bluuebunny/crossref_metadata_2025 huggingface dataset:
Effects on Indscal of Non-Orthogonal Perceptions of Object Space Dimensions
Authors: MacCallum Robert C.
Published: January 2006

A general question is raised concerning the possible consequences of employing the very popular INDSCAL multidimensional scaling model in cases where the assumptions of that model may be violated. Simulated data are generated which violate the INDSCAL assumption that all individuals perceive the dimensions of the common object space to be orthogonal. INDSCAL solutions for these various sets of data are found to exhibit extremely high goodness of fit, but systematically distorted object spaces and negative subject weights. The author advises use of Tucker’s three-mode model for multidimensional scaling, which can account for non-orthogonal perceptions of the object space dimensions. It is shown that the INDSCAL model is a special case of the three-mode model.
A Probabilistic Model for Validation of Behavioral Hierarchies
Authors: Dayton C. Mitchell , Macready George B.
Published: January 2006

A probabilistic model for the validation of behavioral hierarchies is presented. Estimation is by means of iterative convergence to maximum likelihood estimates, and two approaches to assessing the fit of the model to sample data are discussed. The relation of this general probabilistic model to other more restricted models which have been presented previously is explored and three cases of the general model are applied to exemplary data.
A Further Note on Freeman’s Measure of Association
Authors: Freeman Linton C.
Published: January 2006

This note extends and elaborates Hubert’s attempt to provide an interpretation of Freeman’s measure of association, θ. The θ measure is used in a contingency table when observations are ordered on one variable and unordered on the other. No attempt is made explore the distribution of θ.
A Non-Graphical Method for Transforming an Arbitrary Factor Matrix into a Simple Structure Factor Matrix
Authors: Horst Paul
Published: January 2006

The most commonly used method of factoring a matrix of intercorrelations is the centroid method developed by L. L. Thurstone. It is, however, necessary to transform the centroid matrix of factor loadings into a simple structure matrix in order to facilitate the interpretation of the factor loadings. Current methods for effecting this transformation are chiefly graphical and require considerable experience and personal judgment. This paper presents a new method for transforming an arbitrary factor matrix into a simple structure matrix by methods almost completely objective. The theory underlying the method is developed and approximation procedures are derived. The method is applied to a matrix of factor loadings previously analyzed by Thurstone.
Image and Anti-Image Covariance Matrices from a Correlation Matrix that may be Singular
Authors: Kaiser Henry F.
Published: January 2006

Following the work of Tucker, Cooper, and Meredith, image and anti-image covariance matrices from a correlation matrix that may be singular are derived.
Determining the Number of Components from the Matrix of Partial Correlations
Authors: Velicer Wayne F.
Published: January 2006

A common problem for both principal component analysis and image component analysis is determining how many components to retain. A number of solutions have been proposed, none of which is totally satisfactory. An alternative solution which employs a matrix of partial correlations is considered. No components are extracted after the average squared partial correlation reaches a minimum. This approach gives an exact stopping point, has a direct operational interpretation, and can be applied to any type of component analysis. The method is most appropriate when component analysis is employed as an alternative to, or a first-stage solution for, factor analysis.
Extending Generalized Symmetric Means to Arbitrary Matrix Sampling Designs
Authors: Wellington Roger
Published: January 2006

Generalized symmetric means are redefined in a way which allows them to be calculated for any matrix sampling design. It is proved that these sample gsm's are unbiased estimates of the analogous population gsm's. Illustrative examples are given.
Re-Evaluation of Monte Carlo Studies in Nonmetric Multidimensional Scaling
Authors: Clark Andrew K.
Published: January 2006

Critical examination is made of the recent controversy over the value of Monte Carlo techniques in nonmetric multidimensional scaling procedures. The case is presented that the major relevance of Monte Carlo studies is not for the local minima problem but for the meaningfulness of the obtained solutions.
Some Simple Procedures for Handling Missing Data in Multivariate Analysis
Authors: Frane James W.
Published: January 2006

For analyses with missing data, some popular procedures delete cases with missing values, perform analysis with “missing value” correlation or covariance matrices, or estimate missing values by sample means. There are objections to each of these procedures. Several procedures are outlined here for replacing missing values by regression values obtained in various ways, and for adjusting coefficients (such as factor score coefficients) when data are missing. None of the procedures are complex or expensive.
A Test of the Hypothesis that Cronbach's Alpha Reliability Coefficient is the Same for Two Tests Administered to the Same Sample
Authors: Feldt Leonard S.
Published: January 2006

In measurement studies the researcher may wish to test the hypothesis that Cronbach’s alpha reliability coefficient is the same for two measurement procedures. A statistical test exists for independent samples of subjects. In this paper three procedures are developed for the situation in which the coefficients are determined from the same sample. All three procedures are computationally simple and give tight control of Type I error when the sample size is 50 or greater.
A New Solution to the Problem of Finding All Numerical Solutions to Ordered Metric Structures
Authors: Lehner Paul E. , Noma Elliot
Published: January 2006

