bluuebunny/crossref_metadata_2025 huggingface dataset:
Exact Distributions of Intraclass Correlation and Cronbach's Alpha with Gaussian Data and General Covariance
Authors: Kistner Emily O. , Muller Keith E.
Published: February 2006

Intraclass correlation and Cronbach's alpha are widely used to describe reliability of tests and measurements. Even with Gaussian data, exact distributions are known only for compound symmetric covariance (equal variances and equal correlations). Recently, large sample Gaussian approximations were derived for the distribution functions.

New exact results allow calculating the exact distribution function and other properties of intraclass correlation and Cronbach's alpha, for Gaussian data with any covariance pattern, not just compound symmetry. Probabilities are computed in terms of the distribution function of a weighted sum of independent chi-square random variables.

New F approximations for the distribution functions of intraclass correlation and Cronbach's alpha are much simpler and faster to compute than the exact forms. Assuming the covariance matrix is known, the approximations typically provide sufficient accuracy, even with as few as ten observations.

Either the exact or approximate distributions may be used to create confidence intervals around an estimate of reliability. Monte Carlo simulations led to a number of conclusions. Correctly assuming that the covariance matrix is compound symmetric leads to accurate confidence intervals, as was expected from previously known results. However, assuming and estimating a general covariance matrix produces somewhat optimistically narrow confidence intervals with 10 observations. Increasing sample size to 100 gives essentially unbiased coverage. Incorrectly assuming compound symmetry leads to pessimistically large confidence intervals, with pessimism increasing with sample size. In contrast, incorrectly assuming general covariance introduces only a modest optimistic bias in small samples. Hence the new methods seem preferable for creating confidence intervals, except when compound symmetry definitely holds.
An Interactive Multiobjective Programming Approach to Combinatorial Data Analysis
Authors: Brusco Michael J. , Stahl Stephanie
Published: February 2006

Combinatorial optimization problems in the social and behavioral sciences are frequently associated with a variety of alternative objective criteria. Multiobjective programming is an operations research methodology that enables the quantitative analyst to investigate tradeoffs among relevant objective criteria. In this paper, we describe an interactive procedure for multiobjective asymmetric unidimensional seriation problems. This procedure uses a dynamic-programming algorithm to partially generate the efficient set of sequences for small to medium-sized problems, and a multioperation heuristic to estimate the efficient set for larger problems. The interactive multiobjective procedure is applied to an empirical data set from the psychometric literature. We conclude with a discussion of other potential areas of application in combinatorial data analysis.
Mixed-Effects Analyses of Rank-Ordered Data
Authors: Böckenholt Ulf
Published: February 2006

This paper presents a synthesis of Bock's (1972) nominal categories model and Luce's (1959) choice model for mixed-effects analyses of rank-ordered data. It is shown that the proposed ranking model is both parsimonious and flexible in accounting for preference heterogeneity as well as fixed and random effects of covariates. Relationships to other approaches, including Takane's (1987) ideal point discriminant model and Croon's (1989) latent-class version of Luce's ranking model, are also discussed. The application focuses on a ranking study of behavioral traits that parents find desirable in children.
Testing for Local Dependency in Dichotomous and Polytomous Item Response Models
Authors: Ip Edward Hak-sing
Published: February 2006

Researchers studying item response models are often interested in examining the effects of local dependency on the validity of the resulting conclusion from statistical inference. This paper focuses on the detection of local dependency. We provide a framework for viewing local dependency within dichotomous and polytomous items that are clustered by design, and present a testing procedure that allows researchers to specifically identify individual item pairs that exhibit local dependency, while controlling for false positive rate. Simulation results from the study indicate that the proposed method is effective. In addition, a discussion of its relation to other existing methods is provided.
A Bayesian Analysis of Finite Mixtures in the LISREL Model
Authors: Zhu Hong-Tu , Lee Sik-Yum
Published: February 2006

In this paper, we propose a Bayesian framework for estimating finite mixtures of the LISREL model. The basic idea in our analysis is to augment the observed data of the manifest variables with the latent variables and the allocation variables. The Gibbs sampler is implemented to obtain the Bayesian solution. Other associated statistical inferences, such as the direct estimation of the latent variables, establishment of a goodness-of-fit assessment for a posited model, Bayesian classification, residual and outlier analyses, are discussed. The methodology is illustrated with a simulation study and a real example.
Thurstone's Discriminal Processes Fifty Years Later
Authors: Luce R. Duncan
Published: February 2006

