I have a question regarding the relevance of reporting (various) estimates of random effects in mixed models. Having read multiple papers and forum threads on the issue, I don't feel any closer to understanding what should be reported, so I hope this question could be an opportunity to start a discussion as to which values should be reported under what circumstances.
The typical output for a mixed model (lmer in R) provides the variance and standard deviation for each of the random intercepts and/or slopes, as well as correlations between random intercepts and slopes, if these are specified. Some papers seem to report these values, while some choose to report standard deviation only. Other researchers choose to report ICC, although this seem to be applicable only to models containing a single random intercept, according to an answer provided here: Intraclass Correlation Coefficient in mixed model with random slopes
Others yet, choose to report R2 estimations, although there has been some criticisms regarding applicability of 'variance explained' to mixed models. Finally, some people seem to calculate p-values to establish whether the influence of random effects is significant, although the discussions regarding the point of estimating p values for mixed models is, again, ongoing, and seem to favour other solutions.
Importantly, most solutions are discussed in the context of random intercept-models only, and so what is applicable for models containing random slopes as well, is very much a question mark.
Lastly, most of the discusssions/papers seem to relate to situations where the effects of the random effects are of interest. What should one do in a situation where the random effects are there to account for repeated measures (random effect of the subject) and the variability between different stimuli (random effect of the item)? It seems inappropriate not to report them at all, while also inappropriate to focus on them too much.
The question is of a practical interest to me, since I am currently analysing a mixed model containing subject and item as random effects, as well as a by-subject random slope for the effect of predictor X1. However, having spent many hours going through resources available online, I noticed that very little information is available that can be used by people less used to mixed models or generally not as advanced when it comes to linear modelling. Since mixed models seem to be gaining in popularity, I hope this thread could be quite useful for many researchers.
Thank you in advance for all the input!