The convergence criterion used in the Linear Mixed Effects object is that the algorithm has converged if: gT(q)H-1(q)g(q) < i, where i is the convergence criterion specified on the General Options tab. The default is 1´10–10.
The possible convergence outcomes from Newton’s algorithm are:
Newton's algorithm converged with a final Hessian that is positive definite, indicating successful convergence at a local, and hopefully global, minimum.
Newton's algorithm converged with a modified Hessian, indicating that the model may be over-specified. The output is suspect. The algorithm converged but not at a local minimum. It may be in a trough, at a saddle point, or on a flat surface.
Initial variance matrix is not positive definite. This indicates an invalid starting point for the algorithm.
Intermediate variance matrix is not positive definite. The algorithm cannot continue.
Failed to converge in allocated number of iterations.
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