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I'm working on a school project concerning Poisson regresion. I'm trying to build a model for number of cars in household base on American Community Survey. Among explanatory variables are value of property, nb. of people in household, nb. of workers etc. I have about 90k observation.

So I have concerns about the distribution. When I take a look at histogram of nb. of cars in data it is great:

Classic Poisson!

But when it comes to modeling all missing values are removed (also where explanatory variables are missing) and about 2/3 of observations are removed, and looking at the distribution again it doesn't look so Poisson anymore:

Not so Poisson :(

Well it's not that bad, but I'm thinking about data imputation (like using mean of variable for NA's) for explanatory variables in order to keep most information about the car distribution. I'm not sure though what are the effects or risks of doing this. That's why I would ask someone more experienced if this is a good idea or I should not do it and why? Is imputation using mean best method?

Another thing is that, I eventually did the regression for records without missing values and I got this distribution of fitted values:

Fitted

It kind of surprised me because honestly I was expecting something less Normal and more Poisson (of course not discrete, but maybe more positively skewed). Does it look like a correct (common?) result?

Thanks for answers!

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