bluuebunny/crossref_metadata_2025 huggingface dataset:
The Concept of Configuration of Interpersonal Relations in a Group as a Time-Dependent Stochastic Process
Authors: Katz Leo , Proctor Charles H.
Published: January 2006

To explain changes in the sociometric configuration of a group through time, a problem arises of the extent to which such changes may be viewed as the aggregation of part-processes occurring at the level of two-person choice structures. A possible model is a Markov chain in which three possible states are mutual choice, one-way choice, and indifference, one realization for each pair of choosing individuals in the group. Choice data for an eighth-grade classroom are fitted to this model and are used to answer questions of constancy of transition probabilities, order of the chain, and sex differences.
Pattern Variants on a Square Field
Authors: Prokhovnik S. J.
Published: January 2006

A quantitative approach to the psychology of pattern recognition requires knowledge of the number of possible variants of any particular pattern. The general solution for the number [p/m2] of pattern variants that p counters can form on a square network of m2 positions is obtained by elementary group theory. The exact solution is given in terms of the different types (symmetric, asymmetric, etc.) of patterns possible and an approximate formula for the total number of patterns is also developed.
Domain Sampling Formulation of Cluster and Factor Analysis
Authors: Tryon Robert C.
Published: January 2006

Domain sampling principles permit formulation of a general method of multidimensional analysis. Cluster and factor analysis methods are special cases stemming from decisions made at different stages of the general method, especially in defining an independent dimension. Key cluster analyses define a dimension as a selection of s variables drawn from the full n set. Centroid, principal axes, and maximum likelihood analyses define it by the n variables (raw or residual, weighted or unweighted); bifactor and second-order analysis, by both types of selection; square root analysis, by one variable. Key cluster methods can be designed to test hypotheses.
A First-Order Method for Estimating Correlation Coefficients
Authors: Weichelt John A.
Published: January 2006

A rapid method of estimating a correlation coefficient is given. The method expresses the correlation coefficient as the ratio between two differences in sums (or means) of the dependent variable computed only for extremes of the bivariate distribution. A trial shows that this method gives results similar to the product-moment correlation coefficient. Extensions of the method to qualitative data are also suggested.
A Prepunched Master Deck for the Computation of Square Roots on IBM Electrical Accounting Equipment
Authors: Reynolds Wm. A.
Published: January 2006

This paper presents a prepunched deck of cards to enable the extraction of square roots on standard punch card tabulating equipment. Such a deck is valuable in constructing mathematical tables which involve square roots or in obtaining standard deviations in connection with computing correlation coefficients. By using a deck of reciprocals in conjunction with the deck for square roots, correlations may be solved completely on IBM equipment.
A Brief Comment on Thurstone's Note on a Reanalysis of Davis' Reading Tests
Authors: Davis Frederick B.
Published: January 2006

A comparison of factorial analyses made by Thurstone and by the writer shows that they differ in three important respects. The results of the two analyses are compared with respect to their social utility, which is offered as a proper criterion for judging the merit of factorial analyses performed by different mathematical procedures.
A Comparative Study in Multiple-Factor Analysis of “Neurotic” Tendency
Authors: MacCrone I. D. , Starfield A.
Published: January 2006

The original aim of this investigation was to discover what relations exist between race attitudes and certain personality traits. For that purpose, a standard neurotic inventory and an attitude scale were applied to three dissimilar groups of subjects, and the results, obtained by multiple-factor analysis carried out independently for each of the three groups, compared with one another. The components of neurotic tendency, as displayed by each of the three groups, show a high measure of agreement and appear to be reconcilable with other interpretations of neurotic personality. So far as the original aim of the study is concerned, there appears to be a slight but significant tendency for the neurotic factor of hypersensitiveness to affect the race attitudes of Europeans towards the native in South Africa in a negative or unfavorable direction.
Note about the Multiple Group Method
Authors: Thurstone L. L.
Published: January 2006

This note directs attention to the basic similarity between a factor analysis method described by Holzinger in 1944 and what Thurstone has called the multiple group method. With minor modifications and the application of Holzinger's method in several successive cycles until the residuals vanish, the methods are essentially the same.
Identifiability and Statistical Properties of Two-Stage Learning with no Successes in the Initial Stage
Authors: Greeno James G.
Published: January 2006

A model is considered for learning where there is an initial stage with only errors, an intermediate state with errors and correct responses, and an absorbing state with only correct responses. A model with observable states is constructed, and sufficient identifiable parameters are given for the original model. Distribution statistics and other properties of data are derived as functions of the identifiable parameters. Informal estimates and sufficient statistics are given for the identifiable parameters. A number of testable hypotheses about the theoretical parameters are described. Some identifying restrictions for the model are given, along with the estimates for the unrestricted free parameters which follow. An application is made to data from a pairedassociate learning experiment.
Factorial Rotation to Simple Structure and Maximum Similarity
Authors: Bloxom Bruce
Published: January 2006