A new algorithm is used to test and describe the set of all possible solutions for any linear model of an empirical ordering derived from techniques such as additive conjoint measurement, unfolding theory, general Fechnerian scaling and ordinal multiple regression. The algorithm is computationally faster and numerically superior to previous algorithms.
Discovery Algorithms for Hierarchical Relations
Authors: Price Lewis C. , Dayton C. Mitchell , Macready George B.
Published: January 2006

Two algorithms based on a latent class model are presented for discovering hierarchical relations that exist among a set of K dichotomous items. The two algorithms, stepwise forward selection and backward elimination, incorporate statistical criteria for selecting (or deleting) 0-1 response pattern vectors to form the subset of the total possible 2k vectors that uniquely describe the hierarchy. The performances of the algorithms are compared, using computer-constructed data, with those of three competing deterministic approaches based on ordering theory and the calculation of Phi/Phi-max coefficients. The discovery algorithms are also demonstrated on real data sets investigated in the literature.
A Definition for the Common-Factor Analysis Model and the Elimination of Problems of Factor Score Indeterminacy
Authors: Williams James S.
Published: January 2006

A factor analysis model consists of a random sequence of variates defined on a probability space and satisfying the usual descriptive equations of the common-factor analysis in which the common-factor scores are dimensionally independent. Necessary and sufficient conditions are given for a model to exist with essentially unique and hence determinate common factor scores. Parallel results are given for the existence of models with nonunique and hence indeterminate scores. It is then próved that two models cannot exist with essentially unique but different scores for the same common factors. The meaning and application of these results are discussed.
A Monte Carlo Study of Kruskal’s Variance based Measure on Stress
Authors: Levine David M.
Published: January 2006

Researchers in the past ten years have studied various parameters involved in nonmetric multidimensional scaling by utilizing Monte Carlo procedures. This paper develops stress distributions using Kruskal's second stress formula based upon a null hypothesis of equal likelihood in the ranking of a set of proximities. These distributions can serve to determine whether a set of data has other than random structure.
Robust Techniques for Testing Heterogeneity of Variance Effects in Factorial Designs
Authors: O’Brien Ralph G.
Published: January 2006

Several ways of using the traditional analysis of variance to test heterogeneity of spread in factorial designs with equal or unequal n are compared using both theoretical and Monte Carlo results. Two types of spread variables, (1) the jackknife pseudovalues of s2 and (2) the absolute deviations from the cell median, are shown to be robust and relatively powerful. These variables seem to be generally superior to the Z-variance and Box-Scheffé procedures.
Likelihood Methods for Testing Group Problem Solving Models with Censored Data
Authors: Regal Ronald R. , Larntz Kinley
Published: January 2006

Problem solving models relating individual and group solution times under time limit censoring are presented. Maximum likelihood estimates of parameters of the resulting censored distributions are derived and goodness of fit tests for the individual-group models are constructed. The methods are illustrated on data previously analyzed by Restle and Davis.
Multidimensional Scaling of Nominal Data: The Recovery of Metric Information with Alscal
Authors: Young Forrest W. , Null Cynthia H.
Published: January 2006

Multidimensional scaling has recently been enhanced so that data defined at only the nominal level of measurement can be analyzed. The efficacy of ALSCAL, an individual differences multidimensional scaling program which can analyze data defined at the nominal, ordinal, interval and ratio levels of measurement, is the subject of this paper. A Monte Carlo study is presented which indicates that (a) if we know the correct level of measurement then ALSCAL can be used to recover the metric information presumed to underlie the data; and that (b) if we do not know the correct level of measurement then ALSCAL can be used to determine the correct level and to recover the underlying metric structure. This study also indicates, however, that with nominal data ALSCAL is quite likely to obtain solutions which are not globally optimal, and that in these cases the recovery of metric structure is quite poor. A second study is presented which isolates the potential cause of these problems and forms the basis for a suggested modification of the ALSCAL algorithm which should reduce the frequency of locally optimal solutions.
A Theory of Consistency of Ordering Generalizable to Tailored Testing
Authors: Cliff Norman
Published: January 2006

Measures of consistency and completeness of order relations derived from test-type data are proposed. The measures are generalized to apply to incomplete data such as from tailored testing. The measures are based on consideration of the items-plus-persons by items-plus-persons matrix as an adjacency matrix in which a 1 means that the row element, whether item or person, dominated the column element. From this the number of item-item and person-person dominance relations can be derived. Indices of consistency are developed which compare the number of dominance relations in a matrix to the number that would occur if it were perfectly consistent and to the number in a random matrix; relations to other indices are noted.
The Equivalence of Three Statistical Packages for Performing Hierarchical Cluster Analysis
Authors: Blashfield Roger
Published: January 2006

