R: Equivalence between lm and glm
I find difficult to understand why in lm(log(Y) ~ X) Y is assumed lognormal. I know that if Y ~ N then Z=exp(Y) ~ LN, and that if Y ~ LN then Z=log(Y) ~ N. In lm(log(Y) ~ X) I assume Y ~ N(mu, sigma^2), and then exp(Y) would be distributed by a LN, not l og(Y). Where is my mistake? Moreover, in glm(Y ~ X, family=gaussian(link=log)) the regression is log(mu) = beta0 + beta1*X. In lm(log(Y) ~ X) the regression is exp(mu+(1/2)*sigma^2) = beta0 + beta1*X. Correct? Thank you for your help Stefano Sofia
Da: peter dalgaard [pdalgd at gmail.com]
Inviato: mercoled? 29 maggio 2013 18.51 A: Stefano Sofia Cc: r-help at r-project.org Oggetto: Re: [R] Equivalence between lm and glm On May 29, 2013, at 17:23 , Stefano Sofia wrote: > > Dear R-users, > in case of linear model, > lm(Y ~ X) > is equivalent to > glm(Y ~ X, family=gaussian(link=identity)) > > In case of the exponential model > lm(log(Y) ~ X) > why > glm(Y ~ X, family=gaussian(link=log)) > is not equivalent? Y is assumed lognormal in one case, normal in the other. > Is there an equivalent glm to lm(log(Y) ~ X)? > Yes, glm(log(Y) ~ X, family=gaussian(link=identity)) -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com ________________________________ AVVISO IMPORTANTE: Questo messaggio di posta elettronica pu? contenere informazioni confidenziali, pertanto ? destinato solo a persone autorizzate alla ricezione. I messaggi di posta elettronica per i client di Regione Marche possono contenere informazioni confidenziali e con privilegi legali. Se non si ? il destinatario specificato, non leggere, copiare, inoltrare o archiviare questo messaggio. Se si ? ricevuto questo messaggio per errore, inoltrarlo al mittente ed eliminarlo completamente dal sistema del proprio computer. Ai sensi dell?art. 6 della DGR n. 1394/2008 si segnala che, in caso di necessit? ed urgenza, la risposta al presente messaggio di posta elettronica pu? essere visionata da persone estranee al destinatario. IMPORTANT NOTICE: This e-mail message is intended to be received only by persons entitled to receive the confidential information it may contain. E-mail messages to clients of Regione Marche may contain information that is confidential and legally privileged. Please do not read, copy, forward, or store this message unless you are an intended recipient of it. If you have received this message in error, please forward it to the sender and delete it completely from your computer system.