When the regression of factored variates on variates defining subpopulations (or experimental groups) is (a) nonlinear or (b) heteroscedastic, an existing solution to the problem of factorial invariance does not apply. This paper presents an approach which can be used in place of the existing solution and derives a method for obtaining maximally similar orthogonal simple structure factor pattern matrices across subpopulations. The method is applied to data from three experimental groups.
A Semi-Orthogonal Dependent Factor Solution
Authors: Porebski Olgierd R.
Published: January 2006

The paper presents a general framework for the dependent factor method in which judgmental as well as analytic criteria may be employed. The procedure involves a semi-orthogonal transformation of an oblique solution comprising a number of reference factors and a number of experimental factors (composites). It determines analytically the residual factors in the experimental field keeping the reference field constant. The method is shown to be a generalization of the multiple factor procedure [Thurstone, 1947] in so far as it depends on the use of generalized inverse in deriving partial structure from total pattern. It is also shown to provide an example of the previously empty category (Case III) of the Harris-Kaiser generalization [1964]. A convenient computational procedure is provided. It is based on an extension of Aitken's [1937] method of pivotal condensation of a triple-product matrix to the evaluation of a matrix of the form H − VA−1U' (for a nonsingular A).
Statistical Methods for a General Theory of All-or-None Learning
Authors: Polson Peter G.
Published: January 2006

Greeno and Steiner have shown that a three state Markov Chain with a single absorbing state is equivalent to many of the current formalizations of All-or-None learning theories. Distribution statistics and other summary statistics are derived from the general model. Expressions for the maximum likelihood estimators of its parameters and the sampling variances of the estimates are presented. Likelihood ratio tests for several different null hypotheses are derived. These tests permit one to evaluate the usual null hypotheses in terms of the parameters of a process model.
Simple Reaction Time with Markovian Evolution of Gaussian Discriminal Processes
Authors: Emerson Phillip L.
Published: January 2006

If the discriminal distributions of signal-detectability theory evolve in time according to a normal Markov process, they can be characterized by Brownian motion generalized with a constant bias determined by signal strength. If the process is stopped at the first occurrence of a preset criterion displacement, the resulting latency distribution provides a model for the central component of simple reaction time. Discussed are properties of the distribution which should be useful in obtaining experimental predictions from neural-counting assumptions, and in relating reaction times to basic variables of the theory of signal-detectability.
Estimation of True Score and Error Variance for Tests Under Various Equivalence Assumptions
Authors: Kristof Walter
Published: January 2006

Maximum-likelihood estimators of true score variance and error variance for mental tests are derived for six different models of equivalent measurements. Statistical properties of the estimators are examined. Main emphasis is placed upon essentially τ-equivalent measurements. A statistical criterion for this type of measurement is given. The solution of the comparatively simple maximum-likelihood equations is effected by means of a rapid Newton-Raphson procedure. Two different initial estimators are considered and their relative merits in terms of second moments evaluated. Four numerical examples are appended by way of illustration.
Homogeneous Case of the Continuous Response Model
Authors: Samejima Fumiko
Published: January 2006

In line with the latent trait model, the continuous response level is defined and considered, in contrast to the discrete response levels, which have already been explored by the author. Discussions are mainly focused on the homogeneous case and the open response situation. The operating density characteristic of the continuous item score is defined. Also the basic function, information functions and the positive-exponent family are discussed on the continuous response level, in connection with the sufficient condition that a unique maximum estimate is provided for the response pattern, which consists of the continuous item scores.
On the Numerical Approximation of the Bivariate Normal (Tetrachoric) Correlation Coefficient
Authors: Kirk David B.
Published: January 2006

In this paper a rapid and reliable method is found for estimating the value of the Bivariate Normal Correlation Coefficient, ρ, given values of the joint probability and the normal deviates, h and k, or the related areas. This technique finds useful application in the computational approximation of the tetrachoric correlation coefficient, r, when the underlying distributions may be assumed to be normal.
A Note on H = Log2m
Authors: Tuinman J. Jaap
Published: January 2006

When teaching elementary concepts on information theory a problem keeps reoccurring which, if only for pedagogical reasons, deserves discussion.
A Goodness of Fit Test for the Rasch Model
Authors: Andersen Erling B.
Published: January 2006

The Rasch model is an item analysis model with logistic item characteristic curves of equal slope, i.e. with constant item discriminating powers. The proposed goodness of fit test is based on a comparison between difficulties estimated from different scoregroups and over-all estimates.

Based on the within scoregroup estimates and the over-all estimates of item difficulties a conditional likelihood ratio is formed. It is shown that—2 times the logarithm of this ratio is x2-distributed when the Rasch model is true.

