How to account for cluster autocorrelation and spatio-temporal autocorrelation of data?

General
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I would like to design an experiment to measure the behavior response of (non-human) individuals clustered in a group of five individuals. Multiple clusters will be measured independently. Each cluster will be exposed to a continuous, increasing threat; think of it as a deadly drone coming from a distance (say 50 m south of the cluster), then flying close immediately above the cluster, and finally flying away (until 50 m north of the cluster). There will be four different types of “threat” treatments, from harmless to potentially deadly, and each cluster will be exposed to four treatments in no particular order (i.e. the order of challenge is randomized). Each trial will be recorded, and then the individual’s responses will be recorded at fixed distances from the cluster (50, 25, 0, -25, -50 m) +/- some 5 m buffer.

I am grappling with two major issues in conceiving the statistical model that will capture such an experiment:

  1. An individual response might be triggered by the other four individuals in the cluster rather than the perceived threat itself. Could that be solved by including a covariate in the model which captures the order of reaction (so, 1 through to 5)?

  2. The magnitude of the response might be dependent on the anticipation of the threat. As in, if you see a car coming right at you, you will be increasingly alarmed the closer the car gets. Therefore, the responses measured at a given distance have a temporal and spatial correlation with the distance measured previously. What type of model should I use in this instance? An ARMA? Or something else?

The objective is to come up with a statistical approach that let us measure the influence of the different treatment categories and distances of the treatment from the cluster while accounting for the cluster autocorrelation, and the spatial and temporal autocorrelation of the data.

Thanks!

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Hi, @JuanAzofeifa, and welcome to the Stan forums. Sorry for the slow reply, but these “how do I model X” with a short description are very challenging for us to answer because modeling is hard and very domain dependent. This one’s going to be especially challenging because it sounds like a military application.

If you do want help with the model, I’d recommend starting with a description of the shape and constraints on the data you collect. For example, what is a response and is there any group data or is all the data at the individual level (with grouping as a covariate). Do you get multiple responses per attack? Do you expect any group-level interactions and if so, how do you want to model them rather than as fixed correlations (which don’t generalize to new groups)?

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