bluuebunny/crossref_metadata_2025 huggingface dataset:
Conditions for Rasch-Dichotomizability of the Unidimensional Polytomous Rasch Model
Authors: Roskam Edward E. , Jansen Paul G. W.
Published: January 2006

Jansen and Roskam (1986) discussed the compatibility of the unidimensional polytomous Rasch model with dichotomization of the response continuum. They derived a rather strict condition in which dichotomization of multicategory data that fit the unidimensional polytomous Rasch model, results in dichotomous data which fit the dichotomous Research model with effectively the same subject parameter. In this paper a more general dichotomization condition is derived for the polytomous Rasch model, which appears less restrictive, but upholds that the intrinsic logic of the unidimensional polytomous Rasch model defies dichotomization in general. The robustness of dichotomous analysis investigated in a simulation study. It shows a close relation with the two-parameters (Birnbaum) model. Theoretical and methodological implications are discussed.
An Improved Solution for Factals: A Nonmetric Common Factor Analysis
Authors: Nevels Klaas
Published: January 2006

In FACTALS an alternating least squares algorithm is utilized. Mooijaart (1984) has shown that this algorithm is based upon an erroneous assumption. This paper gives a proper solution for the loss function used in FACTALS.
A Bayesian Random Effects Model for Testlets
Authors: Bradlow Eric T. , Wainer Howard , Wang Xiaohui
Published: January 2006

Standard item response theory (IRT) models fit to dichotomous examination responses ignore the fact that sets of items (testlets) often come from a single common stimuli (e.g. a reading comprehension passage). In this setting, all items given to an examinee are unlikely to be conditionally independent (given examinee proficiency). Models that assume conditional independence will overestimate the precision with which examinee proficiency is measured. Overstatement of precision may lead to inaccurate inferences such as prematurely ending an examination in which the stopping rule is based on the estimated standard error of examinee proficiency (e.g., an adaptive test). To model examinations that may be a mixture of independent items and testlets, we modified one standard IRT model to include an additional random effect for items nested within the same testlet. We use a Bayesian framework to facilitate posterior inference via a Data Augmented Gibbs Sampler (DAGS; Tanner & Wong, 1987). The modified and standard IRT models are both applied to a data set from a disclosed form of the SAT. We also provide simulation results that indicates that the degree of precision bias is a function of the variability of the testlet effects, as well as the testlet design.
Uniqueness of Three-Mode Factor Models with Sparse Cores: The 3 × 3 × 3 Case
Authors: Kiers Henk A. L. , ten Berge Jos M. F. , Rocci Roberto
Published: January 2006

Three-Mode Factor Analysis (3MFA) and PARAFAC are methods to describe three-way data. Both methods employ models with components for the three modes of a three-way array; the 3MFA model also uses a three-way core array for linking all components to each other. The use of the core array makes the 3MFA model more general than the PARAFAC model (thus allowing a better fit), but also more complicated. Moreover, in the 3MFA model the components are not uniquely determined, and it seems hard to choose among all possible solutions. A particularly interesting feature of the PARAFAC model is that it does give unique components. The present paper introduces a class of 3MFA models in between 3MFA and PARAFAC that share the good properties of the 3MFA model and the PARAFAC model: They fit (almost) as well as the 3MFA model, they are relatively simple and they have the same uniqueness properties as the PARAFAC model.
Rasch's Model for Reading Speed with Manifest Explanatory Variables
Authors: Jansen Margo G. H.
Published: January 2006

In educational and psychological measurement we find the distinction between speed and power tests. Although most tests are partially speeded, the speed element is usually neglected. Here we consider a latent trait model developed by Rasch for the response time on a (set of) pure speed test(s), which is based on the assumption that the test response times are approximately gamma distributed, with known shape parameters and scale parameters depending on subject “ability” and test “difficulty” parameters. In our approach the subject parameters are treated as random variables having a common gamma distribution. From this, maximum marginal likelihood estimators are derived for the test difficulties and the parameters of the latent subject distribution. This basic model can be extended in a number of ways. Explanatory variables for the latent subject parameters and for the test parameters can be incorporated in the model. Our methods are illustrated by the analysis of a simulated and an empirical data set.
Standard Errors for the Class of Orthomax-Rotated Factor Loadings: Some Matrix Results
Authors: Hayashi Kentaro , Yung Yiu-Fai
Published: January 2006

The partial derivative matrices of the class of orthomax-rotated factor loadings with respect to the unrotated maximum likelihood factor loadings are derived. The reported results are useful for obtaining standard errors of the orthomax-rotated factor loadings, with or without row normalization (standardization) of the initial factor loading matrix for rotation. Using a numerical example, we verify our analytic formulas by comparing the obtained standard error estimates with that from some existing methods. Some advantages of the current approach are discussed.
Quadratic Prediction of Factor Scores
Authors: Meijer Erik , Wansbeek Tom
Published: January 2006

