Possible to model a distribution over time?

[aeiche01]

I'm trying to do something that I'm not sure is possible with mvgam, but I figured if anyone knew it would be you!

I've got data on the size-abundance relationship between a given species over time in multiple plots. So basically, at time t we have measurements of size on the x axis and abundance on the y axis. The relationship between size and abundance can be mapped with a distribution (e.g., power law, weibull, or just a GAM). Then at time t+1 the distribution changes, due to mortality/growth/recruitment. Meaning, trees that were at size x i are now at size x_j, which would shift abundance y, but then we also have new trees coming in at xi...and all of this is influenced by covariates such as disturbance, growth, etc.

Where I'm trying to figure out is whether it's possible to use mvgam to do a state space model where the variable being predicted is really a distribution rather than a one dimensional variable. I feel like this is something a hierarchical model might help with? But I'm not sure. My question boils down to

1. Is this possible, or should I look somewhere else?
2. Are there tutorials/videos you can point me to that explain how to do this?

Thank you!

[aeiche01]

It occurs to me that I might be making this a little too difficult, and could probably just include size as a predictor variable in addition to time...

[nicholasjclark]

Hi @aeiche01, thanks for the question. There are a few ways you can approach this kind of task, namely to predict variation for an entire function. In fact there is an entire field of literature dedicated to this type of function on scalar regression. The literature that I am most familiar with aims to forecast changes in mortality curves over time, see for example the references and worked examples in Rob Hyndman's {vital} package. To make this work in {mvgam}, you could create a set of spline basis functions that evaluate on the size measurements, and use these as time-varying predictors of the abundance measurements. This will allow you to estimate how the size-abundance relationship changes over time, while also allowing you to incorporate other predictors such as disturbances etc... I will have another software package available sometime in the next few months that generalizes this and makes it easier to do within the {mgcv} framework, so let me know if you are interested and I can keep you up to date with any developments

[aeiche01]

Thanks for the answer! I am definitely interested in this, please keep me in the loop!