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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?

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    $\begingroup$ Yes, it would be much better to put all of this in a single model - not just all countries, but all 5 pressures too. And to account for spatial autocorrelation in this single model. If you provide more detail about your pollution model (and perhaps some data?), you may get a more useful answer here. $\endgroup$
    – mkt
    Jul 29 at 5:18
  • $\begingroup$ Just to provide more information on the model - I'm using a very basic model for the pressures, just a linear model with one independent variable (pollution) because the purpose isn't to be able to use pollution to predict biodiversity, but rather to compare how sensitive the biodiversity of each country is, to pollution, and see how this varies geographically - eg are the continents' sensitivities statistically different. $\endgroup$
    – Kayleigh
    Jul 29 at 7:35
  • $\begingroup$ Please edit such information into your question, because most readers won't check comments. Also, by making separate models for each pressure, you are making large (and I would say unjustified) assumptions about the nature of their covariance. That you want to do inference rather than prediction does not change this. $\endgroup$
    – mkt
    Jul 29 at 7:37
  • $\begingroup$ Okay, thank you $\endgroup$
    – Kayleigh
    Jul 29 at 7:39
  • $\begingroup$ "because the purpose isn't to be able to use pollution to predict biodiversity, but rather to compare how sensitive" The purpose doesn't matter here. You might be still better of by adding all variables together in a single model. In that way you obtain a sensitivity that is corrected for the presence of other pressures. $\endgroup$ Jul 29 at 8:01

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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.

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  • $\begingroup$ "But your levels are the countries, and you would have only one gradient coefficient per level." - Would the ANOVA work if I grouped the countries' sensitivity scores ( that I obtained from the coefficients of the gradients from the linear models of each country) into continents (lets say I have data for 100 countries that fit into 5 continents)? Or is the principle of doing an ANOVA on coefficients from linear models (instead of raw data) just not right? $\endgroup$
    – Kayleigh
    Jul 29 at 7:32
  • $\begingroup$ In principle, you can use ANOVA on those coefficients if you know that its assumptions like independence and normality are satisfied, or you can use a less restrictive method like e.g. Kruskal–Wallis. But this might be difficult to verify. So, I would rather go with the methods in the question I linked to. Also note, that if you group for continents, you would only test whether the continents are different, not the individual countries. $\endgroup$
    – frank
    Jul 29 at 8:27

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