Factor scores are naturally predicted by means of their conditional expectation given the indicators y. Under normality this expectation is linear in y but in general it is an unknown function of y. It is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic function of y.
A Model-Based Standardization Approach that Separates True Bias/DIF from Group Ability Differences and Detects Test Bias/DTF as well as Item Bias/DIF
Authors: Shealy Robin , Stout William
Published: January 2006

A model-based modification (SIBTEST) of the standardization index based upon a multidimensional IRT bias modeling approach is presented that detects and estimates DIF or item bias simultaneously for several items. A distinction between DIF and bias is proposed. SIBTEST detects bias/DIF without the usual Type 1 error inflation due to group target ability differences. In simulations, SIBTEST performs comparably to Mantel-Haenszel for the one item case. SIBTEST investigates bias/DIF for several items at the test score level (multiple item DIF called differential test functioning: DTF), thereby allowing the study of test bias/DIF, in particular bias/DIF amplification or cancellation and the cognitive bases for bias/DIF.
Constructing Measures with Maximum Reliability
Authors: Knott M. , Bartholomew D. J.
Published: January 2006

The scoring of response vectors to give maximum test-retest correlation is investigated. Simple sufficiency arguments show that the form of the best scores is very restricted. A general method is given for finding the best scores, deriving the best scores for the normal factor model, and showing by calculation of several particular cases that for a standard model for binary response it is easy to approximate the best scores.
A Generalized Family of Coefficients of Relational Agreement for Numerical Scales
Authors: Fagot Robert F.
Published: January 2006

A family of coefficients of relational agreement for numerical scales is proposed. The theory is a generalization to multiple judges of the Zegers and ten Berge theory of association coefficients for two variables and is based on the premise that the choice of a coefficient depends on the scale type of the variables, defined by the class of admissible transformations. Coefficients of relational agreement that denote agreement with respect to empirically meaningful relationships are derived for absolute, ratio, interval, and additive scales. The proposed theory is compared to intraclass correlation, and it is shown that the coefficient of additivity is identical to one measure of intraclass correlation.
Nonunique Solutions to the Likelihood Equation for the Three-Parameter Logistic Model
Authors: Yen Wendy M. , Burket George R. , Sykes Robert C.
Published: January 2006

Samejima identified the possibility of multiple solutions to the likelihood equation (multiple maxima in the likelihood function) for estimating an examinee's trait value for the three-parameter logistic model. In the practical applications that Lord studied, he found that multiple solutions did not occur when the number of items was ≥20. In the present paper, fourteen multiple-choice achievement tests with from 20 to 50 items were examined to see if it was possible for them to produce item response vectors with multiple maxima; such vectors were found for all the tests. Examination of response vectors for large groups of real examinees found that from 0 to 3.1% of them had response vectors with multiple maxima. The implications of these results for multiple-choice tests are discussed.
More “Tricks of the Trade”: Reparameterizing LISREL Models using Negative Variances
Authors: Green Donald Philip , Palmquist Bradley L.
Published: January 2006

This paper shows how LISREL may be used to estimate simplex models which impose constraints on the variances of endogenous variables. This technique allows us to estimate both the parameters and the standard errors of the correlated measurement error model proposed by Wiley and Wiley (1974).
A General Solution of the Weighted Orthonormal Procrustes Problem
Authors: Mooijaart Ab , Commandeur Jacques J. F.
Published: January 2006

A general solution for weighted orthonormal Procrustes problem is offered in terms of the least squares criterion. For the two-demensional case. this solution always gives the global minimum; for the general case, an algorithm is proposed that must converge, although not necessarily to the global minimum. In general, the algorithm yields a solution for the problem of how to fit one matrix to another under the condition that the dimensions of the latter matrix first are allowed to be transformed orthonormally and then weighted differentially, which is the task encountered in fitting analogues of the IDIOSCAL and INDSCAL models to a set of configurations.
Pseudo Maximum Likelihood Estimation and a Test for Misspecification in Mean and Covariance Structure Models
Authors: Arminger Gerhard , Schoenberg Ronald J.
Published: January 2006

