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I'm working with count data (ticket sales, to be specific) and I'm having trouble fitting a model to it. I've tried a linear one and a transformed linear one, but the residuals end up being non-normal and having a non-constant variance. I've been trying to play around with other models (negative binomial, poisson, etc.) but I can't seem to get anything to fit very well. Here's the histogram for my response variable and what the residual plots look like for my linear model: enter image description here

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  • $\begingroup$ What is the unit of analysis? $\endgroup$
    – dimitriy
    Commented Jun 18, 2014 at 17:44
  • $\begingroup$ It's trying to predict tickets sold. $\endgroup$ Commented Jun 18, 2014 at 19:17
  • $\begingroup$ Per user? Per unit of time? X days before the game? $\endgroup$
    – dimitriy
    Commented Jun 18, 2014 at 19:36
  • $\begingroup$ Oops, sorry. It's x days before the game. $\endgroup$ Commented Jun 18, 2014 at 19:36

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I would try a Negative Binomial Regression model (NBRM), which accounts for a non-negative integer dependent variable. The NBRM is basically an extension of the Poisson regression which introduces a dispersion parameter that allows for over-dispersion. Zero-inflated models, on the other hand, are well suited for situations in which zeros can be the product of two different process (this is well explained in the UCLA site that Stat points out above). Depending on the characteristics of your dependent variable, other models could be appropriate, like a zero-truncated model.

There are several texts on models for count variables, like Cameron & Trivedi 1998, Cameron & Trivedi 2005 (see chapter 20, "Models for Count Data"), or Zeileis, Kleiber & Jackman 2008 for a more practical approach focused on R.

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  • $\begingroup$ C&T Count data book has a 2nd edition. $\endgroup$
    – dimitriy
    Commented Jun 18, 2014 at 17:43
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Maybe you can try to fit a Zero-inflated Poisson Regression. I am not sure how well that model will be, but you can give it a try. An example has been given in here.

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