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5

I would suggest fitting a multilevel model, with company/firm nested within industry and firm also nested within country. This is just a special case of a mixed effects model and could be specified with this kind of formula (using the notation adopted by the lme4 library and others): ESG ~ fixed_effects + (1 | industry) + (1 | industry:firm) + (1| country) +...

5

In models with nonlinear link functions there is indeed a difference in the interpretation of the regression coefficients in GEEs and mixed-effects models. In short, GEEs give you the more usual interpretation of comparing groups of subjects. E.g., for dichotomous outcomes and the logit link you get the log-odds ratio between the group of males and the ...

3

This is all in the documentation of package plm, e.g., the package's vignette. I believe you got confused due to the various fixed effects you would like to estimate. You would need to specify correctly what the observational units (individual dimension) and what the time dimension of your data is and put those into the index argument. If you look at firms, ...

2

It is well-known that the relationship between $R^2$ and adjusted $R^2$ in a linear regression (and ultimately, a fixed-effects regression can also be seen as a linear regression, see e.g. Difference between fixed effects dummies and fixed effects estimator?) is (see e.g. Is $R^2_{adjusted}$ both unbiased and consistent under the alternative in simple ...

2

You can indeed compare the group at specific time points when time is treated as a continuous variable. In general, you can test the following hypothesis $$\begin{eqnarray} H_0: X_1 \beta = X_2 \beta\\ H_a: X_1 \beta \neq X_2 \beta \end{eqnarray}$$ where $\beta$ are the fixed effects of the model, and $X_1$ and $X_2$ are two design matrices specifying the ...

1

The lcmm() function fit a latent class linear mixed-effects model. This postulates that there are some underlying sub-populations in your data that you wish to recover. The model is estimated using maximum likelihood, and therefore it will provide you with correct inferences provides that any missing data in your outcome variable are missing at random and ...

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