Four issues are discussed concerning Thurstone's discriminal processes: the distributions governing the representation, the nature of the response decision rules, the relation of the mean representation to physical characteristics of the stimulus, and factors affecting the variance of the representation. A neural schema underlying the representation is proposed which involves samples in time of pulse trains on individual neural fibers, estimators of parameters of the several pulse trains, samples of neural fibers, and an aggregation of the estimates over the sample. The resulting aggregated estimate is the Thurstonian representation. Two estimators of pulse rate, which is monotonic with signal intensity, are timing and counting ratios and two methods of aggregation are averaging and maximizing. These lead to very different predictions in a speed-accuracy experiment; data indicate that both estimators are available and the aggregation is by averaging. Magnitude estimation data are then used both to illustrate an unusual response rule and to study the psychophysical law. In addition, the pattern of variability and correlation of magnitude estimates on successive trials is interpreted in terms of the sample size over which the aggregation takes place. Neural sample size is equated with selective attention, and is an important factor affecting the variability of the representation. It accounts for the magical number seven phenomenon in absolute identification and predicts the impact of nonuniform distributions of intensities on the absolute identification of two frequencies.
Two simple Classes of Mastery Scores based on the Beta-Binomial Model
Authors: Huynh Huynh
Published: February 2006

Two simple classes of mastery scores which are suitable for hand calculations are presented for beta-binomial test score distributions combined with linear and cubic referral success. The models provide a simple way to explore the consequences of selecting an arbitrary mastery score. Such assessment would be useful whenever the test user is not willing to post a priori a loss ratio, but wishes to look at the various consequences before aiming at a particular score.
The Rasch Model, the Law of Comparative Judgment and Additive Conjoint Measurement
Authors: Brogden H. E.
Published: February 2006

Relationships between the Rasch model and both the law of comparative judgment and additive conjoint measurement are discussed. The distance between the ability of Person a and the difficult of Item i is, in the Rasch model, the baseline value corresponding to the probability that a will respond correctly to i, where this probability is interpreted as the area under a logistic curve (which is substantially equivalent to the normal curve) and is thus an application of the law of comparative judgment. Under certain assumptions, the Rasch model is also a special case of additive conjoint measurement and, properly reinterpreted, may be usefully applied in contexts other than individual differences.
The Estimation of Reliability When Several Trials are Available
Authors: Alexander Howard W.
Published: February 2006

In certain types of experiment it frequently happens that we have a block of data consisting of several trials on the same individuals. Using the methods of estimation provided by the analysis of variance, estimates of reliability are derived for this case, and the conditions under which each is valid are discussed. Various relations between these estimates and the product-moment coefficient of correlation are obtained.
Table of Mean Deviates for Various Portions of the Unit Normal Distribution
Authors: Leverett Hollis M.
Published: February 2006

In the absence of sound units of measurement, the data obtained by use of a psychometric instrument may sometimes be so irregular that they cannot be accepted as a good representation of the true function of the trait measured. Frequently, ordered categorical or ranked data and other irregular distributions are obtained to represent traits that are obviously continuous and probably unskewed functions. In such cases, the data may be improved in the direction of a better approximation of the true function by converting them to normal distribution form. A table of mean deviates of various portions of the unit normal curve is presented to facilitate this conversion.
Note on the Sampling Error of the Difference Between Correlated Proportions or Percentages
Authors: McNemar Quinn
Published: February 2006

Two formulas are presented for judging the significance of the difference between correlated proportions. The chi square equivalent of one of the developed formulas is pointed out.
The Reliability of Linearly Equated Tests
Authors: Segall Daniel O.
Published: February 2006

An asymptotic expression for the reliability of a linearly equated test is developed using normal theory. The reliability is expressed as the product of two terms, the reliability of the test before equating, and an adjustment term. This adjustment term is a function of the sample sizes used to estimate the linear equating transformation. The results of a simulation study indicate close agreement between the theoretical and simulated reliability values for samples greater than 200. Findings demonstrate that samples as small as 300 can be used in linear equating without an appreciable decrease in reliability.
On the Loss of Information in Conditional Maximum Likelihood Estimation of Item Parameters
Authors: Eggen Theo J. H. M.
Published: February 2006

In item response models of the Rasch type (Fischer & Molenaar, 1995), item parameters are often estimated by the conditional maximum likelihood (CML) method. This paper addresses the loss of information in CML estimation by using the information concept of F-information (Liang, 1983). This concept makes it possible to specify the conditions for no loss of information and to define a quantification of information loss. For the dichotomous Rasch model, the derivations will be given in detail to show the use of the F-information concept for making comparisons for different estimation methods. It is shown that by using CML for item parameter estimation, some information is almost always lost. But compared to JML (joint maximum likelihood) as well as to MML (marginal maximum likelihood) the loss is very small. The reported efficiency in the use of information of CML to JML and to MML in several comparisons is always larger than 93%, and in tests with a length of 20 items or more, larger than 99%.
The Asymptotic Bias of Minimum Trace Factor Analysis, with Applications to the Greatest Lower Bound to Reliability
Authors: Shapiro Alexander , Ten Berge Jos M. F.
Published: February 2006

