The TRANSREG Procedure

## Controlling the Number of Iterations

Several a-options in the PROC TRANSREG or MODEL statement control the number of iterations performed. Iteration terminates when any one of the following conditions is satisfied:

• The number of iterations equals the value of the MAXITER= a-option.
• The average absolute change in variable scores from one iteration to the next is less than the value of the CONVERGE= a-option.
• The criterion change is less than the value of the CCONVERGE= a-option.

You can specify negative values for either convergence option if you wish to define convergence only in terms of the other option. The criterion change can become negative when the data have converged so that it is numerically impossible, within machine precision, to increase the criterion. Usually, a negative criterion change is the result of very small amounts of rounding error since the algorithms are (usually) convergent. However, there are other cases where a negative criterion change is a sign of divergence, which is not necessarily an error. When you specify an SSPLINE transformation or the REITERATE or DUMMY a-option, divergence may be perfectly normal.

When there are no monotonicity constraints and there is only one canonical variable in each set, PROC TRANSREG (with the DUMMY a-option) can usually find the optimal solution in only one iteration. (There are no monotonicity constraints when the MONOTONE, MSPLINE, or UNTIE transformations and the UNTIE= and MONOTONE= a-options are not specified. There is only one canonical variable in each set when METHOD=MORALS or METHOD=UNIVARIATE, or when METHOD=REDUNDANCY with only one dependent variable, or when METHOD=CANALS and NCAN=1.)

The initialization iteration is number 0. When there are no monotonicity constraints and there is only one canonical variable in each set, the next iteration shows no change and iteration stops. At least two iterations (0 and 1) are performed with the DUMMY a-option even if nothing changes in iteration 0. The MONOTONE, MSPLINE, and UNTIE variables are not transformed by the dummy variable initialization. Note that divergence with the DUMMY a-option, particularly in the second iteration, is not an error. The initialization iteration is slower and uses more memory than other iterations. However, for many models, specifying the DUMMY a-option can greatly decrease the amount of time required to find the optimal transformations. Furthermore, by solving for the transformations directly instead of iteratively, PROC TRANSREG avoids certain nonoptimal solutions.

You can increase the number of iterations to ensure convergence by increasing the value of the MAXITER= a-option and decreasing the value of the CONVERGE= a-option. Since the average absolute change in standardized variable scores seldom decreases below 1E-11, you should not specify a value for the CONVERGE= a-option less than 1E-8 or 1E-10. Most of the data changes occur during the first few iterations, but the data can still change after 50 or even 100 iterations. You can try different combinations of values for the CONVERGE= and MAXITER= a-options to ensure convergence without extreme overiteration. If the data do not converge with the default specifications, try CONVERGE=1E-8 and MAXITER=50, or CONVERGE=1E-10 and MAXITER=200. Note that you can specify the REITERATE a-option to start iterating where the previous analysis stopped.