Controlling convergence rate


A difficulty with the Average Information algorithm is that it sometimes overestimeates the updates required, especially when there are diverse parameters and the initial values are orders of magnitude from the REML solution.

As an ad hoc procedure, ASReml does not usually take the full AI update for the first few iterations. This is controlled by the !STEPSIZE r and !SLOW n qualifiers.

The size of the parameter updates applied by ASReml is r times the calculated AI updates. The default initial value of r is the reciprocal of the square root of the Maximum number of iterations; r may be set to a value in the range 0.01 to 1. Each iteration it is moved fairly quickly towards 1. For example, starting at 0.1, the sequence would be 0.1, 0.32, 0.56, 1. in the first 4 iterations.

!SLOW n modifies the rate that r is moved toward 1. If specified, ASReml looks at the potential size of the updates and if any are large, it reduces the size of r. If n is greater than 10 ASReml also modifies the Information matrix by multiplying the diagonal elements by n. This has the effect of further reducing the updates.

These qualifiers may help when you do not have good starting values, resulting in convergence failure.

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