Sabre

APPROXIMATE

Sabre manual

Syntax: APPROXIMATE number
where number is a non-negative integer which is less than or equal to MAXITS.

Purpose:
The APPROXIMATE command sets the number of iterations which are to be performed using the Meilijson approximation to the Hessian matrix.

This first derivative based approximation is more robust than the matrix of true second derivatives when the parameter estimates are a long way from their maximum likelihood solutions. For this reason, the first number iterations of any mixture model fit are carried out using the approximation to the Hessian. If the true Hessian is positive semi-definite on the (number+1)st iteration, then the algorithm switches to this matrix. Otherwise, the approximate method is retained until the true Hessian attains positive semi-definiteness. All further iterations continue to make use of the matrix of true second derivatives.

Note that, even if convergence is achieved within the first number iterations, the parameter estimate standard errors are still calculated from the true Hessian since it alone provides consistent estimates of their values.

The default number of approximate iterations is 5. The current setting of the APPROXIMATE parameter may be obtained by issuing the DISPLAY SETTINGS command.

The APPROXIMATE command has no effect on model fitting instigated using the LFIT command.