I am interested in investigating a non-linear temporal trend in a data set and so I would like to use the R package mgcv to fit the following GAM:
model1 <- gam(Variable ~ s(Date, by = Site.Factor), data = data)
where Variable is the continuous variable of interest, Site.Factor is a factor with two levels and Date is a continuous variable.
I have read that know that because of the inclusion of the by factor within the smoothing function, differences in the means of the two factor levels are not accounted for. I should therefore include Site.Factor as a parametric term like so:
model2 <- gam(Variable ~ Site.Factor + s(Date, by = Site.Factor), data = data)
However, whilst I might expect the influence of Site.Factor on the smooth to be significant, I do not expect the means of each level of the factor to be significant. Do I still need to include the factor separately within the model as in model1, or would model2 be okay?
Unless you know that the populations from which your data are drawn have exactly the same mean then yes, you should include the term Site.Factor as a fixed effect term, whether that difference in sample is significant or not.