In theory, the greatest lower bound (g.l.b.) to reliability is the best possible lower bound to the reliability based on single test administration. Yet the practical use of the g.l.b. has been severely hindered by sampling bias problems. It is well known that the g.l.b. based on small samples (even a sample of one thousand subjects is not generally enough) may severely overestimate the population value, and statistical treatment of the bias has been badly missing. The only results obtained so far are concerned with the asymptotic variance of the g.l.b. and of its numerator (the maximum possible error variance of a test), based on first order derivatives and the asumption of multivariate normality. The present paper extends these results by offering explicit expressions for the second order derivatives. This yields a closed form expression for the asymptotic bias of both the g.l.b. and its numerator, under the assumptions that the rank of the reduced covariance matrix is at or above the Ledermann bound, and that the nonnegativity constraints on the diagonal elements of the matrix of unique variances are inactive. It is also shown that, when the reduced rank is at its highest possible value (i.e., the number of variables minus one), the numerator of the g.l.b. is asymptotically unbiased, and the asymptotic bias of the g.l.b. is negative. The latter results are contrary to common belief, but apply only to cases where the number of variables is small. The asymptotic results are illustrated by numerical examples.
MCMC Estimation and Some Model-Fit Analysis of Multidimensional IRT Models
Authors: Béguin A. A. , Glas C. A. W.
Published: February 2006

A Bayesian procedure to estimate the three-parameter normal ogive model and a generalization of the procedure to a model with multidimensional ability parameters are presented. The procedure is a generalization of a procedure by Albert (1992) for estimating the two-parameter normal ogive model. The procedure supports analyzing data from multiple populations and incomplete designs. It is shown that restrictions can be imposed on the factor matrix for testing specific hypotheses about the ability structure. The technique is illustrated using simulated and real data.
Bayesian Inference for Graphical Factor Analysis Models
Authors: Giudici Paolo , Stanghellini Elena
Published: February 2006

We generalize factor analysis models by allowing the concentration matrix of the residuals to have nonzero off-diagonal elements. The resulting model is named graphical factor analysis model. Allowing a structure of associations gives information about the correlation left unexplained by the unobserved variables, which can be used both in the confirmatory and exploratory context. We first present a sufficient condition for global identifiability of this class of models with a generic number of factors, thereby extending the results in Stanghellini (1997) and Vicard (2000). We then consider the issue of model comparison and show that fast local computations are possible for this purpose, if the conditional independence graphs on the residuals are restricted to be decomposable and a Bayesian approach is adopted. To achieve this aim, we propose a new reversible jump MCMC method to approximate the posterior probabilities of the considered models. We then study the evolution of political democracy in 75 developing countries based on eight measures of democracy in two different years.
A Modified Beta Binomial Model with Applications to Multiple Choice and Taste Tests
Authors: Morrison Donald G. , Brockway George
Published: February 2006

A modified beta binomial model is presented for use in analyzing ramdom guessing multiple choice tests and certain forms of taste tests. Detection probabilities for each item are distributed beta across the population subjects. Properties for the observable distribution of correct responses are derived. Two concepts of true score estimates are presented. One, analogous to Duncan’s empirical Bayes posterior mean score, is appropriate for assessing the subject’s performance on that particular test. The second is more suitable for predicting outcomes on similar tests.
Maximum Likelihood Estimation of the Polychoric Correlation Coefficient
Authors: Olsson Ulf
Published: February 2006

The polychoric correlation is discussed as a generalization of the tetrachoric correlation coefficient to more than two classes. Two estimation methods are discussed: Maximum likelihood estimation, and what may be called “two-step maximum likelihood” estimation. For the latter method, the thresholds are estimated in the first step. For both methods, asymptotic covariance matrices for estimates are derived, and the methods are illustrated and compared with artificial and real data.
Binary Programming and Test Design
Authors: Theunissen T. J. J. M.
Published: February 2006

An algorithmic approach to test design, using information functions, is presented. The approach uses a special branch of linear programming, i.e. binary programming. In addition, results of some benchmark problems are presented. Within the same framework, it is also possible to formulate the problem of individualized testing.
Combinatorial Data Analysis: Association and Partial Association
Authors: Hubert Lawrence J.
Published: February 2006

A combinatorial data analysis strategy is reviewed that is designed to compare two arbitrary measures of proximity defined between the objects from some set. Based on a particular cross-product definition of correspondence between these two numerically specified notions of proximity (typically represented in the form of matrices), extensions are then pursued to indices of partial association that relate the observed pattern of correspondence between the first two proximity measures to a third. The attendant issues of index normalization and significance testing are discussed; the latter is approached through a simple randomization model implemented either through a Monte Carlo procedure or distributional approximations based on the first three moments. Applications of the original comparison strategy and its extensions to partial association may be developed for a variety of methodological and substantive tasks. Besides rank correlation, we emphasize the topics of spatial autocorrelation for one variable and spatial association between two and mention the connection to the usual randomization approach for one-way analysis-of-variance.
A Note on the Determination of Configuration and Weights for a Class of Individual Scaling Models
Authors: Vani Vina , Raghavachari M.
Published: February 2006

