"Population-averaged"regression on panel data using Stata

In summary, R^2 may not be a relevant measure for population-averaged analyses as these models do not provide an explanation for individual data points. Additionally, there may be biases present due to the nature of the data being averaged. It is recommended to use a regular linear regression if an R^2 value is desired.
  • #1
monsmatglad
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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
 
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  • #2
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.
 

1. What is "population-averaged" regression on panel data?

"Population-averaged" regression on panel data is a statistical method used to analyze data where the same individuals or groups are observed over multiple time periods. It takes into account both within-individual and between-individual variations, and provides estimates for the average effects of the variables on the outcome variable across the entire population.

2. How is "population-averaged" regression different from "fixed-effects" regression?

In "fixed-effects" regression, the focus is on within-individual variations and the model estimates the effects of variables on the outcome variable for each individual separately. In "population-averaged" regression, the focus is on the average effects of the variables on the outcome variable across the entire population, taking into account both within-individual and between-individual variations.

3. What is the advantage of using "population-averaged" regression on panel data?

The advantage of using "population-averaged" regression is that it allows for the estimation of average effects of variables on the outcome variable across the entire population, rather than just for specific individuals or groups. This can provide a more comprehensive understanding of the relationships between variables and the outcome.

4. What is the appropriate sample size for using "population-averaged" regression on panel data?

The appropriate sample size for using "population-averaged" regression on panel data depends on the number of individuals or groups in the population, the number of time periods observed, and the number of variables included in the model. As a general rule, a larger sample size is preferred to ensure more accurate estimates.

5. Can "population-averaged" regression on panel data be used for causal inference?

Yes, "population-averaged" regression on panel data can be used for causal inference, as long as the necessary assumptions are met. These assumptions include the absence of unobserved confounding variables and the correct specification of the model. Additionally, the use of fixed-effects models or instrumental variables can help to address potential biases in the estimates.

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