Three different software programs which contain hierarchical agglomerative cluster analysis procedures were shown to generate different solutions on the same data set using apparently the same options. The basis for the differences in the solutions was the formulae used to calculate Euclidean distance. Users of statistical software were warned of terminological confusion concerning cluster analysis.
On Keats' Generalization of the Rasch Model
Authors: Colonius Hans
Published: January 2006

Parameter estimation for Keats generalization of the Rasch model that takes account of guessing behavior is investigated. It is shown that no minimal sufficient statistics for the ability parameters independent of the difficulty parameters exist. Thus Andersen's conditional inference technique for consistent estimation is not applicable to Keats' model. The notion of separability of the parameters is generalized.
Minimum Rank and Minimum Trace of Covariance Matrices
Authors: Della Riccia Giacomo , Shapiro Alexander
Published: January 2006

This paper considers some mathematical aspects of minimum trace factor analysis (MTFA). The uniqueness of an optimal point of MTFA is proved and necessary and sufficient conditions for a point x to be optimal are established. Finally, some results about the connection between MTFA and the classical minimum rank factor analysis will be presented.
Nonmetric Individual Differences Multidimensional Scaling: An Alternating Least Squares Method with Optimal Scaling Features
Authors: Takane Yoshio , Young Forrest W. , de Leeuw Jan
Published: January 2006

A new procedure is discussed which fits either the weighted or simple Euclidian model to data that may (a) be defined at either the nominal, ordinal, interval or ratio levels of measurement; (b) have missing observations; (c) be symmetric or asymmetric; (d) be conditional or unconditional; (e) be replicated or unreplicated; and (f) be continuous or discrete. Various special cases of the procedure include the most commonly used individual differences multidimensional scaling models, the familiar nonmetric multidimensional scaling model, and several other previously undiscussed variants.

The procedure optimizes the fit of the model directly to the data (not to scalar products determined from the data) by an alternating least squares procedure which is convergent, very quick, and relatively free from local minimum problems.

The procedure is evaluated via both Monte Carlo and empirical data. It is found to be robust in the face of measurement error, capable of recovering the true underlying configuration in the Monte Carlo situation, and capable of obtaining structures equivalent to those obtained by other less general procedures in the empirical situation.
Some Exact Conditional Tests of Independence for R × C Cross-Classification Tables
Authors: Agresti Alan , Wackerly Dennis
Published: January 2006

Exact conditional tests of independence in cross-classification tables are formulated based on the χ2 statistic and statistics with stronger operational interpretations, such as some nominal and ordinal measures of association. Guidelines for the table dimensions and sample sizes for which the tests are economically implemented on a computer are given. Some selected sample sizes and marginal distributions are used in a numerical comparison between the significance levels of the approximate and exact conditional tests based on the χ2 statistic.
The Relationship between External Variables and Common Factors
Authors: Steiger James H.
Published: January 2006

A theorem is presented which gives the range of possible correlations between a common factor and an external variable (i.e., a variable not included in the test battery factor analyzed). Analogous expressions for component (and regression component) theory are also derived. Some situations involving external correlations are then discussed which dramatize the theoretical differences between components and common factors.
A Method for Simulating Non-Normal Distributions
Authors: Fleishman Allen I.
Published: January 2006

A method of introducing a controlled degree of skew and kurtosis for Monte Carlo studies was derived. The form of such a transformation on normal deviates [X ~ N(0, 1)] is Y = a + bX + cX2 + dX3. Analytic and empirical validation of the method is demonstrated.
Contributions to Factor Analysis of Dichotomous Variables
Authors: Muthén Bengt
Published: January 2006

A new method is proposed for the factor analysis of dichotomous variables. Similar to the method of Christoffersson this uses information from the first and second order proportions to fit a multiple factor model. Through a transformation into a new set of sample characteristics, the estimation is considerably simplified. A generalized least-squares estimator is proposed, which asymptotically is as efficient as the corresponding estimator of Christoffersson, but which demands less computing time.
Scale Freeness in Factor Analysis
Authors: Swaminathan Hariharan , Algina James
Published: January 2006

The notion of scale freeness does not seem to have been well understood in the factor analytic literature. It has been believed that if the loss function that is minimized to obtain estimates of the parameters in the factor model is scale invariant, then the estimates are scale free. It is shown that scale invariance of the loss function is neither a necessary nor a sufficient condition for scale freeness. A theorem that ensures scale freeness in the orthogonal factor model is given in this paper.
Canonical Analysis of Longitudinal and Repeated Measures Data with Stationary Weights
Authors: Meredith William , Tisak John
Published: January 2006

