Matlab tool for nonlinear mixed effects I'm wondering if someone is familiar with the NLMEFITSA algorithm in matlab. This algorithm gives me as result the fixed effects parameters (beta) for a mixed effects model as well as their covariance matrix (psi), but it also gives me, in the "stats" struct, one covariance matrix called "covb" I know this one has to do with the standard errors and it is important for calculating confidence intervals, but to be honest I don't know what is exactly the difference  between this "covb" and the "psi " covariance matrix. And how could I use "covb" when simulating new data?
Thanks if anyone can explain this to me.
 A: I do not know anything about NLMEFITSA but quite a lot about mixed effects modelling. The covariance matrix for beta (psi) is a measure of how the fixed effects parameters are spread over the population whereas covb is a measure of the uncertainty of the parameters.
Consider a one-parameter model for simplicity. If the single parameter b is assumed to be normally distributed over the population beta is its estimated mean and psi its variance (over the population). covb on the other hand is a measure of the uncertainty of the estimated value beta itself, thus an uncertatinty measure of the mean. I'm not sure how the program works, but also the estimated value of the covariance parameter psi is of course uncertain and covb might also inlude an estimate of the uncertainty of psi (making covb a 2x2 matrix in the one-parameter case). The matrix covb is usually computed by using Fisher information theory.
Google "fisher information matrix" AND covariance, or something similar, for more information about parameter uncertainty in likelihood methods.
