I wanted to conduct regression for a count outcome data with under dispersion. Which regression model is appropriate?
Hello Behailu Terefe Tesfaye
Perhaps at first glance, what comes to mind is Poisson regression. Therefore, in my opinion, it is better to present more findings.
It is good to see the links below
https://www.graphpad.com/guides/prism/latest/curve-fitting/reg_poisson-regression.htm
Especially this one.
https://support.minitab.com/en-us/minitab/21/help-and-how-to/statistical-modeling/regression/how-to/fit-poisson-model/before-you-start/overview/
Dear Abolfazl Ghoodjani, thank you for your prompt reaction. Look, I read that poisson regression is not appropriate for handling count outcomes when the variance is less or greater than mean. In my case, the variance is a slightly lower than the mean (under dispersed).
Of course, I do not insist on using Poisson regression. Because I still don't know your study format.
It's good though, see the picture.
Another point is that you can easily test whether your DV (Dependent Variable) has a Poisson distribution or not.
Professor Kelvyn Jones thank you for your reaction in advance. Look, the data was collected prospectively from patients over their hospital stay and the outcome variable has a whole number value randomly running from 0 to 6. When I run a summary statistics for this variable on STATA, the mean value is 1.2... and the variance is 0.9....
The other issue is since the data is collected over hospital stay, the duration over which the data is collected from each patient is variable.
Questions
Can I use models for count outcomes for my data? If so which model?
While Prof Jones is replying see the attached Google search for the possible methods. Best wishes David Booth
I would use over-dispersed NBD model (which is potentially over dispersed compared to Poisson) with an offset to take account of the variable exposure. Not taking account of the different times may induce the under dispersion and you may find that you get over dispersion when you model the situation properly! My experience is that these issues only affect the standard errors of the estimates and not the estimates per se.
see
Hilbe, J. (2011). Negative Binomial Regression (2nd ed.). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511973420
Hilbe, J. (2014). Modeling Count Data. Cambridge: Cambridge University Press. doi:10.1017/CBO9781139236065
the first is more technical, the second is more approachable.
Thank you prof. Kelvyn Jones for your usual informative response for my concerns. I downloaded the first reference 1st ed. freely and I`m exploring it.
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