bluuebunny/crossref_metadata_2025 huggingface dataset:
Application of the Concept of Simple Structure to Alexander's Data
Authors: Yela Mariano
Published: January 2006

A battery of 20 tests originally analyzed by Alexander (1) was reworked according to the principle of simple structure. His results were sustained in general. Both analyses yielded five factors in the first-order domain. Of these, three factors in the re-analysis (v, X and F) have almost exactly the same loadings as the corresponding factors in the original work, and were interpreted in the same way. The loading pattern of a fourth factor, Z, left uninterpreted in the original study, happened to be more clear in the re-analysis, and an interpretation was attempted. It appears to be a factor of perceptual synthesis, and seems to play an important role in intellectual processes. A fifth factor, not present in Alexander's results, appeared in the new analysis: the reasoning factor, involved in inductive and deductive thinking. All four cognitive factors are related to a general factor that can be thought of as representing abstraction and education of relations and correlates, these processes being, therefore, the essential feature underlying intellectual behavior, at least in that sector surveyed by the tests of the present battery.
Sequential Sampling Plans for Use in Psychological Test Work
Authors: Kimball Allyn W.
Published: January 2006

In large-scale psychological testing programs, it happens frequently that a group of items must be checked for accuracy with respect to certain characteristics. In many cases it is not feasible to check each item in the group separately, so that a decision concerning the entire group is usually reached by examining in detail only a small portion of the group. This paper proposes some sequential sampling plans for use in this type of work. A general discussion of the problem is followed by an illustrative example of the method applied to checking scores on groups of psychological test papers.
On the Identifiability of Parameters in Thurstone's Multiple Factor Analysis
Authors: Reiersøl Olav
Published: January 2006

In econometric literature a parameter in a theoretical model has been called identifiable if it can be uniquely determined in terms of the joint probability distribution of the observed variables. In this paper the identifiability of parameters in four different factor analysis models is considered. The last of these four models corresponds to Thurstone's factor analysis. In Sections 7 and 11, the possibility of a statistical testing of the models is discussed. Section 10 deals with the problem of actually determining the parameter r (the number of common factors) in terms of the probability distribution of the observed variables.
The Consistency of the Items of an Activity Preference Blank
Authors: Fowler H. M.
Published: January 2006

Results of an experiment to obtain data on the consistency of the items of two forms of an Activity Preference Blank are presented. Both Form I and Form II, which was a revised edition of Form I, were administered twice, so consistency data are available for both forms. A sub-item is said to be consistent if a high proportion of men marked it the same way, M for preferred Most and L for preferred Least, on both administrations of the test. The data of the experiment were investigated to see what happens to the consistency of sub-items when the items are changed in context, when the number of sub-items in an item is reduced, and when the time-interval between the administration and the re-administration of the test is increased. The author also gives data on the consistency of the responses made to particular combinations of sub-items and data on item consistency when all sub-item combinations are taken into consideration.
Table for Determining phi Coefficients
Authors: Jurgensen C. E.
Published: January 2006

A table is presented which directly gives phi coefficients accurate to three places when entered by the proportion of one sub-group responding in a specified manner and the proportion of a second sub-group responding in the same manner. The table gives coefficients identical with those obtained by formula if the sub-groups are equal in number. The phi coefficients can readily be expressed, if desired, in terms of critical ratio or chi square. The table is more accurate than the use of abacs and eliminates the use of time-consuming formulas. Accurate determination of item validity on the basis of statistically rigorous techniques can be made more quickly by means of the table than validity determined by less efficient methods which have previously been used to save time.
A Quantitative Description of the Stimulus
Authors: Lynch J. A.
Published: January 2006

A formula for the stimulus is derived. The essential postulates and assumptions are based on Gestalt theory.
A Model for the Analysis of Multiple Strategies
Authors: Castellan N. John
Published: January 2006

In many decision problems the decision-maker must ask a series of questions or select cues relevant to but prior to the decision. There are many strategies which would prescribe an order for asking such questions or selecting such cues. It is the purpose of the paper to describe a manner in which the strategy or strategies of the decision-maker can be analyzed. From this model can be derived limits corresponding to the possible use of a particular strategy, and the effective or observed use of the strategy or strategies by the decision-maker.
A Sequence of Limiting Distributions of Response Probabilities
Authors: McGregor J. R. , Zidek J. V.
Published: January 2006

Explicit solutions are obtained for a sequence of limiting distributions of response probabilities for the two experimenter-controlled events learning model of Bush and Mosteller [2]. A generalization to the s experimenter-controlled events model is found.
The Uniqueness and Significance of Simple Structure Demonstrated by Contrasting Organic “Natural Structure” and “Random Structure” Data
Authors: Cattell Raymond B. , Gorsuch Richard L.
Published: January 2006

