Fit switchpoint model with all colonies and covariates (rework bumbl() internals)

[Aariq]

In the case of a dataset of bumblebee worker count over time with possible covariates, we want to estimate different values of tau (the switchpoint) for each colony, but a single value for each covariate (or variance parameter like in a negative binomial model).

The current behavior is to fit as many models as there are colonies to find tau. You could do this with a simple formula, count ~ week supplied to the current version of bumbl(), and then take the resulting tau's and plug them into a model with covariates using all the data. However, the value of tau might depend on covariates or variance parameters.

Elizabeth thinks the solution is to optimize values of tau for all colonies simultaneously (e.g. with optim()) to maximize likelihood of a model including covariates fit to all the data.

I think this involves fitting a model like count ~ time*colony + .post*colony + covariates where .post is 0 before tau and time-tau after tau. The goal would be to optimize the values of tau for each colony to maximize the likelihood of that GLM.

[Aariq]

This should possibly exist as a separate function for backwards compatibility (e.g. bumbl2())

[Aariq]

The insight package might be useful for manipulating model formulae https://github.com/easystats/insight

[Aariq]

A "sketch" of this rework is available here: https://github.com/Aariq/bumbl/blob/master/notes/single-model-rework-notes.Rmd