I am having a hard time figuring what Nakagawa's R² really "means". I understand that in simple linear regressions, R² indicates the amount of variance in the dependent variable explained by the predictor variables. For the diverse pseudo-R² measures available for different types of non-linear regression models, it is stated in various ressources that they cannot be interpreted in the same manner as the R² for linear regressions. But what do they mean, then?
From experience I know for example, that McFadden's pseudo-R² generally yields lower values than Nagelkerke's pseudo-R². I understand that Nakagawa's pseudo-R² is available for mixed models in two versions: a) conditional, taking into account fixed and random effects and b) marginal, considering only fixed effects. But I have no idea what these numbers do excatly tell me and, more importantly for me, how to deal with them in practice.
- Are there (+- accurate) thresholds for stating that conditional or marginal pseudo-R² is low / high? In other words: is there a sensible starting point to state that a model is somehow "meaningful" (or not)?
- Are Nakagawa's pseudo-R² values directly comparable between models with different structure (such as sample size, number/porperty of fixed and/or random effects etc.)?
- Am I right to assume that the combination of "high" conditional and relatively "low" marginal pseudo-R² indicates that the random effects are decisive factors, whereas the fixed effects do not have much explanatory power? (and vice versa: small differences in conditional and marginal pseudo-R² should then indicate low explanatory power of the random effects)?