Using the theory of pseudo maximum likelihood estimation the asymptotic covariance matrix of maximum likelihood estimates for mean and covariance structure models is given for the case where the variables are not multivariate normal. This asymptotic covariance matrix is consistently estimated without the computation of the empirical fourth order moment matrix. Using quasi-maximum likelihood theory a Hausman misspecification test is developed. This test is sensitive to misspecification caused by errors that are correlated with the independent variables. This misspecification cannot be detected by the test statistics currently used in covariance structure analysis.
Alternating Least Squares Algorithms for Simultaneous Components Analysis with Equal Component Weight Matrices in Two or More Populations
Authors: Kiers Henk A. L. , ten Berge Jos M. F.
Published: January 2006

Millsap and Meredith (1988) have developed a generalization of principal components analysis for the simultaneous analysis of a number of variables observed in several populations or on several occasions. The algorithm they provide has some disadvantages. The present paper offers two alternating least squares algorithms for their method, suitable for small and large data sets, respectively. Lower and upper bounds are given for the loss function to be minimized in the Millsap and Meredith method. These can serve to indicate whether or not a global optimum for the simultaneous components analysis problem has been attained.
Influential Observations in Principal Factor Analysis
Authors: Tanaka Yutaka , Odaka Yoshimasa
Published: January 2006

We propose a method for detecting influential observations in iterative principal factor analysis. For this purpose we derive the influence functions I(x; LLT) and I(x; Δ) for the common variance matrix T =LLT and the unique variance matrix Δ, respectively, in the common factor decomposition Σ =LLT + Δ. A numerical example is given for illustration.
Three-Mode Orthomax Rotation
Authors: Kiers Henk A. L.
Published: January 2006

Factor analysis and principal components analysis (PCA) are often followed by an orthomax rotation to rotate a loading matrix to simple structure. The simple structure is usually defined in terms of the simplicity of the columns of the loading matrix. In Three-mode PCA, rotational freedom of the so called core (a three-way array relating components for the three different modes) can be used similarly to find a simple structure of the core. Simple structure of the core can be defined with respect to all three modes simultaneously, possibly with different emphases on the different modes. The present paper provides a fully flexible approach for orthomax rotation of the core to simple structure with respect to three modes simultaneously. Computationally, this approach relies on repeated (two-way) orthomax applied to supermatrices containing the frontal, lateral or horizontal slabs, respectively. The procedure is illustrated by means of a number of exemplary analyses. As a by-product, application of the Three-mode Orthomax procedures to two-way arrays is shown to reveal interesting relations with and interpretations of existing two-way simple structure rotation techniques.
Multicategorical Spline Model for Item Response Theory
Authors: Abrahamowicz Michal , Ramsay James O.
Published: January 2006

Additional information contained in incorrect responses calls for a multicategorical rather than a binary analysis of multiple choice data. A nonparametric divided-by-total model for joint maximum likelihood estimation of probability-of-choice functions (for particular responses) and of latent ability is proposed. The model approximates probability functions by rational splines. Some illustrative examples of real test data analysis and the results of a Monte Carlo study are presented.
Comparing One-Step M-Estimators of Location Corresponding to Two Independent Groups
Authors: Wilcox Rand R.
Published: January 2006

Experience with real data indicates that psychometric measures often have heavy-tailed distributions. This is known to be a serious problem when comparing the means of two independent groups because heavy-tailed distributions can have a serious effect on power. Another problem that is common in some areas is outliers. This paper suggests an approach to these problems based on the one-step M-estimator of location. Simulations indicate that the new procedure provides very good control over the probability of a Type I error even when distributions are skewed, have different shapes, and the variances are unequal. Moreover, the new procedure has considerably more power than Welch's method when distributions have heavy tails, and it compares well to Yuen's method for comparing trimmed means. Wilcox's median procedure has about the same power as the proposed procedure, but Wilcox's method is based on a statistic that has a finite sample breakdown point of only 1/n, where n is the sample size. Comments on other methods for comparing groups are also included.
Convergence Theory for Partial Images and Revision of the Definition of Total Images
Authors: Findeisen Peter
Published: January 2006

Guttman's assumption underlying his definition of “total images” is rejected: Partial images are not generally convergent everywhere. Even divergence everywhere is shown to be possible. The convergence type always found on partial images is convergence in quadratic mean; hence, total images are redefined as quadratic mean-limits. In determining the convergence type in special situations, the asymptotic properties of certain correlations are important, implying, in some cases, convergence almost everywhere, which is also effected by a countable population or multivariate normality or independent variables. The interpretations of a total image as a predictor, and a “common-factor score”, respectively, are made precise.
Note on Two Generalizations of Coefficient Alpha
Authors: Raju Nambury S.
Published: January 2006

An important relationship is given for two generalizations of coefficient alpha, Rajaratnam, Cronbach and Gleser's generalizability formula for stratified-parallel tests and Raju's coefficient beta.
The Role of Secondary Covariates when Estimating latent Trait Population Distributions
Authors: Thomas Neal
Published: January 2006

