bluuebunny/crossref_metadata_2025 huggingface dataset:
Application of the Bootstrap Methods in Factor Analysis
Authors: Ichikawa Masanori , Konishi Sadanori
Published: January 2006

A Monte Carlo experiment is conducted to investigate the performance of the bootstrap methods in normal theory maximum likelihood factor analysis both when the distributional assumption is satisfied and unsatisfied. The parameters and their functions of interest include unrotated loadings, analytically rotated loadings, and unique variances. The results reveal that (a) bootstrap bias estimation performs sometimes poorly for factor loadings and nonstandardized unique variances; (b) bootstrap variance estimation performs well even when the distributional assumption is violated; (c) bootstrap confidence intervals based on the Studentized statistics are recommended; (d) if structural hypothesis about the population covariance matrix is taken into account then the bootstrap distribution of the normal theory likelihood ratio test statistic is close to the corresponding sampling distribution with slightly heavier right tail.
An Extension of the Concept of Specific Objectivity
Authors: Irtel Hans
Published: January 2006

Comparisons of subjects are specifically objective if they do not depend on the items involved. Such comparisons are not restricted to the 1-parameter logistic latent trait model, but may also be defined within ordinal independence models and even within the 2-parameter logistic model.
Optimum Examinee Samples for Item Parameter Estimation in Item Response Theory: A Multi-Objective Programming Approach
Authors: Timminga Ellen
Published: January 2006

This paper proposes a multi-objective programming method for determining samples of examinees needed for estimating the parameters of a group of items. In the numerical experiments, optimum samples are compared to uniformly and normally distributed samples. The results show that the samples usually recommended in the literature are well suited for estimating the difficulty parameters. Furthermore, they are also adequate for estimating the discrimination parameters in the three-parameter model, but not for the guessing parameters.
Identifiability of Nonlinear Logistic Test Models
Authors: Bechger Timo M. , Verhelst Norman D. , Verstralen Huub H. F. M.
Published: January 2006

The linear logistic test model (LLTM) specifies the item parameters as a weighted sum of basic parameters. The LLTM is a special case of a more general nonlinear logistic test model (NLTM) where the weights are partially unknown. This paper is about the identifiability of the NLTM. Sufficient and necessary conditions for global identifiability are presented for a NLTM where the weights are linear functions, while conditions for local identifiability are shown to require a model with less restrictions. It is also discussed how these conditions are checked using an algorithm due to Bekker, Merckens, and Wansbeek (1994). Several illustrations are given.
Effect Size, Power, and Sample Size Determination for Structured means Modeling and Mimic Approaches to between-groups Hypothesis Testing of means on a Single Latent Construct
Authors: Hancock Gregory R.
Published: January 2006

While effect size estimates, post hoc power estimates, and a priori sample size determination are becoming a routine part of univariate analyses involving measured variables (e.g., ANOVA), such measures and methods have not been articulated for analyses involving latent means. The current article presents standardized effect size measures for latent mean differences inferred from both structured means modeling and MIMIC approaches to hypothesis testing about differences among means on a single latent construct. These measures are then related to post hoc power analysis, a priori sample size determination, and a relevant measure of construct reliability.
Compact Integer-Programming Models for Extracting Subsets of Stimuli from Confusion Matrices
Authors: Brusco Michael J. , Stahl Stephanie
Published: January 2006

This paper presents an integer linear programming formulation for the problem of extracting a subset of stimuli from a confusion matrix. The objective is to select stimuli such that total confusion among the stimuli is minimized for a particular subset size. This formulation provides a drastic reduction in the number of variables and constraints relative to a previously proposed formulation for the same problem. An extension of the formulation is provided for a biobjective problem that considers both confusion and recognition in the objective function. Demonstrations using an empirical interletter confusion matrix from the psychological literature revealed that a commercial branch-and-bound integer programming code was always able to identify optimal solutions for both the single-objective and biobjective formulations within a matter of seconds. A further extension and demonstration of the model is provided for the extraction of multiple subsets of stimuli, wherein the objectives are to maximize similarity within subsets and minimize similarity between subsets.
Standard Errors of Fit Indices using Residuals in Structural Equation Modeling
Authors: Ogasawara Haruhiko
Published: January 2006

The asymptotic standard errors of the correlation residuals and Bentler's standardized residuals in covariance structures are derived based on the asymptotic covariance matrix of raw covariance residuals. Using these results, approximations of the asymptotic standard errors of the root mean square residuals for unstandardized or standardized residuals are derived by the delta method. Further, in mean structures, approximations of the asymptotic standard errors of residuals, standardized residuals and their summary statistics are derived in a similar manner. Simulations are carried out, which show that the asymptotic standard errors of the various types of residuals and the root mean square residuals in covariance, correlation and mean structures are close to actual ones.
A Weighted Procrustes Criterion
Authors: Koschat Martin A. , Swayne Deborah F.
Published: January 2006

