I have a group of participants (Subj) all of whom have a covariate measure (Pars). Each participant saw a series of images (Image) that belonged to one of three categories (Stim). To each image, participants made a response (Resp) that was classified as a behavior (Beh). I have combined Stim and Beh (StimBeh), and for each of these Stimulus-Behaviors I have a parameter estimate (Est). I would like to see what the effect of the covariate is in the parameter estimate for the different types of behaviors associated with the different stimuli types, when treating subject and image as random effects. I believe StimBeh should be a fixed effect. I have been unable to make the model converge.
Combining Stim and Beh is a strange approach. I may be missing something, but I would have incorporated Stim and Beh (or possibly Resp) as covariates. Combining them imposes an interaction without allowing each in the model as a main effect. Finally, if your parameter lies in $[0,1]$, you might want to transform the response.