The U.S. National Assessment of Educational Progress (NAEP), the Third International Mathematics and Science Study (TIMSS), and the U.S. Adult Literacy Survey collect probability samples of students (or adults) who are administered brief examinations in subject areas such as mathematics and reading (cognitive variables), along with background demographic (primary) and educational environment (secondary) questions. The demographic questions are used in the primary reporting, while the numerous “explanatory” secondary variables, or “covariates”, are only directly utilized in subsequent secondary analyses. The covariates are also used indirectly to create the plausible values (multiple imputations) that are an integral part of analyses because of the use of sparse matrix sampling of cognitive items. The improvement in the precision of the primary reporting due to the inclusion of the covariates is assessed here and contrasted with the precision of reporting using plausible values created using only the primary demographic variables.

The results demonstrate that the improvement in precision depends on the matrix sampling designs for the cognitive assessments. The improvements range from essentially none for the most common designs, to moderate for some less common designs. Consequently, two potential changes in the reporting procedures that could improve the statistical and operational efficiency of primary reporting are (a) eliminate or reduce the collection of covariates and increase the number of cognitive items, (b) to avoid delays, eliminate the covariates from the creation of plausible values used for the primary reports, but include them later when creating public-use files for secondary analyses. The potential improvements in statistical and operational efficiency must be weighed against the intrinsic interest in the covariates, and the potential for small discrepancies in the primary and secondary reporting.
Equivalent Linear Logistic Test Models
Authors: Bechger Timo M. , Verstralen Huub H. F. M. , Verhelst Norman D.
Published: January 2006

This paper is about the Linear Logistic Test Model (LLTM). We demonstrate that there are infinitely many equivalent ways to specify a model. An implication is that there may well be many ways to change the specification of a given LLTM and achieve the same improvement in model fit. To illustrate this phenomenon, we analyze a real data set using a Lagrange multiplier test for the specification of the model. This Lagrange multiplier test is similar to the modification index used in structural equation modeling.
On the Need for Negative Local Item Dependence
Authors: Habing Brian , Roussos Louis A.
Published: January 2006

While negative local item dependence (LID) has been discussed in numerous articles, its occurrence and effects often go unrecognized. This is due in part to confusion over what unidimensional latent trait is being utilized in evaluating the LID of multidimensional testing data. This article addresses this confusion by using an appropriately chosen latent variable to condition on. It then provides a proof that negative LID must occur when unidimensional ability estimates (such as number right score) are obtained from data which follow a very general class of multidimensional item response theory models. The importance of specifying what unidimensional latent trait is used, and its effect on the sign of the LIDs are shown to have implications in regard to a variety of foundational theoretical arguments, to the simulation of LID data sets, and to the use of testlet scoring for removing LID.
The Robustness of the Usual Correction for Restriction in Range Due to Explicit Selection
Authors: Holmes D. J.
Published: January 2006

Corrections for restriction in range due to explicit selection assume the linearity of regression and homoscedastic array variances. This paper develops a theoretical framework in which the effects of some common forms of violation of these assumptions on the estimation of the unrestricted correlation can be investigated. Simple expressions are derived for both the restricted and corrected correlations in terms of the target (unrestricted) correlation in these situations.
Interpreting Canonical Correlation Analysis through Biplots of Structure Correlations and Weights
Authors: ter Braak Cajo J. F.
Published: January 2006

This paper extends the biplot technique to canonical correlation analysis and redundancy analysis. The plot of structure correlations is shown to the optimal for displaying the pairwise correlations between the variables of the one set and those of the second. The link between multivariate regression and canonical correlation analysis/redundancy analysis is exploited for producing an optimal biplot that displays a matrix of regression coefficients. This plot can be made from the canonical weights of the predictors and the structure correlations of the criterion variables. An example is used to show how the proposed biplots may be interpreted.
Distractor Selection Ratios
Authors: Love Thomas E.
Published: January 2006

A latent variable representation for multiple-choice item and option characteristic curves is presented. Under standard assumptions of conditional independence of item responses and monotonicity of item characteristic curves, a criterion for distractors is proposed based on distractor selection ratios. A connection is made between the proposed criterion and the theory of individual choice behavior, providing new insight. The main results allow for the testing of the criterion from observable data without first specifying a parametric form for the characteristic curves. A series of examples apply the method.
Cluster Differences Scaling with a Within-Clusters Loss Component and a Fuzzy Successive Approximation Strategy to Avoid Local Minima
Authors: Heiser Willem J. , Groenen Patrick J. F.
Published: January 2006

