Best way to model time series with autocorelation and parameters colinearlity?

Modeling
,
1

Hi All,

I’m a beginner in Bayesian statistics in general and want to try brms to answer my research question. My data consist of time-series measurements that were collected using continuos moving averages, resulting in highly correlated data points. Different interventions (categorical variables) were applied in four blocks during data collection, and we’re investigating how these interventions influence changes in measurements.

My current brms model specification is:

brm(formula = bf(measurement ~ block + (1 | id)+ ar(gr=id, p=1)),  
    family = gaussian())

I fit above model but the end results showed the parameters collinearity between the intervention types of block3 and block4, which may be invalidate ROPE.

My questions are:

  1. Is the ar() term in the model specification sufficient, or is it a suitable choice, to account for autocorrelation between the data points collected using this measurement method? How can I determine if the correlation structure adequately captures the autocorrelation?

  2. How should I address parameter multicollinearity, especially when it might be influenced by how the data was measured (e.g., moving average causing overlap between measurements for different interventions at different time point)? Although I could combining the correlated categorical predictors, doing so would contradict my research goal of distinguishing between intervention types.

  3. If I decided to leave parameters with multicollinearity in the model, what caution you would suggest when interpreting the results? I have read through Collinearity isn’t a disease that needs curing and https://avehtari.github.io/modelselection/collinear.html.

  4. Is there a better way to model this problem?

Thank you for taking the time to read this. Apologies for any potential misunderstandings or misspecifications. Any suggestions or learning resources on time series modeling would be greatly appreciated!