The study compares the extent to which naturally structured data and artificial, relatively random data (both with the same basic parameters) produce simple structure factors which are uniquely determined. Two examples of unstructured matrices were compared with the ball problem matrix. The results show that an oblique position of maximum hyperplane count in the structured data differs from that in the unstructured by reaching a significantly more unique position in terms of the exactitude with which it is re-discoverable when starting from different positions, and by reaching (at the maximum) a significantly higher hyperplane count.
Maximum Likelihood Estimation of Parameters of Signal Detection Theory–A Direct Solution
Authors: Dorfman Donald D. , Alf Edward
Published: January 2006

Ogilvie and Creelman have recently attempted to develop maximum likelihood estimates of the parameters of signal-detection theory from the data of yes-no ROC curves. Their method involved the assumption of a logistic distribution rather than the normal distribution in order to make the mathematics more tractable. The present paper presents a method of obtaining maximum likelihood estimates of these parameters using the assumption of underlying normal distributions.
A Choice Theory Analysis of Similarity Judgments
Authors: Luce R. Duncan
Published: January 2006

The selection of one of several stimuli as most similar to a reference stimulus is assumed to satisfy a choice axiom that permits assigning ratio scale values to each variable-reference stimuli pair. The logarithm of this scale is treated as a distance measure, leading to the following testable conclusions about the pairwise choice probabilities as the reference stimulus is varied. First, the plot is a symmetrically truncated ogive with horizontal tails. Second, if two pairs of choice stimuli have the same midpoint, the ogive of one pair is part of the ogive of the other. In terms of this model, the hysteresis and midpoint displacement effects in the method of bisection are discussed, and relations with Coombs' unfolding techniques are explored.
Some Implications of the Logical Calculus for Empirical Classes for Social Science Methodology
Authors: Schutz William C.
Published: January 2006

An exposition of a calculus for empirical classes (CEC), one of the few attempts by logicians to deal with the problem of constructs and indicators, is presented. The CEC provides the groundwork for a formal structure for the situation in which individuals have a degree of membership in various classes rather than having either membership or nonmembership—a situation nearly always true in empirical research. The CEC is presented and its relation to various social science concepts is mentioned. An application of the CEC model to latent structure analysis (LSA) suggests alternatives to the local independence assumption including one called the local scale assumption, which has a close relation to a Guttman scale.
A Modification of Kendall's Tau for Measuring Association in Contingency Tables
Authors: Karon Bertram P. , Alexander Irving E.
Published: January 2006

A coefficient of association τ′ is described for a contingency table containing data classified into two sets of ordered categories. Within each of the two sets the number of categories or the number of cases in each category need not be the same. τ′=+1 for perfect positive association and has an expectation of 0 for chance association. In many cases τ′ also has a -1 as a lower limit. The limitations of Kendall&s τ′a and τ′b and Stuart&s τ′c are discussed, as is the identity of these coefficients to τ′ under certain conditions. Computational procedure for τ′ is given.
Estimating Item Indices by Nomographs
Authors: Colver Robert M.
Published: January 2006

Two nomographs are presented for estimating item validity indices identical in value to those obtained from Flanagan 's table and to those obtained from Davis' chart. Experience has shown that the use of the nomographs results in the saving of a significant amount of time with no loss in accuracy. The nomographs also provide a method of quick conversion between the familiar coefficients and the Davis indices, which are less familiar but which offer greater flexibility.
Fitting a Simplex Symmetrically
Authors: Schönemann Peter H.
Published: January 2006

A method for fitting a perfect simplex [Guttman, 1954] is suggested which, in contrast to Kaiser's [1962], is independent of the order of the manifest variables. It is based on a procedure for scaling a set of points from their pairwise distances [Torgerson, 1958; Young & Householder, 1938] which is reviewed in compact notation in the Appendix. The method is extended to an iterative algorithm for fitting a quasi-simplex. Some empirical results are included.
A Set Theoretic Analysis of Group Interactions
Authors: Mackenzie Kenneth D.
Published: January 2006

Prior to the statistical treatment of experimentally derived data the experimenter must obtain the data. In many studies in psychology, the content of group interactions is obtained by a data coding scheme. Coding schemes are shown to possess hierarchical structures and can be characterized by a hierarchy of fields. Three examples of coding schemes as hierarchies of fields are given. Techniques for extracting numbers from the set are presented. Problems associated with the improper assignment of elements of a data coding scheme to a theoretical structure are examined. The main result is that there will be errors in assignment of data to theory unless the structure of the data coding scheme is identical with that structure which is relevant to the theory being tested. Whenever the structures are not equal, the results are hard to interpret. In fact, any size of assignment error can be obtained. Since these errors precede the usual statistical treatment of data, it would appear that reported empirical findings are only valid when there exists no assignment errors.
Longitudinal Factor Analysis
Authors: Corballis M. C. , Traub R. E.
Published: January 2006