Cluster differences scaling is a method for partitioning a set of objects into classes and simultaneously finding a low-dimensional spatial representation of K cluster points, to model a given square table of dissimilarities among n stimuli or objects. The least squares loss function of cluster differences scaling, originally defined only on the residuals of pairs of objects that are allocated to different clusters, is extended with a loss component for pairs that are allocated to the same cluster. It is shown that this extension makes the method equivalent to multidimensional scaling with cluster constraints on the coordinates. A decomposition of the sum of squared dissimilarities into contributions from several sources of variation is described, including the appropriate degrees of freedom for each source. After developing a convergent algorithm for fitting the cluster differences model, it is argued that the individual objects and the cluster locations can be jointly displayed in a configuration obtained as a by-product of the optimization. Finally, the paper introduces a fuzzy version of the loss function, which can be used in a successive approximation strategy for avoiding local minima. A simulation study demonstrates that this strategy significantly outperforms two other well-known initialization strategies, and that it has a success rate of 92 out of 100 in attaining the global minimum.
Exploring the Set-Theoretical Structure of Objects by Additive Trees
Authors: Candel Math J. J. M.
Published: January 2006

Arrangements of feature sets that have been proposed to represent qualitative and quantitative variation among objects are shown to generate identical sets of set-symmetric distances. The set-symmetric distances for these feature arrangements can be represented by path lengths in an additive linear tree. Imperfect versions of these feature arrangements are proposed, which also are indistinguishable by the set-symmetric distance model. The distances for the imperfect versions can be represented by path lengths in an additive imperfectly linear tree. When dissimilarities are defined by the more general contrast model and a constant may be added to proximity data, then for both the perfect and imperfect arrangements an additive tree analysis obtains a perfect fit with an imperfectly linear tree. However, in the case of the contrast model also the distinction between the perfect and imperfect arrangements disappears in that also for the perfect arrangements the resulting tree need no longer be linear.
A Person-Fit Index for Polytomous Rasch Models, Latent Class Models, and Their Mixture Generalizations
Authors: von Davier Matthias , Molenaar Ivo W.
Published: January 2006

A normally distributed person-fit index is proposed for detecting aberrant response patterns in latent class models and mixture distribution IRT models for dichotomous and polytomous data.

This article extends previous work on the null distribution of person-fit indices for the dichotomous Rasch model to a number of models for categorical data. A comparison of two different approaches to handle the skewness of the person-fit index distribution is included.
Multilevel Logistic Regression for Polytomous Data and Rankings
Authors: Skrondal Anders , Rabe-Hesketh Sophia
Published: January 2006

We propose a unifying framework for multilevel modeling of polytomous data and rankings, accommodating dependence induced by factor and/or random coefficient structures at different levels. The framework subsumes a wide range of models proposed in disparate methodological literatures. Partial and tied rankings, alternative specific explanatory variables and alternative sets varying across units are handled. The problem of identification is addressed. We develop an estimation and prediction methodology for the model framework which is implemented in the generally available gllamm software. The methodology is applied to party choice and rankings from the 1987–1992 panel of the British Election Study. Three levels are considered: elections, voters and constituencies.
Analysis of Contingency Tables by Ideal Point Discriminant Analysis
Authors: Takane Yoshio
Published: January 2006

Cross-classified data are frequently encountered in behavioral and social science research. The loglinear model and dual scaling (correspondence analysis) are two representative methods of analyzing such data. An alternative method, based on ideal point discriminant analysis (DA), is proposed for analysis of contingency tables, which in a certain sense encompasses the two existing methods. A variety of interesting structures can be imposed on rows and columns of the tables through manipulations of predictor variables and/or as direct constraints on model parameters. This, along with maximum likelihood estimation of the model parameters, allows interesting model comparisons. This is illustrated by the analysis of several data sets.
An Incomplete Data Approach to the Analysis of Covariance Structures
Authors: Kiiveri H. T.
Published: January 2006

In this paper, linear structural equation models with latent variables are considered. It is shown how many common models arise from incomplete observation of a relatively simple system. Subclasses of models with conditional independence interpretations are also discussed. Using an incomplete data point of view, the relationships between the incomplete and complete data likelihoods, assuming normality, are highlighted. For computing maximum likelihood estimates, the EM algorithm and alternatives are surveyed. For the alternative algorithms, simplified expressions for computing function values and derivatives are given. Likelihood ratio tests based on complete and incomplete data are related, and an example on using their relationship to improve the fit of a model is given.
Network Models for Social Influence Processes
Authors: Robins Garry , Pattison Philippa , Elliott Peter
Published: January 2006