The Procrustes criterion is a common measure for the distance between two matrices X and Y, and can be interpreted as the sum of squares of the Euclidean distances between their respective column vectors. Often a weighted Procrustes criterion, using, for example, a weighted sum of the squared distances between the column vectors, is called for. This paper describes and analyzes the performance of an algorithm for rotating a matrix X such that the column-weighted Procrustes distance to Y is minimized. The problem of rotating X into Y such that an aggregate measure of Tucker's coefficient of congruence is maximized is also discussed.
The Rowwise Correlation between Two Proximity Matrices and the Partial Rowwise Correlation
Authors: de Vries Han
Published: January 2006

This paper discusses rowwise matrix correlation, based on the weighted sum of correlations between all pairs of corresponding rows of two proximity matrices, which may both be square (symmetric or asymmetric) or rectangular. Using the correlation coefficients usually associated with Pearson, Spearman, and Kendall, three different rowwise test statistics and their normalized coefficients are discussed, and subsequently compared with their nonrowwise alternatives like Mantel's Z. It is shown that the rowwise matrix correlation coefficient between two matrices X and Y is the partial correlation between the entries of X and Y controlled for the nominal variable that has the row objects as categories. Given this fact, partial rowwise correlations (as well as multiple regression extensions in the case of Pearson's approach) can be easily developed.
The Partial Credit Model and Null Categories
Authors: Wilson Mark , Masters Geofferey N.
Published: January 2006

A category where the frequency of responses is zero, either for sampling or structural reasons, will be called a null category. One approach for ordered polytomous item response models is to downcode the categories (i.e., reduce the score of each category above the null category by one), thus altering the relationship between the substantive framework and the scoring scheme for items with null categories. It is discussed why this is often not a good idea, and a method for avoiding the problem is described for the partial credit model while maintaining the integrity of the original response framework. This solution is based on a simple reexpression of the basic parameters of the model.
Analysis of Asymmetry by a Slide-Vector
Authors: Zielman Berrie , Heiser Willem J.
Published: January 2006

The slide-vector scaling model attempts to account for the asymmetry of a proximity matrix by a uniform shift in a fixed direction imposed on a symmetric Euclidean representation of the scaled objects. Although no method for fitting the slide-vector model seems available in the literature, the model can be viewed as a constrained version of the unfolding model, which does suggest one possible algorithm. The slide-vector model is generalized to handle three-way data, and two examples from market structure analysis are presented.
An Alternating Least Squares Method for the Weighted Approximation of a Symmetric Matrix
Authors: Berge Jos M. F. , Kiers Henk A. L.
Published: January 2006

Bailey and Gower examined the least squares approximation C to a symmetric matrix B, when the squared discrepancies for diagonal elements receive specific nonunit weights. They focussed on mathematical properties of the optimal C, in constrained and unconstrained cases, rather than on how to obtain C for any given B. In the present paper a computational solution is given for the case where C is constrained to be positive semidefinite and of a fixed rank r or less. The solution is based on weakly constrained linear regression analysis.
Fitting Longitudinal Reduced-Rank Regression Models by Alternating Least Squares
Authors: Bijleveld Catrien C. J. H. , De Leeuw Jan
Published: January 2006

An alternating least squares method for iteratively fitting the longitudinal reduced-rank regression model is proposed. The method uses ordinary least squares and majorization substeps to estimate the unknown parameters in the system and measurement equations of the model. In an example with cross-sectional data, it is shown how the results conform closely to results from eigenanalysis. Optimal scaling of nominal and ordinal variables is added in a third substep, and illustrated with two examples involving cross-sectional and longitudinal data.
Exact and Best Confidence Intervals for the Ability Parameter of the Rasch Model
Authors: Klauer Karl Christoph
Published: January 2006

A commonly used method to evaluate the accuracy of a measurement is to provide a confidence interval that contains the parameter of interest with a given high probability. Smallest exact confidence intervals for the ability parameter of the Rasch model are derived and compared to the traditional, asymptotically valid intervals based on the Fisher information. Tables of the exact confidence intervals, termed Clopper-Pearson intervals, can be routinely drawn up by applying a computer program designed by and obtainable from the author. These tables are particularly useful for tests of only moderate lengths where the asymptotic method does not provide valid confidence intervals.
Beyond Principal Component Analysis: A Trilinear Decomposition Model and Least Squares Estimation
Authors: Pham Tuan Dinh , Möcks Joachim
Published: January 2006

The paper derives sufficient conditions for the consistency and asymptotic normality of the least squares estimator of a trilinear decomposition model for multiway data analysis.
Ordinal Test Fidelity Estimated by an Item Sampling Model
Authors: Cliff Norman , Donoghue John R.
Published: January 2006