A model is presented for factor analysing scores on a set of psychological tests administered as both pre- and postmeasures in a study of change. The model assumes that the same factors underlie the tests on each occasion, but that factor scores as well as factor loadings may change between occasions. Factors are defined to be orthogonal between as well as within occasions. A two-stage least squares procedure for fitting the model is described, and generally provides a unique rotation solution for the factors on each occasion.
Three Common Factor Models for Groups of Variables
Authors: McDonald Roderick P.
Published: January 2006

For the case of two or more groups of variables (batteries), generalizations on three common factor models, the Equal Residual Variances model, the Image model of Jöreskog, and the Canonical Factor Analysis model, are described and illustrated with empirical examples.
Extensions of the Significance Test for One-Parameter Signal Detection Hypotheses
Authors: Marascuilo Leonard A.
Published: January 2006

The basic models of signal detection theory involve the parametric measure, d′, generally interpreted as a detectability index. Given two observers, one might wish to know whether their detectability indices are equal or unequal. Gourevitch and Galanter (1967) proposed a large sample statistical test that could be used to test the hypothesis of equal d′ values. In this paper, their large two sample test is extended to a K-sample detection test. If the null hypothesis d1′ = d2′ = ... = dK′ is rejected, one can employ the post hoc confidence interval procedure described in this paper to locate possible statistically significant sources of variance and differences. In addition, it is shown how one can use the Gourevitch and Galanter statistics to test d′ = 0 for a single individual.
A Scalar Product Model for the Multidimensional Scaling of Choice
Authors: Bechtel Gordon G. , Tucker Ledyard R , Chang Wei-Ching
Published: January 2006

A multidimensional scaling analysis is presented for replicated layouts of pairwise choice responses. In most applications the replicates will represent individuals who respond to all pairs in some set of objects. The replicates and the objects are scaled in a joint space by means of an inner product model which assigns weights to each of the dimensions of the space. Least squares estimates of the replicates' and objects' coordinates, and of unscalability parameters, are obtained through a manipulation of the error sum of squares for fitting the model. The solution involves the reduction of a three-way least squares problem to two subproblems, one trivial and the other solvable by classical least squares matrix factorization. The analytic technique is illustrated with political preference data and is contrasted with multidimensional unfolding in the domain of preferential choice.
Statistical Analysis of Sets of Congeneric Tests
Authors: Jöreskog K. G.
Published: January 2006

Various models for sets of congeneric tests are considered, including models appropriate for the analysis of multitrait-multimethod data. All models are illustrated with real data. The special cases when two or more tests within a set are tau-equivalent or parallel are also considered. All data analyses are done within the framework of a general model by Jöreskog [1970].
A Comparison of Computer Routines for the Calculation of the Tetrachoric Correlation Coefficient
Authors: Froemel Ernest C.
Published: January 2006

In calculations of the discriminating-power parameter of the normal ogive model, Bock and Lieberman compared estimates derived from their maximum-likelihood solution with those derived from the heuristic solution. The two sets of estimates were in excellent agreement provided the heuristic solution used accurate tetrachoric correlation coefficients. Three computer methods for the calculation of the tetrachoric correlation were examined for accuracy and speed. The routine by Saunders was identified as an acceptably accurate method for calculating the tetrachoric correlation coefficient.
Significant Category Clustering in Free Recall
Authors: Arnold Barry C.
Published: January 2006

Frender and Doubilet suggest that Bousfield’s ratio of repetitions (RR) is the best measure of clustering in free recall presently available. Conditioning only on the number of words recalled, they determine the mean of RR in the absence of clustering. In this note the null variance of RR is presented. This permits development of conservative significance tests based on the Cramér inequality.
The ‘Ability’ Scale in Item Characteristic Curve Theory
Authors: Lord Frederic M.
Published: January 2006

For the six available sets of empirical data, the discrimination (slope) parameter of the logistic item characteristic curve was found to have a significant positive correlation over items with the difficulty (location) parameter. This unpleasant situation can be eliminated by a suitably chosen transformation of the ability scale. An example of the transformation is given and some empirical results of using the transformed scale are shown.
Probabilistic, Multidimensional Unfolding Analysis
Authors: Zinnes Joseph L. , Griggs Richard A.
Published: January 2006

