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I have a question towards an analysis of purchasing decisions. I have a data set where I investigate the amount of previous purchases last week (predictor) on the amount of purchases today (response variable). Because it is count data I use a negative binomial panel regression (random effects). However, I also tried a linear panel regression. The coefficients of my predictor variable are 0,008 in the negative binomial and 0,4 in the linear regression. Studying the literature I saw many researchers using a linear regression in this context. I am wondering how such a huge difference can be explained between those results. Of course, I am aware that interpretation is different one unit increase in previous purchases results in 0,4 increase in the linear regression. While the Incidence Rate Ratio in the negative binomial suggests a one unit increase of previous purchases results in a factor of 1,008 of the response variable. Any comments or help would be appreciated :)

kjetil b halvorsen
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Steven Heinrich
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    What link function are you using in the negative binomial regression? – whuber Jun 14 '15 at 17:32
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    I guess a usual log link. In stata I just operated the normal negative binomial regression (count data/negative binomial). When I transform the independent variables in log form (according to Cameron and Trivedi that is allowed), I have a 0,7 coefficient for my main predictor. I am really confused, this does not really make sense – Steven Heinrich Jun 16 '15 at 08:06
  • Have a look at https://stats.stackexchange.com/questions/142338/goodness-of-fit-and-which-model-to-choose-linear-regression-or-poisson/142353#142353 to understand the differences in interpretation – kjetil b halvorsen Apr 03 '18 at 14:04

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