In my analysis I am running two versions of the same linear mixed model, the only difference is that in one model the response variable is observed and in the second the response variable is simulated. My goal is to 1) compare the parameter estimates of the two models and 2) compare the predictions generated by the two models. More specifically, I want to know over what range of values of the predictor variables do the observed and simulated models have different predicted responses.
My simulations encompass 1000 independent generations of the response variable. Hence I have 1000 parameter estimates and predictions from which I can calculate a 95% confidence interval.
My question is about generating the confidence intervals of the parameter estimates and predictions for the observed data mixed model. There are a plethora of options: Wald, parametric bootstrap, nonparametric bootstrap, and then the package "boot" in R generates five types of intervals (e.g. basic, studentized, adjusted percentile). Further, one can generate confidence intervals taking into account solely the uncertainty in the fixed effects or add in the uncertainty due to the random effects. I am unsure what procedure is most comparable to how I generated confidence intervals from the 1000 simulated mixed models.
Thank you in advance for your help with this rather long-winded question.