A probabilistic, multidimensional version of Coombs' unfolding model is obtained by assuming that the projections of each stimulus and each individual on each axis are normally distributed. Exact equations are developed for the single dimensional case and an approximate one for the multidimensional case. Both types of equations are expressed solely in terms of univariate normal distribution functions and are therefore easy to evaluate. A Monte Carlo experiment, involving 9 stimuli and 3 subjects in a 2 dimensional space, was run to determine the degree of accuracy of the multidimensional equation and the feasibility of using iterative methods to obtain maximum likelihood estimates of the stimulus and subject coordinates. The results reported here are gratifying in both respects.
On the Factor Score Controversy
Authors: Green Bert F.
Published: January 2006

A summary and interpretation of the recent literature on the indeterminacy of factor scores is given in simple terms. A good index of factor score determinacy is the squared multiple correlation of the factor with the observed variables.
Fast Regression Estimates of Missing Data
Authors: Koopman Raymond F.
Published: January 2006

A recent comparison of methods for estimating missing data concluded that when there is sufficient redundancy to justify using a more elaborate method than the mean of each variable, the principal components and regression methods are equally good and superior to the other methods investigated. Principal components was preferred because of its “tremendous computational savings over the regression method.” This note proposes an alternate implementation of the regression method which should be slightly faster than the principal components method.
The Difficulty of a Test and its Factor Composition
Authors: Guilford J. P.
Published: January 2006

A factor analysis of the ten sub-tests of the Seashore test of pitch discrimination revealed that more than one ability is involved. One factor, which accounted for the greater share of the variances, had loadings that decreased systematically with increasing difficulty. A second factor had strongest loadings among the more difficult items, particularly those with frequency differences of 2 to 5 cycles per second. A third had strongest loadings at differences of 5 to 12 cycles per second. No explanation for the three factors is apparent, but the hypothesis is accepted that they represent distinct abilities. In tests so homogeneous as to content and form, where a single common factor might well have been expected, the appearance of additional common factors emphasizes the importance of considering the difficulty level of test items, both in the attempt to interpret new factors and in the practice of testing. The same kind of item may measure different abilities according as it is easy or difficult for the individuals to whom it is applied.
A Note on Keats' Generalization of the Rasch Model
Authors: White P. O.
Published: January 2006

An alternative derivation is given for a simple test model which incorporates an ability parameter for the subject and difficulty level and guessing parameters for the problem. The probability of a correct response to the problem is a projective transformation of the problem difficulty. The ability and difficulty parameters separate into additive components.
Multicomponent Latent Trait Models for Ability Tests
Authors: Whitely Susan E.
Published: January 2006

A major research direction for ability measurement has been to identify the information-processes that are involved in solving test items through mathematical modeling of item difficulty. However, this research has had limited impact on ability measurement, since person parameters are not included in the process models. The current paper presents some multicomponent latent trait models for reproducing test performance from both item and person parameters on processing components. Components are identified from item subtasks, in which performance is a logistic function (i.e., Rasch model) of person and item parameters, and then are combined according to a mathematical model of processing on the composite item.
Tests of Symmetry in Three-Way Contingency Tables
Authors: Read Campbell B.
Published: January 2006

Three-dimensional contingency tables are analyzed, with one variable (e.g., sex) as a factor, and with a natural relation between the other variables (e.g. left and right eye vision). Models of special interest, like symmetry and proportional symmetry between the related variables, and homogeneity across the factor levels, are investigated. Maximum likelihood estimators of parameters and partitions of chi-square goodness-of-fit statistics are explicitly presented; the independence of certain models is noted, and an example is discussed.
Approximate Uniqueness Estimates for Singular Correlation Matrices
Authors: Finkbeiner C. T. , Tucker L. R.
Published: January 2006

The residual variance (one minus the squared multiple correlation) is often used as an approximation to the uniqueness in factor analysis. An upper bound approximation to the residual variance is given for the case when the correlation matrix is singular. The approximation is computationally simpler than the exact solution, especially since it can be applied routinely without prior knowledge as to the singularity or nonsingularity of the correlation matrix.
The Linear Utility Model for Optimal Selection
Authors: Mellenbergh Gideon J. , van der Linden Wim J.
Published: January 2006

A linear utility model is introduced for optimal selection when several subpopulations of applicants are to be distinguished. Using this model, procedures are described for obtaining optimal cutting scores in subpopulations in quota-free as well as quota-restricted selection situations. The cutting scores are optimal in the sense that they maximize the overall expected utility of the selection process. The procedures are demonstrated with empirical data.
A Note on the Minres Method
Authors: Nosal Miloslav
Published: January 2006

This paper discusses the advantages and problems related to factor analysis by minimizing residuals (minres). It is shown that this method fails if the starting point of iterations is not well chosen. A suitable starting point is suggested.
Comparing Examinees to a Control
Authors: Wilcox Rand R.
Published: January 2006

