bluuebunny/crossref_metadata_2025 huggingface dataset:
Estimating True Score in the Compound Binomial Error Model
Authors: Wilcox Rand R.
Published: January 2006

Several procedures have been proposed in the statistical literature for estimating simultaneously the mean of each of k binomial populations. In terms of mental test theory, however, it is not clear that these procedures should be used when an item sampling model applies since the binomial error model is usually viewed as an oversimplification of the “true” situation. In this study we compare empirically several of these estimation techniques. Particular attention is given to situations where observations are generated according to a two-term approximation to the compound binomial distribution.
Approximate Interval Estimation for a Certain Intraclass Correlation Coefficient
Authors: Fleiss Joseph L. , Shrout Patrick E.
Published: January 2006

When the raters participating in a reliability study are a random sample from a larger population of raters, inferences about the intraclass correlation coefficient must be based on the three mean squares from the analysis of variance table summarizing the results: between subjects, between raters, and error. An approximate confidence interval for the parameter is presented as a function of these three mean squares.
Optimal Scaling of Paired Comparison and Rank Order Data: An Alternative to Guttman's Formulation
Authors: Nishisato Shizuhiko
Published: January 2006

A formulation, which is different from Guttman's is presented. The two formulations are both called the optimal scaling approach, and are proven to provide identical scale values. The proposed formulation has at least two advantages over Guttman's. Namely, (i) the former serves to clarify close relations of the optimal scaling approach to those of Slater and the vector model of preferential choice, and (ii) in addition to the stimulus scale values, it provides scores for the subjects, which indicate the degrees of response consistency (transitivity), relative to the optimum solution. The method is assumption-free and capable of multidimensional analysis.
Procrustean Analysis of Matrices with Different Row Order
Authors: Borg Ingwer
Published: January 2006

Procrustean analysis is extended here to the case where matrices have different row order. Using a definition system in the sense of facet theory, fitting transformations are determined for the set of centroids that represent common substantive equivalence classes of all or some matrices. The resulting operators are used to transform the original matrices. An index, Δ, which is consistent with this approach expresses the goodness of fit.
The Principal Components of Mixed Measurement Level Multivariate Data: An Alternating Least Squares Method with Optimal Scaling Features
Authors: Young Forrest W. , Takane Yoshio , de Leeuw Jan
Published: January 2006

A method is discussed which extends principal components analysis to the situation where the variables may be measured at a variety of scale levels (nominal, ordinal or interval), and where they may be either continuous or discrete. There are no restrictions on the mix of measurement characteristics and there may be any pattern of missing observations. The method scales the observations on each variable within the restrictions imposed by the variable's measurement characteristics, so that the deviation from the principal components model for a specified number of components is minimized in the least squares sense. An alternating least squares algorithm is discussed. An illustrative example is given.
Note on the Squared Multiple Correlation as a Lower Bound to Communality
Authors: Harris Chester W.
Published: January 2006

A simple proof that the squared multiple correlation of a variable with the remaining variables in the set of variables is a lower bound to the communality of that variable is presented.
Two Logit Models for External Analysis of Preferences
Authors: Cooper Lee G. , Nakanishi Masao
Published: January 2006

A logit vector model and a logit ideal point model are presented for external analysis of paired comparison preference judgments aggregated over a homogeneous group. The logit vector model is hierarchically nested within the logit ideal point model so that statistical tests are available to distinguish between these two models. Generalized least squares estimation procedures are developed to account for heteroscedastic sampling error variances and specification error variances. Two numerical illustrations deal with judgments concerning employee compensation plans and preferences for salt and sugar in the brine of canned green beans.
Computational Aspects of the Greatest Lower Bound to the Reliability and Constrained Minimum Trace Factor Analysis
Authors: ten Berge Jos M. F. , Snijders Tom A. B. , Zegers Frits E.
Published: January 2006

In the last decade several algorithms for computing the greatest lower bound to reliability or the constrained minimum-trace communality solution in factor analysis have been developed. In this paper convergence properties of these methods are examined. Instead of using Lagrange multipliers a new theorem is applied that gives a sufficient condition for a symmetric matrix to be Gramian. Whereas computational pitfalls for two methods suggested by Woodhouse and Jackson can be constructed it is shown that a slightly modified version of one method suggested by Bentler and Woodward can safely be applied to any set of data. A uniqueness proof for the solution desired is offered.
Linear Structural Equations with Latent Variables
Authors: Bentler P. M. , Weeks David G.
Published: January 2006