A test theory using only ordinal assumptions is presented. It is based on the idea that the test items are a sample from a universe of items. The sum across items of the ordinal relations for a pair of persons on the universe items is analogous to a true score. Using concepts from ordinal multiple regression, it is possible to estimate the tau correlations of test items with the universe order from the taus among the test items. These in turn permit the estimation of the tau of total score with the universe. It is also possible to estimate the odds that the direction of a given observed score difference is the same as that of the true score difference. The estimates of the correlations between items and universe and between total score and universe are found to agree well with the actual values in both real and artificial data.
An Automated Test Development of Parallel Tests from a Seed Test
Authors: Armstrong Ronald D. , Jones Douglas H. , Wu Ing-Long
Published: January 2006

Binary programming models are presented to generate parallel tests from an itembank. The parallel tests are created to match item for item an existing seed test and match user supplied taxonomic specifications. The taxonomic specifications may be either obtained from the seed test or from some other user requirement. An algorithm is presented along with computational results to indicate the overall efficiency of the process. Empirical findings based on an itembank for the Arithmetic Reasoning section of the Armed Services Vocational Aptitude Battery are given.
The Asymptotic Posterior Normality of the Latent Trait for Polytomous IRT Models
Authors: Chang Hua-Hua
Published: January 2006

Chang and Stout (1993) presented a derivation of the asymptotic posterior normality of the latent trait given examinee responses under nonrestrictive nonparametric assumptions for dichotomous IRT models. This paper presents an extention of their results to polytomous IRT models in a fairly straightforward manner. In addition, a global information function is defined, and the relationship between the global information function and the currently used information functions is discussed. An information index that combines both the global and local information is proposed for adaptive testing applications.
A Stochastic Multidimensional Unfolding Approach for Representing Phased Decision Outcomes
Authors: DeSarbo Wayne S. , Lehmann Donald R. , Carpenter Gregory , Sinha Indrajit
Published: January 2006

This paper presents a stochastic multidimensional unfolding (MDU) procedure to spatially represent individual differences in phased or sequential decision processes. The specific application or scenario to be discussed involves the area of consumer psychology where consumers form judgments sequentially in their awareness, consideration, and choice set compositions in a phased or sequential manner as more information about the alternative brands in a designated product/service class are collected. A brief review of the consumer psychology literature on these nested congnitive sets as stages in phased decision making is provided. The technical details of the proposed model, maximum likelihood estimation framework, and algorithm are then discussed. A small scale Monte Carlo analysis is presented to demonstrate estimation proficiency and the appropriateness of the proposed model selection heuristic. An application of the methodology to capture awareness, consideration, and choice sets in graduate school applicants is presented. Finally, directions for future research and other potential applications are given.
Modeling Within-Subject Dependencies in Ordinal Paired Comparison Data
Authors: Böckenholt Ulf , Dillon William R.
Published: January 2006

This paper presents two probabilistic models based on the logistic and the normal distribution for the analysis of dependencies in individual paired comparison judgments. It is argued that a core assumption of latent class choice models, independence of individual decisions, may not be well-suited for the analysis of paired comparison data. Instead, the analysis and interpretation of paired comparison data may be much simplified by allowing for within-person dependencies that result from repeated evaluations of the same options in different pairs. Moreover, by relating dependencies among the individual-level responses to (in)consistencies in the judgmental process, we show that the proposed graded paired comparison models reduce to ranking models under certain conditions. Three applications are presented to illustrate the approach.
A Latent Class Approach to Fitting the Weighted Euclidean Model, Clascal
Authors: Winsberg Suzanne , De Soete Geert
Published: January 2006

A weighted Euclidean distance model for analyzing three-way proximity data is proposed that incorporates a latent class approach. In this latent class weighted Euclidean model, the contribution to the distance function between two stimuli is per dimension weighted identically by all subjects in the same latent class. This model removes the rotational invariance of the classical multidimensional scaling model retaining psychologically meaningful dimensions, and drastically reduces the number of parameters in the traditional INDSCAL model. The probability density function for the data of a subject is posited to be a finite mixture of spherical multivariate normal densities. The maximum likelihood function is optimized by means of an EM algorithm; a modified Fisher scoring method is used to update the parameters in the M-step. A model selection strategy is proposed and illustrated on both real and artificial data.
Principal Component Analysis with External Information on both Subjects and Variables
Authors: Takane Yoshio , Shibayama Tadashi
Published: January 2006

A method for structural analysis of multivariate data is proposed that combines features of regression analysis and principal component analysis. In this method, the original data are first decomposed into several components according to external information. The components are then subjected to principal component analysis to explore structures within the components. It is shown that this requires the generalized singular value decomposition of a matrix with certain metric matrices. The numerical method based on the QR decomposition is described, which simplifies the computation considerably. The proposed method includes a number of interesting special cases, whose relations to existing methods are discussed. Examples are given to demonstrate practical uses of the method.
On the use of Ridit Analysis
Authors: Beder Jay H. , Heim Robert C.
Published: January 2006