When comparing examinees to a control, the examiner usually does not know the probability of correctly classifying the examinees based on the number of items used and the number of examinees tested. Using ranking and selection techniques, a general framework is described for deriving a lower bound on this probability. We illustrate how these techniques can be applied to the binomial error model. New exact results are given for normal populations having unknown and unequal variances.
The Problem of the Additive Constant and Eigenvalues in Metric Multidimensional Scaling
Authors: Saito Takayuki
Published: January 2006

This paper is concerned with the additive constant problem in metric multidimensional scaling. First the influence of the additive constant on eigenvalues of a scalar product matrix is discussed. The second part of this paper is devoted to the introduction of a new formulation of the additive constant problem. A solution is given for fixed dimensionality, by maximizing a normalized index of fit with a gradient method. An experimental computation has shown that the author's solution is accurate and easy to follow.
Simultaneous Optimization of Factor Assessibility and Representativeness: An Old Solution to a New Problem
Authors: Greene Vernon L.
Published: January 2006

P. M. Bentler has shown that Rao's canonical factor analysis is in effect a psychometric analysis, leading to factors that are maximally assessible from the data. He contrasts this with Kaiser and Caffrey's alpha factor analysis that leads to factors that maximally represent the true factors in the content domain. Noting the problems associated with factors that may be highly assessible, but not very representative, or vice versa, Bentler suggests the need for a technique that would, insofar as possible, be optimal with respect to both criteria. Such a technique is presented here, and is shown to resolve into a traditional scaling method, which in turn acquires a richer psychometric interpretation.
A New Algorithm for the Least-Squares Solution in Factor Analysis
Authors: Okamoto Masashi , Ihara Masamori
Published: January 2006

A new algorithm to obtain the least-squares or MINRES solution in common factor analysis is presented. It is based on the up-and-down Marquardt algorithm developed by the present authors for a general nonlinear least-squares problem. Experiments with some numerical models and some empirical data sets showed that the algorithm worked nicely and that SMC (Squared Multiple Correlation) performed best among four sets of initial values for common variances but that the solution might sometimes be very sensitive to fluctuations in the sample covariance matrix.
On the Existence and Uniqueness of Maximum-Likelihood Estimates in the Rasch Model
Authors: Fischer Gerhard H.
Published: January 2006

Necessary and sufficient conditions for the existence and uniqueness of a solution of the so-called “unconditional” (UML) and the “conditional” (CML) maximum-likelihood estimation equations in the dichotomous Rasch model are given. The basic critical condition is essentially the same for UML and CML estimation. For complete data matrices A, it is formulated both as a structural property of A and in terms of the sufficient marginal sums. In case of incomplete data, the condition is equivalent to complete connectedness of a certain directed graph. It is shown how to apply the results in practical uses of the Rasch model.
A Note on the Relation between Coefficient Alpha and Guttman’s “split-half” Lower Bounds
Authors: Jackson Paul H.
Published: January 2006

Use of the same term “split-half” for division of an n-item test into two subtests containing equal [Cronbach], and possibly unequal [Guttman], numbers of items sometimes leads to a misunderstanding about the relation between Guttman’s maximum split-half bound and Cronbach’s coefficient alpha.

Coefficient alpha is the average of split-half bounds in the Cronbach sense and so is not larger than the maximum split-half bound in either sense when n is even. When n is odd, however, splithalf bounds exist only in the Guttman sense and the largest of these may be smaller than coefficient alpha.
Present at the Birth
Authors: Horst Paul , Stalnaker John
Published: January 2006

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.
Models, Computers and Policies: Fifty Years of Psychometrika
Authors: Green Bert F.
Published: January 2006

Mathematical models have been represented in Psychometrika first in biophysics, then in stochastic models of behavior, and later in computer simulations of behavior. Other specialized journals now attract many articles in these areas, but Psychometrika's policy of broad interest in all aspects of quantitative psychology remains sound. This paper reviews Psychometrika's coverage of mathematical models and computation, and discusses some matters of editorial policy.
Improved Bounds for Optimal Intervals in Weakly Constrained Regression Problems
Authors: ten Berge Jos M. F.
Published: January 2006

The solution of weakly constrained regression problems typically requires the iterative search, in a given interval, of a point where a certain function has a zero derivative. This note deals with improved bounds for the interval to be searched.
Maximum Likelihood Estimation in Multidimensional Scaling
Authors: Ramsay J. O.
Published: January 2006

A variety of distributional assumptions for dissimilarity judgments are considered, with the lognormal distribution being favored for most situations. An implicit equation is discussed for the maximum likelihood estimation of the configuration with or without individual weighting of dimensions. A technique for solving this equation is described and a number of examples offered to indicate its performance in practice. The estimation of a power transformation of dissimilarity is also considered. A number of likelihood ratio hypothesis tests are discussed and a small Monte Carlo experiment described to illustrate the behavior of the test of dimensionality in small samples.
Effects of Conditionality on INDSCAL and ALSCAL Weights
Authors: MacCallum Robert C.
Published: January 2006