When measuring the same variables on different “occasions”, two procedures for canonical analysis with stationary compositing weights are developed. The first, SUMCOV, maximizes the sum of the covariances of the canonical variates subject to norming constraints. The second, COLLIN, maximizes the largest root of the covariances of the canonical variates subject to norming constraints. A characterization theorem establishes a model building approach. Both methods are extended to allow for Cohort Sequential Designs. Finally a numerical illustration utilizing Nesselroade and Baltes data is presented.
EM Algorithms for ML Factor Analysis
Authors: Rubin Donald B. , Thayer Dorothy T.
Published: January 2006

The details of EM algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models. The algorithm is essentially the same for both cases and involves only simple least squares regression operations; the largest matrix inversion required is for a q × q symmetric matrix where q is the matrix of factors. The example that is used demonstrates that the likelihood for the factor analysis model may have multiple modes that are not simply rotations of each other; such behavior should concern users of maximum likelihood factor analysis and certainly should cast doubt on the general utility of second derivatives of the log likelihood as measures of precision of estimation.
On the Use of Bisection Procedures in Animal Psychophysical Scaling
Authors: Raslear Thomas G.
Published: January 2006

The ability of bisection procedures to specify the form of the psychophysical scale depends upon the precision of the technique. It is demonstrated that the precision of bisection techniques is a function of the stimulus interval bisected. Consequently, the choice of stimuli in a bisection experiment may predispose the ability of the experiment to distinguish between alternative psychophysical scales. The testing of interval scale properties of derived scales and the assessment of context effects in bisection experiments was also discussed.
On Testing the Equality of Proportions in the Paired Case with Incomplete Data
Authors: Ekbohm Gunnar
Published: January 2006

The problem of testing two correlated proportions with incomplete data is considered by means of Monte Carlo simulations studies. A test proposed in this paper, which can be regarded as a generalization of McNemar’s test, is recommended in all cases with incomplete data and not too small samples.
Monotone Spline Transformations for Dimension Reduction
Authors: Winsberg S. , Ramsay J. O.
Published: January 2006

Consider a set of data consisting of measurements of n objects with respect to p variables displayed in an n × p matrix. A monotone transformation of the values in each column, represented as a linear combination of integrated basis splines, is assumed determined by a linear combination of a new set of values characterizing each row object. Two different models are used: one, an Eckart-Young decomposition model, and the other, a multivariate normal model. Examples for artificial and real data are presented. The results indicate that both methods are helpful in choosing dimensionality and that the Eckart-Young model is also helpful in displaying the relationships among the objects and the variables. Also, results suggest that the resulting transformations are themselves illuminating.
Denoting the Base-Free Measure of Change
Authors: Messick Samuel
Published: January 2006

Bond criticized the base-free measure of change proposed by Tucker, Damarin, and Messick by pointing to an incorrect derivation which is here viewed instead as a correct derivation entailing an inadequately specified tacit assumption. Bond's revision leads to estimates of the correlation between initial position and change which are negatively biased by correlated errors, whereas the original approach, with the tacit assumption properly denoted, leads to unbiased values.
An Examination of the Effect of Six Types of Error Perturbation on Fifteen Clustering Algorithms
Authors: Milligan Glenn W.
Published: January 2006

An evaluation of several clustering methods was conducted. Artificial clusters which exhibited the properties of internal cohesion and external isolation were constructed. The true cluster structure was subsequently hidden by six types of error-perturbation. The results indicated that the hierarchical methods were differentially sensitive to the type of error perturbation. In addition, generally poor recovery performance was obtained when random seed points were used to start the K-means algorithms. However, two alternative starting procedures for the nonhierarchical methods produced greatly enhanced cluster recovery and were found to be robust with respect to all of the types of error examined.
Approximate Confidence Intervals for a Robust Scale Parameter
Authors: Budescu David V.
Published: January 2006

A recent paper by Wainer and Thissen has renewed the interest in Gini’s mean difference, G, by pointing out its robust characteristics. This note presents distribution-free asymptotic confidence intervals for its population value, γ, in the one sample case and for the difference Δ = (γ1 − γ2) in the two sample situations. Both procedures are based on a technique of jackknifing U-statistics developed by Arvesen.
Multidimensional Successive Categories Scaling: A Maximum Likelihood Method
Authors: Takane Yoshio
Published: January 2006

A single-step maximum likelihood estimation procedure is developed for multidimensional scaling of dissimilarity data measured on rating scales. The procedure can fit the euclidian distance model to the data under various assumptions about category widths and under two distributional assumptions. The scoring algorithm for parameter estimation has been developed and implemented in the form of a computer program. Practical uses of the method are demonstrated with an emphasis on various advantages of the method as a statistical procedure.
A Note on the Uniqueness of Minimum Rank Solutions in Factor Analysis
Authors: Williams James S.
Published: January 2006

A revised theorem is presented concerning uniqueness of minimum rank solutions in common factor analysis.
Three Technical Word Processors
Authors: Cudeck Robert , McGuire Dennis P.
Published: January 2006

If Gutenberg had been a psychometrician, the invention of movable type would have occured much later than the year 1456. As anyone who has ever approached the problem knows, the requirements for automating technical writing are much greater than those for standard prose. A writer of technical documents needs all standard Roman letters, plus the full array of Greek characters, mathematical symbols, and the ability to freely half space for superscripts and subscripts. It is not known when the first scientific or technical manuscript was produced with movable type, but one can be sure that it came decades after Gutenberg's Bible.

