I'm running a bunch of GAM analyses on time series data (measurements of my own weight). Unlike many examples I see online, my data is not spaced evenly in time. In fact, time points can come minutes (if not seconds) apart, and the entire range of the data is about a year (currently about 500 data points).
Taking the helpful advice of Gavin Simpson's blog posts on the matter, I am looking to make my model aware of the autocorrelation in the data, using something like:
m <- gamm(Y ~ s(time) + s(...) + ..., correlation = corCAR1(form = ~time))
However, after struggling for a long time trying to make sense of things, I realized that the results of my model are wildly different depending on the scale of the time covariate.
I initially just converted the datetimes into EPOCH time, which resulted in very large numbers---for example 1569201817. Using this covariate, the AR1 component of my model did little to nothing.
But when I scaled the same variable (ie. as.vector(scale(time)), after converting it into a numeric), the model was completely different, with the AR1 component playing a major role.
Playing around with it, I found that whenever I scale the range of the time covariate to greater than 70, the behavior changes to disfavoring the AR1 model.
What gives? The example the corCAR1() docs use has a time covariate that ranges from -0.16 to 1.16, so that suggests I should scale my data, but the fact that everything changes with an arbitrary scale doesn't make much sense to me.
How do I know the proper scale to use?