The power of the proposed goodness of fit test is discussed for alternative models with logistic item characteristic curves, but unequal discriminating items from a scholastic aptitude test.
A Note on a Sufficiency Condition for Uniqueness of a Restricted Factor Matrix
Authors: Dunn James E.
Published: January 2006

A counterexample is produced to a conjecture by K. G. Jöreskog concerning sufficiency conditions for uniqueness of a restricted factor matrix. A substitute condition is stated and proved for the most common situation where the restricted elements are specified to be zero.
Interactive Scaling with Individual Subjects
Authors: Young Forrest W. , Cliff Norman
Published: January 2006

A metric multidimensional scaling (MDS) procedure based on computer-subject interaction is developed, and an experiment designed to validate the procedure is presented. The interactive MDS system allows generalization of current MDS systems in two directions: (a) very large numbers of stimuli may be scaled; and (b) the scaling is performed with individual subjects, facilitating the investigation of individual as well as group processes. The experiment provided positive support for the interactive MDS system. Specifically, (a) individual data are amenable to meaningful interpretation, and they provide a tentative basis for quantitative investigation; and (b) grouped data provide meaningful interpretive and quantitative results which are equivalent to results from standard paired-comparisons methods.
Measurement as Structural Theory
Authors: Guttman Louis
Published: January 2006

Definitions are of course arbitrary. Following Lewis Carroll, one can make words mean what one wishes [cf. Gardner, 1960]. Basically, all that is formally required of a definition is that it be clear: that it enable reliable use of the concept concerned. A more informal, heuristic, desideratum is that it actually influence theorists and researchers to progress in their work.

A strategy for attaining reliability is to make a list of related concepts which might be confused with the one intended, and then to define all the concepts simultaneously in one facet framework. Such a mapping helps to make explicit what the target concept has in common with the others, and how it differs from them. This facet strategy has proved to be useful for distinguishing, for example, among varieties of intelligence [Guttman, 1965; Schlesinger and Guttman, 1969], among varieties of attitude [Guttman, 1959; Elizur, 1970; Jordan, 1971], and even between intelligence and attitude [Guttman, in press]. Evidence is accumulating as to the stimulating effect of the approach for the development of new insights and for the discovery of new forms of lawfulness in data.
Bias and Runs in Dice Throwing and Recording: A Few Million Throws
Authors: Iversen Gudmund R. , Longcor Willard H. , Mosteller Frederick , Gilbert John P. , Youtz Cleo
Published: January 2006

An experimenter threw individually 219 different dice of four different brands and recorded even and odd outcomes for one block of 20,000 trials for each die—4,380,000 throws in all. The resulting data on runs offer a basis for comparing the observed properties of such a physical randomizing process with theory and with simulations based on pseudo-random numbers and RAND Corporation random numbers. Although generally the results are close to those forecast by theory, some notable exceptions raise questions about the surprise value that should be associated with occurrences two standard deviations from the mean. These data suggest that the usual significance level may well actually be running from 7 to 15 percent instead of the theoretical 5 percent.

The data base is the largest of its kind. A set generated by one brand of dice contains 2,000,000 bits and is the first handmade empirical data of such size to fail to show a significant departure from ideal theory in either location or scale.
The Effect of Unequal Group Size on Tukey's HSD Procedure
Authors: Smith Robert A.
Published: January 2006

A limitation of the Tukey HSD procedure for multiple comparison has been the requirement of equal number of observations for each group. Three approximation techniques have been suggested when the group sizes are unequal. Each of these techniques was empirically analyzed to determine its effect on Type I error. Two of the considered variables, average group size and differences in group size, caused differing actual probabilities of Type I error. One of the three techniques (Kramer's) consistently provided actual probabilities in close agreement with corresponding nominal probabilities.
A Covariance Analysis of Multiple Paired Comparisons
Authors: Bechtel Gordon G.
Published: January 2006

In the method of multiple paired comparisons the dominance of object j over object k is observed upon p attributes. The present paper develops a covariance analysis for these paired comparisons in terms of a linear model which includes scale, bias, and interaction effects, along with s covariants upon which the comparisons are presumably dependent. The covariance model gives rise to adjusted parameter estimates and hypothesis tests for the residual pairwise layout from which the effects of the s covariants have been removed. These estimation and testing procedures are illustrated with an analysis of political judgment data, and their relevance to the general problem of residual scaling is discussed.
A Posterior Region for Parallel Profile Differentials
Authors: Geisser Seymour , Kappenman Russell F.
Published: January 2006

A simple Bayesian solution for the joint estimation of several parallel profile differentials for multivariate normal populations is obtained. This generalizes a previous result for a single profile differential.
On Browne's Solution for Oblique Procrustes Rotation
Authors: Cramer Elliot M.
Published: January 2006

Browne [1967] has given a method of solving the problem (originally stated by Mosier, [1939]) of finding a least squares fit to a specified factor structure. The problem is one of minimizing the sum of squared residuals of Φ — FT with Diag (T'T)= I. Browne's solution involves the eigenvectors and values of F'F and leads to an iterative solution.