This paper generalizes the p* class of models for social network data to predict individual-level attributes from network ties. The p* model for social networks permits the modeling of social relationships in terms of particular local relational or network configurations. In this paper we present methods for modeling attribute measures in terms of network ties, and so construct p* models for the patterns of social influence within a network. Attribute variables are included in a directed dependence graph and the Hammersley-Clifford theorem is employed to derive probability models whose parameters can be estimated using maximum pseudo-likelihood. The models are compared to existing network effects models. They can be interpreted in terms of public or private social influence phenomena within groups. The models are illustrated by an empirical example involving a training course, with trainees' reactions to aspects of the course found to relate to those of their network partners.
Maximum Likelihood Estimation of Nonlinear Structural Equation Models
Authors: Lee Sik-Yum , Zhu Hong-Tu
Published: January 2006

The existing maximum likelihood theory and its computer software in structural equation modeling are established based on linear relationships among manifest variables and latent variables. However, models with nonlinear relationships are often encountered in social and behavioral sciences. In this article, an EM type algorithm is developed for maximum likelihood estimation of a general nonlinear structural equation model. To avoid computation of the complicated multiple integrals involved, the E-step is completed by a Metropolis-Hastings algorithm. It is shown that the M-step can be completed efficiently by simple conditional maximization. Standard errors of the maximum likelihood estimates are obtained via Louis's formula. The methodology is illustrated with results from a simulation study and two real examples.
Analysis of Structural Equation Model with Ignorable Missing Continuous and Polytomous Data
Authors: Song Xin-Yuan , Lee Sik-Yum
Published: January 2006

The main purpose of this article is to develop a Bayesian approach for structural equation models with ignorable missing continuous and polytomous data. Joint Bayesian estimates of thresholds, structural parameters and latent factor scores are obtained simultaneously. The idea of data augmentation is used to solve the computational difficulties involved. In the posterior analysis, in addition to the real missing data, latent variables and latent continuous measurements underlying the polytomous data are treated as hypothetical missing data. An algorithm that embeds the Metropolis-Hastings algorithm within the Gibbs sampler is implemented to produce the Bayesian estimates. A goodness-of-fit statistic for testing the posited model is presented. It is shown that the proposed approach is not sensitive to prior distributions and can handle situations with a large number of missing patterns whose underlying sample sizes may be small. Computational efficiency of the proposed procedure is illustrated by simulation studies and a real example.
Psychometrics: from Practice to Theory and Back
Authors: Stout William
Published: January 2006

The paper surveys 15 years of progress in three psychometric research areas: latent dimensionality structure, test fairness, and skills diagnosis of educational tests. It is proposed that one effective model for selecting and carrying out research is to chose one's research questions from practical challenges facing educational testing, then bring to bear sophisticated probability modeling and statistical analyses to solve these questions, and finally to make effectiveness of the research answers in meeting the educational testing challenges be the ultimate criterion for judging the value of the research. The problem-solving power and the joy of working with a dedicated, focused, and collegial group of colleagues is emphasized. Finally, it is suggested that the summative assessment testing paradigm that has driven test measurement research for over half a century is giving way to a new paradigm that in addition embraces skills level formative assessment, opening up a plethora of challenging, exciting, and societally important research problems for psychometricians.
On Normal Theory Based Inference for Multilevel Models with Distributional Violations
Authors: Yuan Ke-Hai , Bentler Peter M.
Published: January 2006

Data in social and behavioral sciences are often hierarchically organized though seldom normal, yet normal theory based inference procedures are routinely used for analyzing multilevel models. Based on this observation, simple adjustments to normal theory based results are proposed to minimize the consequences of violating normality assumptions. For characterizing the distribution of parameter estimates, sandwich-type covariance matrices are derived. Standard errors based on these covariance matrices remain consistent under distributional violations. Implications of various covariance estimators are also discussed. For evaluating the quality of a multilevel model, a rescaled statistic is given for both the hierarchical linear model and the hierarchical structural equation model. The rescaled statistic, improving the likelihood ratio statistic by estimating one extra parameter, approaches the same mean as its reference distribution. A simulation study with a 2-level factor model implies that the rescaled statistic is preferable.
Tests of Homogeneity of Means and Covariance Matrices for Multivariate Incomplete Data
Authors: Kim Kevin H. , Bentler Peter M.
Published: January 2006

