The TRANSREG Procedure
- Overview
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Getting Started
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Syntax
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Details
Model Statement Usage Box-Cox Transformations Using Splines and Knots Scoring Spline Variables Linear and Nonlinear Regression Functions Simultaneously Fitting Two Regression Functions Penalized B-Splines Smoothing Splines Smoothing Splines Changes and Enhancements Iteration History Changes and Enhancements ANOVA Codings Missing Values Missing Values, UNTIE, and Hypothesis Tests Controlling the Number of Iterations Using the REITERATE Algorithm Option Avoiding Constant Transformations Constant Variables Character OPSCORE Variables Convergence and Degeneracies Implicit and Explicit Intercepts Passive Observations Point Models Redundancy Analysis Optimal Scaling OPSCORE, MONOTONE, UNTIE, and LINEAR Transformations SPLINE and MSPLINE Transformations Specifying the Number of Knots SPLINE, BSPLINE, and PSPLINE Comparisons Hypothesis Tests Output Data Set OUTTEST= Output Data Set Computational Resources Unbalanced ANOVA without CLASS Variables Hypothesis Tests for Simple Univariate Models Hypothesis Tests with Monotonicity Constraints Hypothesis Tests with Dependent Variable Transformations Hypothesis Tests with One-Way ANOVA Using the DESIGN Output Option Discrete Choice Experiments: DESIGN, NORESTORE, NOZERO Centering Displayed Output ODS Table Names ODS Graphics
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Examples
- References
| Convergence and Degeneracies |
When you specify the SSPLINE transformation, divergence is normal. The rest of this section assumes that you did not specify SSPLINE. For all the methods available in PROC TRANSREG, the algorithms are convergent, in terms of both the criterion being optimized and the parameters being estimated. The value of the criterion being maximized (squared multiple correlation, average squared multiple correlation, or average squared canonical correlation) can, theoretically, never decrease from one iteration to the next. The values of the parameters being solved for (the scores and weights of the transformed variables) become stable after sufficient iteration.
In practice, the criterion being maximized can decrease with overiteration. When the statistic has very nearly reached its maximum, further iterations might report a decrease in the criterion in the last few decimal places. This is a normal result of very small amounts of rounding error. By default, iteration terminates when this occurs because, by default, CCONVERGE=0.0. Specifying CCONVERGE=–1, an impossible change, turns off this check for convergence.
Even though the algorithms are convergent, they might not converge to a global optimum. Also, under extreme circumstances, the solution might degenerate. Because two points always form a straight line, the algorithms sometimes try to reach this degenerate optimum. This sometimes occurs when one observation is an ordinal outlier (when one observation has the extreme rank on all variables). The algorithm can reach an optimal solution that ties all other categories producing two points. Similar results can occur when there are many missing values. More generally, whenever there are very few constraints on the scoring of one or more points, degeneracies can be a problem. In a well-behaved analysis, the maximum data change, average data change, and criterion change all decrease at a rapid rate with each iteration. When the rate of change increases for several iterations, the solution might be degenerating.