Data: I have monthly temperature data for 90 years along with a climate index ('pdo') that influences temperature.
- Scientific question: is there a linear trend in temperature across time?
I've fit the following models using the
gls() function in R:
temp ~ I(year - 1950) temp ~ I(year - 1950) + factor(month) temp ~ I(year - 1950) + factor(month) + pdo temp ~ I(year - 1950) + factor(month) + pdo + factor(month):pdo
Each subsequent model does better (has a lower AIC), but are these subsequent models necessary given my question?
How necessary is it to account for these other variables? How necessary is it to include interaction terms??
- Sure they create better models, but do they change or improve the way I interpret the coefficients?
Does the fact that I'm using time variables as predictors affect my approach here? Does an interaction with month even make sense?
I assume if the added variables are not significant, then I do not choose that more complicated model. what if only some of the categorical variables are significant -- do I remove those that are not?
Note: I understand I also have to account for temporal autocorrelation to get accurate p values.