Ridit analysis is statistical method for comparing ordinal-scale responses. In this paper, the extact variance and asymptotic distribution of the average ridit is developed, including the cases in which the reference group is sampled or the comparison group is finite. The appropriate use and interpretation of ridit analysis is also discussed.
A Note on Distributional Properties of the Jöreskog-Sörbom Fit Indices
Authors: Maiti Sadhan Samar , Mukherjee Bishwa Nath
Published: January 2006

In introducing the LISREL model for systems of linear structural equations, Jöreskog and Sörbom proposed two goodness-of-fit indices, GFI and AGFI. Their asymptotic distributions and some statistical properties are discussed.
Departure from Normal Assumptions: A Promise for Future Psychometrics with Substantive Mathematical Modeling
Authors: Samejima Fumiko
Published: January 2006

Normal assumptions have been used in many psychometric methods, to the extent that most researchers do not even question their adequacy. With the rapid advancement of computer technologies in recent years, psychometrics has extended its territory to include intensive cognitive diagnosis, etcetera, and substantive mathematical modeling has become essential. As a natural consequence, it is time to consider departure from normal assumptions seriously. As examples of models which are not based on normality or its approximation, the logistic positive exponent family of models is discussed. These models include the item task complexity as the third parameter, which determines the single principle of ordering individuals on the ability scale.
Item Information and Discrimination Functions for Trinary PCM Items
Authors: Akkermans Wies , Muraki Eiji
Published: January 2006

For trinary partial credit items the shape of the item information and the item discrimination function is examined in relation to the item parameters. In particular, it is shown that these functions are unimodal if δ2 − δ1 < 4 ln 2 and bimodal otherwise The locations and values of the maxima are derived. Furthermore, it is demonstrated that the value of the maximum is decreasing in δ2 − δ1. Consequently, the maximum of a unimodal item information function is always larger than the maximum of a bimodal one, and similarly for the item discrimination function.
The Nontruncated Marginal of a Truncated Bivariate Normal Distribution
Authors: Arnold Barry C. , Beaver Robert J. , Groeneveld Richard A. , Meeker William Q.
Published: January 2006

Inference is considered for the marginal distribution of X, when (X, Y) has a truncated bivariate normal distribution. The Y variable is truncated, but only the X values are observed. The relationship of this distribution to Azzalini's “skew-normal” distribution is obtained. Method of moments and maximum likelihood estimation are compared for the three-parameter Azzalini distribution. Samples that are uniformative about the skewness of this distribution may occur, even for large n. Profile likelihood methods are employed to describe the uncertainty involved in parameter estimation. A sample of 87 Otis test scores is shown to be well-described by this model.
The Application of Latent Class Models in Adaptive Testing
Authors: Macready George B. , Dayton C. Mitchell
Published: January 2006

This paper provides a description of a new adaptive testing algorithm based on a latent class modeling framework. The algorithm incorporates a four-stage iterative procedure that conditionally minimizes expected loss in classification of respondents across different content domains. The classification decisions relate to the membership of a person in a category of a latent variable for each of the separate domains considered. The algorithm appears to be particularly effective when latent class membership is related across the various domains of interest, since classification decisions on domains assessed early in the process are used to revise the probabilities for latent class membership on domains for which classification decisions have not yet been made. To assess the effectiveness of the proposed algorithm, a simulation based upon real data was conducted. For this example, the algorithm proved to be relatively efficient, requiring only 40% of the number of items needed under a nonadaptive approach. In addition, the algorithm provided classification decisions which, in 96% of the cases, were consistent with decisions based upon all available items when the maximum acceptable classification error rate was set at 5%.
A Bayesian Alternative to Least Squares and Equal Weighting Coefficients in Regression
Authors: Laughlin James E.
Published: January 2006

This paper details a Bayesian alternative to the use of least squares and equal weighting coefficients in regression. An equal weight prior distribution for the linear regression parameters is described with regard to the conditional normal regression model, and resulting posterior distributions for these parameters are detailed. Some interesting connections between this Bayesian procedure and several other methods for estimating optimal weighting coefficients are discussed. In addition, results are presented of a Monte Carlo investigation which compared the effectiveness of the Bayesian procedure relative to least squares, equal weight, ridge, and Bayesian exchangeability estimations.
A Simple General Method for Oblique Rotation
Authors: Jennrich Robert I.
Published: January 2006

