"Population-averaged"regression on panel data using Stata

[monsmatglad]

TL;DR

using population-averaged as regression approach on panel data in Stata

Hey. I am running regression on panel data. I test different approaches using Stata. When using "population-averaged" no squared R measures are reported. The approach is equal to running a regular linear regression on the panel data, and according to my professor, a squared R is statistically "allowed." When I run a regular linear regression on the data, the coefficients and significance-levels are almost completely identical to "population-averaged", but a squared R and adjusted squared R is reported. is there a reason why Stata does not provide a squared R estimate (within, between, overall) when applying "population-averaged"? Is there a way to make it report such a measure? and if not, can I use the Squared R from a regular linear regression as a "substitute"?

Mons

 

[Dale]

I am not sure that R^2 makes sense for a population averaged analysis. In general, R^2 measures the proportion of the variance in the data explained by fitting the model to the data. However, in a population averaged analysis you don't really produce a model that explains the data at all, so there isn't anything against which to measure the variance.

For example, suppose you have a control and a treatment group of seeds with several different characteristics of the seeds and your outcome is sprouting or not sprouting and you are doing a logit regression. A normal regression will give you the odds of a given control seed sprouting vs the odds of that same seed sprouting under the treatment. So it is an explanation about that given individual seed data point and can be used to explain the actual outcome of that specific data point. In contrast, the population averaged regression will give you the odds of an average control seed sprouting vs the odds of an average treatment seed sprouting. It does not explain any of the individual data points, and if your experimental assignment is not random then there can be biases due to the population biases.

I think that if you want an R^2 value you should not use a population averaged regression. It just doesn't seem to make sense to me.