Consider the typical problem in individual scaling, namely finding a common configuration and weights for each individual from the given interpoint distances or scalar products. Within the STRAIN framework it is shown that the problem of determining weights for a given configuration can be posed as a standard quadratic programming problem. A set of necessary conditions for an optimal configuration to satisfy are given. A closed form expression for the configuration is obtained for the one dimensional case and an approach is given for the two dimensional case.
Rank-Reducibility of a Symmetric Matrix and Sampling Theory of Minimum Trace Factor Analysis
Authors: Shapiro Alexander
Published: February 2006

One of the intriguing questions of factor analysis is the extent to which one can reduce the rank of a symmetric matrix by only changing its diagonal entries. We show in this paper that the set of matrices, which can be reduced to rank r, has positive (Lebesgue) measure if and only if r is greater or equal to the Ledermann bound. In other words the Ledermann bound is shown to be almost surely the greatest lower bound to a reduced rank of the sample covariance matrix. Afterwards an asymptotic sampling theory of so-called minimum trace factor analysis (MTFA) is proposed. The theory is based on continuous and differential properties of functions involved in the MTFA. Convex analysis techniques are utilized to obtain conditions for differentiability of these functions.
Restricted Multidimensional Scaling Models for Asymmetric Proximities
Authors: Weeks David G. , Bentler P. M.
Published: February 2006

Restricted multidimensional scaling models [Bentler & Weeks, 1978] allowing constraints on parameters, are extended to the case of asymmetric data. Separate functions are used to model the symmetric and antisymmetric parts of the data. The approach is also extended to the case in which data are presumed to be linearly related to squared distances. Examples of several models are provided, using journal citation data. Possible extensions of the models are considered.
Factor Analysis by Instrumental Variables Methods
Authors: Hägglund Gösta
Published: February 2006

Three alternative estimation procedures for factor analysis based on the instrumental variables method are presented. These procedures are justified by the method of least squares. Formulas for asymptotic standard errors of factor loadings are derived. The procedures are empirically compared to the method of maximum likelihood. The conclusion, based on the data used in this study, is that two of the procedures seem to work well.
A Test-Theoretic Approach to Observed-Score Equating
Authors: van der Linden Wim J.
Published: February 2006

Observed-score equating using the marginal distributions of two tests is not necessarily the universally best approach it has been claimed to be. On the other hand, equating using the conditional distributions given the ability level of the examinee is theoretically ideal. Possible ways of dealing with the requirement of known ability are discussed, including such methods as conditional observed-score equating at point estimates or posterior expected conditional equating. The methods are generalized to the problem of observed-score equating with a multivariate ability structure underlying the scores.
Maximum Likelihood Estimation of Latent Interaction Effects with the LMS Method
Authors: Klein Andreas , Moosbrugger Helfried
Published: February 2006

In the context of structural equation modeling, a general interaction model with multiple latent interaction effects is introduced. A stochastic analysis represents the nonnormal distribution of the joint indicator vector as a finite mixture of normal distributions. The Latent Moderated Structural Equations (LMS) approach is a new method developed for the analysis of the general interaction model that utilizes the mixture distribution and provides a ML estimation of model parameters by adapting the EM algorithm. The finite sample properties and the robustness of LMS are discussed. Finally, the applicability of the new method is illustrated by an empirical example.
Optimal Scaling by Alternating Length-Constrained Nonnegative Least Squares, with Application to Distance-Based Analysis
Authors: Groenen Patrick J. F. , van Os Bart-Jan , Meulman Jacqueline J.
Published: February 2006

An important feature of distance-based principal components analysis, is that the variables can be optimally transformed. For monotone spline transformation, a nonnegative least-squares problem with a length constraint has to be solved in each iteration. As an alternative algorithm to Lawson and Hanson (1974), we propose the Alternating Length-Constrained Non-Negative Least-Squares (ALC-NNLS) algorithm, which minimizes the nonnegative least-squares loss function over the parameters under a length constraint, by alternatingly minimizing over one parameter while keeping the others fixed. Several properties of the new algorithm are discussed. A Monte Carlo study is presented which shows that for most cases in distance-based principal components analysis, ALC-NNLS performs as good as the method of Lawson and Hanson or sometimes even better in terms of the quality of the solution.
A Note on the Geometric Interpretation of the EM Algorithm in Estimating Item Characteristics and Student Abilities
Authors: Ip Edward H. , Lalwania Neal
Published: February 2006