A simple and very general algorithm for oblique rotation is identified. While motivated by the rotation problem in factor analysis, it may be used to minimize almost any function of a not necessarily square matrix whose columns are restricted to have unit length. The algorithm has two steps. The first is to compute the gradient of the rotation criterion and the second is to project this onto a manifold of matrices with unit length columns. For this reason it is called a gradient projection algorithm. Because the projection step is very simple, implementation of the algorithm involves little more than computing the gradient of the rotation criterion which for many applications is very simple. It is proven that the algorithm is strictly monotone, that is as long as it is not already at a stationary point, each step will decrease the value of the criterion. Examples from a variety of areas are used to demonstrate the algorithm, including oblimin rotation, target rotation, simplimax rotation, and rotation to similarity and simplicity simultaneously. While it may be, the algorithm is not intended for use as a standard algorithm for well established problems, but rather as a tool for investigating new methods where its generality and simplicity may save an investigator substantial effort.
A Unified Approach to Exploratory Factor Analysis with Missing Data, Nonnormal Data, and in the Presence of Outliers
Authors: Yuan Ke-Hai , Marshall Linda L. , Bentler Peter M.
Published: January 2006

Factor analysis is regularly used for analyzing survey data. Missing data, data with outliers and consequently nonnormal data are very common for data obtained through questionnaires. Based on covariance matrix estimates for such nonstandard samples, a unified approach for factor analysis is developed. By generalizing the approach of maximum likelihood under constraints, statistical properties of the estimates for factor loadings and error variances are obtained. A rescaled Bartlett-corrected statistic is proposed for evaluating the number of factors. Equivariance and invariance of parameter estimates and their standard errors for canonical, varimax, and normalized varimax rotations are discussed. Numerical results illustrate the sensitivity of classical methods and advantages of the proposed procedures.
Tucker3 Hierarchical Classes Analysis
Authors: Ceulemans Eva , Van Mechelen Iven , Leenen Iwin
Published: January 2006

This paper presents a new model for binary three-way three-mode data, called Tucker3 hierarchical classes model (Tucker3-HICLAS). This new model generalizes Leenen, Van Mechelen, De Boeck, and Rosenberg's (1999) individual differences hierarchical classes model (INDCLAS). Like the INDCLAS model, the Tucker3-HICLAS model includes a hierarchical classification of the elements of each mode, and a linking structure among the three hierarchies. Unlike INDCLAS, Tucker3-HICLAS (a) does not restrict the hierarchical classifications of the three modes to have the same rank, and (b) allows for more complex linking structures among the three hierarchies. An algorithm to fit the Tucker3-HICLAS model is described and evaluated in an extensive simulation study. An application of the model to hostility data is discussed.
The Optimality of the Centroid Method
Authors: Choulakian Vartan
Published: January 2006

The aim of this note is to show that the centroid method has two optimality properties. It yields loadings with the highest sum of absolute values, even in absence of the constraint that the squared component weights be equal. In addition, it yields scores with maximum variance, subject to the constraint that none of the squared component weights be larger than 1.
Least Squares Metric, Unidimensional Scaling of Multivariate Linear Models
Authors: Poole Keith T.
Published: January 2006

The squared error loss function for the unidimensional metric scaling problem has a special geometry. It is possible to efficiently find the global minimum for every coordinate conditioned on every other coordinate being held fixed. This approach is generalized to the case in which the coordinates are polynomial functions of exogenous variables. The algorithms shown in the paper are linear in the number of parameters. They always descend and, at convergence, every coefficient of every polynomial is at its global minimum conditioned on every other parameter being held fixed. Convergence is very rapid and Monte Carlo tests show the basic procedure almost always converges to the overall global minimum.
A Generalization of Takane's Algorithm for Dedicom
Authors: Kiers Henk A. L. , ten Berge Jos M. F. , Takane Yoshio , de Leeuw Jan
Published: January 2006

An algorithm is described for fitting the DEDICOM model for the analysis of asymmetric data matrices. This algorithm generalizes an algorithm suggested by Takane in that it uses a damping parameter in the iterative process. Takane's algorithm does not always converge monotonically. Based on the generalized algorithm, a modification of Takane's algorithm is suggested such that this modified algorithm converges monotonically. It is suggested to choose as starting configurations for the algorithm those configurations that yield closed-form solutions in some special cases. Finally, a sufficient condition is described for monotonic convergence of Takane's original algorithm.
Continuous and Discrete Latent Structure Models for Item Response Data
Authors: Haertel Edward H.
Published: January 2006

Relations are examined between latent trait and latent class models for item response data. Conditions are given for the two-latent class and two-parameter normal ogive models to agree, and relations between their item parameters are presented. Generalizations are then made to continuous models with more than one latent trait and discrete models with more than two latent classes, and methods are presented for relating latent class models to factor models for dichotomized variables. Results are illustrated using data from the Law School Admission Test, previously analyzed by several authors.
Joint Consistency of Nonparametric Item Characteristic Curve and Ability Estimation
Authors: Douglas Jeff
Published: January 2006

