I want to use GAM to analyze my experimental data. In my experiment, participants basically play a game for 40 experimental years. In total I have 6 different conditions and I have a between-subject design: one participant only experiences one condition.
I want to analyze a variable which is the output of participants' annual decisions. What I want to show is that:
- Year has an impact on this output variable for all the conditions.
- The path of this output variable over 40 experimental years is significantly different across 6 conditions.
To this end, I run the following model and get this result:
Abbr is my categorical variable which has 6 levels. My question is mostly on the interpretation. The "Approximate significance of smooth terms" part of the table tells me that Year has a significant effect on pr in all conditions. Is it correct?
What does the "Parametric coefficients" part tell me? How can I compare these 6 conditions and tell that the paths are significantly different?
Thank you for the great reply! It is much more clear now in terms of smooths.
What I try to do is to test that the smooths are significantly different from each other for my 6 categories. To this end, I followed your blog post and end up with ordered factors with the following model and the results, where OC is my ordered categorical variable:
Now, I can say that there is a significant difference between the smooths of F-G1P1 and F-G5P1. And when I plot, I get the following: The first plot gives me the smooth for my category F (reference category), while others are the difference smooths. How should I interpret them?
Now, I would like to extend this analysis to have a pairwise comparison between my 6 categories. To do this, I try to follow this post but I didn't succeed. Do all my categories need to have the same number of observations for these comparisons?