Re: different result in two nb reg and pisson reg

Posted by Andy W on Sep 16, 2014; 12:26pm
URL: http://spssx-discussion.165.s1.nabble.com/different-result-in-two-nb-reg-and-pisson-reg-tp5727252p5727265.html

I'm not quite sure what "The reciprocal will be a bit stronger than taking the log" means. I suggested log because it results in a similar model to that of the Poisson regression i.e. for Poisson regression the equation is the log of the expected value of Y:

log(E[Y|X]) = B*X

Whereas for a regression with the dependent variable logged it is the expected value of the transformed variable:

E[log(Y)|X] = B*X

Unfortunately these won't results in the same estimates -- but I hope people see the resemblance!

Like I said it is a bit arm-chair to be suggesting models without more knowledge (I doubt someone is travelling the same distance for times ranging between 5 minutes and 4.5 hours though! The variables clearly suggest we are dealing with humans, not animal measurements). Typically the researcher can specify a generic theory of the form Y = f(X) - that is the outcome is some function of a set of explanatory variables. The form of the function can be guided by prior research and/or purely data driven curve fitting.

Poisson and negative binomial models are standard fare for models of counts and rates -- especially when they have low counts. These models have positive probability for all positive values though, hence my hesitation of its appropriateness in this situation in which there are no zero values of travel times.  If this was say a survey and it asked "For the last 10 hours you have driven, how many minutes were travelling to work?" then this is likely not appropriate for Poisson, as it has a cap at 10 hours (and I would expect many people to cap out near the 10 hour mark). If it was a survey and asked "In the past week, how many minutes have you spent travelling to work?" - this could plausibly be appropriate for a Poisson model. (The choice between Poisson and Neg. Bin. is typically data driven.)