The simultaneous and nonparametric estimation of latent abilities and item characteristic curves is considered. The asymptotic properties of ordinal ability estimation and kernel smoothed nonparametric item characteristic curve estimation are investigated under very general assumptions on the underlying item response theory model as both the test length and the sample size increase. A large deviation probability inequality is stated for ordinal ability estimation. The mean squared error of kernel smoothed item characteristic curve estimates is studied and a strong consistency result is obtained showing that the worst case error in the item characteristic curve estimates over all items and ability levels converges to zero with probability equal to one.
Pairwise Partitioning: A Nonmetric Algorithm for Identifying Feature-Based Similarity Structures
Authors: Hutchinson J. Wesley , Mungale Amitabh
Published: January 2006

Pairwise partitioning is a nonmetric, divisive algorithm, for identifying feature structures based on pairwise similarities. For errorless data, this algorithm is shown to identify only (and sometimes all) valid features for certain hierarchical and multidimensional feature structures. Unfortunately, the algorithm is also extremely sensitive to error in the data. Fortunately, several modifications of the algorithm are shown to compensate significantly for this deficiency. The algorithm is illustrated with simulations and analyses of three sets of similarity data. The results suggest that this algorithm will be most useful (a) as an exploratory tool for generating a relatively large set of potential features that can be reduced using other criteria (either statistical or substantive) and (b) as a source of confirmatory or disconfirmatory evidence.
Measurement Invariance, Factor Analysis and Factorial Invariance
Authors: Meredith William
Published: January 2006

Several concepts are introduced and defined: measurement invariance, structural bias, weak measurement invariance, strong factorial invariance, and strict factorial invariance. It is shown that factorial invariance has implications for (weak) measurement invariance. Definitions of fairness in employment/admissions testing and salary equity are provided and it is argued that strict factorial invariance is required for fairness/equity to exist. Implications for item and test bias are developed and it is argued that item or test bias probably depends on the existence of latent variables that are irrelevant to the primary goal of test constructers.
A Latent Class Unfolding Model for Analyzing Single Stimulus Preference Ratings
Authors: De Soete Geert , Heiser Willem J.
Published: January 2006

A multidimensional unfolding model is developed that assumes that the subjects can be clustered into a small number of homogeneous groups or classes. The subjects that belong to the same group are represented by a single ideal point. Since it is not known in advance to which group or class a subject belongs, a mixture distribution model is formulated that can be considered as a latent class model for continuous single stimulus preference ratings. A GEM algorithm is described for estimating the parameters in the model. The M-step of the algorithm is based on a majorization procedure for updating the estimates of the spatial model parameters. A strategy for selecting the appropriate number of classes and the appropriate number of dimensions is proposed and fully illustrated on some artificial data. The latent class unfolding model is applied to political science data concerning party preferences from members of the Dutch Parliament. Finally, some possible extensions of the model are discussed.
A Monotonically Convergent Algorithm for Factals
Authors: Kiers Henk A. L. , Takane Yoshio , Mooijaart Ab
Published: January 2006

Takane, Young, and de Leeuw proposed a procedure called FACTALS for the analysis of variables of mixed measurement levels (numerical, ordinal, or nominal). Mooijaart pointed out that their algorithm does not necessarily converge, and Nevels proposed a new algorithm for the case of nominal variables. In the present paper it is shown that Nevels' procedure is incorrect, and a new procedure for handling nominal variables is proposed. In addition, a procedure for handling ordinal variables is proposed. Using these results, a monotonically convergent algorithm is constructed for FACTALS of any mixture of variables.
Fisher Transformations for Correlations Corrected for Selection and Missing Data
Authors: Mendoza Jorge L.
Published: January 2006

The validity of a test is often estimated in a nonrandom sample of selected individuals. To accurately estimate the relation between the predictor and the criterion we correct this correlation for range restriction. Unfortunately, this corrected correlation cannot be transformed using Fisher's Z transformation, and asymptotic tests of hypotheses based on small or moderate samples are not accurate. We developed a Fisher r to Z transformation for the corrected correlation for each of two conditions: (a) the criterion data were missing due to selection on the predictor (the missing data were MAR); and (b) the criterion was missing at random, not due to selection (the missing data were MCAR). The two Z transformations were evaluated in a computer simulation. The transformations were accurate, and tests of hypotheses and confidence intervals based on the transformations were superior to those that were not based on the transformations.
What can we Learn from the Path Equations?: Identifiability, Constraints, Equivalence
Authors: McDonald Roderick P.
Published: January 2006