In our time it has taken substantially longer for word processing software that is used in conjunction with a microcomputer to be developed for the technical writer than for the writer of standard prose.
Repeated Measurements Analysis of Variance when the Correlations have a Certain Pattern
Authors: Wallenstein Sylvan , Fleiss Joseph L.
Published: January 2006

Consider a repeated measurements study in which a single observation is taken at each of t(t > 2) equally spaced time points for each of n subjects. This paper uses a result of Box to find the appropriate multiplicative correction term for the degrees of freedom in the analysis of variance table for the case when there is equal variability per time point, and when the correlation between observations u time units apart is equal to ρu. For large values of t, the multiplicative correction has a lower bound approximately equal to 2.5/(t − 1).
Scaling a Conditional Proximity Matrix to Symmetry
Authors: Levin Joseph , Brown Morton
Published: January 2006

Two least squares procedures for symmetrization of a conditional proximity matrix are derived. The solutions provide multiplicative constants for scaling the rows or columns of the matrix to maximize symmetry. It is suggested that the symmetrization is applicable for the elimination of bias effects like response bias, or constraints on the marginal frequencies imposed by the experimental design, as in confusion matrices.
Bayes Modal Estimation in Item Response Models
Authors: Mislevy Robert J.
Published: January 2006

This article describes a Bayesian framework for estimation in item response models, with two-stage prior distributions on both item and examinee populations. Strategies for point and interval estimation are discussed, and a general procedure based on the EM algorithm is presented. Details are given for implementation under one-, two-, and three-parameter binary logistic IRT models. Novel features include minimally restrictive assumptions about examinee distributions and the exploitation of dependence among item parameters in a population of interest. Improved estimation in a moderately small sample is demonstrated with simulated data.
A Gauss-Newton Algorithm for Exploratory Factor Analysis
Authors: Jennrich Robert I.
Published: January 2006

It is shown that the scoring algorithm for maximum likelihood estimation in exploratory factor analysis can be developed in a way that is many times more efficient than a direct development based on information matrices and score vectors. The algorithm offers a simple alternative to current algorithms and when used in one-step mode provides the simplest and fastest method presently available for moving from consistent to efficient estimates. Perhaps of greater importance is its potential for extension to the confirmatory model. The algorithm is developed as a Gauss-Newton algorithm to facilitate its application to generalized least squares and to maximum likelihood estimation.
Structural Modeling and Psychometrika: An Historical Perspective on Growth and Achievements
Authors: Bentler P. M.
Published: January 2006

The field of linear structural equation modeling with continuous variables is reviewed. Trends in psychometric theory and data analysis across the five decades of publication of Psychometrika are discussed, especially the clarification of concepts of population and sample, explication of the parametric structure of models, delineation of concepts of exploratory and confirmatory data analysis, expansion of statistical theory in psychometrics, estimation via optimization of an explicit objective function, and implementation of general function minimization methods. Developments in the ideas of factor analysis, latent variables, as well as structural and causal modeling are noted. Some major conceptual achievements involving general covariance structure representations, multiple population models, and moment structures are reviewed. The major statistical achievements of normal theory generalized least squares estimation, elliptical and distribution-free estimation, and higher-moment estimation are discussed. Computer programs that implement some of the theoretical developments are described.
Estimation for Structural Equation Models with Missing Data
Authors: Lee Sik-Yum
Published: January 2006

A direct method in handling incomplete data in general covariance structural models is investigated. Asymptotic statistical properties of the generalized least squares method are developed. It is shown that this approach has very close relationships with the maximum likelihood approach. Iterative procedures for obtaining the generalized least squares estimates, the maximum likelihood estimates, as well as their standard error estimates are derived. Computer programs for the confirmatory factor analysis model are implemented. A longitudinal type data set is used as an example to illustrate the results.
A Note on Structural Models for the Circumplex
Authors: Cudeck Robert
Published: January 2006

Jöreskog (1974) developed a latent variable model for the covariance structure of the circumplex which, under certain conditions, includes a model for a patterned correlation matrix (Browne, 1977). This model is of limited usefulness, however, in that it employs a known matrix that is rank deficient for many problems. Furthermore, the model is inappropriate for the circumplex which contains negative covariances. This paper presents alternative models for the perfect circumplex and quasi-circumplex that avoids these difficulties, and that includes the important model for a patterned correlation circumplex matrix. Two numerical examples are provided.
An Approximation of the K out N Reliability of a Test, and a Scoring Procedure for Determining which Items an Examinee Knows
Authors: Wilcox Rand R.
Published: January 2006

