I'm trying to understand heteroscedasticity and the influence this may have on GAMs fitted to palaeo data (or other time series).
My understanding of heteroscedasticity is as follows (please correct me if this is wrong): A sediment core has been sampled every 1 cm, but due to sediment compression, we expect deeper samples to represent many years (so have a large error), whilst surface samples represent few years (so have a smaller error). Therefore, the variation in error is not constant over the time/depth series.
I have fitted a GAM for my palaeo data (measurement of interest vs estimated year). The GAM appears to have a good fit (to my understanding of GAMs), but I am concerned that the GAM is not reliable due to potential heteroscedasticity.
If it helps, I used the mgcv package and this was my call:
measure is my measurement of interest e.g. a concentration
These are some plots of my data which (from googling) I think are useful for determining if data is heteroscedastic. I am not 100% whether these indicate heteroscedasticity, but I think the second plot (residuals vs year) does because it has a cone shape with more points clustering as year increases?
My questions are:
- Do my plots indicate heteroscedasticity?
- Do GAMs rely on an assumption that the data are homoscedastic? Or, are they robust enough to overcome the effects of heteroscedasticity, and can I proceed with a GAM as usual?
- If the data must be homoscedastic, and my data is heteroscedastic, is there a correction I can apply to the data either prior to GAM fitting, or something I can add within the GAM call to account for this issue?
I hope this all makes sense - I am in no way a statistician, so any advice on using GAMs with (potentially) heteroscedastic palaeo data is appreciated!