How to compare the sensitivity of many countries? My thesis question is asking whether biodiversity sensitivity differs geographically. I will assess all 5 pressures individually, but take 1 (pollution) as an example.
My data contains time series for how biodiversity and pollution change in each country, over time.
I ran a linear model, lm(Biodiversity~Pollution), for each of 180 countries, and for the countries demonstrating a significant effect (158 countries), pulled out the coefficient of the gradient as a 'sensitivity score', representing how sensitive that country's biodiversity is, to pollution. I want to compare the countries and see whether they are different. I'm thinking about grouping the sensitivity scores (coefficients of gradient) into continents, then using an ANOVA to test whether the sensitivity scores (Gradients) are different between continents. Would the use of gradients in an ANOVA this way be viable?
Upon looking online, I saw some other threads suggesting that instead of doing a model for each country, to do one model and include country as a dummy variable. Would this work for my situation?
 A: Your question: "Would the use of gradients in an ANOVA this way be viable?"
You could consider doing ANOVA for each of the coefficients of the gradients separately. But your levels are the countries, and you would have only one gradient coefficient per level. That would not give you viable results.
In general, if you have coefficients from different datasets and you want to compare them, see the answers to this question.
Your question: "... do one model and include country as a dummy variable. Would this work for my situation?"
You could do this, but just a single additional linear term containing the dummy variable would give you only different offsets for different countries, while all the other coefficients would be fitted for all countries together. However, if I understood you correctly, you want all your coefficients to be fitted separately for each country. That means you would have to use your dummy variable as an interaction for each of your other independent variables, too, which would again be equivalent to fitting separate models for separate countries. Using a single (fixed effect) model for all countries together only makes sense if you would want some of the coefficients to be the same for all countries.
Another possibility is to use mixed effect models by introducing random effects. If you design one of your coefficients as a random effect, it would be different for different countries, but, when fitting the coefficient for one country, the method would try to take the information of other countries into account. This increases the complexity of your model, but it might make sense.