This note uses the EM-algorithm in an item response model as an illustration of a general method of parameter estimation, which geometrically can be described as an alternating projection method.
An Estimate of the Covariance between Variables which are not Jointly Observed
Authors: Cudeck Robert
Published: February 2006

Situations sometimes arise in which variables collected in a study are not jointly observed. This typically occurs because of study design. An example is an equating study where distinct groups of subjects are administered different sections of a test. In the normal maximum likelihood function to estimate the covariance matrix among all variables, elements corresponding to those that are not jointly observed are unidentified. If a factor analysis model holds for the variables, however, then all sections of the matrix can be accurately estimated, using the fact that the covariances are a function of the factor loadings. Standard errors of the estimated covariances can be obtained by the delta method. In addition to estimating the covariance matrix in this design, the method can be applied to other problems such as regression factor analysis. Two examples are presented to illustrate the method.
On the Bock-Aitkin Procedure—from an EM Algorithm Perspective
Authors: Hsu Yaowen
Published: February 2006

The relationship between the EM algorithm and the Bock-Aitkin procedure is described with a continuous distribution of ability (latent trait) from an EM-algorithm perspective. Previous work has been restricted to the discrete case from a probit-analysis perspective.
Latent Variable Modeling in Heterogeneous Populations
Authors: Muthén Bengt O.
Published: February 2006

Common applications of latent variable analysis fail to recognize that data may be obtained from several populations with different sets of parameter values. This article describes the problem and gives an overview of methodology that can address heterogeneity. Artificial examples of mixtures are given, where if the mixture is not recognized, strongly distorted results occur. MIMIC structural modeling is shown to be a useful method for detecting and describing heterogeneity that cannot be handled in regular multiple-group analysis. Other useful methods instead take a random effects approach, describing heterogeneity in terms of random parameter variation across groups. These random effects models connect with emerging methodology for multilevel structural equation modeling of hierarchical data. Examples are drawn from educational achievement testing, psychopathology, and sociology of education. Estimation is carried out by the LISCOMP program.
Minimizing the Number of Observations: A Generalization of the Spearman-Brown Formula
Authors: Sanders P. F. , Theunissen T. J. J. M. , Baas S. M.
Published: February 2006

A new method for determining the minimum number of observations per subject needed to achieve a specific generalizability coefficient is presented. This method, which consists of a branch-and-bound algorithm, allows for the employment of constraints specified by the investigator.
Extensions of the Partial Credit Model
Authors: Glas C. A. W. , Verhelst N. D.
Published: February 2006

The partial credit model, developed by Masters (1982), is a unidimensional latent trait model for responses scored in two or more ordered categories. In the present paper some extensions of the model are presented. First, a marginal maximum likelihood estimation procedure is developed which allows for incomplete data and linear restrictions on both the item and the population parameters. Secondly, two statistical tests for evaluating model fit are presented: the former test has power against violation of the assumption about the ability distribution, the latter test offers the possibility of identifying specific items that do not fit the model.
The Role of Collateral Information about Examinees in Item Parameter Estimation
Authors: Mislevy Robert J. , Sheehan Kathleen M.
Published: February 2006

Standard procedures for estimating item parameters in item response theory (IRT) ignore collateral information that may be available about examinees, such as their standing on demographic and educational variables. This paper describes circumstances under which collateral information about examinees may be used to make inferences about item parameters more precise, and circumstances under which it must be used to obtain correct inferences.
A Simulated Annealing Methodology for Clusterwise Linear Regression
Authors: DeSarbo Wayne S. , Oliver Richard L. , Rangaswamy Arvind
Published: February 2006

In many regression applications, users are often faced with difficulties due to nonlinear relationships, heterogeneous subjects, or time series which are best represented by splines. In such applications, two or more regression functions are often necessary to best summarize the underlying structure of the data. Unfortunately, in most cases, it is not known a priori which subset of observations should be approximated with which specific regression function. This paper presents a methodology which simultaneously clusters observations into a preset number of groups and estimates the corresponding regression functions' coefficients, all to optimize a common objective function. We describe the problem and discuss related procedures. A new simulated annealing-based methodology is described as well as program options to accommodate overlapping or nonoverlapping clustering, replications per subject, univariate or multivariate dependent variables, and constraints imposed on cluster membership. Extensive Monte Carlo analyses are reported which investigate the overall performance of the methodology. A consumer psychology application is provided concerning a conjoint analysis investigation of consumer satisfaction determinants. Finally, other applications and extensions of the methodology are discussed.
The Equivalence of Two Methods of Parameter Estimation for the Rasch Model
Authors: Blackwood Larry G. , Bradley Edwin L.
Published: February 2006

Two methods of estimating parameters in the Rasch model are compared. It is shown that estimates for a certain loglinear model for the score × item × response table are equivalent to the unconditional maximum likelihood estimates for the Rasch model.
Principals Versus Osmod: A Comment on Saito and Otsu
Authors: Kuhfeld Warren F. , Young Forrest W.
Published: February 2006

