I am fitting data from a repeated-meausures design by means of a (generalized) mixed model (lme4) including a fixed effect (2level factor), as well as a random intercept and a random slope for subjects ("keeping it maximal" as recommended by Barr et al. 2013, Journal of Language and Memory).
My random effect correlation is "perfect" , i.e. 1 or -1 (while intercept-/slope variances are close to but not 0), which is apparently indicative of "overparameterization" (Baayen, 2008,Journal of Language and Memory). I see some strange behavior coming along with this: Eg., plotting random effects essentially draws parallel lines, although this doesnt fit the data very well. Also, comparing the full model to a simpler one via PBmodecomp returns an convergence error. I suspect this is all related but may also result from other issues with my data.
.... Thus my question(s): Are results reliable/sound with random effects correlation of 1/-1 ? Can I savely ingore this kind "overfitting" (as it has no further effects) or should I start to remove random effects such as the slope ? Any proposals?