Consider any scoring procedure for determining whether an examinee knows the answer to a test item. Let xi = 1 if a correct decision is made about whether the examinee knows the i th item; otherwise xi = 0. The k out of n reliability of a test is ρk = Pr (Σxi ≥k). That is, ρk is the probability of making at least k correct decisions for a typical (randomly sampled) examinee. This paper proposes an approximation of ρk that can be estimated with an answer-until-correct test. The paper also suggests a scoring procedure that might be used when ρk is judged to be too small under a conventional scoring rule where it is decided an examinee knows if and only if the correct response is given.
A Comparison of Factor Analysis Programs in SPSS, BMDP, and SAS
Authors: MacCallum Robert
Published: January 2006

Factor analysis programs in SAS, BMDP, and SPSS are discussed and compared in terms of documentation, methods and options available, internal logic, computational accuracy, and results provided. Some problems with respect to logic and output are described. Based on these comparisons, recommendations are offered which include a clear overall preference for SAS, and advice against general use of SPSS for factor analysis.
Redundancy Analysis an Alternative for Canonical Correlation Analysis
Authors: van den Wollenberg Arnold L.
Published: January 2006

A component method is presented maximizing Stewart and Love's redundancy index. Relationships with multiple correlation and principal component analysis are pointed out and a rotational procedure for obtaining bi-orthogonal variates is given. An elaborate example comparing canonical correlation analysis and redundancy analysis on artificial data is presented.
Extended Similarity Trees
Authors: Corter James E. , Tversky Amos
Published: January 2006

Proximity data can be represented by an extended tree, which generalizes traditional trees by including marked segments that correspond to overlapping clusters. An extended tree is a graphical representation of the distinctive features model. A computer program (EXTREE) that constructs extended trees is described and applied to several sets of conceptual and perceptual proximity data.
Nominal Scale Agreement Among Observers
Authors: Schouten Hubert J. A.
Published: January 2006

Experiments are considered where each of a sample of subjects is assigned to one of C categories separately by each of a fixed or varying group of observers. Building on earlier publications, general procedures are proposed to analyze agreements and disagreements among observers. In the case of a varying group of observers, it is shown that it is not necessary to demand a constant number of observers per subject. In the case of a fixed group of observers, the problem of missing data is considered.

The procedures are illustrated within the context of two clinical diagnosis examples. In the first example it is investigated which categories are relatively hard to distinguish from one another; a new theorem is applied that shows a useful property of the statistic kappa. In the second example it is investigated if a subgroup of observers can be found with a significantly higher degree of interobserver agreement.
On the Reliability of the Extreme Score
Authors: Huynh Huynh
Published: January 2006

Under the assumption of normality, a formula is derived for the reliability of the maximum score. It is shown that the maximum score is more reliable than each of the single observations, but less reliable than their composite score.
A Note on Roy's Largest Root
Authors: Kuhfeld Warren F.
Published: January 2006

The name “Roy's largest root” and similar names are used in practice to label two different but functionally related statistics—one proportional to anF, and the other, a squared canonical correlation. This note presents the logic that leads to the two formulations, states which statistic some popular statistical packages use, and shows the possible source of this inconsistency in the original work of Roy (1953) and Heck (1960).
The Joint Analysis of Direct Ratings, Pairwise Preferences, and Dissimilarities
Authors: Ramsay J. O.
Published: January 2006

In studies involving judgments of similarity or dissimilarity, a variety of other variables may also be measured. Examples might be direct ratings of the stimuli, pairwise preference judgments, and physical measurements of the stimuli with respect to various properties. In such cases, there are important advantages to joint analyses of the dissimilarity and collateral variables. A variety of models are described for relating these and algorithms described for fitting these to data. A number of hypothesis tests are developed and an example offered.
Note on the Squared Multiple Correlation as a Lower Bound to Communality
Authors: Jackson David J. , Tweed Dan L.
Published: January 2006

It is demonstrated that the squared multiple correlation of a variable with the remaining variables in a set of variables is a function of the communalities and the squared canonical correlations between the observed variables and common factors. This equation is shown to imply a strict inequality between the squared multiple correlation and communality.
Applications of Combinatorial Programming to Data Analysis: The Traveling Salesman and Related Problems
Authors: Hubert Lawrence J. , Baker Frank B.
Published: January 2006

The “Traveling Salesman” and similar combinatorial programming tasks encountered in operations research are discussed as possible data analysis models in psychology, for example, in developmental scaling, Guttman scaling, profile smoothing, and data array clustering. In addition, a short overview of the various computational approaches from this area of combinatorial optimization is included.
Binary Action Based Estimation of Propensities
Authors: Duncan George T.
Published: January 2006