Existing test statistics for assessing whether incomplete data represent a missing completely at random sample from a single population are based on a normal likelihood rationale and effectively test for homogeneity of means and covariances across missing data patterns. The likelihood approach cannot be implemented adequately if a pattern of missing data contains very few subjects. A generalized least squares rationale is used to develop parallel tests that are expected to be more stable in small samples. Three factors were varied for a simulation: number of variables, percent missing completely at random, and sample size. One thousand data sets were simulated for each condition. The generalized least squares test of homogeneity of means performed close to an ideal Type I error rate for most of the conditions. The generalized least squares test of homogeneity of covariance matrices and a combined test performed quite well also.
Building an Identifiable Latent Class Model with Covariate Effects on Underlying and Measured Variables
Authors: Huang Guan-Hua , Bandeen-Roche Karen
Published: January 2006

In recent years, latent class models have proven useful for analyzing relationships between measured multiple indicators and covariates of interest. Such models summarize shared features of the multiple indicators as an underlying categorical variable, and the indicators' substantive associations with predictors are built directly and indirectly in unique model parameters. In this paper, we provide a detailed study on the theory and application of building models that allow mediated relationships between primary predictors and latent class membership, but that also allow direct effects of secondary covariates on the indicators themselves. Theory for model identification is developed. We detail an Expectation-Maximization algorithm for parameter estimation, standard error calculation, and convergent properties. Comparison of the proposed model with models underlying existing latent class modeling software is provided. A detailed analysis of how visual impairments affect older persons' functioning requiring distance vision is used for illustration.
The Repeated Insertion Model for Rankings: Missing Link between Two Subset Choice Models
Authors: Doignon Jean-Paul , Pekeč Aleksandar , Regenwetter Michel
Published: January 2006

Several probabilistic models for subset choice have been proposed in the literature, for example, to explain approval voting data. We show that Marley et al.'s latent scale model is subsumed by Falmagne and Regenwetter's size-independent model, in the sense that every choice probability distribution generated by the former can also be explained by the latter. Our proof relies on the construction of a probabilistic ranking model which we label the “repeated insertion model.” This model is a special case of Marden's orthogonal contrast model class and, in turn, includes the classical Mallows φ-model as a special case. We explore its basic properties as well as its relationship to Fligner and Verducci's multistage ranking model.
A Multivariate Reduced-Rank Growth Curve Model with Unbalanced Data
Authors: Hwang Heungsun , Takane Yoshio
Published: January 2006

A multivariate reduced-rank growth curve model is proposed that extends the univariate reducedrank growth curve model to the multivariate case, in which several response variables are measured over multiple time points. The proposed model allows us to investigate the relationships among a number of response variables in a more parsimonious way than the traditional growth curve model. In addition, the method is more flexible than the traditional growth curve model. For example, response variables do not have to be measured at the same time points, nor the same number of time points. It is also possible to apply various kinds of basis function matrices with different ranks across response variables. It is not necessary to specify an entire set of basis functions in advance. Examples are given for illustration.
Locally Dependent Latent Trait Model for Polytomous Responses with Application to Inventory of Hostility
Authors: Ip Edward H. , Wang Yuchung J. , de Boeck Paul , Meulders Michel
Published: January 2006

Psychological tests often involve item clusters that are designed to solicit responses to behavioral stimuli. The dependency between individual responses within clusters beyond that which can be explained by the underlying trait sometimes reveals structures that are of substantive interest. The paper describes two general classes of models for this type of locally dependent responses. Specifically, the models include a generalized log-linear representation and a hybrid parameterization model for polytomous data. A compact matrix notation designed to succinctly represent the system of complex multivariate polytomous responses is presented. The matrix representation creates the necessary formulation for the locally dependent kernel for polytomous item responses. Using polytomous data from an inventory of hostility, we provide illustrations as to how the locally dependent models can be used in psychological measurement.
Asymptotic Biases in Exploratory Factor Analysis and Structural Equation Modeling
Authors: Ogasawara Haruhiko
Published: January 2006

Formulas for the asymptotic biases of the parameter estimates in structural equation models are provided in the case of the Wishart maximum likelihood estimation for normally and nonnormally distributed variables. When multivariate normality is satisfied, considerable simplification is obtained for the models of unstandardized variables. Formulas for the models of standardized variables are also provided. Numerical examples with Monte Carlo simulations in factor analysis show the accuracy of the formulas and suggest the asymptotic robustness of the asymptotic biases with normality assumption against nonnormal data. Some relationships between the asymptotic biases and other asymptotic values are discussed.
Rotation to Simple Loadings Using Component Loss Functions: The Orthogonal Case
Authors: Jennrich Robert I.
Published: January 2006

