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From |
jverkuilen <jverkuilen@gc.cuny.edu> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: glm and reg produce different results for loglinear model? |

Date |
Mon, 3 Nov 2008 10:27:18 -0500 |

Log link and log transform are not the same model. On what scale do you expect the errors to operate? Log transform implies lognormal errors which are multiplicative. Log link is log in expected value but additive in errors. -----Original Message----- From: "Matthew Mercurio (matthewmercurio)" <matthewmercurio@fscgroup.com> To: statalist@hsphsun2.harvard.edu Sent: 10/31/2008 5:43 PM Subject: st: glm and reg produce different results for loglinear model? I have two variables, (1) outagecost (estimated costs to each customer of a short electrical power interuuption) (2) mwhannual (annual megawatt hours of electricity consumption fpr each customer) Since these variables appear approximately lognormal, I have been estimating the following simple model: reg lnoutagecost lnmwhannual where lnoutagecost and lnmwhannual represent the natural log of the two variables desribed above. The results are: . reg lnoutagecost lnmwhannual Source | SS df MS Number of obs = 32345 -------------+------------------------------ F( 1, 32343) = 9370.20 Model | 34151.9301 1 34151.9301 Prob > F = 0.0000 Residual | 117881.722 32343 3.6447368 R-squared = 0.2246 -------------+------------------------------ Adj R-squared = 0.2246 Total | 152033.652 32344 4.70052104 Root MSE = 1.9091 ------------------------------------------------------------------------ ---- lnoutagecost | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------- ---- lnmwhannual | .3824726 .0039512 96.80 0.000 .3747282 .3902171 _cons | 5.370938 .0232302 231.21 0.000 5.325406 5.41647 ------------------------------------------------------------------------ ---- I then tried the following model in glm which I had expected to produce identical results: glm outagecost lnmwhannual, link(log) Generalized linear models No. of obs = 52418 Optimization : ML Residual df = 52416 Scale parameter = 7.59e+09 Deviance = 3.97873e+14 (1/df) Deviance = 7.59e+09 Pearson = 3.97873e+14 (1/df) Pearson = 7.59e+09 Variance function: V(u) = 1 [Gaussian] Link function : g(u) = ln(u) [Log] AIC = 25.5881 Log likelihood = -670636.5416 BIC = 3.98e+14 ------------------------------------------------------------------------ ---- | OIM outagecost | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------- ---- lnmwhannual | .5568004 .0130092 42.80 0.000 .5313029 .5822979 _cons | 5.355758 .1384432 38.69 0.000 5.084414 5.627102 ------------------------------------------------------------------------ ---- Obviously the results are very similar, but not identical. I read the Stata Manual section on GLM and checked a large number of posts on Statalist related to loglinear models, but I was not able to understand exactly why glm using link(log) doesn't produce the same results as logging both variables and using reg. Based on my reading of the Stata manual it appears to have someing to do with the fact that the link() option relates to the expectation od the dependent variable, not the dependent variable itself. Can anyone tell me why the results are different? Matthew G. Mercurio, Ph.D. Senior Consultant Freeman, Sullivan & Co. * * 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/ * * 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/

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