This paper gives a form of the solution which does not involve solution of an eigenvalue problem but does require an iteration similar to Browne's. It suggests the possible existence of a singularity, and a simple modification of Browne's computational procedure is proposed which deals with this case. A better starting value for the iteration is also proposed for which convergence is guaranteed using the ordinary Newton iteration.
Testing Pattern Hypotheses for Covariance Matrices
Authors: McDonald R. P.
Published: January 2006

Maximum likelihood estimates of the free parameters, and an asymptotic likelihood-ratio test, are given for the hypothesis that one or more elements of a covariance matrix are zero, and/or that two or more of its elements are equal. The theory applies immediately to a transformation of the covariance matrix by a known nonsingular matrix. Estimation is by Newton's method, starting conveniently from a closed-form least-squares solution.

Numerical illustrations include a test for equality of diagonal blocks of a covariance matrix, and estimation of quasi-simplex structures.
The Measurement of Factor Indeterminacy
Authors: McDonald Roderick P.
Published: January 2006

Results obtained by Guttman [1955] on the determinacy of common factors have been thought to have disturbing consequences for the common factor model. It is argued that factors must be thought of as unobservable, and uniquely defined but numerically indeterminate. It follows that Guttman's measure of indeterminacy is inconsistent with the foundations of the factor model in probability theory, and the traditional measures of factor indeterminacy used by earlier writers should be reinstated. These yield no disturbing conclusions about the model.
Factor Analysis of Dichotomized Variables
Authors: Christoffersson Anders
Published: January 2006

An approach for multiple factor analysis of dichotomized variables is presented. It is based on the distribution of the first and second order joint probabilities of the binary scored items. The estimator is based on the generalized least squares principle. Standard errors and a test of the fit of the model is given.
Marginal Distributions for the Estimation of Proportions in m Groups
Authors: Lewis Charles , Wang Ming-mei , Novick Melvin R.
Published: January 2006

A Bayesian Model II approach to the estimation of proportions in m groups (discussed by Novick, Lewis, and Jackson) is extended to obtain posterior marginal distributions for the proportions. It is anticipated that these will be useful in applications (such as Individually Prescribed Instruction) where decisions are to be made separately for each proportion, rather than jointly for the set of proportions. In addition, the approach is extended to allow greater use of prior information than previously and the specification of this prior information is discussed.
A Model Relating Transfer of Learning and Correlation
Authors: Flammer August
Published: January 2006

The theoretical and practical importance of a double undertaking is discussed: the development of learning and transfer taxonomies with psychometric relevance and the building of psychometric classificatory systems with implications for learning and instruction. Psychometric classifications of human performances are most often based on the covariation of individual differences. The model presented justifies the expectation that the transfer from learning one task to learning another is linearly dependent on the coefficient of intercorrelation between the two tasks when the coefficient is corrected for attenuation. Two studies so far have explicitly confirmed the main deductions from this model. Contrary to the predictions, however, the regression curves yielded negative intercepts. Two empirically testable explanations are offered, one of which would be in full accordance with the model, while the other would call for a further assumption.
Estimation of the Reliability of a Test Divided into Two Parts of Unequal Length
Authors: Feldt Leonard S.
Published: January 2006

In some situations where reliability must be estimated it is impossible to divide the measuring instrument into more than two separately scoreable parts. When this is the case, the parts may be homogeneous in content but clearly unequal in length. The resultant scores will not be essentially τ-equivalent, and hence total test reliability cannot be satisfactorily estimated via Cronbach's coefficient alpha. Limitation on the number of parts rules out Kristof's three-part approach. A technique is developed for estimating reliability in such situations. The approach is shown to function very well when applied to five achievement tests.
The Weighted Varimax Rotation and the Promax Rotation
Authors: Cureton Edward E. , Mulaik Stanley A.
Published: January 2006

Kaiser’s iterative algorithm for the varimax rotation fails when (a) there is a substantial cluster of test vectors near the middle of each bounding hyperplane, leading to non-bounding hyperplanes more heavily overdetermined than those at the boundaries of the configuration of test vectors, and/or (b) there are appreciably more than m (m factors) tests whose loadings on one of the factors of the initial F- matrix, usually the first, are near-zero, leading to overdetermination of the hyperplane orthogonal to this initial F- axis before rotation. These difficulties are overcome by weighting the test vectors, giving maximum weights to those likely to be near the primary axes, intermediate weights to those likely to be near hyperplanes but not near primary axes, and near-zero weights to those almost collinear with or almost orthogonal to the first initial F- axis. Applications to the Promax rotation are discussed, and it is shown that these procedures solve Thurstone’s hitherto intractable “invariant” box problem as well as other more common problems based on real data.
On Small World Statistics
Authors: Fienberg Stephen E. , Lee S. Keith
Published: January 2006

The small-world problem revolves around the tracing of a line of acquaintances linking any two persons chosen at random. This paper discusses the statistical analysis of data arising out of two experimental studies of the small-world problem. The estimation of parameters in two previously proposed models is discussed, and the goodness-of-fit of these models is considered.
A Proposal for Handling Missing Data
Authors: Gleason Terry C. , Staelin Richard
Published: January 2006

A method for dealing with the problem of missing observations in multivariate data is developed and evaluated. The method uses a transformation of the principal components of the data to estimate missing entries. The properties of this method and four alternative methods are investigated by means of a Monte Carlo study of 42 computer-generated data matrices. The methods are compared with respect to their ability to predict correlation matrices as well as missing entries.

