I am just a beginner. I have a sample of 71. I wish to do a Poisson regression. Is this sufficient for estimating a Poisson model? Should I use only counts as $Y$ variable or should I use percentages (i.e., counts converted into percentages)? For the given sample size up to how many $X$ variables could I use in a single model?
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$\begingroup$ Well, I just now fitted a Poisson regression to three observations - both parameter estimates were within about 1.3 standard errors of the population parameters. (It even managed to fit 2, but of course that leaves no degrees of freedom for anything but the fit.) $\endgroup$– Glen_bCommented May 3, 2014 at 9:18
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I'm not aware of any special problems occurring with Poisson regression with small samples. I would not try to transform your data into percentages; I don't even know how that would work. With a smaller sample, you may want to just use a negative binomial model (instead of a straight Poisson) by default. I don't know if it might be more difficult to assess overdispersion with fewer data. A general rule of thumb regarding sample sizes and the number of variables in regression models is that you can have 1 variable for each 10 data. As far as I know, that would be the same for Poisson regression, although I take such rules of thumb with a grain of salt personally.
answered May 3, 2014 at 3:57