I find you question a bit confusing - your interactions would appear to be in the fixed part of the model - while the variance partitioning  concerns the random part ( of course conditional on what is in the fixed part). The issue is of course that the level 1 variance is not an estimable  parameter in general mixed models such as binary logistic models but there are ways to calculate variance partitioning coefficients akin to intra-class correlations of the random part

see under VPC in

http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#discrete

and more generally for binomial models

https://www.researchgate.net/publication/4993175_Variance_partitioning_in_multilevel_logistic_models_that_exhibit_overdispersion

My reading of what you say about the referee's comments is that s/he wants you  to report this VPC - and it does not generally matter for its calculation whether there are interactions or not - of course the value is likely to change as variables and their interactions are include in the model.

Also see a previous post

https://www.researchgate.net/post/How_can_I_calculate_ICC_for_a_dichotomous_dependent_variable_in_a_multi_level_analysis

Article Variance Partitioning in Multilevel Logistic Models That Exh...

Ahh, indeed my post may be confusing (I corrected it) as the hierarchical variance partitioning is often used in mixed models. I meant hierarchical partitioning sensu : Chevan, A. and Sutherland, M. 1991 Hierarchical Partitioning. The American Statistician 45, 90–

96. 

This method is being used for linear models to split R2 into (1) joint effect of an explanatory variable of interest with other variables and (2) individual contribution of the variable of interest. This method assume additive effects of explanatory variables so I am not sure how to cope with interaction terms. 

Hi Piotr! I personally (working on binomial models) have used the function 'importance' from MuMIN package to calculate the relative importance of each variable, that works using the sum of ‘Akaike weights’ over all models including the explanatory variable.

In your case, working on mixed models I don't know. Maybe you can use something similar to 'variation partitioning' (from vegan), to show the single and shared contribute of each variable predictor.

Things are complicated with multilevel logit models as the level -1 variance can never go down and indeed level 2 variance can go up as important predictor variables are included.

The most approachable account - and they try to develop a R-squared - I know of is in  Chapter 17 of

An Introduction to Basic and Advanced Multilevel Modeling Tom A B Snijders,

Roel J Bosker (2012).. - second edition

This is how it works

Snijders andd Bosker (2012, equation 14.21) have proposed the following procedure for calculating a R2 for the binary outcome model.[

 1.   Having estimated the model, maked predictions based only on the fixed part of the model  and including no random effects))

 2.   Calculate the variance of these fixed-part predictions; this is the required ‘explained’ variance.

 3.   Calculate the ratio of this explained variance to the sum of the explained variance plus the unexplained variance from level 1 (a value of 3.29) and the higher-level random parts.

 All three elements have to be on the same scale, which here is the logit.

Federico, yes, I would prefer to use multimodel inference rather than hierarchical partitioning - I was just curious how to cope such problem. And probably  I will use the MumIn package, however I have to work out specific code for model building procedure. I do not want to built all possible models and want always keep main 1-order effects in models with interactions (I am quite new and naive user of R). 

Hi Piotr, Perhaps you have solved the problem already, just a few tips: MuMIn works with mixed effect models as well, however for me the theoretical background of using the importance() function is not clear. But I also suggest using multimodel inference, because it gives you a clear idea about the relative 'importance' of the explanatory variables.

I see no problems with the interactions, you can estimate their contribution to the explained variance like for the explanatory variables. Of course, they will not be independent, because a model with an interaction term makes sense if the interacting terms are also included as fixed effects. But at least you can see if a given explanatory variable per se, or its interaction with another variable is more important. However, I don't know if hier.part works with mixed effect models.