This article is concerned with a subset of numerically stable and scalable algorithms useful to support computationally complex psychometric models in the era of machine learning and massive data. The subset selected here is a core set of numerical methods that should be familiar to computational psychometricians and considers whitening transforms…

The Multi-Attribute Consensus Building (MACB) method is a quantitative approach for determining a group's opinion about the importance of each item (strategy, decision, recommendation, policy, priority, etc.) on a list (Vanderwood, & Erickson, 1994). This process enables a small or large group of participants to generate and discuss a set…

The preference scaling of a group of subjects may not be homogeneous, but different groups of subjects with certain characteristics may show different preference scalings, each of which can be derived from paired comparisons by means of the Bradley-Terry model. Usually, either different models are fit in predefined subsets of the sample or the…

Indefinite symmetric matrices that are estimates of positive-definite population matrices occur in a variety of contexts such as correlation matrices computed from pairwise present missing data and multinormal based methods for discretized variables. This note describes a methodology for scaling selected off-diagonal rows and columns of such a…

The process of constructing assessment scales for performance testing is complex and multi-dimensional. As a result, a number of different approaches, both empirically and intuitively based, are open to developers. In this paper we outline the approach taken in the revision of a set of assessment scales used with speaking tests, and present the…

Combining diverse methods in a single study raises a problem: What should be done when the findings of one method of investigation conflict with those of another? The authors illustrate this problem using an example in which three study phases--quantitative, qualitative, and intervention--are applied. The findings from the quantitative phase did…

This paper discusses how a seldom-used statistical procedure, recursive regression (RR), can numerically and graphically illustrate data-driven nonlinear relationships and interaction of variables. This routine falls into the family of exploratory techniques, yet a few interesting features make it a valuable compliment to factor analysis and…

Some problems associated with the criteria of reproducibility and scalability as they are used in Guttman scalogram analysis to evaluate cumulative, nonparametric scales of dichotomous items are discussed. A computer program is presented which analyzes response patterns elicited by dichotomous scales designed to be cumulative. (Author/DWH)

Reducing the arbitrariness of a metric is distinct from the pursuit of validity, rational zero points, data transformations, standardization, and the types of statistical procedures one uses to analyze interval-level versus ordinal-level data. A variety of theoretical, methodological, and statistical tools can assist researchers who wish to make…

Certain definitions introduce appropriate concepts, among which are the definitions of the counting functions of the primes and twin primes, along with definitions of the correlation coefficient in a bivariate sample space. It is argued conjecturally that the characteristic functions of the prime "p" and of the quantity "p"+2 are highly…

The computer program WEIGAN makes the weighted G analysis available for computer users. The input and output of the program are described. (Author/JKS)

Provides a nontechnical explanation of the family of multivariate statistical techniques known as multidimensional scaling (MDS). Explains the purpose of MDS, and the advantages of using these techniques in the study of musical perception. Discusses two approaches to the interpretation of MDS solutions. Lists examples of musical studies using MDS.…

This paper overviews technical developments in data analysis procedures for the National Assessment of Educational Progress (NAEP) reading data during 1984. The highlight of the reshaping of the NAEP data has been the scaling using item response theory (IRT). AT this point in the data analysis, an IRT-based scale appears appropriate for reading…