Count outcome with exposure vs. rate outcome

[Matt Piszczek]

Dear Forum Members,

I am estimating models of organizational turnover (i.e. quit rates). My outcome data is in the form of "number of quits." Most organizations report zero quits, but the range is quite large. The data is most definitely not normally distributed. I also have data on the number of employees in each organization.

My inclination is to use zero-inflated negative binomial regression with total number of employees as the exposure variable, but it this type of modeling is not common practice in my field. More commonly, researchers will divide turnover by total number of employees to construct a turnover rate variable, add one, take the log, and then model it using OLS regression.

Can anyone help me understand the implications of these two approaches for modeling the data so I can produce the most accurate estimates? I have found plenty of information on how to conduct regression for count outcomes, but have not been able to find any advice comparing these two approaches. Thanks for any help you might be able to provide.

-Matt

[Joao Santos Silva]

Dear Matt,

First of all, I would say that the approach you describe as standard in your field is totally inappropriate, so stay away from it.

Using a zero-inflated negative binomial regression with total number of employees as the exposure variable also does not sound like a good choice to me. To start with, Stata's implementation of the ZINB has some problems that may lead you to spurious results. Also, zero-inflated models are designed for cases where for some individual we'll always observe zeros, which does not sound reasonable in your case. Finally, I do not think that using the number of employees as an exposure will ensure that the fitted values will always be smaller than the number of employees.

My suggestion is that you model the ratio using the fractional logit introduced by Papke and Wooldridge and implemented in -fracreg-

Best wishes,

Joao

[Matt Piszczek]

Thank you Joao, I appreciate your time. I will look into this option.