Raymond F. Koopman

Evaluation of factor analytic research procedures by means of simulated correlation matrices

In order to study the effectiveness of factor analytic methods, a procedure was developed for computing simulated correlation matrices which are more similar to real data correlation matrices than are those matrices computed from the factor analysis structural model. In the present investigation, three methods of factor extraction were studied as applied to 54 simulated correlation matrices which varied in proportion of variance derived from a major factor domain, number of factors in the major domain, and closeness of the simulation procedure to the factor analysis structural model. While the factor extraction methods differed little from one another in quality of results for matrices more dissimilar to the factor analytic model, major differences in quality of results were associated with fewer factors in the major domain, higher proportion of variance from the major domain, and closeness of the simulation procedure to the factor analysis structural model.

The bias in regression-based indices of premorbid IQ.

Formulas for premorbid intelligence estimates are typically derived by linear regression and are therefore biased in individual cases because of regression to the mean. It is shown that it is inappropriate to compare such IQ estimates with current IQ scores to determine whether a decline from premorbid levels has occurred. This widespread practice grossly overestimates the probability of an IQ decline in the below-average range and grossly underestimates it in the above-average range, with serious implications for clinical practice. The authors present a formula for computing unbiased estimates of IQ decline as well as a test of the null hypothesis of no decline. Corresponding tables for several combinations of test indices and estimation methods are included for practical reference.

On Bayesian estimation in unrestricted factor analysis

It is shown that the common and unique variance estimates produced by Martin & McDonalds Bayesian estimation procedure for the unrestricted common factor model have a predictable sum which is always greater than the maximum likelihood estimate of the total variance. This fact is used to justify a suggested simple alternative method of specifying the Bayesian parameters required by the procedure.

On the sensitivity of a composite to its weights

A method is presented for investigating two aspects of the sensitivity of a linear composite to the values of its weights.

Fast Regression Estimates of Missing Data.

A recent comparison of methods for estimating missing data concluded that when there is sufficient redundancy to justify using a more elaborate method than the mean of each variable, the principal components and regression methods are equally good and superior to the other methods investigated. Principal components was preferred because of its “tremendous computational savings over the regression method.” This note proposes an alternate implementation of the regression method which should be slightly faster than the principal components method.

The orders of equidistribution of subsequences of some asymptotically random sequences

The orders of equidistribution of subsequences of every nth term of the asymptotically random sequence given by Tootill, Robinson, and Eagle [5], and of six other asymptotically random sequences, were determined for various values of n and of the number of bits to which each term in the sequence is read. Deficiencies in equidistribution were found to be small enough to qualify the sequences for use in applications with fixed, as well as variable, dimensionality requirements. An improved initialization algorithm is also given.

On the standard error of the modified biserial correlation

A paradoxical implication of Kraemers expression for the large-sample standard error of Brogdens form of the biserial correlation is identified, and a new expression is given which does not imply the paradox. However, numerical evidence is presented which calls into question the correctness of the expression.

Biased estimators, biased experts, and the Ivory Tower: a reply to Grove (2001).

This reply responds to W. M. Groves (2001) critique of H. O. F. Veiel and R. F. Koopmans (2001) article on bias in widely used methods of estimating premorbid IQ. In this reply, the authors show that Grove is misrepresenting part of Veiel and Koopmans arguments, extend them to show that the proposed adjustment to regression estimates of IQ not only is unbiased but also is the maximum-likelihood estimate of the true IQ, and argue that Groves notion of the acceptability of biased methods in judicial proceedings reflects a fundamental misapprehension of their nature and purpose.

Determining parameter values in the generalized image system

Generalized image analysis is considered as a logical algebraic extension of Guttmanian image analysis. Under the assumption that a reduced-rank description of the images is desired, a procedure is developed which achieves the scale-free property by simultaneously rescaling in the metrics of both the images and anti-images, and which produces images and anti-images that are maximally independent in terms of the dimensions needed to account for them.