The role of conditionality in the INDSCAL and ALSCAL procedures is explained. The effects of conditionality on subject weights produced by these procedures is illustrated via a single set of simulated data. Results emphasize the need for caution in interpreting subject weights provided by these techniques.
Multiple-Answer Multiple-Choice Test Items: Responding and Scoring Through Bayes and Minimax Strategies
Authors: Duncan George T. , Milton E. O.
Published: January 2006

A multiple-answer multiple-choice test item has a certain number of alternatives, any number of which might be keyed. The examinee is also allowed to mark any number of alternatives. This increased flexibility over the one keyed alternative case is useful in practice but raises questions about appropriate scoring rules. In this article a certain class of item scoring rules called the binary class is considered. The concepts of standard scoring rules and equivalence among these scoring rules are introduced in the “misinformation” model for which the traditional “knowledge” model is a special case. The examinee’s strategy with respect to a scoring rule is examined. The critical role of a quantity called the scoring ratio is emphasized. In the case of examinee uncertainty about the number of correct alternatives on an item, a Bayes and a minimax strategy for the examinee are developed. Also an appropriate response for the examiner to the minimax strategy is outlined.
Statistical Inference Based on Ranks
Authors: Hettmansperger Thomas P. , McKean Joseph W.
Published: January 2006

This paper develops a unified approach, based on ranks, to the statistical analysis of data arising from complex experimental designs. In this way we answer a major objection to the use of rank procedures as a major methodology in data analysis. We show that the rank procedures, including testing, estimation and multiple comparisons, are generated in a natural way from a robust measure of scale. The rank methods closely parallel the familiar methods of least squares, so that estimates and tests have natural interpretations.
A Comparison of Several k Sample Tests for Ordered Alternatives in Completely Randomized Designs
Authors: Berenson Mark L.
Published: January 2006

The importance of appropriate test selection for a given research endeavor cannot be overemphasized. Using samples drawn from eleven populations (differing in shape, peakedness, and density in the tails), this study investigates the small sample empirical powers of nine k-sample tests against ordered location alternatives under completely randomized designs. The results then are intended to aid the researcher in the selection of a particular procedure appropriate for a given endeavor. To highlight this an industrial psychology application involving work productivity is presented.
A Simplified Accurate Algorithm for the Fisher-Yates Exact Test
Authors: Phillips J. P. N.
Published: January 2006

An algorithm, using a short cut due to Feldman and Klingler, for the Fisher-Yates exact test is presented: the algorithm is quick, simple and accurate.
A Note on Latent Trait Theory and Bowker's Test
Authors: Meredith William , Sands Laura Prouty
Published: January 2006

Bowker's test for marginal equality in contingency tables provides a familiar chi-square test to determine whether the marginal distributions are the same across two or more factors or occasions. In this note it is shown how latent trait theory provides a theoretical framework for the development and application of this test.
Identification of Inconsistent Variates in Factor Analysis
Authors: Kano Yutaka , Ihara Masamori
Published: January 2006

When some of observed variates do not conform to the model under consideration, they will have a serious effect on the results of statistical analysis. In factor analysis the model with inconsistent variates may result in improper solutions. In this article a useful method for identifying a variate as inconsistent is proposed in factor analysis. The procedure is based on the likelihood principle. Several statistical properties such as the effect of misspecified hypotheses, the problem of multiple comparisons, and robustness to violation of distributional assumptions are investigated. The procedure is illustrated by some examples.
Modification Indices for the 2-PL and the Nominal Response Model
Authors: Glas Cees A. W.
Published: January 2006

In this paper, it is shown that various violations of the 2-PL model and the nominal response model can be evaluated using the Lagrange multiplier test or the equivalent efficient score test. The tests presented here focus on violation of local stochastic independence and insufficient capture of the form of the item characteristic curves. Primarily, the tests are item-oriented diagnostic tools, but taken together, they also serve the purpose of evaluation of global model fit. A useful feature of Lagrange multiplier statistics is that they are evaluated using maximum likelihood estimates of the null-model only, that is, the parameters of alternative models need not be estimated. As numerical examples, an application to real data and some power studies are presented.
Retrieving the Correlation Matrix from a Truncated PCA Solution: The Inverse Principal Component Problem
Authors: ten Berge Jos M. F. , Kiers Henk A. L.
Published: January 2006

