3 ms·

For point (3), in most of my academic research and work in industry, I have used Generalized Additive Models with great technical success (i.e., they fit the da

For point (3), in most of my academic research and work in industry, I have used Generalized Additive Models with great technical success (i.e., they fit the data well). Still, I have noticed that they have been rarely understood or given the proper appreciation by--it is a broad category--stakeholders. Out of laziness and habit, mostly.

SubiculumCode 2y ago
I've looked at additive models, but I have so far shied away because I've read that they are not super equipped to deal with non-additive interactions.
- levocardia 2y ago
  They actually deal with non-additive "low-order" interactions quite well. In R's mgcv for example, let's say you had data from many years of temperature readings across a wide geographic area, so your data are (lat, long, year, temperature). mgcv lets you fit a model like: gam(temperature ~ te(long, lat) + s(year) + ti(long, lat,year)) where you have (1) a nonlinear two-way interaction (i.e. a smooth surface) across two spatial dimensions, (2) a univariate nonlinear effect of time, and (3) a three-way nonlinear interaction, i.e. "does the pattern of temperature distributions shift over time?" You still can't do arbitrary high-order interactions like you can get out of tree-based methods (xgboost & friends) but that's a small price to pay for valid confidence intervals and p-values. For example, the model above will give you a p-value for the ti() term, which you can use as formal statistical evidence to say -- at what level of confidence -- a spatiotemporal trend exists. This Rmarkdown file (not rendered sadly) shows how to do this and other tricks https://github.com/eric-pedersen/mgcv-esa-workshop/blob/master/example-spatio-temporal%20data.Rmd https://github.com/eric-pedersen/mgcv-esa-workshop/blob/mast...
  - SubiculumCode 2y ago
    Hey cool. I'll take a closer look then. Thanks! I assume that there are mixed model variants out there too.

SubiculumCode 2y ago

I've looked at additive models, but I have so far shied away because I've read that they are not super equipped to deal with non-additive interactions.

levocardia 2y ago
They actually deal with non-additive "low-order" interactions quite well. In R's mgcv for example, let's say you had data from many years of temperature readings across a wide geographic area, so your data are (lat, long, year, temperature). mgcv lets you fit a model like: gam(temperature ~ te(long, lat) + s(year) + ti(long, lat,year)) where you have (1) a nonlinear two-way interaction (i.e. a smooth surface) across two spatial dimensions, (2) a univariate nonlinear effect of time, and (3) a three-way nonlinear interaction, i.e. "does the pattern of temperature distributions shift over time?" You still can't do arbitrary high-order interactions like you can get out of tree-based methods (xgboost & friends) but that's a small price to pay for valid confidence intervals and p-values. For example, the model above will give you a p-value for the ti() term, which you can use as formal statistical evidence to say -- at what level of confidence -- a spatiotemporal trend exists. This Rmarkdown file (not rendered sadly) shows how to do this and other tricks https://github.com/eric-pedersen/mgcv-esa-workshop/blob/master/example-spatio-temporal%20data.Rmd https://github.com/eric-pedersen/mgcv-esa-workshop/blob/mast...
- SubiculumCode 2y ago
  Hey cool. I'll take a closer look then. Thanks! I assume that there are mixed model variants out there too.