, dp/dx_ij, differs by observation and average marginal effects are calculated. The marginal effect can be shown to be dp_ij/dx_ij = b*p_ij*(1-p_ij) Is it kosher to do the following if the independent variable is the natural log of the "original" (i.e., untransformed) independent variable? For example, let the model be p_ij = e^b*ln(x_ij)/[sum e^b*ln(x_ik)]. (2) Now the marginal effect, with respect to the untransformed variable ought to be dp_ij/dx_ij = (b/x_ij)*p_ij*(1 - p_ij) Now, the elasticity of p with respect to x_ij in (1) is epsilon = (dp_ij/dx_ij)*(x_ij/p_ij) = (marginal effect)*(x_ij/p_ij) = [b*p_ij*(1 - p_ij)]*(x_ij/p_ij) = b*(1 - p_ij)*x_ij, while for (2) it is epsilon = (dp_ij/dx_ij)*(x_ij/p_ij) = (marginal effect)*(x_ij/p_ij) = [(b/x_ij)*p_ij*(1 - p_ij)]*(x_ij/p_ij) = b*(1 - p_ij) One benefit I see is that the variable, x_ij, doesn't appear in this expression. Thanks for taking the time to read this, not to mention for any help or suggestions. Cheers, Misha * * 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: Marginal effects with natural log of independent variable***From:*Austin Nichols <austinnichols@gmail.com>

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