An interdependent multivariate linear relations model based on manifest, measured variables as well as unmeasured and unmeasurable latent variables is developed. The latent variables include primary or residual common factors of any order as well as unique factors. The model has a simpler parametric structure than previous models, but it is designed to accommodate a wider range of applications via its structural equations, mean structure, covariance structure, and constraints on parameters. The parameters of the model may be estimated by gradient and quasi-Newton methods, or a Gauss-Newton algorithm that obtains least-squares, generalized least-squares, or maximum likelihood estimates. Large sample standard errors and goodness of fit tests are provided. The approach is illustrated by a test theory model and a longitudinal study of intelligence.
A Technique for the Nonmetric Analysis of Paired Comparisons of Psychological Intervals
Authors: Schneider Bruce
Published: January 2006

A nonmetric coordinate adjustment technique is developed which determines scale values for objects whose interobject intervals (differences in subjective value) have been directly compared. In Monte Carlo simulations, the degree of metric determinancy of the scale values is shown to be quite high even when the amount of error is relatively high. This robustness under high-error conditions permitted the analysis of individual subject data in experiments on the direct comparison of loudness differences and loudness ratios where only one judgment per interval comparison was obtained per subject.
Calculation of the Tetrachoric Correlation Coefficient
Authors: Divgi D. R.
Published: January 2006

A new subroutine has been developed for calculating the terachoric correlation coefficient. Recent advances in computing inverse normal and bivariate normal distributions have been utilized. The iterative procedure is started with an approximation with an error less than ±.0135.
Axiomatic and Numerical Conjoint Measurement: An Evaluation of Diagnostic Efficacy
Authors: Emery Douglas R. , Barron F. Hutton
Published: January 2006

Synthetic data are used to examine how well axiomatic and numerical conjoint measurement methods, individually and comparatively, recover simple polynomial generators in three dimensions. The study illustrates extensions of numerical conjoint measurement (NCM) to identify and model distributive and dual-distributive, in addition to the usual additive, data structures. It was found that while minimum STRESS was the criterion of fit, another statistic, predictive capability, provided a better diagnosis of the known generating model. That NCM methods were able to better identify generating models conflicts with Krantz and Tversky's assertion that, in general, the direct axiom tests provide a more powerful diagnostic test between alternative composition rules than does evaluation of numerical correspondence. For all methods, dual-distributive models are most difficult to recover, while consistent with past studies, the additive model is the most robust of the fitted models.
Bayesian Estimation of Item Response Curves
Authors: Tsutakawa Robert K. , Lin Hsin Ying
Published: January 2006

Item response curves for a set of binary responses are studied from a Bayesian viewpoint of estimating the item parameters. For the two-parameter logistic model with normally distributed ability, restricted bivariate beta priors are used to illustrate the computation of the posterior mode via the EM algorithm. The procedure is illustrated by data from a mathematics test.
Latent Trait Models and Dichotomization of Graded Responses
Authors: Jansen Paul G. W. , Roskam Edward E.
Published: January 2006

This paper discusses the compatibility of the polychotomous Rasch model with dichotomization of the response continuum. It is argued that in the case of graded responses, the response categories presented to the subject are essentially an arbitrary polychotomization of the response continuum, ranging for example from total rejection or disagreement to total acceptance or agreement of an item or statement. Because of this arbitrariness, the measurement outcome should be independent of the specific polychotomization applied, for example, presenting a specific multicategory response format should not affect the measurement outcome. When such is the case, the original polychotomous model is called “compatible” with dichotomization.

A distinction is made between polychotomization or dichotomization “before the fact,” that is, in constructing the response format, and polycho- or dichotomization “after the fact,” for example in dichotomizing existing graded response data.

It is shown that, at least in case of dichotomization after-the-fact, the polychotomous Rasch model is not compatible with dichotomization, unless a rather special condition of the model parameters is met. Insofar as it may be argued that dichotomization before the fact is not essentially different from dichotomization after the fact, the value of the unidimensional polychotomous Rasch model is consequently questionable. The impact of our conclusion on related models is also discussed.
On Scaling Models Applied to Data from Several Groups
Authors: Clogg Clifford C. , Goodman Leo A.
Published: January 2006

Statistical methods are presented to facilitate a more complete analysis of results obtained when a scaling model is applied to data from two or more groups. These methods can be used to (a) compare the corresponding estimated latent distributions obtained using the scaling model applied to the different groups, (b) compare the corresponding estimated item reliabilities (or item response error rates) for the different groups, and (c) test whether the scaling model applied to the several groups can be replaced by a more parsimonious scaling model that includes various homogeneity constraints (i.e., constraints that describe which parameters in the model are the same for the several groups). Various kinds of scaling models are considered here in the multiple-group context.
A PROC MATRIX Program for Preference-Dissimilarity Multidimensional Scaling
Authors: Ramsey J. O.
Published: January 2006