Saito and Otsu (1988) compared their OSMOD method of nonmetric principal-component analysis to an early and incorrect implementation of the PRINCIPALS algorithm of Young, Takane, and de Leeuw (1978). In this comment we present results from the current, correct implementations of the algorithm.
Model Comparison of Nonlinear Structural Equation Models with Fixed Covariates
Authors: Lee Sik-Yum , Song Xin-Yuan
Published: February 2006

Recently, it has been recognized that the commonly used linear structural equation model is inadequate to deal with some complicated substantive theory. A new nonlinear structural equation model with fixed covariates is proposed in this article. A procedure, which utilizes the powerful path sampling for computing the Bayes factor, is developed for model comparison. In the implementation, the required random observations are simulated via a hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm. It is shown that the proposed procedure is efficient and flexible; and it produces Bayesian estimates of the parameters, latent variables, and their highest posterior density intervals as by-products. Empirical performances of the proposed procedure such as sensitivity to prior inputs are illustrated by a simulation study and a real example.
A Taxonomy of Latent Structure Assumptions for Probability Matrix Decomposition Models
Authors: Meulders Michel , De Boeck Paul , Van Mechelen Iven
Published: February 2006

A taxonomy of latent structure assumptions (LSAs) for probability matrix decomposition (PMD) models is proposed which includes the original PMD model (Maris, De Boeck, & Van Mechelen, 1996) as well as a three-way extension of the multiple classification latent class model (Maris, 1999). It is shown that PMD models involving different LSAs are actually restricted latent class models with latent variables that depend on some external variables. For parameter estimation a combined approach is proposed that uses both a mode-finding algorithm (EM) and a sampling-based approach (Gibbs sampling). A simulation study is conducted to investigate the extent to which information criteria, specific model checks, and checks for global goodness of fit may help to specify the basic assumptions of the different PMD models. Finally, an application is described with models involving different latent structure assumptions for data on hostile behavior in frustrating situations.
Marginal Maximum Likelihood Estimation for a Psychometric Model of Discontinuous Development
Authors: Mislevy Robert J. , Wilson Mark
Published: February 2006

Item response theory models posit latent variables to account for regularities in students' performances on test items. Wilson's “Saltus” model extends the ideas of IRT to development that occurs in stages, where expected changes can be discontinuous, show different patterns for different types of items, or even exhibit reversals in probabilities of success on certain tasks. Examples include Piagetian stages of psychological development and Siegler's rule-based learning. This paper derives marginal maximum likelihood (MML) estimation equations for the structural parameters of the Saltus model and suggests a computing approximation based on the EM algorithm. For individual examinees, empirical Bayes probabilities of learning-stage are given, along with proficiency parameter estimates conditional on stage membership. The MML solution is illustrated with simulated data and an example from the domain of mixed number subtraction.
Rasch's Multiplicative Poisson Model with Covariates
Authors: Ogasawara Haruhiko
Published: February 2006

As a multivariate model of the number of events, Rasch's multiplicative Poisson model is extended such that the parameters for individuals in the prior gamma distribution have continuous covariates. The parameters for individuals are integrated out and the hyperparameters in the prior distribution are estimated by a numerical method separately from difficulty parameters that are treated as fixed parameters or random variables. In addition, a method is presented for estimating parameters in Rasch's model with missing values.
An Alternative Two Stage Least Squares (2SLS) Estimator for Latent Variable Equations
Authors: Bollen Kenneth A.
Published: February 2006

The Maximum-likelihood estimator dominates the estimation of general structural equation models. Noniterative, equation-by-equation estimators for factor analysis have received some attention, but little has been done on such estimators for latent variable equations. I propose an alternative 2SLS estimator of the parameters in LISREL type models and contrast it with the existing ones. The new 2SLS estimator allows observed and latent variables to originate from nonnormal distributions, is consistent, has a known asymptotic covariance matrix, and is estimable with standard statistical software. Diagnostics for evaluating instrumental variables are described. An empirical example illustrates the estimator.
Some Uniqueness Results for PARAFAC2
Authors: ten Berge Jos M. F. , Kiers Henk A. L.
Published: February 2006

Whereas the unique axes properties of PARAFAC1 have been examined extensively, little is known about uniqueness properties for the PARAFAC2 model for covariance matrices. This paper is concerned with uniqueness in the rank two case of PARAFAC2. For this case, Harshman and Lundy have recently shown, subject to mild assumptions, that PARAFAC2 is unique when five (covariance) matrices are analyzed. In the present paper, this result is sharpened. PARAFAC2 is shown to be usually unique with four matrices. With three matrices it is not unique unless a certain additional assumption is introduced. If, for instance, the diagonal matrices of weights are constrained to be non-negative, three matrices are enough to have uniqueness in the rank two case of PARAFAC2.
Additive Structure in Qualitative Data: An Alternating Least Squares Method with Optimal Scaling Features
Authors: de Leeuw Jan , Young Forrest W. , Takane Yoshio
Published: February 2006