When r Principal Components are available for k variables, the correlation matrix is approximated in the least squares sense by the loading matrix times its transpose. The approximation is generally not perfect unless r =k. In the present paper it is shown that, when r is at or above the Ledermann bound, r principal components are enough to perfectly reconstruct the correlation matrix, albeit in a way more involved than taking the loading matrix times its transpose. In certain cases just below the Ledermann bound, recovery of the correlation matrix is still possible when the set of all eigenvalues of the correlation matrix is available as additional information.
Simulating Correlated Multivariate Nonnormal Distributions: Extending the Fleishman Power Method
Authors: Headrick Todd C. , Sawilowsky Shlomo S.
Published: January 2006

A procedure for generating multivariate nonnormal distributions is proposed. Our procedure generates average values of intercorrelations much closer to population parameters than competing procedures for skewed and/or heavy tailed distributions and for small sample sizes. Also, it eliminates the necessity of conducting a factorization procedure on the population correlation matrix that underlies the random deviates, and it is simpler to code in a programming language (e.g., FORTRAN). Numerical examples demonstrating the procedures are given. Monte Carlo results indicate our procedure yields excellent agreement between population parameters and average values of intercorrelation, skew, and kurtosis.
The Conjunctive Model of Hierarchical Classes
Authors: Van Mechelen Iven , De Boeck Paul , Rosenberg Seymour
Published: January 2006

This paper describes the conjunctive counterpart of De Boeck and Rosenberg's hierarchical classes model. Both the original model and its conjunctive counterpart represent the set-theoretical structure of a two-way two-mode binary matrix. However, unlike the original model, the new model represents the row-column association as a conjunctive function of a set of hypothetical binary variables. The conjunctive nature of the new model further implies that it may represent some conjunctive higher order dependencies among rows and columns. The substantive significance of the conjunctive model is illustrated with empirical applications. Finally, it is shown how conjunctive and disjunctive hierarchical classes models relate to Galois lattices, and how hierarchical classes analysis can be useful to construct lattice models of empirical data.
On the Relationship between iTem Response Theory and Factor Analysis of Discretized Variables
Authors: Takane Yoshio , de Leeuw Jan
Published: January 2006

Equivalence of marginal likelihood of the two-parameter normal ogive model in item response theory (IRT) and factor analysis of dichotomized variables (FA) was formally proved. The basic result on the dichotomous variables was extended to multicategory cases, both ordered and unordered categorical data. Pair comparison data arising from multiple-judgment sampling were discussed as a special case of the unordered categorical data. A taxonomy of data for the IRT and FA models was also attempted.
Does Adaptive Testing Violate Local Independence?
Authors: Mislevy Robert J. , Chang Hua-Hua
Published: January 2006

Item response theory posits “local independence,” or conditional independence of item responses given item parameters and examinee proficiency parameters. The usual definition of local independence, however, addresses the context of fixed tests, and initially appears to yield incorrect response-pattern probabilities in the context of adaptive testing. The paradox is resolved by introducing additional notation to deal with the item selection mechanism.
Estimating Correlations with Missing Data, a Bayesian Approach
Authors: Gross Alan L. , Torres-Quevedo Rocio
Published: January 2006

The posterior distribution of the bivariate correlation is analytically derived given a data set where x is completely observed but y is missing at random for a portion of the sample. Interval estimates of the correlation are then constructed from the posterior distribution in terms of highest density regions (HDRs). Various choices for the form of the prior distribution are explored. For each of these priors, the resulting Bayesian HDRs are compared with each other and with intervals derived from maximum likelihood theory.
Robust and Powerful Nonorthogonal Analyses
Authors: Keselman H. J. , Carriere K. C. , Lix Lisa M.
Published: January 2006

Numerous types of analyses for factorial designs having unequal cell frequencies have been discussed in the literature. These analyses test either weighted or unweighted marginal means which, in turn, correspond to different model comparisons. Previous research has indicated, however, that these analyses result in biased (liberal or conservative) tests when cell variances are heterogeneous. We show how to obtain a generally robust and powerful analysis with any of the recommended nonorthogonal solutions by adapting a modification of the Welch-James procedure for comparing means when population variances are heterogeneous.
Suppressing Permutations or Rigid Planar Rotations: A Remedy Against Nonoptimal Varimax Rotations
Authors: ten Berge Jos M. F.
Published: January 2006

Varimax rotation consists of iteratively rotating pairs of columns of a matrix to a maximal sum (over columns) of variances of squared elements of the matrix. Without loss of optimality, the two rotated columns can be permuted and/or reflected. Although permutations and reflections are harmless for each planar rotation per se, they can be harmful in Varimax rotation. Specifically, they often give rise to the phenomenon that certain pairs of columns are consistently skipped in the iterative process, whence Varimax will be terminated at a nonstationary point. The skipping phenomenon is demonstrated, and it is shown how to prevent it.
Simplimax: Oblique Rotation to an Optimal Target with Simple Structure
Authors: Kiers Henk A. L.
Published: January 2006