A computer program can be a means of communicating the structure of an algorithm as well as a tool for data analysis. From this perspective high-level matrix-oriented languages like PROC MATRIX in the SAS system are especially useful because of their readability and compactness. An algorithm for the joint analysis of dissimilarity and preference data using maximum likelihood estimation is presented in PROC MATRIX code.
Indclus: An Individual differences Generalization of the Adclus Model and the Mapclus Algorithm
Authors: Carroll J. Douglas , Arabie Phipps
Published: January 2006

We present a new model and associated algorithm, INDCLUS, that generalizes the Shepard-Arabie ADCLUS (ADditive CLUStering) model and the MAPCLUS algorithm, so as to represent in a clustering solution individual differences among subjects or other sources of data. Like MAPCLUS, the INDCLUS generalization utilizes an alternating least squares method combined with a mathematical programming optimization procedure based on a penalty function approach to impose discrete (0,1) constraints on parameters defining cluster membership. All subjects in an INDCLUS analysis are assumed to have a common set of clusters, which are differentially weighted by subjects in order to portray individual differences. As such, INDCLUS provides a (discrete) clustering counterpart to the Carroll-Chang INDSCAL model for (continuous) spatial representations. Finally, we consider possible generalizations of the INDCLUS model and algorithm.
Asymptotic Comparison of Missing Data Procedures for Estimating Factor Loadings
Authors: Brown C. Hendricks
Published: January 2006

Large sample properties of four methods of handling multivariate missing data are compared. The criterion for comparison is how well the loadings from a single factor model can be estimated. It is shown that efficiencies of the methods depend on the pattern or arrangement of missing data, and an evaluation study is used to generate predictive efficiency equations to guide one's choice of an estimating procedure. A simple regression-type estimator is introduced which shows high efficiency relative to the maximum likelihood method over a large range of patterns and covariance matrices.
On the Investigation of Local Identifiability: A Counterexample
Authors: Shapiro A. , Browne M. W.
Published: January 2006

An assertion that the parameters of a covariance structure are locally identified at a certain point only if the rank of the Jacobian matrix at that point equals the number of parameters, is shown to be false by means of a counterexample.
Fitting Cross-Classification Table Data to Models when Observations are Subject to Classification Error
Authors: Thomas Hoben
Published: January 2006

Individuals are classified in a cross-classification table where two behavioral observations on each individual determine the classification. The problem is to test certain structural models assumed to underlie the cross-classified observations. A minimum chi-square test procedure is proposed.
Orthogonal Procrustes Rotation for Two or More Matrices
Authors: Ten Berge Jos M. F.
Published: January 2006

Necessary and sufficient conditions for rotating matrices to maximal agreement in the least-squares sense are discussed. A theorem by Fischer and Roppert, which solves the case of two matrices, is given a more straightforward proof. A sufficient condition for a best least-squares fit for more than two matrices is formulated and shown to be not necessary. In addition, necessary conditions suggested by Kristof and Wingersky are shown to be not sufficient. A rotation procedure that is an alternative to the one by Kristof and Wingersky is presented. Upper bounds are derived for determining the extent to which the procedure falls short of attaining the best least-squares fit. The problem of scaling matrices to maximal agreement is discussed. Modifications of Gower’s method of generalized Procrustes analysis are suggested.
A Note on Moran’s Measure of Multiple Rank Correlation
Authors: Bobko Philip
Published: January 2006

A measure of multiple rank correlation, Ty.122, is proposed for the situation with no tied observations in the variables. The measure is a weighted average of two squared Kendall taus. It is shown that Ty.122 is equivalent to a statistic previously proposed by Moran and thus a new interpretation is given to Moran’s statistic.
Comparing Variances of Correlated Variables
Authors: Cohen Ayala
Published: January 2006

A test is proposed for the equality of the variances of k ≥ 2 correlated variables. Pitman's test for k = 2 reduces the null hypothesis to zero correlation between their sum and their difference. Its extension, eliminating nuisance parameters by a bootstrap procedure, is valid for any correlation structure between the k normally distributed variables. A Monte Carlo study for several combinations of sample sizes and number of variables is presented, comparing the level and power of the new method with previously published tests. Some nonnormal data are included, for which the empirical level tends to be slightly higher than the nominal one. The results show that our method is close in power to the asymptotic tests which are extremely sensitive to nonnormality, yet it is robust and much more powerful than other robust tests.
A Binomial Test for Hierarchical Dependency
Authors: Guay Roland B. , McCabe George P.
Published: January 2006

A binomial test for hierarchical dependency is presented. The null hypothesis is that all members of a population who possess a certain skill are a subset of the members who possess another skill. This hypothesis is basic to the writings of several prominent theorists, such as Gagné and Piaget. The model, assumptions, formula derivations, and procedures for the test are explained. An illustrative example is also provided.
A Two-Stage Algorithm for Assessing Violations of Additivity Via Axiomatic and Numerical Conjoint Analysis
Authors: Nygren Thomas E.
Published: January 2006