A method is developed to investigate the additive structure of data that (a) may be measured at the nominal, ordinal or cardinal levels, (b) may be obtained from either a discrete or continuous source, (c) may have known degrees of imprecision, or (d) may be obtained in unbalanced designs. The method also permits experimental variables to be measured at the ordinal level. It is shown that the method is convergent, and includes several previously proposed methods as special cases. Both Monte Carlo and empirical evaluations indicate that the method is robust.
A Solution to the Weighted Procrustes Problem in which the Transformation is in Agreement with the Loss Function
Authors: Lissitz Robert W. , Schönemann Peter H. , Lingoes James C.
Published: February 2006

This paper provides a generalization of the Procrustes problem in which the errors are weighted from the right, or the left, or both. The solution is achieved by having the orthogonality constraint on the transformation be in agreement with the norm of the least squares criterion. This general principle is discussed and illustrated by the mathematics of the weighted orthogonal Procrustes problem.
On the Theory of a Set of Tests which differ Only in Length
Authors: Kristof Walter
Published: February 2006

This paper presents a contribution to the sampling theory of a set of homogeneous tests which differ only in length, test length being regarded as an essential test parameter. Observed variance-covariance matrices of such measurements are taken to follow a Wishart distribution. The familiar true score-and-error concept of classical test theory is employed. Upon formulation of the basic model it is shown that in a combination of such tests forming a “total” test, the singal-to-noise ratio of the components is additive and that the inverse of the population variance-covariance matrix of the component measures has all of its off-diagonal elements equal, regardless of distributional assumptions. This fact facilitates the subsequent derivation of a statistical sampling theory, there being at most m + 1 free parameters when m is the number of component tests. In developing the theory, the cases of known and unknown test lengths are treated separately. For both cases maximum-likelihood estimators of the relevant parameters are derived. It is argued that the resulting formulas will remain reasonable even if the distributional assumptions are too narrow. Under these assumptions, however, maximum-likelihood ratio tests of the validity of the model and of hypotheses concerning reliability and standard error of measurement of the total test are given. It is shown in each case that the maximum-likelihood equations possess precisely one acceptable solution under rather natural conditions. Application of the methods can be effected without the use of a computer. Two numerical examples are appended by way of illustration.
Stochastic Processes and the Guttman Simplex
Authors: Groen Guy J.
Published: February 2006

The problem of whether a precise connection exists between stochastic processes of the type considered in mathematical learning theory and the Guttman simplex is investigated. The approach is to consider a class of models that characterize the sequential properties of discrete data, and to derive a set of conditions which a model must satisfy in order to generate inter-trial correlations r
ij
with the ‘perfect simplex’ property: r
ik
= r
ij
r
jk
for all trials i < j < k. It is shown that the Chapman-Kolomogorov Equations provide a necessary and sufficient condition for this property to hold. It follows that a process which is Markovian in the errors and successes will have this property. It is also shown that, if certain reliability assumptions are introduced, then the all-or-none model has the simplex property if the appropriate correlation coefficients are corrected for attenuation.
On the Robustness of Maximum Likelihood Scaling for Violations of the Error Model
Authors: Storms Gert
Published: February 2006

A Monte Carlo study was conducted to investigate the robustness of the assumed error distribution in maximum likelihood estimation models for multidimensional scaling. Data sets generated according to the lognormal, the normal, and the rectangular distribution were analysed with the log-normal error model in Ramsay's MULTISCALE program package. The results show that violations of the assumed error distribution have virtually no effect on the estimated distance parameters. In a comparison among several dimensionality tests, the corrected version of the x2 test, as proposed by Ramsay, yielded the best results, and turned out to be quite robust against violations of the error model.
Component Analysis with Different Sets of Constraints on Different Dimensions
Authors: Takane Yoshio , Kiers Henk A. L. , de Leeuw Jan
Published: February 2006

Many of the “classical” multivariate data analysis and multidimensional scaling techniques call for approximations by lower dimensional configurations. A model is proposed, in which different sets of linear constraints are imposed on different dimensions in component analysis and “classical” multidimensional scaling frameworks. A simple, efficient, and monotonically convergent algorithm is presented for fitting the model to the data by least squares. The basic algorithm is extended to cover across-dimension constraints imposed in addition to the dimensionwise constraints, and to the case of a symmetric data matrix. Examples are given to demonstrate the use of the method.
A Note on Dual Scaling of Successive Categories Data
Authors: Nishisato Shizuhiko , Sheu Wen-Jenn
Published: February 2006