Factor analysis and principal component analysis are usually followed by simple structure rotations of the loadings. These rotations optimize a certain criterion (e.g., varimax, oblimin), designed to measure the degree of simple structure of the pattern matrix. Simple structure can be considered optimal if a (usually large) number of pattern elements is exactly zero. In the present paper, a class of oblique rotation procedures is proposed to rotate a pattern matrix such that it optimally resembles a matrix which has an exact simple pattern. It is demonstrated that this method can recover relatively complex simple structures where other well-known simple structure rotation techniques fail.
Multivariate Analysis with Linearizable Regressions
Authors: de Leeuw Jan
Published: January 2006

We study the class of multivariate distributions in which all bivariate regressions can be linearized by separate transformation of each of the variables. This class seems more realistic than the multivariate normal or the elliptical distributions, and at the same time its study allows us to combine the results from multivariate analysis with optimal scaling and classical multivariate analysis. In particular a two-stage procedure which first scales the variables optimally, and then fits a simultaneous equations model, is studied in detail and is shown to have some desirable properties.
The Area between Two Item Characteristic Curves
Authors: Raju Nambury S.
Published: January 2006

Formulas for computing the exact signed and unsigned areas between two item characteristic curves (ICCs) are presented. It is further shown that when thec parameters are unequal, the area between two ICCs is infinite. The significance of the exact area measures for item bias research is discussed.
Properties of the Maximum Likelihood Solution in Factor Analysis Regression
Authors: Browne Michael W.
Published: January 2006

Algebraic properties of the normal theory maximum likelihood solution in factor analysis regression are investigated. Two commonly employed measures of the within sample predictive accuracy of the factor analysis regression function are considered: the variance of the regression residuals and the squared correlation coefficient between the criterion variable and the regression function. It is shown that this within sample residual variance and within sample squared correlation may be obtained directly from the factor loading and unique variance estimates, without use of the original observations or the sample covariance matrix.
Imputation of Missing Categorical Data by Maximizing Internal Consistency
Authors: van Buuren Stef , van Rijckevorsel Jan L. A.
Published: January 2006

This paper suggests a method to supplant missing categorical data by “reasonable” replacements. These replacements will maximize the consistency of the completed data as measured by Guttman's squared correlation ratio. The text outlines a solution of the optimization problem, describes relationships with the relevant psychometric theory, and studies some properties of the method in detail. The main result is that the average correlation should be at least 0.50 before the method becomes practical. At that point, the technique gives reasonable results up to 10–15% missing data.
Factor Analysis for Clustered Observations
Authors: Longford N. T. , Muthén B. O.
Published: January 2006

Classical factor analysis assumes a random sample of vectors of observations. For clustered vectors of observations, such as data for students from colleges, or individuals within households, it may be necessary to consider different within-group and between-group factor structures. Such a two-level model for factor analysis is defined, and formulas for a scoring algorithm for estimation with this model are derived. A simple noniterative method based on a decomposition of the total sums of squares and crossproducts is discussed. This method provides a suitable starting solution for the iterative algorithm, but it is also a very good approximation to the maximum likelihood solution. Extensions for higher levels of nesting are indicated. With judicious application of quasi-Newton methods, the amount of computation involved in the scoring algorithm is moderate even for complex problems; in particular, no inversion of matrices with large dimensions is involved. The methods are illustrated on two examples.
Models for Measurement, Precision, and the Nondichotomization of Graded Responses
Authors: Andrich David
Published: January 2006

It is common in educational, psychological, and social measurement in general, to collect data in the form of graded responses and then to combine adjacent categories. It has been argued that because the division of the continuum into categories is arbitrary, any model used for analyzing graded responses should accommodate such action. Specifically, Jansen and Roskam (1986) enunciate a joining assumption which specifies that if two categories j and k are combined to form category h, then the probability of a response in h should equal the sum of the probabilities of responses in j and k. As a result, they question the use of the Rasch model for graded responses which explicitly prohibits the combining of categories after the data are collected except in more or less degenerate cases. However, the Rasch model is derived from requirements of invariance of comparisons of entities with respect to different instruments, which might include different partitions of the continuum, and is consistent with fundamental measurement. Therefore, there is a strong case that the mathematical implication of the Rasch model should be studied further in order to understand how and why it conflicts with the joining assumption. This paper pursues the mathematics of the Rasch model and establishes, through a special case when the sizes of the categories are equal and when the model is expressed in the multiplicative metric, that its probability distribution reflects the precision with which the data are collected, and that if a pair of categories is collapsed after the data are collected, it no longer reflects the original precision. As a consequence, and not because of a qualitative change in the variable, the joining assumption is destroyed when categories are combined. Implications of the choice between a model which satisfies the joining assumption or one which reflects on the precision of the data collection considered are discussed.