Why linear mixed effect regression over multiple linear regressions for individual random effect? I have a dataset on green-up days pan-Arctic and relate this to weather variables.
I therefore want to use a linear mixed effect model where region (e.g. Alaska, Yukon, Northwest Territories, Eastern Siberia etc.) is the random effect, and weather variables are fixed effects. I am looking for, how the weather influences the day of green-up (given in day of the year). I know there is some random effect involved from spatial differences across the Arctic.
library(lme4)
reg.result = lmer(greenup ~ precip+temp+windspeed+relativehumidity+(1+precip+temp+windspeed+relativehumidity|region), data = greenup, REML = F)

I do not want to have variable intercept but fixed slope for each random effect. So I add the term (1+precip+temp+windspeed+relativehumidity|region).
This gives me different intercepts and slopes for each random effect (region).
Alternatively, I could just perform a linear regression per region e.g.
Alaska <- lm(greenup ~ precip+temp+windspeed+relativehumidity, data = AK)
Yukon <- lm(greenup ~ precip+temp+windspeed+relativehumidity, data = YK)
NWT <- lm(greenup ~ precip+temp+windspeed+relativehumidity, data = NWT)
...
ESib <- lm(greenup ~ precip+temp+windspeed+relativehumidity, data = ESib)

My question is then, why would I not just make multiple different linear regressions for each region and thereby take out this random effect myself?
Would it give me a different result?

The difference between your random effects (RE) approach and your multiple model (MM) approach, is that with MM each model doesn't use any data from the other regions, while with RE the models also use the data belonging to the other regions. So if the data for say AK would result in learned linear coefficients that are very different from those for the other regions, those coefficients would be adjusted to be "more equal" to those of the other regions.
So you should use random effects if you think that the submodels for all the different levels (in your case the levels are the regions) are similar.
This is particularly helpful if a certain region, e.g. NWT, has only very little data. With RE you then borrow information from the other regions and use it for NWT, too.
By the way, what do you think is it that changes your values of greenup in different regions if it is not the different weather in those regions?
