Statistics Toolbox includes two different algorithms (nlmefit and nlmefitsa) for fitting nonlinear mixed effects model.
nlmefitsa uses stochastic expectation maximization.
beta = nlmefit(X,y,group,V,fun,beta0) fits a nonlinear mixed-effects regression model and returns estimates of the fixed effects in beta. By default, nlmefit fits a model in which each parameter is the sum of a fixed and a random effect, and the random effects are uncorrelated (their covariance matrix is diagonal).
[BETA,PSI,STATS,B] = nlmefitsa(X,Y,GROUP,V,MODELFUN,BETA0) fits a nonlinear mixed-effects regression model and returns estimates of the fixed effects in BETA. By default, nlmefitsa fits a model where each model parameter is the sum of a corresponding fixed and random effect, and the covariance matrix of the random effects is diagonal, i.e., uncorrelated random effects.
The BETA, PSI, and other values this function returns are the result of a random (Monte Carlo) simulation designed to converge to the maximum likelihood estimates of the parameters. Because the results are random, it is advisable to examine the plot of simulation to results to be sure that the simulation has converged. It may also be helpful to run the function multiple times, using multiple starting values, or use the 'Replicates' parameter to perform multiple simulations.
