I'm doing an analysis of how error committement in a particular task influences some numerical reports. I use linear mixed effects models from lmer package. I can formulate a model such as:
lmer(report ~ error + (1+error|id), data)
However, there are actually two kinds of errors which can influence participant's reports: error from current trial (currerror) but also error from previous trial (preverror). I'd like to see how both kinds of these errors influence participants reports. Crucially, it seems that both errors are not independent - i.e. committement of error in previous trial is related to higher chance of committing error also in current trial. In other words, my dependent variable (report) is loaded by two corelated factors. It seems to me that I have two options:
1) First is to make a model with two factors (possibly, although not necessarily, with interaction term), like:
lmer(report ~ currerror * preverror + (1 + currerror * preverror|id), data)
2) Second option is to run two separate analyses for two kinds of errors:
lmer(report ~ currerror + (1+currerror|id), data) lmer(report ~ preverror + (1+preverror|id), data)
My question is: is this lack of independence a problem for mixed models? Should I then choose second option (two separate models) over the first? And COULD I do it given that this second option is also somewhat more justified by my experimental plan, because I was originally interested only in the effect of previous-trial error, and the effect of current error came up later and is somewhat more exploratory.
Could I make two "lines" of analyses - first investigating effects of previous error (main interest) and second investigating effects of current error? Or should I include both factors in any analysis that I'll do?