This article describes a Bayesian framework for estimation in item response models, with two-stage prior distributions on both item and examinee populations. Strategies for point and interval estimation are discussed, and a general procedure based on the EM algorithm is presented. Details are given for implementation under one-, two-, and three-parameter binary logistic IRT models. Novel features include minimally restrictive assumptions about examinee distributions and the exploitation of dependence among item parameters in a population of interest. Improved estimation in a moderately small sample is demonstrated with simulated data.

Regression estimation and poststratification are methods used in survey sampling to estimate a population mean, when additional information is available for some auxiliary variables. The extension of these methods to factor analysis is considered. These methods may be used either to improve the efficiency of estimation or to adjust for the effects of nonrandom selection. The estimation procedure may be formulated in a LISREL framework.

There is a unity underlying the diversity of models for the analysis of multivariate data. Essentially, they constitute a family models, most generally nonlinear, for structural/functional relations between variables drawn from a behavior domain.

Conjunctive item response models are introduced such that (a) sufficient statistics for latent traits are not necessarily additive in item scores; (b) items are not necessarily locally independent; and (c) existing compensatory (additive) item response models including the binomial, Rasch, logistic, and general locally independent model are special cases. Simple estimates and hypothesis tests for conjunctive models are introduced and evaluated as well. Conjunctive models are also identified with cognitive models that assume the existence of several individually necessary component processes for a global ability. It is concluded that conjunctive models and methods may show promise for constructing improved tests and uncovering conjunctive cognitive structure. It is also concluded that conjunctive item response theory may help to clarify the relationships between local dependence, multidimensionality, and item response function form.

This paper presents a bimatrix structure for examining ordinal partial rankings. A set of axioms is given similar to those of Kemeny and Snell (1962) and Bogart (1973), which uniquely determines the distance between any pair of such rankings. The l1 norm is shown to satisfy this set of axioms, and to be equivalent to the Kemeny and Snell distance on their subspace of weak orderings. Consensus formation is discussed.

In introducing the founders, Jones noted that the first organizational meeting of the Society occurred in February of 1935 and the first professional meeting occurred in September 1935, in connection with the convention of the American Psychological Association. In the Psychometric Society's first year, the president was L. L. Thurstone, the secretary was Paul Horst, the treasurer was Jack Dunlap, and the chairman of the membership committee was John Stalnaker. The editorial council consisted of Thurstone, chairman, Horst and Albert Kurtz, editors, and Marion Richardson, managing editor. The editorial board was noteworthy for its great breadth of interest, and its international and multidisciplinary character.

The purpose of the Psychometric Society is to encourage mathematical psychology. This article justifies the emphasis on quantification, and upon rationalization in science, as well as the Society's conception of the fundamental nature of science.

By reference to nominated attributes, a genus, being a population of objects of one specified kind, may be partitioned into species, being subpopulations of different kinds. A prototype is an object representative of its species within the genus. Using this framework, the paper describes how objects can be relatively differentiated with respect to attributes, and how attributes can be relatively differentiating with respect to objects. Methods and rationale for such differential ordering of objects and attributes are presented by example, formal development, and application.

For a genus Ω comprising n species of object there is a subset P ofn distinct prototypes. With respect to m nominated attributes, each object in Ω has an m-element characterization. Together these determine an n × m objects × attributes matrix, the rows of which are the characterizations of the prototypical objects. Over then species in Ω, an associated relative frequency vector gives the distribution of objects (and of their characterizations). The matrix and vector associate the objects in Ω with points in a metric space (P, δ); and it is with respect to various sums of distances in this attribute space that one can differentially order objects and attributes.

The definition of the distance function δ is generalized across kinds of difference, types of characterization, scale-types of measurement, Minkowski index ≧ 1, and any form of distribution of objects over species. Explanatory and taxonomic applications in psychology and other fields are discussed, with focus on classification, identification, recognition, and search. The Braille code and the identification of its characters provide illustration.

Meredith's method of extracting a factorially invariant solution is adapted to longitudinal settings. An explorational estimation procedure is presented which attempts to identify the longitudinal factor components of an across occasion variance-covariance matrix. This is effected by transforming an initial factor pattern matrix to stationarity. The estimation is performed in two parts, the first employing a stepwise algorithm to ascertain the dimensionality and existence of the longitudinal components and the second being the direct estimation of the existing factor pattern.