An algorithm for assessing additivity conjunctively via both axiomatic conjoint analysis and numerical conjoint scaling is described. The algorithm first assesses the degree of individual differences among sets of rankings of stimuli, and subsequently examines either individual or averaged data for violations of axioms necessary for an additive model. The axioms are examined at a more detailed level than has been previously done. Violations of the axioms are broken down into different types. Finally, a nonmetric scaling of the data can be done based on either or both of two different badness-of-fit scaling measures. The advantages of combining all of these features into one algorithm for improving the diagnostic value of axiomatic conjoint measurement in evaluating additivity are discussed.
On Simulating Non-Normal Distributions
Authors: Tadikamalla Pandu R.
Published: January 2006

Six different algorithms to generate widely different non-normal distributions are reviewed. These algorithms are compared in terms of speed, simplicity and generality of the technique. The advantages and disadvantages of using these algorithms are briefly discussed.
Relating Tests Given to Different Samples
Authors: Rubin Donald B. , Thayer Dorothy
Published: January 2006

Suppose a collection of standard tests is given to all subjects in a random sample, but a different new test is given to each group of subjects in nonoverlapping subsamples. A simple method is developed for displaying the information that the data set contains about the correlational structure of the new tests. This is possible to some extent, even though each subject takes only one new test. The method uses plausible values of the partial correlations among the new tests given the standard tests in order to generate plausible simple correlations among the new tests and plausible multiple correlations between composites of the new tests and the standard tests. The real data example included suggests that the method can be useful in practical problems.
Evaluating the Conformity of Sociometric Measurements
Authors: Hubert Lawrence J. , Baker Frank B.
Published: January 2006

The problem of comparing two sociometric matrices, as originally discussed by Katz and Powell in the early 1950’s, is reconsidered and generalized using a different inference model. In particular, the proposed indices of conformity are justified by a regression argument similar to the one used by Somers in presenting his well-known measures of asymmetric ordinal association. A permutation distribution and an associated significance test are developed for the specific hypothesis of “no conformity” reinterpreted as a random matching of the rows and (simultaneously) the columns of one sociometric matrix to the rows and columns of a second. The approximate significance tests that are presented and illustrated with a simple numerical example are based on the first two moments of the permutation distribution, or alternatively, on a random sample from the complete distribution.
U-Statistic Hierarchical Clustering
Authors: D’Andrade Roy G.
Published: January 2006

A monotone invariant method of hierarchical clustering based on the Mann-Whitney U-statistic is presented. The effectiveness of the complete-link, single-link, and U-statistic methods in recovering tree structures from error perturbed data are evaluated. The U-statistic method is found to be consistently more effective in recovering the original tree structures than either the single-link or complete-link methods.
On Bayesian Estimation in Unrestricted Factor Analysis
Authors: Koopman Raymond F.
Published: January 2006

It is shown that the common and unique variance estimates produced by Martin & McDonald’s Bayesian estimation procedure for the unrestricted common factor model have a predictable sum which is always greater than the maximum likelihood estimate of the total variance. This fact is used to justify a suggested simple alternative method of specifying the Bayesian parameters required by the procedure.
A Note on the Factor Analysis of Partial Covariance Matrices
Authors: McDonald Roderick P.
Published: January 2006

A relationship is given between the joint common factor structure of two sets of variables, and the factor structure of the partial covariance matrix of one of the sets with the other partialled out.
Goodness of Fit Tests for Paired Comparison Models
Authors: Douglas Graham A.
Published: January 2006

A goodness of fit test presented by Andersen is shown to be incorrect. The correct test is described and a re-analysis of Andersen's data is provided.
Allowing for Infeasible Pairings in the Matching Paradigm
Authors: Gillett Raphael
Published: January 2006

The objective of research in the matching paradigm is to determine whether a one-to-one pairing configuration between objects in two arrays contains more pairings of a particular kind than expected under the null hypothesis. The presence of infeasible pairings, that is, of particular pairings which can not possibly take place, has the effect of altering the null distribution that would otherwise obtain. To enable researchers to determine the appropriate null distribution, a generalization of classical rook methodology is developed which can accommodate infeasible pairings in the matching paradigm.
A Still Further Note on Freeman's Measure of Association
Authors: Buck Jane L. , Finner Stephen L.
Published: January 2006

This article demonstrates that Freeman's theta, a measure of association between a nominal variable and an ordinal variable, has a sampling distribution identical with the sampling distribution of Mann-Whitney's U.
An Algorithm for Generating Artificial Test Clusters
Authors: Milligan Glenn W.
Published: January 2006

