Computing Aspects of a Nonlinear Method of Sire Evaluation for Categorical Data

Abstract

The threshold model equations are shown to correspond to a pseudo-linear model. A modification of Jacobi iteration “on data” is presented that does not require setting up the system of equations explicitly. Two iterative threshold model programs were developed; these involve absorption-inversion and iteration “on data”. The programs were applied to a set of simulated data. Normal termination did not occur when the data contained fixed effects with observations only in an extreme category, and methods for solving such problems are described. The absorption-inversion program behaved erratically when the model was not of full rank; numerical accuracy problems precluded detection of dependencies between thresholds and other effects. The iteration “on data” version was fastest when only a single round of modified Jacobi was performed for each Newton-Raphson round. A round of iteration for the absorption-inversion program consumed 837, 11.8, and 1.24s of central processing unit time on a Personal Computer AT, an IBM 3081 mainframe, and a CRAY X-MP/48 supercomputer, respectively. Corresponding times for the iteration “on data” program were 55.2, 2.6, and .57s. The cost of a threshold model analysis would be three to five times larger than that of a linear model.