Do I have to add extra terms to a regression model?

Question

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

Questions:

1. Each subsequent model does better (has a lower AIC), but are these subsequent models necessary given my question?

2. 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?

3. Does the fact that I'm using time variables as predictors affect my approach here? Does an interaction with month even make sense?

4. 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?

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Note: I understand I also have to account for temporal autocorrelation to get accurate p values.

Answer 1

I agree with you added interaction terms may not necessarily mean better interpretation. I usually add interaction terms when i can interpret the model or if i am getting significant gain in accuracy. You can go through following 2 tutorial they may be relevant to you on the topic.

http://analyticspro.org/2016/03/01/r-tutorial-basic-2-variable-linear-regression/

and

http://analyticspro.org/2016/03/02/r-tutorial-multiple-linear-regression/