The results indicate that whenever there exists modest intercorrelations among the variables (i.e., average off diagonal correlation above .2) the proposed method is at least as good as the best alternative (a regression method) while being considerably faster and simpler computationally. Models for determining the best alternative based upon easily calculated characteristics of the matrix are given. The generality of these models is demonstrated using the previously published results of Timm.
Testing Pattern Hypotheses for Correlation Matrices
Authors: McDonald Roderick P.
Published: January 2006

McDonald [1974] obtained Maximum Likelihood (ML) estimates of the free parameters, and an asymptotic likelihood-ratio test, for the hypothesis that one or more elements of a covariance matrix are zero, and/or that groups of two or more of its elements are equal. Estimation was by Newton's method, starting from a closed-form Least Squares (LS) solution that is typically close to the ML solution point. The hypothesis can also be tested using the general model for the analysis of covariance structures given by Jöreskog [1970], but the combination of a closed-form LS starting point and the classical Newton method given by McDonald yields estimates in about a quarter of the computer time needed by JOreskog's program, ACØVS.
Statistical Methods for Absorbing Markov-Chain Models for Learning: Estimation and Identification
Authors: Polson Peter G. , Huizinga David
Published: January 2006

General algorithms for computing the likelihood of any sequence generated by an absorbing Markov-chain are described. These algorithms enable an investigator to compute maximum likelihood estimates of parameters using unconstrained optimization techniques. The problem of parameter identifiability is reformulated into questions concerning the behavior of the likelihood function in the neighborhood of an extremum. An alternative characterization of the concept of identifiability is proposed. A procedure is developed for deciding whether or not this definition is satisfied.
On Linear Combinations of Binary Item Scores
Authors: Krishnan T.
Published: January 2006

A method is given for finding a linear combination of binary item scores that minimizes the expected frequency of misclassification, in discriminating between two groups. The item scores are not assumed to be stochastically independent. The method uses the theory of threshold functions, developed by electrical engineers. Since psychometricians may not be familiar with this theory an elementary introduction to the required material is also given.
Representation of Structure in Similarity Data: Problems and Prospects
Authors: Shepard Roger N.
Published: January 2006

Conclusion

After struggling with the problem of representing structure in similarity data for over 20 years, I find that a number of challenging problems still remain to be overcome—even in the simplest case of the analysis of a single symmetric matrix of similarity estimates. At the same time, I am more optimistic than ever that efforts directed toward surmounting the remaining difficulties will reap both methodological and substantive benefits. The methodological benefits that I forsee include both an improved efficiency and a deeper understanding of “discovery” methods of data analysis. And the substantive benefits should follow, through the greater leverage that such methods will provide for the study of complex empirical phenomena—perhaps particularly those characteristic of the human mind.
Alternative Measures of Fit for the Schönemann-Carroll Matrix Fitting Algorithm
Authors: Lingoes James C. , Schönemann Peter H.
Published: January 2006

In connection with a least-squares solution for fitting one matrix, A, to another, B, under optimal choice of a rigid motion and a dilation, Schönemann and Carroll suggested two measures of fit: a raw measure, e, and a refined similarity measure, es, which is symmetric. Both measures share the weakness of depending upon the norm of the target matrix, B, e.g., e(A, kB) ≠ e(A, B) for k ≠ 1. Therefore, both measures are useless for answering questions of the type: “Does A fit B better than A fits C?”. In this note two new measures of fit are suggested which do not depend upon the norms of A and B, which are (0, 1)-bounded, and which, therefore, provide meaningful answers for comparative analyses.
Correcting for Unreliability in Nonlinear Models of Attitude Change
Authors: Hunter John E. , Cohen Stanley H.
Published: January 2006

The paper opens with a brief discussion of the problems in testing nonlinear models of attitude change. The regression artifacts produced by unreliability are shown in both the linear and nonlinear case. Classical solutions for the linear case are quickly reviewed. A “new” solution to the linear case is presented and applied to the nonlinear case. It is shown to work well under a broad set of conditions. Regression artifacts in bivariate regression are then discussed. If the predictors are independent, then the univariate correction procedure can be applied to each predictor separately. But if the predictors are correlated, a joint correction procedure must be used. One such procedure is defined and shown to work perfectly in the case of linear regression and reasonably well in a broad set of conditions in which the regression is nonlinear.
Single Subject Incomplete Designs for Nonmetric Multidimensional Scaling
Authors: Spence Ian , Domoney Dennis W.
Published: January 2006