Bentler and Bonett's nonnormed fit index is a widely used measure of goodness of fit for the analysis of covariance structures. This note shows that contrary to what has been claimed the nonnormed fit index is dependent on sample size. Specifically for a constant value of a fitting function, the nonnormed index is inversely related to sample size. A simple alternative fit measure is proposed that removes this dependency. In addition, it is shown that this new measure as well as the old nonnormed fit index can be applied to any fitting function that measures the deviation of the observed covariance matrix from the covariance matrix implied by the parameter estimates for a model.

A test is proposed for the equality of the variances of k ≥ 2 correlated variables. Pitman's test for k = 2 reduces the null hypothesis to zero correlation between their sum and their difference. Its extension, eliminating nuisance parameters by a bootstrap procedure, is valid for any correlation structure between the k normally distributed variables. A Monte Carlo study for several combinations of sample sizes and number of variables is presented, comparing the level and power of the new method with previously published tests. Some nonnormal data are included, for which the empirical level tends to be slightly higher than the nominal one. The results show that our method is close in power to the asymptotic tests which are extremely sensitive to nonnormality, yet it is robust and much more powerful than other robust tests.

We consider the problem of least-squares fitting of squared distances in unfolding. An alternating procedure is proposed which fixes the row or column configuration in turn and finds the global optimum of the objective criterion with respect to the free parameters, iterating in this fashion until convergence is reached. A considerable simplification in the algorithm results, namely that this conditional global optimum is identified by performing a single unidimensional search for each point, irrespective of the dimensionality of the unfolding solution.

On the occasion of Psychometrika's fiftieth anniversary, the past twenty-five years' developments in mental test theory are reviewed, with special emphasis on the topics receiving attention in the pages of this journal. (Analogous reviews for Psychometrika's first quarter century were given by Gulliksen and Guilford in 1961.) Much of the recent progress in test theory (and in other branches of psychometrics as well) has been made by treating the problems in this field as being essentially ones of statistical inference. It is concluded that (a) research in test theory is in a healthy state and (b) Psychometrika is an important source of information about that research.

Janson and Vegelius have recently suggested a family of correlations for variables of mixed scale types, including nominal scales. The resulting correlations are E- coefficients, which means that they are unity if the variables involved are identical up to permissible transformations, and that they can be considered as inner products in a Euclidian space. Some of the coefficients of the correlation family suggested by Janson and Vegelius are generalized squared product-moment correlations and some are not. In the present paper, a family of correlations for variables of mixed scale types is advocated all members of which are generalized squared product-moment correlations. Some practical advantages of the latter family are explained.

A chance-corrected version of the family of association coefficients for metric scales proposed by Zegers and ten Berge is presented. It is shown that a matrix with chance-corrected coefficients between a number of variables is Gramian. The members of the chance-corrected family are shown to be partially ordered.

In a variety of measurement situations, the researcher may wish to compare the reliabilities of several instruments administered to the same sample of subjects. This paper presents eleven statistical procedures which test the equality of m coefficient alphas when the sample alpha coefficients are dependent. Several of the procedures are derived in detail, and numerical examples are given for two. Since all of the procedures depend on approximate asymptotic results, Monte Carlo methods are used to assess the accuracy of the procedures for sample sizes of 50, 100, and 200. Both control of Type I error and power are evaluated by computer simulation. Two of the procedures are unable to control Type I errors satisfactorily. The remaining nine procedures perform properly, but three are somewhat superior in power and Type I error control.

Item response curves for a set of binary responses are studied from a Bayesian viewpoint of estimating the item parameters. For the two-parameter logistic model with normally distributed ability, restricted bivariate beta priors are used to illustrate the computation of the posterior mode via the EM algorithm. The procedure is illustrated by data from a mathematics test.

Papers on factor analysis appearing in Psychometrika reflect the initial efforts of the Thurstonians to reformulate psychology as a quantitative science. The Thurstonians' emphasis on the development of factor analysis as an exploratory methodology was not new with them but was taken from British statisticians and psychologists who preceded them, whose literature the Thurstonians otherwise tended to ignore. The Thurstonians' rejection of general factors and focus on rotation to simple structure reflected an attempt to avoid statistical artifact and to identify factors with psychological substance. Much of the literature on factor analysis in Psychometrika concerned solving technical problems in the exploratory factor analysis method. Factor analysis took a major shift in direction in the 1970's with the development of confirmatory methodologies, many of which now receive greater attention than the method of exploratory factor analysis, most of the problems of which are now resolved.