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

Whirly123A

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? My hunch was doing just model comparisons of of models where only the specified random slopes vary. I thought for frequentist models I should do likelihood ratio tests to determine the best model and for Bayesian models I would 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 even being able to test the fixed effects. If so it would be cool to automate the process so R / JASP spits out right set of random slopes?

EJ

This topic is discussed in a recent special issue, see https://link.springer.com/article/10.1007/s42113-021-00113-2 for the introductory paper.

My own preference would be not to make an all or none choice, but model-average across all relevant models in play. You can even do this in a frequentist framework (sort of) by means of AIC.

Cheers,

E.J.