Appropriate Counts Model

[Siddharth Rao]

Hello,

I am unsure of the appropriate counts model to use in the case of an overdispersed response variable, with an unbalanced, panel structure data set. The unit variable is electoral constituency, and the time variable is financial years. I considered using a negative binomial panel regression with -xtnbreg- but have read (in the Rabe-Hesketh and Skrondal text on multilevel modelling) that this is a poor option for panel data because the coefficients are difficult to interpret. As my main variable of interest is an indicator variable, and as the effects of the are clearer to me on examining fitted values for them (mainly for margin of victory), this does not seem that much of a concern for me. They recommend random-intercept poisson model with a sandwich estimator for the standard errors, which I don't think I can do because I use stata on university computers and can not use gllamm.

I am trying to see the effects of many electoral variables including turnout, margin of victory, legislators' membership of the ruling coalition (coded as an indicator variable), and the main variable of interest, partisan affiliation with a higher level of government (again coded as an indicator variable), on the number of infrastructure projects initiated by legislators in a state legislative assembly in India.

I am using Stata 14.
I have included a summary of the response variable below:

Projects

Mean 38.87229
Largest Std. Dev. 31.73026
Variance 1006.81
Skewness 5.646863
Kurtosis 92.75536

I would be very grateful for any suggestions on how to deal with this, potential alternative models and robustness checks. Thank You!

Edit: tags

[Joao Santos Silva]

Dear Siddharth,

I would certainly start with a simple Poisson regression and consider adding fixed effects. The commands you need for that are standard in Stata (-poisson- and -xtpoisson- with the option fe). You do not provide any evidence that there is overdispersion in your model, but even if that is the case it is probably not a big problem as long as you use clustered standard errors.

Best wishes,

Joao

[Siddharth Rao]

Thank you so much for your prompt reply and your kind advice, Joao!

I got the idea that a Poisson model would be inappropriate when earlier, I fitted a negative binomial model and saw the following results for the likelihood ratio test for the overdispersion parameter:

Likelihood-ratio test of alpha=0: chibar2(01) = 1.8e+04 Prob>=chibar2 = 0.000

This is what led me to believe that a Poisson model is inappropriate. I am unfortunately unaware of any better way to test for overdispersion, especially one more appropriate given the panel structure of the data, in addition to which I am unaware of any methods to assess goodness of fit for panel data analysis.

Thanks for your help and suggestions!

Best wishes,
Siddharth

[Joao Santos Silva]

Dear Siddharth,

The overdispersion will be reduced if you include fixed effects. Anyway, for what you want to do, overdispersion is not very relevant; it is relevant only if you need to compute the probability of a certain count.

Best wishes,

Joao

[Siddharth Rao]

Once again, thanks very much for your help Joao! I am definitely using fixed effects to deal with heterogeneity already. I really appreciate your advice, thanks!