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We are trying to decide between using crime per capita as a dependent variable in our model versus including population on the right hand side. The basic analysis is about crime's relationship with economic activity (business revenues, etc).

Our crime data is yearly, but our population data is decennial so the yearly numbers in between are interpolated. Since they are interpolated, I feel more comfortable using pop on the right hand side, since it is my understanding that interpolated data causes less bias when used as a control than when used as a dependent variable (mismeasurement in a dependent variable being more serious than in a control). If both are logged, shouldn't they be exactly the same anyway? ($\ln(crime/pop)=\ln(crime)-\ln(pop)$, so $\ln(pop)$  can be moved to the rhs).

The model is a fixed effects model with both year and geographic fixed effects. Also, population is just nighttime population (ie, people who live there), whereas our analysis is about daytime population (people who shop there, work there, etc). Any suggestions on which way to go?

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  • $\begingroup$ I ran into the same issue. In my case, using the per capita version resulted in extremely skewed data which made the models misbehave. Using population size as a predictor gave much more sensible results. You can see the discussion here: openpsych.net/forum/showthread.php?tid=298 $\endgroup$ Commented Feb 25, 2017 at 22:56

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This could benefit from some more detailed information ... but assuming that the crime data consists of counts, that is usually modeled by a Poisson regression, with (log) population as an offset. Details are given at Goodness of fit and which model to choose linear regression or Poisson and elsewhere ... and I think that should be the way to go.

But your post also indicates some other problems, such as

population is just nighttime population (ie, people who live there), whereas our analysis is about daytime population (people who shop there, work there, etc)

which would be a problem if difference between night and day population differs between the districts (as it surely does ...). You would need to get some information about the relationship between the two populations, maybe.

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