An observer is to make inference statements about a quantity p, called a propensity and bounded between 0 and 1, based on the observation that p does or does not exceed a constant c. The propensity p may have an interpretation as a proportion, as a long-run relative frequency, or as a personal probability held by some subject. Applications in medicine, engineering, political science, and, most especially, human decision making are indicated. Bayes solutions for the observer are obtained based on prior distributions in the mixture of beta distribution family; these are then specialized to power-function prior distributions. Inference about log p and log odds is considered. Multiple-action problems are considered in which the focus of inference shifts to the process generating the propensities p, both in the case of a process parameter π known to the subject and unknown. Empirical Bayes techniques are developed for observer inference about c when π is known to the subject. A Bayes rule, a minimax rule and a beta-minimax rule are constructed for the subject when he is uncertain about π.
Monte Carlo Studies in Nonmetric Scaling
Authors: Spence Ian , Young Forrest W.
Published: January 2006

In response to Arabie several random ranking studies are compared and discussed. Differences are typically very small, however it is noted that those studies which used arbitrary configurations tend to produce slightly higher stress values. The choice of starting configuration is discussed and we suggest that the use of a principal components decomposition of the doubly centered matrix of dissimilarities, or some transformation thereof, will yield an initial configuration which is superior to a randomly chosen one.
A Note on Parameter Estimation for Lazarsfeld's Latent Class Analysis
Authors: Formann Anton K.
Published: January 2006

As the literature indicates, no method is presently available which takes explicitly into account that the parameters of Lazarsfeld's latent class analysis are defined as probabilities and are therefore restricted to the interval [0, 1]. In the present paper an appropriate transform on the parameters is performed in order to satisfy this constraint, and the estimation of the transformed parameters according to the maximum likelihood principle is outlined. In the sequel, a numerical example is given for which the basis solution and the usual maximum likelihood method failed. The different results are compared and the advantages of the proposed method discussed.
A Note on Analyzing Ordered Alternatives
Authors: Marcus Ruth
Published: January 2006

A general method of devising stepwise multiple testing procedures with fixed experimentwise error is applied to the problem of non-parametric randomized block design with ordered alternatives. In addition, the method is applied to other models with ordered alternatives.
Three-Way Metric Unfolding Via Alternating Weighted Least Squares
Authors: DeSarbo Wayne S. , Douglas Carroll J.
Published: January 2006

Three-way unfolding was developed by DeSarbo (1978) and reported in DeSarbo and Carroll (1980, 1981) as a new model to accommodate the analysis of two-mode three-way data (e.g., nonsymmetric proximities for stimulus objects collected over time) and three-mode, three-way data (e.g., subjects rendering preference judgments for various stimuli in different usage occasions or situations). This paper presents a revised objective function and new algorithm which attempt to prevent the common type of degenerate solutions encountered in typical unfolding analysis. We begin with an introduction of the problem and a review of three-way unfolding. The three-way unfolding model, weighted objective function, and new algorithm are presented. Monte Carlo work via a fractional factorial experimental design is described investigating the effect of several data and model factors on overall algorithm performance. Finally, three applications of the methodology are reported illustrating the flexibility and robustness of the procedure.
On more Powerful Tests of Judge Agreement with a known Standard
Authors: Robinson David H.
Published: January 2006

To establish the existence of his abilities, a judge is given the task of classifying each of N= rs subjects into one of r known categories, each containing s of the subjects. An incomplete design is proposed whereby the judge is presented with b groups, each one containing n= rs/b<r subjects. The n different categories corresponding to members of the group are known. Using the total number of correct classifications, this method of grouping is compared to that in which the group size is equal to the number of categories. The incomplete grouping is shown to yield a more powerful test for discriminating between the null hypothesis that the judge is guessing the classifications and the alternative hypothesis that he has some definite abilities. The incomplete design is found to be most effective (powerful) when the number of subjects in a group is limited to two or three.
Correspondence Analysis of Incomplete Contingency Tables
Authors: de Leeuw Jan , van der Heijden Peter G. M.
Published: January 2006

Correspondence analysis can be described as a technique which decomposes the departure from independence in a two-way contingency table. In this paper a form of correspondence analysis is proposed which decomposes the departure from the quasi-independence model. This form seems to be a good alternative to ordinary correspondence analysis in cases where the use of the latter is either impossible or not recommended, for example, in case of missing data or structural zeros. It is shown that Nora's reconstitution of order zero, a procedure well-known in the French literature, is formally identical to our correspondence analysis of incomplete tables. Therefore, reconstitution of order zero can also be interpreted as providing a decomposition of the residuals from the quasi-independence model. Furthermore, correspondence analysis of incomplete tables can be performed using existing programs for ordinary correspondence analysis.
Exploratory Analysis of Contingency Tables by Loglinear Formulation and Generalizations of Correspondence Analysis
Authors: Choulakian Vartan
Published: January 2006