Monte Carlo procedures were used to investigate the properties of a nonmetric multidimensional scaling algorithm when used to scale an incomplete matrix of dissimilarities. Various recommendations for users who wish to scale incomplete matrices are made: (a) recovery was found to be satisfactory provided that the “degrees of freedom” ratio exceeded 3.5, irrespective of error level; (b) cyclic designs were found to provide best recovery, although random patterns of deletion performed almost as well; and (c) strongly locally connected designs, specifically overlapping cliques, were generally inferior. These conclusions are based on 837 scaling solutions and are applicable to stimulus sets containing more than 30 objects.
Alternative Methods of Constructing Strict Weak Orders from Interval Orders
Authors: Fishburn Peter C. , Gehrlein William V.
Published: January 2006

Let n stimuli be linearly ordered by a physical attribute. Consider an individual's “more than” relation based on perceived attribute values. Assuming that the individual's relation agrees with the linear order and is an interval order, the paper examines the extent to which ordered pairs in the linear order but not in the interval order (due to nondetection of “small” differences) can be correctly identified on the basis of the interval order alone. Different methods of constructing strict weak orders from interval orders are compared by the degree of agreement with the underlying linear order.
A Note on Freeman's Measure of Association for Relating an Ordered to an Unordered Factor
Authors: Hubert Lawrence
Published: January 2006

Within the context of a contingency table, this note describes the relationship between Freeman's measure of association θ and the asymmetric association measures developed by Somers. The θ coefficient is appropriate for a contingency table in which the levels of one factor are ordered and the levels of the other factor are unordered; the indices defined by Somers are usually used when the levels of both factors are ordered and one is assumed to be the independent factor.
A Confirmatory Analysis of the Factor Stability Hypothesis
Authors: Bechtoldt Harold P.
Published: January 2006

The procedures recently developed by Jöreskog for studying similarities and differences in factor structures between different groups were applied to data from a study designed by Thurstone to investigate the sampling stability of a hypothesized isolated configuration. The hypothesis of an isolated configuration was rejected but not by much. The results represent a restricted and unique simple structure solution with the factor loadings and uniqueness values invariant over the two samples.
The Relative Efficiency of Two Tests as a Function of Ability Level
Authors: Lord Frederic M.
Published: January 2006

A new formula is developed for the relative efficiency of two tests measuring the same trait. The formula expresses relative efficiency solely in terms of the standard errors of measurement and, surprisingly, the frequency distributions of true scores. Approximate methods for estimating relative efficiency may make this function routinely available. A numerical illustration compares new and old estimates of relative efficiency for subtests from the Scholastic Aptitude Test.
Applications of Projective Transformations to Test Theory
Authors: Keats J. A.
Published: January 2006

Various writers have suggested the use of projective transformations in psychological theories. Among them are Herbst [t970], Atkin [1972] and Levine [in press]. In general these suggestions relate to scaling problems in psychophysics and in social psychology. The purpose of the present note is to extend these applications to test theory. One of the models proposed by Rasch [1960] can be seen as a special case of the projective transformation and this fact has certain implications for the use of the model.
The Additive Difference Model and a Metric and an Ordering on Sets
Authors: Becker Johannes , Pipahl Werner
Published: January 2006

On the basis of the idea of common elements to account for similarity, Restle [1959] developed a set-theoretical model on the generation of similarity judgments. Restle differentiates between his “more qualitative discussion” (p. 207), regarding stimuli as sets of elements and using no geometric concepts or assumptions, and metric quantitative developments of similarity, regarding stimuli as points in a geometric space. To the latter we can count the additive difference model of Beals, Krantz, & Tversky [1968] and Tversky & Krantz [1970].

Despite these differences the two models lead to the same conclusions on the characteristics of similarity judgments.
An Alternative Method of Fitting a Model of Individual Differences in Multidimensional Scaling
Authors: Bloxom Bruce
Published: January 2006

In articles by Homn [1969] and Carroll and Chang [1970] and in a memorandum by Bloxom [1968], a model was proposed for individual differences in multidimensional scaling. The distance in a p-dimensional space between stimuli j and k for person i is assumed to be given by

for N persons and for all pairs of n stimuli, where wim, is the “weight” given to axis m by person i and ajm, is the projection of stimulus j on that axis.
Determination of Joint Distributions from Marginal Distributions in Dichotomous Systems
Authors: Castellan N. John
Published: January 2006

