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In doing a count data model using a Poisson distribution, should the estimate (output) be rounded (or the ceiling) if your target variable is always a whole number in the input training target data and is there a way to do this in the model? (i.e. I enter the integer 0-9, it outputs floats)

To put in practical terms I cannot have 1.22 people or 3.89 people, should this become 1 and 4 within the model.

If so, how do you account for this in your model so the model parameters and outputs so the coefficients and other diagnostic information are in line with the output as the model itself in SAS is not going to round up or down for you and adjust automatically (at least I do not believe so in SAS) and it has to do it after the fact.. creating an inconsistency?

If not, just output it and allow the end user to interpret?

I am still a newbie so I may just be over thinking this ... any input would be appreciated. Yes or No's with some additional detail/reference even more appreciated.

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  • $\begingroup$ You are conflating parameters with data. A Poisson parameter can be non-integral. There is no inherent inconsistency or contradiction in that. Although you cannot have 1.22 people, you certainly can have a population that averages 1.22 people per household, for instance. Or, for another common example, it would be useless to insist that the probability of heads in a coin flip (a parameter) be either 0 or 1 (the only possible data values)! Insisting that parameters be integral will greatly limit your options and virtually guarantees that you obtain inferior estimates and predictions. $\endgroup$ – whuber Feb 28 '15 at 21:44
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    $\begingroup$ @whuber Thanks. I think that was the kind of sanity check I was really looking for.. that makes sense. If you put it in an answer I would accept it. $\endgroup$ – CRSouser Feb 28 '15 at 21:46
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This answer is basically copying the comments of whuber.

The OP is conflating parameters with data. With count data and a Poisson model, the data must be integers, but even if 1.22 people is impossible, one can have a population that averages 1.22 people per household, say.

Insisting that parameters must be integers will only limit options, make numerical maximization more difficult, and gain you nothing. Your estimations and predictions will be inferior.

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