Goodman's (1979, 1981, 1985) loglinear formulation for bi-way contingency tables is extended to tables with or without missing cells and is used for exploratory purposes. A similar formulation is done for three-way tables and generalizations of correspondence analysis are deduced. A generalized version of Goodman's algorithm, based on Newton's elementary unidimensional method is used to estimate the scores in all cases.
Weighted Minimum Trace Factor Analysis
Authors: Shapiro Alexander
Published: January 2006

In the last decade several authors discussed the so-called minimum trace factor analysis (MTFA), which provides the greatest lower bound (g.l.b.) to reliability. However, the MTFA fails to be scale free. In this paper we propose to solve the scale problem by maximization of the g.l.b. as the function of weights. Closely related to the primal problem of the g.l.b. maximization is the dual problem. We investigate the primal and dual problems utilizing convex analysis techniques. The asymptotic distribution of the maximal g.l.b. is obtained provided the population covariance matrix satisfies sone uniqueness and regularity assumptions. Finally we outline computational algorithms and consider numerical examples.
An Interactive Preference Ordering Model and its Monte Carlo Evaluation
Authors: Reynolds Thomas J. , Cliff Norman
Published: January 2006

A computer-interactive preference ordering procedure that is based on assumed transitivity of relations is described. The procedure includes features that are designed to make it robust in the presence of inconsistency. With errorless data, the method will find the underlying order in close to log2n! comparisons. Two simulation studies are described where the responses are assumed to follow the Thurstone Case V model. It was found that the method produces orders that are more valid than does a considerably larger preselected subset of pairs.
Sample Size Requirements for Estimating Pearson, Kendall and Spearman Correlations
Authors: Bonett Douglas G. , Wright Thomas A.
Published: January 2006

Interval estimates of the Pearson, Kendall tau-a and Spearman correlations are reviewed and an improved standard error for the Spearman correlation is proposed. The sample size required to yield a confidence interval having the desired width is examined. A two-stage approximation to the sample size requirement is shown to give accurate results.
Exact Person Fit Indexes for the Rasch Model for Arbitrary Alternatives
Authors: Poncny Ivo
Published: January 2006

A new algorithm for obtaining exact person fit indexes for the Rasch model is introduced which realizes most powerful tests for a very general family of alternative hypotheses, including tests concerning DIF as well as model-deviating item correlations. The method is also used as a goodness-of-fit test for whole data sets where the item parameters are assumed to be known. For tests with 30 items at most, exact values are obtained, for longer tests a Monte Carlo-algorithm is proposed. Simulated examples and an empirical investigation demonstrate test power and applicability to item elimination.
Robust Mean and Covariance Structure Analysis Through Iteratively Reweighted Least Squares
Authors: Yuan Ke-Hai , Bentler Peter M.
Published: January 2006

Robust schemes in regression are adapted to mean and covariance structure analysis, providing an iteratively reweighted least squares approach to robust structural equation modeling. Each case is properly weighted according to its distance, based on first and second order moments, from the structural model. A simple weighting function is adopted because of its flexibility with changing dimensions. The weight matrix is obtained from an adaptive way of using residuals. Test statistic and standard error estimators are given, based on iteratively reweighted least squares. The method reduces to a standard distribution-free methodology if all cases are equally weighted. Examples demonstrate the value of the robust procedure.
On the Relations Among Regular, Equal Unique Variances, and Image Factor Analysis Models
Authors: Hayashi Kentaro , Bentler Peter M.
Published: January 2006

We investigate under what conditions the matrix of factor loadings from the factor analysis model with equal unique variances will give a good approximation to the matrix of factor loadings from the regular factor analysis model. We show that the two models will give similar matrices of factor loadings if Schneeweiss' condition, that the difference between the largest and the smallest value of unique variances is small relative to the sizes of the column sums of squared factor loadings, holds. Furthermore, we generalize our results and discus the conditions under which the matrix of factor loadings from the regular factor analysis model will be well approximated by the matrix of factor loadings from Jöreskog's image factor analysis model. Especially, we discuss Guttman's condition (i.e., the number of variables increases without limit) for the two models to agree, in relation with the condition we have shown, and conclude that Schneeweiss' condition is a generalization of Guttman's condition. Some implications for practice are discussed.
Adjusting for Information Inflation Due to Local Dependency in Moderately Large Item Clusters
Authors: IP Edward Hak-sing
Published: January 2006

When multiple items are clustered around a reading passage, the local independence assumption in item response theory is often violated. The amount of information contained in an item cluster is usually overestimated if violation of local independence is ignored and items are treated as locally independent when in fact they are not. In this article we provide a general method that adjusts for the inflation of information associated with a test containing item clusters. A computational scheme was presented for the evaluation of the factor of adjustment for clusters in the restrictive case of two items per cluster, and the general case of more than two items per cluster. The methodology was motivated by a study of the NAEP Reading Assessment. We present a simulated study along with an analysis of a NAEP data set.