In many areas of research in which the experimenter deals with a set of dichotomous dimensions it is often desirable to specify them in terms of marginal distributions and some conditional distributions. This paper develops a set of systematic procedures for determination of joint distributions with an arbitrary number of dimensions. Most of these procedures require only addition and/or subtraction. An extension of the procedures permits easy determination of covariance and correlation matrices.
Nonmetric Multidimensional Scaling: Recovery of Metric Information
Authors: Young Forrest W.
Published: January 2006

The degree of metric determinancy afforded by nonmetric multidimensional scaling was investigated as a function of the number of points being scaled, the true dimensionality of the data being scaled, and the amount of error contained in the data being scaled. It was found 1) that if the ratio of the degrees of freedom of the data to that of the coordinates is sufficiently large then metric information is recovered even when random error is present; and 2) when the number of points being scaled increases the stress of the solution increases even though the degree of metric determinacy increases.
Some Developments in Multivariate Generalizability
Authors: Joe George W. , Woodward J. Arthur
Published: January 2006

This article is concerned with estimation of components of maximum generalizability in multifacet experimental designs involving multiple dependent measures. Within a Type II multivariate analysis of variance framework, components of maximum generalizability are defined as those composites of the dependent measures that maximize universe score variance for persons relative to observed score variance. The coefficient of maximum generalizability, expressed as a function of variance component matrices, is shown to equal the squared canonical correlation between true and observed scores. Emphasis is placed on estimation of variance component matrices, on the distinction between generalizability- and decision-studies, and on extension to multifacet designs involving crossed and nested facets. An example of a two-facet partially nested design is provided.
Two-Matrix Orthogonal Rotation Procedures
Authors: Hakstian A. Ralph
Published: January 2006

Examples are presented in which it is either desirable or necessary to transform two sets of orthogonal axes to simple structure positions by means of the same transformation matrix. A solution is then outlined which represents a two-matrix extension of the general “orthomax” orthogonal rotation criterion. In certain circumstances, oblique two-matrix solutions are possible using the procedure outlined and the Harris-Kaiser [1964] logic. Finally, an illustrative example is presented in which the preceding technique is applied in the context of an inter-battery factor analysis.
The Solution of Simultaneous Equations
Authors: Dwyer P. S.
Published: January 2006

This paper is an attempt to integrate the various methods which have been developed for the numerical solution of simultaneous linear equations. It is demonstrated that many of the common methods, including the Doolittle Method, are variations of the method of “single division.” The most useful variation of this method, in case symmetry is present, appears to be the Abbreviated Doolittle method. The method of multiplication and subtraction likewise can be abbreviated in various ways of which the most satisfactory form appears to be the new Compact method. These methods are then applied to such problems as the solution of related equations, the solution of groups of equations, and the evaluation of the inverse of a matrix.
A Procedure for Ordering Object Pairs Consistent with the Multidimensional Unfolding Model
Authors: Rabinowitz George
Published: January 2006

A procedure for ordering object (stimulus) pairs based on individual preference ratings is described. The basic assumption is that individual responses are consistent with a nonmetric multidimensional unfolding model. The method requires data where a numerical response is independently generated for each individual-object pair. In conjunction with a nonmetric multidimensional scaling procedure, it provides a vehicle for recovering meaningful object configurations.
A Model and Algorithm for Multidimensional Scaling with External Constraints on the Distances
Authors: Borg Ingwer , Lingoes James C.
Published: January 2006

A method for externally constraining certain distances in multidimensional scaling configurations is introduced and illustrated. The approach defines an objective function which is a linear composite of the loss function of the point configuration X relative to the proximity data P and the loss of X relative to a pseudo-data matrix R. The matrix R is set up such that the side constraints to be imposed on X’s distances are expressed by the relations among R’s numerical elements. One then uses a double-phase procedure with relative penalties on the loss components to generate a constrained solution X. Various possibilities for constructing actual MDS algorithms are conceivable: the major classes are defined by the specification of metric or nonmetric loss for data and/or constraints, and by the various possibilities for partitioning the matrices P and R. Further generalizations are introduced by substituting R by a set of R matrices, Ri, i = 1, …r, which opens the way for formulating overlapping constraints as, e.g., in patterns that are both row- and column-conditional at the same time.
A Significance Test for Multisample Sphericity
Authors: Mendoza Jorge L.
Published: January 2006

The paper obtains a maximum likelihood criterion test for multisample sphericity. The test contains Mauchly’s sphericity test as a special case.
Estimating the Parameters of the Latent Population Distribution
Authors: Andersen Erling , Madsen Mette
Published: January 2006

Under consideration is a test battery of binary items. The responses of n individuals are assumed to follow a Rasch model. It is further assumed that the latent individual parameters are distributed within a given population in accordance with a normal distribution. Methods are then considered for estimating the mean and variance of this latent population distribution. Also considered are methods for checking whether a normal population distribution fits the data. The developed methods are applied to data from an achievement test and from an attitude test.
Two-Step Weighted Least Squares Factor Analysis of Dichotomized Variables
Authors: Christoffersson Anders
Published: January 2006

