When a model with all random slopes will not converge, what is the best way to choose which random effects to include? Imagine the following model:
lmer(DV ~ Control Variable A + Control Variable B + Control Variable C + 
         Variable of Interest A + Variable of Interest B + Variable of Interest C + 
         Variable of Interest A x Variable of Interest B + 
         Variable of Interest A x Variable of Interest C + (1|Subject) + (1|Item)

(I only included random intercepts for the purpose of the example.)
If a model with all possible random slopes does not converge, what's the best way to decide which random slopes to include. Should it only be based on theory, and which effects are more likely to vary by subject/item?
Edit: I am fitting an lmer() model using lme4. I know that might make this seem like a stackoverflow issue, but I'm really interested in the theory of how to decide which random slopes to include when I can't include all of them (as Barr er al., 2013 recommend). It is a linear mixed effects model for data in which participants responded to various stimuli. Thus the model includes random subject and item intercepts. The variables of interest were manipulated within subjects but not within items. There are 120 observations per participant. I used whatever optimized is the default for lmer(). 
 A: Note that random effects are used to capture correlations in the data. In particular, when you include a random effect for a grouping variable (i.e., the variable that you put after the | symbol), you postulate that measurements of your outcome variable that have the same value for the grouping variable are correlated. What you put in front of the | symbol determines how these correlations look like. For example, 


*

*if you put only an intercept (i.e., 1 | id), you assume the same correlation for all pairs of measurements with the same value of the grouping variable;

*if you put a random slope (i.e., x | id), you postulate that outcome measurements that have x values closer in magnitude are more strongly correlated than measurements for which the difference between corresponding x values is of larger magnitude. E.g., in a longitudinal study if x is time, then you say that measurements closer in time are more strongly correlated than measurements further apart in time.


In that regard, you have to carefully think what random effects you put in your model, and which random slopes you really need to begin with. Hence, putting all random slopes may result in an overly complicated, not realistic model.
If you want to have a closer on how random effects model correlations, you may have a look in the shiny app for my Repeated Measurements course, in particular check Section 3.3 in both the slides and the app.