An algorithm for generating artificial data sets which contain distinct nonoverlapping clusters is presented. The algorithm is useful for generating test data sets for Monte Carlo validation research conducted on clustering methods or statistics. The algorithm generates data sets which contain either 1, 2, 3, 4, or 5 clusters. By default, the data are embedded in either a 4, 6, or 8 dimensional space. Three different patterns for assigning the points to the clusters are provided. One pattern assigns the points equally to the clusters while the remaining two schemes produce clusters of unequal sizes. Finally, a number of methods for introducing error in the data have been incorporated in the algorithm.
Latent Class Models for Nonmonotone Dichotomous Items
Authors: Formann Anton K.
Published: January 2006

Starting from perfectly discriminating nonmonotone dichotomous items, a class of probabilistic models with or without response errors and with or without intrinsically unscalable respondents is described. All these models can be understood as simply restricted latent class analysis. Thus, the estimation and identifiability of the parameters (class sizes and item latent probabilities) as well as the chi-squared goodness-of-fit tests (Pearson and likelihood-ratio) are free of the problems. The applicability of the proposed variants of latent class models is demonstrated on real attitudinal data.
Forced Classification: A Simple Application of a Quantification Method
Authors: Nishisato Shizuhiko
Published: January 2006

This study formulates a property of a quantification method, the principle of equivalent partitioning (PEP). When the PEP is used together with Guttman's principle of internal consistency (PIC) in a simple way, the combination offers an interesting way of analyzing categorical data in terms of the variate(s) chosen by the investigator, a type of canonical analysis. The study discusses applications of the technique to multiple-choice, rank-order, and paired comparison data.
Items Bundles
Authors: Rosenbaum Paul R.
Published: January 2006

An item bundle is a small group of multiple choice items that share a common reading passage or graph, or a small group of matching items that share distractors. Item bundles are easily identified by paging through a copy of a test. Bundled items may violate the latent conditional independence assumption of unidimensional item response theory (IRT), but such a violation would not typically suggest the existence of a new fundamental human ability to read one specific reading passage or to interpret one specific graph. It is important, therefore, to have theoretical concepts and empirical checks that distinguish between, on the one hand, anticipated violations of latent conditional independence within item bundles, and, on the other hand, violations that cannot be attributed to idiosyncratic features of test format and instead suggest departures from unidimensionalty. To this end, two theorems on unidimensional IRT are extended to describe observable item response distributions when there is conditional independence between but not necessarily within item bundles.
FACAIC: Model Selection Algorithm for the Orthogonal Factor Model using AIC and CAIC
Authors: Bozdogan Hamparsum , Ramirez Donald E.
Published: January 2006

This paper describes the authors' FORTRAN algorithm FACAIC for choosing the number of factors for an orthogonal factor model using Akaike's Information Criterion. FACAIC utilizes the IMSL subroutine OFCOMM.
The Adjusted Rand Statistic: A SAS Macro
Authors: Fisher Dennis G. , Hoffman Paul
Published: January 2006

A macro for calculating the Hubert and Arabie (1985) adjusted Rand statistic is presented. The adjusted Rand statistic gives a measure of classification agreement between two partitions of the same set of objects. The macro is written in the SAS macro language and makes extensive use of SAS/IML software (SAS Institute, 1985a, 1985b). The macro uses two different methods of handling missing values. The default method assumes that each object that has a missing value for the classification category is in its own separate category or cluster for that classification. The optional method places all objects with a missing value for the classification category into the same category for that classification.
Mathematical Formulation of Multivariate Euclidean Models for Discrimination Methods
Authors: Mullen Kenneth , Ennis Daniel M.
Published: January 2006

Multivariate models for the triangular and duo-trio methods are described in this paper. In both cases, the mathematical formulation of Euclidean models for these methods is derived and evaluated for the bivariate case using numerical quadrature. Theoretical results are compared with those obtained using Monte Carlo simulation which is validated by comparison with previously published theoretical results for univariate models of these methods. This work is discussed in light of its importance to the development of a new theory for multidimensional scaling in which the traditional assumption can be eliminated that proximity measures and perceptual distances are monotonically related.
Understanding Correlates of Change by Modeling Individual Differences in Growth
Authors: Rogosa David R. , Willett John B.
Published: January 2006

The study of correlates of change is the investigation of systematic individual differences in growth. Our representation of systematic individual differences in growth is built up in two parts: (a) a model for individual growth and, (b) a model for the dependence of parameters in the individual growth models on individual characteristics. First, explicit representations of correlates of change are constructed for various models of individual growth. Second, for the special case of initial status as a correlate of change, properties of collections of growth curves provide new results on the relation between change and initial status. Third, the shortcomings of previous approaches to the assessment of correlates of change are demonstrated. In particular, correlations of residual change measures with exogenous individual characteristics are shown to be poor indicators of systematic individual differences in growth.
Similarities Derived from 3-d Nonlinear Psychophysics: Variance Distributions
Authors: Gregson Robert A. M.
Published: January 2006

