How to test for support for random slopes using both frequentist methods and Bayesian methods

[Whirly123]

In the (Bayesian) paper: https://pubmed.ncbi.nlm.nih.gov/35357978/ and also the famous (frequentist) Bar paper: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3881361/ we want to specify all random slopes in so far as the data support the hypothesis that this variance exists.

The recommendation given in the cited paper says:

"I recommend starting analysis by testing the support for random slopes in the data and removing them from the models only if there is clear evidence against them."


What are the appropriate Frequentist and Bayesian tests for support of random slopes? I usually just specify them all in Gamlj and remove until the model converges but is there a more rigorous way of doing this? My hunch was doing just model comparisons of of models where only the specified random slopes vary. I thought for frequentist models I would do likelihood ratio tests to determine the best model and for Bayesian models just compare Bayes Factors. Maybe there is a more appropriate test for this?

Is this correct? It seems like one would have to do a fair bit of model comparison before I could even test the fixed effects. If so it would be cool to automate the process so R / Gamlj spits out right set of random slopes?

[mcfanda@gmail.com]

In gamlj you have the LR test for random slopes variances. We do not have bayesian lmm yet, but I do not expect results to be very different between maximum likelihood (what people would call frequentist) and average likelihood (what people call bayesian)