Hi Rick_SAS, 1. I have seen that for some simulated data set, reparameterization helps. For example, instead of modeling the variance of the random effect of A0 as: sigma_A0*sigma_A0, instead I used: exp(2*logsigmaA0), so A0_i ~ normal(0, exp(2*logsigmaA0)), then the convergence is fine, there is also no warning message and the standard errors are well achieved. 2. Of course, it does not work for all data sets. I have tried to re-write the code, where I directly estimated the variance of the random effect of A0: A0_i ~ normal(0, sigma2_A0) and then put sigma2_A0 >=0 into a bound statement, now there is another warning: " NOTE: FCONV convergence criterion satisfied. NOTE: At least one element of the (projected) gradient is greater than 1e-3. WARNING: The final Hessian matrix is full rank but has at least one negative eigenvalue. Second-order optimality condition violated. " 3. I am thinking of other re-parameterization for the variance of the random effect as it seems that this causes the problem, but have not come up with any positive solution now. Thanks.
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