Nlmefit covb and PSI
4 views (last 30 days)
When using nlmefit or nlmefitsa for estimating a mixed effects model, the algorithm gives me 2 covariance matrices as result: PSI and stats.covb. Anyone can tell me what is the difference between these two? The help says this: PSI, an r-by-r estimated covariance matrix for the random effects. covb — The estimated covariance matrix of the parameter estimates
I know that if I want to simulate a population using nlmefitsa's results I should generate random samples using beta and PSI. But, how can I use covb?
Thanks if anyone can help me.
Star Strider on 15 Sep 2012
Edited: Star Strider on 15 Sep 2012
I haven't done much with nmlefitsa, so I don't have much experience with it. As a general rule however, COVB (the covariance matrix of the parameter estimates), provides one rather important bit of information on the parameters themselves: it allows you to calculate the confidence intervals on the parameters.
With Beta a column vector of the parameter values, and CovB the covariance matrix, the 95% confidence intervals are given by:
CI95 = [Beta-1.96*sqrt(diag(CovB)) Beta+1.96*sqrt(diag(CovB))];
The 1.96 value is the ‘critical value’ (the z-statistic or z-score) corresponding to the 95% confidence interval:
cv = norminv(0.975, 0, 1);
The usual interpretation of the confidence intervals on the parameters is that if the confidence interval for a particular parameter includes zero, that parameter is not needed in the model.