Procedures are given for determining identified parameters, finding constraints on the covariances, and checking equivalence, in acyclic (recursive) linear path models with correlated error terms (disturbances), by inspection of the path equations, aided by simple recursions. This provides a useful and general alternative to the employment of directed acyclic graph theory for such purposes.
Testing Unidimensionality in Polytomous Rasch Models
Authors: Christensen Karl Bang , Bjorner Jakob Bue , Kreiner Svend , Petersen Jørgen Holm
Published: January 2006

A fundamental assumption of most IRT models is that items measure the same unidimensional latent construct. For the polytomous Rasch model two ways of testing this assumption against specific multidimensional alternatives are discussed. One, a marginal approach assuming a multidimensional parametric latent variable distribution, and, two, a conditional approach with no distributional assumptions about the latent variable. The second approach generalizes the Martin-Löf test for the dichotomous Rasch model in two ways: to polytomous items and to a test against an alternative that may have more than two dimensions. A study on occupational health is used to motivate and illustrate the methods.
An Ordinal Coefficient of Relational Agreement for Multiple Judges
Authors: Fagot Robert F.
Published: January 2006

In a recent article, Fagot proposed a generalized family of coefficients of relational agreement for multiple judges, focusing on the concept of empirically meaningful relationships. In this paper an ordinal coefficient of relational agreement, based on ranking data, is presented as a special case of the generalized family. It is shown that the proposed ordinal coefficient encompasses other ordinal coefficients, such as the Kendall coefficient of concordance, the average Spearman rank-order coefficient, and intraclass correlation based on ranks. It is also shown that the Kendall coefficient of concordance, corrected for chance agreement, is equivalent to the ordinal coefficient proposed in this paper.
Analyzing Sequential Categorical Data: Individual Variation in Markov Chains
Authors: Gardner William
Published: January 2006

Markov chains are probabilistic models for sequences of categorical events, with applications throughout scientific psychology. This paper provides a method for analyzing data consisting of event sequences and covariate observations. It is assumed that each sequence is a Markov process characterized by a distinct transition probability matrix. The objective is to use the covariate data to explain differences between individuals in the transition probability matrices characterizing their sequential data. The elements of the transition probability matrices are written as functions of a vector of latent variables, with variation in the latent variables explained through a multivariate regression on the covariates. The regression is estimated using the EM algorithm, and requires the numerical calculation of a multivariate integral. An example using simulated cognitive developmental data is presented, which shows that the estimation of individual variation in the parameters of a probability model may have substantial theoretical importance, even when individual differences are not the focus of the investigator's concerns.
A New Item Response Theory Modeling Approach with Applications to Unidimensionality Assessment and Ability Estimation
Authors: Strout William F.
Published: January 2006

Using an infinite item test framework, it is argued that the usual assumption of local independence be replaced by a weaker assumption, essential independence. A fortiori, the usual assumption of unidimensionality is replaced by a weaker and arguably more appropriate statistically testable assumption of essential unidimennsionality. Essential unidimennsionnality implies the existence of a “unique” unidimensional latent ability. Essential unidimensionality is equivalent to the “consistent” estimation of this latnet ability in an ordinal scaling sense using any Balanced empirical scaling. A variation of this estimation approach allows consistent estimation of ability on the given latent ability scale.
A Widely Applicable Extension of the Random Effects Two-Way Layout: Its Definition and Statistical Analysis Based on Group Invariance
Authors: Li Heng
Published: January 2006

A type of data layout that may be considered as an extension of the two-way random effects analysis of variance is characterized and modeled based on group invariance. The data layout seems to be suitable for several scenarios in psychometrics, including the one in which multiple measurements are taken on each of a set of variables, and the measurements can be divided into exchangeable subsets. The algebraic structure of the model is studied, which leads to results that are applicable to such problems as estimating correlation matrix corrected for attenuation and testing symmetry hypotheses.
An EM Algorithm for Fitting Two-Level Structural Equation Models
Authors: Liang Jiajuan , Bentler Peter M.
Published: January 2006

Maximum likelihood is an important approach to analysis of two-level structural equation models. Different algorithms for this purpose have been available in the literature. In this paper, we present a new formulation of two-level structural equation models and develop an EM algorithm for fitting this formulation. This new formulation covers a variety of two-level structural equation models. As a result, the proposed EM algorithm is widely applicable in practice. A practical example illustrates the performance of the EM algorithm and the maximum likelihood statistic.
Measuring the Ability of Transitive Reasoning, using Product and Strategy Information
Authors: Bouwmeester Samantha , Sijtsma Klaas
Published: January 2006