Many-one mappings between stimulus properties and pairwise generated similarities are intrinsic to definitions of similarity. This of itself is not sufficient as a basis for predicting the variance associated with any single similarity judgment. An extension to cover this has to be made either by making ancillary assumptions about noise, or by using nonlinear models. The derivation of the variance of similarity judgments is made from the 3Γ process in nonlinear psychophysics. The idea of separability of dimensions in metric space theories of similarity is replaced by one parameter which represents the degree of a form of interdimensional crosscoupling
Identification with Deficient Rank Loading Matrices in Confirmatory Factor Analysis: Multitrait-Multimethod Models
Authors: Grayson David , Marsh Herbert W.
Published: January 2006

This paper presents some results on identification in multitrait-multimethod (MTMM) confirmatory factor analysis (CFA) models. Some MTMM models are not identified when the (factorial-patterned) loadings matrix is of deficient column rank. For at least one other MTMM model, identification does exist despite such deficiency. It is also shown that for some MTMM CFA models, Howe's (1955) conditions sufficient for rotational uniqueness can fail, yet the model may well be identified and rotationally unique. Implications of these results for CFA models in general are discussed.
Indclas: A Three-Way Hierarchical Classes Model
Authors: Leenen Iwin , Van Mechelen Iven , De Boeck Paul , Rosenberg Seymour
Published: January 2006

A three-way three-mode extension of De Boeck and Rosenberg's (1988) two-way two-mode hierarchical classes model is presented for the analysis of individual differences in binary object × attribute arrays. In line with the two-way hierarchical classes model, the three-way extension represents both the association relation among the three modes and the set-theoretical relations among the elements of each model. An algorithm for fitting the model is presented and evaluated in a simulation study. The model is illustrated with data on psychiatric diagnosis. Finally, the relation between the model and extant models for three-way data is discussed.
Comment on Fitting MA Time Series by Structural Equation Models
Authors: Molenaar Peter C. M.
Published: January 2006

In a recent paper by van Buuren (1997) it is concluded that parameter estimates in pure moving-average (MA) models, obtained by software for fitting structural equation models (SEMs), are biased and inefficient. In this comment it is shown that this negative finding may be due to a particular feature of van Buuren's simulation experiment. A modified procedure for fitting MA models by means of SEM software is proposed, and some of its implications are discussed.
Generalized Bilinear Models
Authors: Choulakian Vartan
Published: January 2006

Generalized bilinear models are presented for the statistical analysis of two-way arrays. These models combine bilinear models and generalized linear modeling, and yield a family of models that includes many existing models, as well as suggest other potentially useful ones. This approach both unifies and extends models for two-way arrays, including the ability to treat response and explanatory variables differently in the models, and the incorporation of external information about the variables directly into the analysis. A unifying framework for the generalized bilinear models is provided by considering four particular cases which have been proposed and used in the existing statistical literature. A three-step procedure is proposed to analyze data sets by generalized bilinear models. Two data sets of different nature are analyzed.
Model Selection and Akaike's Information Criterion (AIC): The General Theory and its Analytical Extensions
Authors: Bozdogan Hamparsum
Published: January 2006

During the last fifteen years, Akaike's entropy-based Information Criterion (AIC) has had a fundamental impact in statistical model evaluation problems. This paper studies the general theory of the AIC procedure and provides its analytical extensions in two ways without violating Akaike's main principles. These extensions make AIC asymptotically consistent and penalize overparameterization more stringently to pick only the simplest of the “true” models. These selection criteria are called CAIC and CAICF. Asymptotic properties of AIC and its extensions are investigated, and empirical performances of these criteria are studied in choosing the correct degree of a polynomial model in two different Monte Carlo experiments under different conditions.
Tableau Algorithms for Factor Analysis by Instrumental Variable Methods
Authors: Jennrich Robert I.
Published: January 2006

Simple tableau algorithms are given for the noniterative instrumental variable (FABIN 2) and two stage regression (FABIN 3) factor loading estimates of Hägglund. Corresponding generalized least squares estimates of factor covariances and unique variances are introduced. An example is given for the purpose of illustration and comparison.
Kelley's Formula as a Basis for the Assessment of Reliable Change
Authors: Maassen Gerard H.
Published: January 2006

In the literature on the measurement of change, reliable change is usually determined by means of a confidence interval around an observed value of a statistic that estimates the true change. In recent literature on the efficacy of psychotherapies, attention has been particularly directed at the improvement of the estimation of the true change. Reliable Change Indices, incorporating the reliability-weighted measure of individual change, also known as Kelley's formula, have been proposed. According to current practice, these indices are defined as the ratio of such an estimator and an intuitively appealing criterion and then regarded as standard normally distributed statistics. However, because the authors fail to adopt an adequate standard error of the estimator, the statistical properties of their indices are unclear. In this article, it is shown that this can lead to paradoxical conclusions. The adjusted standard error is derived.
Residualanalysis in the Polytomous Rasch Model
Authors: Andersen Erling B.
Published: January 2006

