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From |
<jrfranke@illinois.edu> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: count regression with product & power terms |

Date |
Tue, 3 Feb 2009 12:54:31 -0600 (CST) |

I'm running a count regression with x1 and x1^2 terms using the "poisson" command (I expect a nonlinear effect of x1), and want to compute marginal effects. The "mfx" and "margeff" commands appear to not be well-suited for computing the marginal effects of such product or power terms (see http://www.unc.edu/%7Eenorton/NortonWangAi.pdf). Ideally, I'd like to be able to graph the marginal effects and their statistical significance (perhaps in a similar manner as in the above paper). Ironically, if graph the "mfx" marginal effects on y, I get the concave shape that I expect, but if I replace these with marginal effects calculated by my own derivitives I don't get similar results. I was wondering if I've made a mistake in the code below or if I'm way off base in my approach/understanding of the issues at hand. Also, I haven't even gotten around to attempting to calculate the significance of the marginal effects, so help with that would be great. Thanks, Jason Franken CODE FOLLOWS: *1st, I run the count regression y = e^(X'B), where X'B = b0 + b1x1 + b2(x1)^2 + b3x3 ... . poisson y x1 x1squared x3 x4 x5 x6 x7 *Then "mfx" gives marginal effects at mean values of other explanatory variables. mfx *And "margeff" computes the average of the marginal effects for each observation in the sample. margeff, dummies(x6) replace *But the marginal effects for x1 and x1squared are incorrect (see http://www.unc.edu/%7Eenorton/NortonWangAi.pdf). *The problem is that derivatives w.r.t x1 (dy/dx1 and d2y/dx1dx1) are incorrect. *For other variables, like x3, we can show that STATA results are correct. poisson y x1 x1squared x3 x4 x5 x6 x7 *REPRODUCE THE "mfx" RESULT egen x1bar = mean(x1) egen x1squaredbar = mean(x1squared) egen x3bar = mean(x3) egen x4bar = mean(x4) egen x5bar = mean(x5) egen x6bar = mean(x6) egen x7bar = mean(x7) gen eBXbar = exp(_b[_cons] + _b[x1]*x1bar + _b[x1squared]*x1squaredbar + _b[x3]*x3bar + _b[x4]*x4bar + _b[x5]*x5bar + _b[x6]*x6bar + _b[x7]*x7bar) gen mf_x3MEAN = _b[x3]*eBXbar list mf_x3MEAN *REPRODUCE THE "margeff" RESULT gen eBX = exp(_b[_cons] + _b[x1]*x1 + _b[x1squared]*x1squared + _b[x3]*x3 + _b[x4]*x4 + _b[x5]*x5 + _b[x6]*x6 + _b[x7]*x7) gen mf_x3 = _b[x3]*eBX sum mf_x3 *Now, I want to compute true marginal effects for x1 (and x1squared), so that I can graph its nonlinear effect. *FOLLOWING SHOULD GIVE TRUE MARGINAL EFFECT FOR "x1" ... *for the average of marginal effects for all observations (like "margeff"): gen mf_x1 = (_b[x1]+(2*_b[x1squared]*x1))*eBX sum mf_x1 *for the marginal effect at mean values of other explanatory variables (like "mfx"): gen mf_rpMEAN = (_b[x1]+(2*_b[x1squared]*x1bar))*eBXbar list mf_rpMEAN *FOLLOWING SHOULD GIVE TRUE MARGINAL EFFECT FOR "x1squared". *for the average of marginal effects for all observations (like "margeff"): gen mf_x1squared = (2*_b[x1squared]*eBX) + (((_b[x1]+(2*_b[x1squared]*x1))^2)*eBX) sum mf_x1squared *for the marginal effect at mean values of other explanatory variables (like "mfx"): gen mf_x1squaredMEAN = (2*_b[x1squared]*eBXbar) + (((_b[x1]+(2*_b[x1squared]*x1bar))^2)*eBXbar) list mf_x1squaredMEAN *Here's the graph computed using "mfx" marginal effects (Am I "out of line" treating the marginal effects like coefficients to predict a value of y at the mean?). poisson y x1 x1squared x3 x4 x5 x6 x7 mfx gen yMEAN = _b[_cons] + (1.297568*rpfactoramos1) + (-.1066019*rp2) + (.083736*x3bar) + (.0003309*x4bar) + (-.0615128*x5bar) + (-.0954496*x6bar) + (.2182201*x7bar) graph twoway (scatter ymean x1, ms(O)) (line yMEAN x1, sort) * * 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: count regression with product & power terms***From:*Austin Nichols <austinnichols@gmail.com>

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