I'm building a model that estimates the effect of a firm level variable (x) on its financial performance (y). It is a cross-classified three-level model with yearly measures of a firm in level-1 and firms in level-2. Firms are then cross-classified by countries and industries in level 3. To account for the contextual factors that moderate the x->y relationship, the model includes terms that interact (x) with moderators at firm level and industry/country level.

I'm able to estimate the model using frequentist HLM via LME4 on R and bayesian HLM via RStan.

Now, I'm interested in ranking the firms based on magnitude of effect that variable (x) has on financial performance (y). While some literature I came across ranked the individual effects using median values of the random effects, posterior means, or empirical bayes estimates, the models in these papers did not include any interaction terms.

I would appreciate any thoughts on ways in which such ranking can be done, while including the effect of various firm level and cross-level interaction terms.

Thank you!