Residuals for check of model fit in the polytomous Rasch model are examined. Comparisons are made between using counts for all response pattern and using item totals for score groups for the construction of the residuals. Comparisons are also, for the residuals based on score group totals, made between using as basis the item totals, or using the estimated item parameters. The developed methods are illustrated by two examples, one from a psychiatric rating scale, one from a Danish Welfare Study.
A Study of the Classification Capabilities of Neural Networks Using Unsupervised Learning: A Comparison with K-means Clustering
Authors: (Sundar) Balakrishnan P. V. , Cooper Martha C. , Jacob Varghese S. , Lewis Phillip A.
Published: January 2006

Several neural networks have been proposed in the general literature for pattern recognition and clustering, but little empirical comparison with traditional methods has been done. The results reported here compare neural networks using Kohonen learning with a traditional clustering method (K-means) in an experimental design using simulated data with known cluster solutions. Two types of neural networks were examined, both of which used unsupervised learning to perform the clustering. One used Kohonen learning with a conscience and the other used Kohonen learning without a conscience mechanism. The performance of these nets was examined with respect to changes in the number of attributes, the number of clusters, and the amount of error in the data. Generally, the K-means procedure had fewer points misclassified while the classification accuracy of neural networks worsened as the number of clusters in the data increased from two to five.
A Parametric Procedure for Ultrametric Tree Estimation from Conditional Rank Order Proximity Data
Authors: Young Martin R. , DeSarbo Wayne S.
Published: January 2006

The psychometric and classification literatures have illustrated the fact that a wide class of discrete or network models (e.g., hierarchical or ultrametric trees) for the analysis of ordinal proximity data are plagued by potential degenerate solutions if estimated using traditional nonmetric procedures (i.e., procedures which optimize a STRESS-based criteria of fit and whose solutions are invariant under a monotone transformation of the input data). This paper proposes a new parametric, maximum likelihood based procedure for estimating ultrametric trees for the analysis of conditional rank order proximity data. We present the technical aspects of the model and the estimation algorithm. Some preliminary Monte Carlo results are discussed. A consumer psychology application is provided examining the similarity of fifteen types of snack/breakfast items. Finally, some directions for future research are provided.
Alternative Test Criteria in Covariance Structure Analysis: A Unified Approach
Authors: Satorra Albert
Published: January 2006

In the context of covariance structure analysis, a unified approach to the asymptotic theory of alternative test criteria for testing parametric restrictions is provided. The discussion develops within a general framework that distinguishes whether or not the fitting function is asymptotically optimal, and allows the null and alternative hypothesis to be only approximations of the true model. Also, the equivalent of the information matrix, and the asymptotic covariance matrix of the vector of summary statistics, are allowed to be singular. When the fitting function is not asymptotically optimal, test statistics which have asymptotically a chi-square distribution are developed as a natural generalization of more classical ones. Issues relevant for power analysis, and the asymptotic theory of a testing related statistic, are also investigated.
An Exact and Optimal Standardized Person Test for Assessing Consistency with the Rasch Model
Authors: Klauer Karl Christoph
Published: January 2006

The Rasch model predicts that an individual's ability level is invariant over subtests of the total test, and thus, all subtests measure the same latent trait. A person test of this invariance hypothesis is discussed that is uniformly most powerful and standardized in the sense that the conditional distribution of the test statistic, given a particular level of ability, does not depend on the absolute value of the examinee's ability parameter. The test can be routinely performed by applying a computer program designed by and obtainable from the author. Finally, a suboptimal test is derived that is extremely easy to use, and an overall group test of the invariance hypothesis discussed. All tests considered do not rely on asymptotic approximations; hence, they may be applied when the test is of only moderate length and the group of examinees is small.
A Numerical Approach to the Approximate and the Exact Minimum Rank of a Covariance Matrix
Authors: ten Berge Jos M. F. , Kiers Henk A. L.
Published: January 2006

A concept of approximate minimum rank for a covariance matrix is defined, which contains the (exact) minimum rank as a special case. A computational procedure to evaluate the approximate minimum rank is offered. The procedure yields those proper communalities for which the unexplained common variance, ignored in low-rank factor analysis, is minimized. The procedure also permits a numerical determination of the exact minimum rank of a covariance matrix, within limits of computational accuracy. A set of 180 covariance matrices with known or bounded minimum rank was analyzed. The procedure was successful throughout in recovering the desired rank.
Points of View Analysis Revisited: Fitting Multidimensional Structures to Optimal Distance Components with Cluster Restrictions on the Variables
Authors: Meulman Jacqueline J. , Verboon Peter
Published: January 2006