A two-step weighted least squares estimator for multiple factor analysis of dichotomized variables is discussed. The estimator is based on the first and second order joint probabilities. Asymptotic standard errors and a model test are obtained by applying the Jackknife procedure.
Tau-Equivalence and Equipercentile Equating
Authors: Yen Wendy M.
Published: January 2006

Test scores that are not perfectly reliable cannot be strictly equated unless they are strictly parallel [Lord, 1980]. This fact implies that tau-equivalence can be lost if an equipercentile equating is applied to observed scores that are not strictly parallel. Seventy-two simulated testing conditions are produced to simulate equating tests with different difficulties and discriminations. Number-correct and trait metrics are examined. When an equipercentile equating is applied to these data, locally biased (i.e., non-tau-equivalent) results are produced for tests of unequal difficulty. Differences between the criteria of tau-equivalence and equipercentile equivalence are discussed.
Alternative Weights and Invariant Parameters in Optimal Scaling
Authors: McDonald Roderick P.
Published: January 2006

Under conditions that are commonly satisfied in optimal scaling problems, arbitrary sets of optimal weights can be obtained by choices of generalized inverse procedures. A simple relationship holds between these and the corresponding invariant item scores. The case of optimal scaling originally treated by Guttman [1941] yields a restricted form of multicategory factor analysis. It is suggested that the invariant parameters of optimal scaling should be interpreted, according to the principles of latent trait theory, rather than the arbitrary weights.
Asymptotic Clarifications, Generalizations, and Concerns Regarding an Extended Class of Matched Pairs Tests based on Powers of Ranks
Authors: Mielke Paul W. , Berry Kenneth J.
Published: January 2006

Recent studies pertaining to an extended class of matched pairs tests based on powers of ranks are discussed. Previous questions regarding the asymptotic properties for this class of tests are clarified and a generalization of this class is described. This generalization raises a previously unanticipated concern about whether or not the analytic comparisons resulting from these tests correspond with an intuitive notion of what is being compared.
Some Standard Errors in Item Response Theory
Authors: Thissen David , Wainer Howard
Published: January 2006

The mathematics required to calculate the asymptotic standard errors of the parameters of three commonly used logistic item response models is described and used to generate values for some common situations. It is shown that the maximum likelihood estimation of a lower asymptote can wreak havoc with the accuracy of estimation of a location parameter, indicating that if one needs to have accurate estimates of location parameters (say for purposes of test linking/equating or computerized adaptive testing) the sample sizes required for acceptable accuracy may be unattainable in most applications. It is suggested that other estimation methods be used if the three parameter model is applied in these situations.
Statistical Evaluation of Measures of Fit in the Lingoes-Borg Procrustean Individual Differences Scaling
Authors: Langeheine Rolf
Published: January 2006

PINDIS, as recently presented by Lingoes and Borg [1978] not only marks the latest development within the scope of individual differences scaling, but, may be of benefit in some closely related topics, such as target analysis. Decisions on whether the various models available from PINDIS fit fallible data are relatively arbitrary, however, since a statistical theory of the fit measures is lacking. Using Monte Carlo simulation, expected fit measures as well as some related statistics were therefore obtained by scaling sets of 4(4)24 random configurations of 5(5)30 objects in 2, 3, and 4 dimensions (individual differences case) and by fitting one random configuration to a fixed random target for 5(5)30 objects in 2, 3, and 4 dimensions (target analysis case). Applications are presented.
A Note on Partitioned Determinants
Authors: de Leeuw Jan
Published: January 2006

A formula for the determinant of a partitioned matrix, possibly with singular submatrices, is derived and applied to some psychometric and numerical problems.
A Priori Tests in Repeated Measures Designs: Effects of Nonsphericity
Authors: Boik Robert J.
Published: January 2006

The validity conditions for univariate repeated measures designs are described. Attention is focused on the sphericity requirement. For a v degree of freedom family of comparisons among the repeated measures, sphericity exists when all contrasts contained in the v dimensional space have equal variances. Under nonsphericity, upper and lower bounds on test size and power of a priori, repeated measures, F tests are derived. The effects of nonsphericity are illustrated by means of a set of charts. The charts reveal that small departures from sphericity (.97 ≤ ε < 1.00) can seriously affect test size and power. It is recommended that separate rather than pooled error term procedures be routinely used to test a priori hypotheses.
Constrained Least Squares Estimators of Oblique Common Factors
Authors: McDonald Roderick P.
Published: January 2006

An expression is given for weighted least squares estimators of oblique common factors, constrained to have the same covariance matrix as the factors they estimate. It is shown that if as in exploratory factor analysis, the common factors are obtained by oblique transformation from the Lawley-Rao basis, the constrained estimators are given by the same transformation. Finally a proof of uniqueness is given.