This monograph provides an epistemological rational for the design of an advanced novel analysis metric. The metric is designed to analyze the outcomes of the Tri-Squared Test. This methodology is referred to as: "Tri-Squared Mean Cross Comparative Analysis" (given the acronym TSMCCA). Tri-Squared Mean Cross Comparative Analysis involves…

General diagnostic models (GDMs) and Bayesian networks are mathematical frameworks that cover a wide variety of psychometric models. Both extend latent class models, and while GDMs also extend item response theory (IRT) models, Bayesian networks can be parameterized using discretized IRT. The purpose of this study is to examine similarities and…

Rasch's psychometric model is presented as a special case of additive conjoint measurement. Two data sets, each of which was analyzed using Rasch scaling methods as well as some of the methods of conjoint measurement, are compared. (Author/JKS)

There are two complementary approaches to conjoint measurement: axiomatic and numerical. In this article, synthetic data are used to examine how well axiomatic and conjoint measurement methods, individually and comparatively, recover parameters from data with three dimensions. (JKS)

Simulation techniques were used to generate conventional test responses and track the proportion of alternatives examinees could classify independently before and after taking the test. Finite-state scores were compared with these actual values and with number-correct and formula scores. Finite-state scores proved useful. (TJH)

A method of comparing one-step M-estimates of location for heavy tailed distributions is proposed and investigated. Simulations indicate that the new procedure provides good control over Type I errors and has more power than do some other methods for dealing with heavy tailed distributions. (SLD)

Based on the usual factor analysis model, this paper investigates the relationship between improper solutions and the number of factors. The properties of the noniterative estimation method of M. Ihara and Y. Kano in exploratory factor analysis are also discussed. The estimators were compared in a Monte Carlo experiment. (TJH)

A class of models is presented for gamma distributed random variables. These additive, multiplicative, and combined additive-multiplicative models are more flexible than classical linear models with respect to the structure that can be imposed on expected values. As a special case, a class of psychometric models for reaction times is presented.…

Multiple matrix sampling (MMS) theory indicates how data may be gathered to most efficiently convey information about levels of attainment in a population, but standard analyses of these data require random sampling of items from a fixed pool of items. This assumption proscribes the retirement of flawed or obsolete items from the pool as well as…

A detailed description of five latent structure models of achievement measurement is presented. The first project paper, by David L. McArthur, analyzes the history of mental testing to show how conventional item analysis procedures were developed, and how dissatisfaction with them has led to fragmentation. The range of distinct conceptual and…

The many methodological contributions of Raymond B. Cattell to multivariate analysis are discussed in terms of contemporary issues in structural equation modeling. His factor analytic approach is compared with current modeling practices. A critical evaluation finds much of Cattell's work still innovative, technically advanced, and valuable to…

This book discusses constructing variables and making measures. It begins by outlining the qualities a number must meet before it qualifies as a measure of something. The basis is the measurement philosophy of G. Rasch. The first requirement for making good measures is good raw material. To achieve the possibility of comparisons, the data must…

Two sets of real sorting data from 50 college students are used to compare results of multidimensional scaling of raw co-occurrence frequencies or dissimilarity measures (D) and profile distances (delta) to determine which yields a better representation of the underlying structure of 2 sets of stimuli. Slight differences are discussed. (SLD)

A Monte Carlo study was conducted to estimate the small sample standard errors and statistical bias of psychometric statistics commonly used in the analysis of achievement tests. The statistics examined in this research were: (1) the index of item difficulty; (2) the index of item discrimination; (3) the corrected item-total point-biserial…

The assumptions of the Criterion-Referenced Test (CRT) model proposed by Kriewall are compared to those of Emrick and Adam's Mastery-Learning (ML) model. Testing, in the context of instructional management, serves three general purposes: performance evaluation (achievement of objectives), placement (classification of students for instruction), and…