Using Bayesian methods to evaluate Thurstone's simple structure concept
The current thesis proposed a new procedure for evaluating the structure of a pattern matrix. The procedure used Bayes' theorem to estimate the posterior probability that sample information described a pattern matrix with simple structure. Sample information included the inner product correlation between the observed pattern matrix and its simple structure target, Fisher's r to z transformation of this correlation, and a jackknife estimate of the standard error for this comparison. The prior probability distribution was assumed to be uniform and the posterior probability distribution was assumed to be Normal. Bayesian decision theory was used to evaluate whether or not the posterior probability demonstrated simple structure. The procedure allowed the user to select a threshold and loss function that was appropriate for their particular evaluation of simple structure. ^ The results of Experiment 1 (simulation study) appeared to indicate that the proposed procedure was adequate for distinguishing between random structure and simple structure pattern matrices. The results of Experiment 2 (application to real data) seemed to support the usefulness of the proposed procedure for evaluating a simple structure hypothesis for actual test data. ^
Milewski, Glenn B, "Using Bayesian methods to evaluate Thurstone's simple structure concept" (2004). ETD Collection for Fordham University. AAI3125020.