Three methods for dual scaling of successive categories data are formulated. They are mathematically equivalent, and provide an appropriate technique to determine stimulus values and category boundaries on a joint scale, a problem that Nishisato's method (1980a) failed to handle.
A Response Model for Multiple Choice Items
Authors: Thissen David , Steinberg Lynne
Published: February 2006

We introduce an extended multivariate logistic response model for multiple choice items; this model includes several earlier proposals as special cases. The discussion includes a theoretical development of the model, a description of the relationship between the model and data, and a marginal maximum likelihood estimation scheme for the item parameters. Comparisons of the performance of different versions of the full model with more constrained forms corresponding to previous proposals are included, using likelihood ratio statistics and empirical data.
The Analysis of Structural Equation Models by Means of Derivative Free Nonlinear Least Squares
Authors: Lee Sik-Yum , Jennrich Robert I.
Published: February 2006

It is shown that the PAR Derivative-Free Nonlinear Regression program in BMDP can be used to fit structural equation models, producing generalized least squares estimates, standard errors, and goodness-of-fit test statistics. Covariance structure models more general than LISREL can be analyzed. The approach is particularly useful for dealing with new non-standard models and experimenting with alternate methods of estimation.
The Essential Process in a Family of Measurement Models
Authors: Masters Geofferey N. , Wright Benjamin D.
Published: February 2006

Five members of the Rasch family of latent trait models which have appeared more or less independently in the literature are brought together and identified as one model. In addition to sharing the distinguishing characteristic of the dichotomous Rasch model—separable person and item parameters and hence sufficient statistics—all five models share a common algebraic form and have as their basic element the fundamental process defined by Rasch's simple logistic expression. In these models, the sufficient statistics for person and item parameters are counts of events constructed to be indicative of the variable being measured, and the measures they enable are ‘fundamental’.
Doppler Adson’s Test: Predictor of Outcome of Surgery in Non‐Specific Thoracic Outlet Syndrome
Authors: Lee A.D. , Agarwal S. , Sadhu D.
Published: February 2006

Introduction

Outcome of surgery in non‐specific thoracic outlet syndrome (TOS) is variable. Duplex imaging of the subclavian artery during Adson’s maneuvre may help predict outcome.

Patients and methods

A retrospective study of 16 cases of non‐specific TOS who had pre‐operative duplex imaging of the subclavian artery during Adson’s maneuvre was done and their outcomes following surgical decompression of the thoracic outlet studied.

Results

Of the eight cases with a positive Adson’s test, seven (87.5%) had a complete response of symptoms following surgery while in the eight cases with a negative test, only four (50%) had a favorable response to surgery.

Conclusion

Duplex scanning of the thoracic outlet during Adson’s maneuvre may help predict outcome of thoracic outlet decompression surgery in cases of non‐specific TOS.
New Indication for Reduction Surgery in Patients with Advanced Hepatocellular Carcinoma with Major Vascular Involvement
Authors: Gotohda Naoto , Kinoshita Taira , Konishi Masaru , Nakagohri Toshio , Takahashi Shinichiro , Furuse Junji , Ishii Hiroshi , Yoshino Masahiro
Published: February 2006

Background

The prognosis of advanced hepatocellular carcinoma (HCC) remains poor, particularly in patients with tumor thrombi (TT) in the major vessels.

Patients and Methods

From July 1992 to October 2004, 161 patients diagnosed as having advanced HCC with major vascular involvement were seen consecutively at our hospital. Among these patients, 32 (20%) underwent surgical resection [16 complete resection (CR), 16 reductive resection (RR)]. Eighteen patients (11%) received radiotherapy (RT), 73 (45%) underwent transcatheter arterial chemoembolization (TACE) or transcatheter arterial infusion chemotherapy (TAI), 8 (5%) with distant metastases received systemic chemotherapy, and 30 (19%) received palliative therapy.

Results

Excluding the CR group, the patients in the RR group had a higher 1‐year survival rate than the other treatment groups. However, there was no significant difference in the overall survival rates of the RR, RT, and TACE/TAI groups. When we evaluated prognostic factors to clarify the indications for RR in the multidisciplinary treatment of patients with advanced HCC with TT, prothrombin activity (PA) was identified as a significant independent preoperative factor for overall survival in the RR group. The survival rate in patients with PA of ≤78% was significantly lower than that of patients with PA of >78% (P = 0.0004). The median survival time of patients with serum PA of >78% who underwent RR was 13.9 months and that of patients who underwent CR was 9.1 months, with no survival difference between the groups.

Conclusion

In advanced HCC with major vascular involvement, patients who had RR with PA of greater 78% achieved a similar survival to those who had CR. The surgeon should still proceed with RR in those patients with serum PA of >78% if CR does not seem feasible on preoperative evaluation.