Points of view analysis (PVA), proposed by Tucker and Messick in 1963, was one of the first methods to deal explicitly with individual differences in multidimensional scaling, but at some point was apparently superceded by the weighted Euclidean model, well-known as the Carroll and Chang INDSCAL model. This paper argues that the idea behind points of view analysis deserves new attention, especially as a technique to analyze group differences. A procedure is proposed that can be viewed as a streamlined, integrated version of the Tucker and Messick Process, which consisted of a number of separate steps. At the same time, our procedure can be regarded as a particularly constrained weighted Euclidean model. While fitting the model, two types of nonlinear data transformations are feasible, either for given dissimilarities, or for variables from which the dissimilarities are derived. Various applications are discussed, where the two types of transformation can be mixed in the same analysis; a quadratic assignment framework is used to evaluate the results.
Maximum Marginal Likelihood Estimation for Semiparametric Item Analysis
Authors: Ramsay J. O. , Winsberg S.
Published: January 2006

The item characteristic curve (ICC), defining the relation between ability and the probability of choosing a particular option for a test item, can be estimated by using polynomial regression splines. These provide a more flexible family of functions than is given by the three-parameter logistic family. The estimation of spline ICCs is described by maximizing the marginal likelihood formed by integrating ability over a beta prior distribution. Some simulation results compare this approach with the joint estimation of ability and item parameters.
Was Euclid an Unnecessarily Sophisticated Psychologist?
Authors: Arabie Phipps
Published: January 2006

A survey of the current state of multidimensional scaling using the city-block metric is presented. Topics include substantive and theoretical issues, recent algorithmic developments and their implications for seemingly straightforward analyses, isometries with other metrics, links to graph-theoretic models, and future prospects.
A General Solution for a Class of Weakly Constrained Linear Regression Problems
Authors: ten Berge Jos M. F.
Published: January 2006

This paper contains a globally optimal solution for a class of functions composed of a linear regression function and a penalty function for the sum of squared regression weights. Global optimality is obtained from inequalities rather than from partial derivatives of a Lagrangian function. Applications arise in multidimensional scaling of symmetric or rectangular matrices of squared distances, in Procrustes analysis, and in ridge regression analysis. The similarity of existing solutions for these applications is explained by considering them as special cases of the general class of functions addressed.
The EM Algorithm for Latent Class Analysis with Equality Constraints
Authors: Mooijaart AB , van der Heijden Peter G. M.
Published: January 2006

The EM algorithm is a popular iterative method for estimating parameters in the latent class model where at each step the unknown parameters can be estimated simply as weighted sums of some latent proportions. The algorithm may also be used when some parameters are constrained to equal given constants or each other. It is shown that in the general case with equality constraints, the EM algorithm is not simple to apply because a nonlinear equation has to be solved. This problem arises, mainly, when equality constraints are defined over probabilities in different combinations of variables and latent classes. A simple condition is given in which, although probabilities in different variable-latent class combinations are constrained to be equal, the EM algorithm is still simple to apply.
On the Misuse of Manifest Variables in the Detection of Measurement Bias
Authors: Meredith William , Millsap Roger E.
Published: January 2006

Measurement invariance (lack of bias) of a manifest variable Y with respect to a latent variable W is defined as invariance of the conditional distribution of Y given W over selected subpopulations. Invariance is commonly assessed by studying subpopulation differences in the conditional distribution of Y given a manifest variable Z, chosen to substitute for W. A unified treatment of conditions that may allow the detection of measurement bias using statistical procedures involving only observed or manifest variables is presented. Theorems are provided that give conditions for measurement invariance, and for invariance of the conditional distribution of Y given Z. Additional theorems and examples explore the Bayes sufficiency of Z, stochastic ordering in W, local independence of Y and Z, exponential families, and the reliability of Z. It is shown that when Bayes sufficiency of Z fails, the two forms of invariance will often not be equivalent in practice. Bayes sufficiency holds under Rasch model assumptions, and in long tests under certain conditions. It is concluded that bias detection procedures that rely strictly on observed variables are not in general diagnostic of measurement bias, or the lack of bias.
Factor and Ideal Point Analysis for Interpersonally Incomparable Data
Authors: Brady Henry E.
Published: January 2006

Interpersonally incomparable responses pose a significant problem for survey researchers. If the manifest responses of individuals differ from their underlying true responses by monotonic transformations which vary from person to person, then the covariances of the manifest responses tools such as factor analysis may yield incorrect results. Satisfactory results for interpersonally incomparable ordinal responses can be obtained by assuming that rankings are based upon a set of multivariate normal latent variables which satisfy the factor or ideal point models of choice. Two statistical methods based upon these assumptions are described; their statistical properties are explored; and their computational feasibility is demonstrated in some simulations. We conclude that is possible to develop methods for factor and ideal point analysis of interpersonally incomparable ordinal data.