Based on seminal work by Lord and Hambleton, Swaminathan, and Rogers, this article is an analytical, graphical, and conceptual reminder that item response theory (IRT) parameter invariance only holds for perfect model fit in multiple populations or across multiple conditions and is thus an ideal state. In practice, one attempts to quantify the…

Measurement is prescriptive in that the model required to produce the numbers from the phenomena is known in advance. Statistical theory is descriptive because the model required to explain the numbers is inferred from the numbers and any other information the researcher can bring to bear. There are well-known families of measurement models and…

Item response theory (IRT) has proven to be a very powerful and useful measurement tool. However, most of the IRT models that have been proposed, and all of the models commonly used, require the assumption of unidimensionality, which prevents their application to a wide range of tests. The few models that have been proposed for use with…

In previous research, no relationship was found between test factor structure and test hierarchical structure. This study found some correspondence between test factor structure and test inter-item dependency structure, as measured by a log-linear model. There was an inconsistency, however, which warrants further study: more significant two-item…

Langmuir's model is studied for the situation where epsilon is independently and identically normally distributed. The "Y/x" versus "Y" plot had a 90% mid-range that did not contain the true curve in a vast portion of the range of "x". The "1/Y" versus "1/chi" plot had undefined expected values,…

The purpose of this study was to develop a model for the distribution of authorships--based on the initial hypothesis that the distribution of authorships follows a shifted Waring distribution--and to test the derived model and some other discrete probability models for goodness-of-fit against empirical data. Bibliographic data from 15 abstracting…

The author contends that model misspecification can occur even after researchers have selected the generally most appropriate class of methods, or general linear model techniques. It is suggested specifically that canonical correlation analysis may provide more meaningful results, as compared with regression, particularly if analysis is augmented…

Three techniques for estimating Kuder Richardson reliability (KR20) coefficients for incomplete data are contrasted. The methods are: (1) Henderson's Method 1 (analysis of variance, or ANOVA); (2) Henderson's Method 3 (FITCO); and (3) Koch's method of symmetric sums (SYSUM). A Monte Carlo simulation was used to assess the precision of the three…

This study attempts to determine which media-exposure models available today are the best. A survey of the literature of the last 20 years is used to provide the basis for assessment of the state of the art of media planning and to draw distinctions between the implicit, naive, subjective, and sophisticated media-exposure models. Discussion of the…

Work performed persuant to grant number 1-06, 1819-2240 from the U.S. Office of Education.

Increasing the level of educational attainment of the population may not always increase the social benefits for those who receive the education. In fact, when a high percentage of the population attains a certain level of education, that attainment ceases to provide socioeconomic benefits; instead, those few who have not reached that educational…

The relatively hard problem of transforming a given set of curves to curves with the same shape can sometimes be reduced to the easier problem of rendering curves parallel. In this paper a group is associated with the given curves, and it is shown that the reduction from the hard problem to the easy problem is valid whenever the group is…

THE FINAL STAGE OF A PROGRAM FOR ACHIEVING A BALANCE BETWEEN THE AGGREGATE SUPPLY AND DEMAND FOR LABOR IS THE DISTRIBUTION OF THE INDUSTRY EMPLOYMENT ESTIMATES INTO OCCUPATIONAL REQUIREMENTS BASED ON PROJECTIONS OF OCCUPATIONAL PATTERNS BY INDUSTRY. THIS CAN BE USED TO EVALUATE POTENTIAL AREAS OF SUBSTANTIAL SURPLUS OR SHORTAGE, AND PROVIDE THE…

This report explains the following mathematical techniques which may be used for relating search requests to documents contained in a library: (1) Boolean Algebraic Retrieval, (2) Linear Statistical Retrieval, (3) Statistical Association Techniques for expanding a query and/or for expanding the set of retrieval documents, (4) Vector Space…

The scientific implications and practical applications of the Stein estimator approach for estimating true scores from observed scores are of potentially great importance. The conceptual complexity is not much greater than that required for more conventional regression models. The empirical Bayesian aspect allows the examiner to incorporate…