Cognitive theories disagree about the processes and the number of abilities involved in transitive reasoning. This led to controversies about the influence of task characteristics on individuals' performance and the development of transitive reasoning. In this study, a computer test was constructed containing 16 transitive reasoning tasks having different characteristics with respect to presentation form, task format, and task content. Both product and strategy information were analyzed to measure the performance of 6- to 13-year-old children. Three methods (MSP, DETECT, and Improved DIMTEST) were used to determine the number of abilities involved and to test the assumptions imposed on the data by item response models. Nonparametric IRT models were used to construct a scale for transitive reasoning. Multiple regression was used to determine the influence of task characteristics on the difficulty level of the tasks. It was concluded that: (1) the qualitatively distinct abilities predicted by Piaget's theory could not be distinguished by means of different dimensions in the data structure; (2) transitive reasoning could be described by one ability, and some task characteristics influenced the difficulty of a task; and (3) strategy information provided a stronger scale than product information.
Analysis of Distractor Difficulty in Multiple-Choice Items
Authors: Revuelta Javier
Published: January 2006

Two psychometric models are presented for evaluating the difficulty of the distractors in multiple-choice items. They are based on the criterion of rising distractor selection ratios, which facilitates interpretation of the subject and item parameters. Statistical inferential tools are developed in a Bayesian framework: modal a posteriori estimation by application of an EM algorithm and model evaluation by monitoring posterior predictive replications of the data matrix. An educational example with real data is included to exemplify the application of the models and compare them with the nominal categories model.
Renal function in tyrosinaemia type I after liver transplantation: A long‐term follow‐up
Authors: Pierik L. J. W. M. , van Spronsen F. J. , Bijleveld C. M. A. , van Dael C. M. L.
Published: January 2006

Hereditary tyrosinaemia type I is an autosomal recessive inborn error of tyrosine catabolism caused by a deficiency of the enzyme fumarylacetoacetase that results in liver failure, hepatocellular carcinoma, renal tubular dysfunction and acute intermittent porphyria. When treated with liver transplantation, tyrosinaemia type I was considered to be cured. Some years after the first liver transplantations in these patients, some reports focused on the renal function after transplantation. These reports showed that urinary succinylacetone excretion remained but that tubular function normalized. In this report we discuss the long‐term renal follow‐up (mean follow‐up time 11 years, range 7–14 years) after liver transplantation in 9 patients with tyrosinaemia type I treated by liver transplantation in our centre. An evaluation was made of renal function and succinylacetone excretion in urine. In all patients we found a persistent excretion of succinylacetone in the urine. With respect to the glomerular function, we can conclude that there is no clear change in GFR. At the same time, tubulopathy persisted in some patients. We consider that excretion of metabolites such as succinylacetone will be an important contributing factor to tubular dysfunction after liver transplantation in patients with tyrosinaemia type I. Therefore, notwithstanding the major effect of liver transplantation on tyrosine metabolism, renal tubular dysfunction remains at risk and needs careful monitoring. Progressive tubular dysfunction can cause glomerular damage. The use of low‐dose NTBC might be considered after liver transplantation in case of tubulopathy to prevent progression of tubular and glomerular dysfunction.
Marrow stromal cells from patients affected by MPS I differentially support haematopoietic progenitor cell development
Authors: Baxter M. A. , Wynn R. F. , Schyma L. , Holmes D. K. , Wraith J. E. , Fairbairn L. J. , Bellantuono I.
Published: January 2006

Bone marrow transplantation is the therapy of choice in patients affected by MPS I (Hurler syndrome), but a high incidence of rejection limits the success of this treatment. The deficiency of α‐L‐iduronidase (EC 1.2.3.76), one of the enzymes responsible for the degradation of glycosaminoglycans, results in accumulation of heparan and dermatan sulphate in these patients. Heparan sulphate and dermatan sulphate are known to be important components of the bone marrow microenvironment and critical for haematopoietic cell development. In this study we compared the ability of marrow stromal cells from MPS I patients and healthy donors to support normal haematopoiesis in Dexter‐type long term culture. We found an inverse stroma/supernatant ratio in the number of clonogenic progenitors, particularly the colony‐forming unit granulocyte–machrophage in MPS I cultures when compared to normal controls. No alteration in the adhesion of haematopoietic cells to the stroma of MPS I patients was found, suggesting that the altered distribution in the number of clonogenic progenitors is probably the result of an accelerated process of differentiation and maturation. The use of α‐L‐iduronidase gene‐corrected marrow stromal cells re‐established normal haematopoiesis in culture, suggesting that correction of the bone marrow microenvironment with competent enzyme prior to transplantation might help establishment of donor haematopoiesis.
Normal very‐long‐chain fatty acids in peroxisomal D‐bifunctional protein deficiency: A diagnostic pitfall
Authors: Soorani‐Lunsing R. J. , van Spronsen F. J. , Stolte‐Dijkstra I. , Wanders R. J. , Ferdinandusse S. , Waterham H. R. , Poll‐The B. T. , Rake J. P.
Published: January 2006

We present a relatively mild case of peroxisomal D‐bifunctional protein deficiency with inconsistent screening results in plasma for peroxisomal disorders.