AIC / BIC for xtgee

[Joe Ward]

Dear Stata users

Please may I ask a question regarding comparing models after using xtgee?

My data are longitudinal mortality rates estimates for different countries, for every year from 2001. I would like to compare the UK (UK=1) with a group of different countries (UK=0).

log_mortality = mortally rate logged for each country and year.
country = country identifier number
yearc = year centred on 2001
UK = If the country is UK this is 1; if the country is not the UK this is 0

I have declared data to be panel data using
xtset country year

My model is
xtgee log_mortality yearc i.uk, i(country) family(poisson) link(log) robust

Previously I have used estat ic to then compare models using AIC and BIC after including (for example) quadratic terms in the model, but this does not seem to work with xtgee. Are there equivalent commands to compare models in this way for use with xtgee?

Many thanks for your help!

Joe

[Clyde Schechter]

The definitions of both AIC and BIC involve the log likelihood ratio. But GEE does not use likelihood maximization, so there is no log-likelihood, hence no information criteria.

Model selection is, in any case, always a difficult problem. While AIC and BIC can give some guidance about when we are moving towards overfitting the noise instead of improving capture of the signal, neither they nor any other statistics are sufficient, and model selection should never rely solely on statistics. Prior information about the form of the model is really crucial in model selections.

The model you show is quite unusual in that you both have log-transformed mortality as the outcome, and then you use a Poisson model (which incorporates a log link). So you have, in a sense, modeled log log mortality. Is that intentional? I'm not saying it couldn't be a correct model, but I've never seen one like that before. Is there a reason you think that the time trend in mortality is linear in the log of the log of mortality? Have others used this model successfully in the past? Do you have a theory that predicts that it should be of this form?

[Joe Ward]

Dear Clyde

Thank you so much for your response. I did not intend to log log mortality - thank you for pointing this out. I apologise for my ignorance, but if I include the log link and just use mortality rather than mortality logged as the outcome, are the coefficients displayed by the model logged? (in which case I should exponentiate them for interpreting the results?)

Thank you again

Joe

[Clyde Schechter]

With the use of the log link on the untransformed mortality rate, you should exponentiate the coefficients if you want to interpret/calculate rates, rate ratios, numbers of cases, etc.

[Joe Ward]

Thats really useful Clyde thank you