Component loss functions (CLFs) are used to generalize the quartimax criterion for orthogonal rotation in factor analysis. These replace the fourth powers of the factor loadings by an arbitrary function of the second powers. Criteria of this form were introduced by a number of authors, primarily Katz and Rohlf (1974) and Rozeboom (1991), but there has been essentially no follow-up to this work. A method so simple, natural, and general deserves to be investigated more completely. A number of theoretical results are derived including the fact that any method using a concave CLF will recover perfect simple structure whenever it exists, and there are methods that will recover Thurstone simple structure whenever it exists. Specific CLFs are identified and it is shown how to compare these using standardized plots. Numerical examples are used to illustrate and compare CLF and other methods. Sorted absolute loading plots are introduced to aid in comparing results and setting parameters for methods that require them.
Interval Estimation of Gamma for an R×S table
Authors: Lui Kung-Jong , Cumberland William G.
Published: January 2006

When the underlying responses are on an ordinal scale, gamma is one of the most frequently used indices to measure the strength of association between two ordered variables. However, except for a brief mention on the use of the traditional interval estimator based on Wald's statistic, discussion of interval estimation of the gamma is limited. Because it is well known that an interval estimator using Wald's statistic is generally not likely to perform well especially when the sample size is small, the goal of this paper is to find ways to improve the finite-sample performance of this estimator. This paper develops five asymptotic interval estimators of the gamma by employing various methods that are commonly used to improve the normal approximation of the maximum likelihood estimator (MLE). Using Monte Carlo simulation, this paper notes that the coverage probability of the interval estimator using Wald's statistic can be much less than the desired confidence level, especially when the underlying gamma is large. Further, except for the extreme case, in which the underlying gamma is large and the sample size is small, the interval estimator using a logarithmic transformation together with a monotonic function proposed here not only performs well with respect to the coverage probability, but is also more efficient than all the other estimators considered here. Finally, this paper notes that applying an ad hoc adjustment procedure—whenever any observed frequency equals 0, we add 0.5 to all cells in calculation of the cell proportions—can substantially improve the traditional interval estimator. This paper includes two examples to illustrate the practical use of interval estimators considered here.
Testing methods for X-machines: a review
Authors: Bogdanov K. , Holcombe M. , Ipate F. , Seed L. , Vanak S.
Published: January 2006

The X-machine testing method has been developed as an application of the W-method to testing the control structure of an implementation, against a specification. The method was proven to demonstrate the equivalence of the behaviour of the two, subject to a number of conditions both a specification and an implementation are expected to satisfy, such as (1) determinism of the two and (2) that functions labelling arcs on a transition diagram of a specification control structure have been tested in advance. Since the original publication of the testing method, a number of extensions have been published, removing the restrictions mentioned above. This paper surveys the extensions of the X-machine testing method, for (1) testing of functions together with testing of a transition diagram, (2) equivalence testing of a non-deterministic implementation against a non-deterministic specification, (3) conformance testing of a deterministic implementation against a non-deterministic specification and (4) equivalence testing of a system of concurrently executing and communicating X-machines, against a specification.
Nonviral in vivo gene transfer in the mucopolysaccharidosis I murine model
Authors: Camassola M. , Braga L. M. , Delgado‐Cañedo A. , Dalberto T. P. , Matte U. , Burin M. , Giugliani R. , Nardi N. B.
Published: January 2006

Mucopolysaccharidosis I (MPS I) is a lysosomal disorder characterized by a deficiency of the enzyme α‐L‐iduronidase (IDUA), which is responsible for the degradation of glycosaminoglycans (GAGs). This deficiency leads to the accumulation of dermatan and heparan sulphate in lysosomes. Presently available treatments include bone marrow transplantation and enzyme replacement therapies, both of which are limited in their effects. In this work, knockout (KO) MPS I mice were treated with a nonviral vector containing the human IDUA cDNA. KO mice were transfected by hydrodynamic injection of pRIDUA in the caudal vein (i.v., n = 3) or by intraperitoneal injection of pRIDUA/Superfect complexes (i.p., n = 3). GAG concentration and IDUA activity were analysed in the kidneys, spleen, lungs, brain and liver. The expression of IDUA in the organs of i.v.‐ and i.p.‐treated mice was also analysed by real‐time reverse‐transcription (RT) PCR and compared by relative quantification. The concentration of GAGs in the organs differed between KO and wild‐type mice. In the spleen and liver, GAG levels were lower in i.v.‐ and i.p.‐treated KO mice than in control nontreated animals. Real‐time RT‐PCR showed that the transgene is expressed in all the analysed organs of i.p.‐ and i.v.‐treated KO mice. Enzyme activity was similarly observed in all the organs analysed. Our data suggest that this kind of transfection may be a useful tool for studies of nonviral protocols for gene therapy of MPS.
Influence of D‐arabitol and ribitol on neuronal network activity
Authors: Klusmann A. , Fleischer W. , Waldhaus A. , Siebler M. , Mayatepek E.
Published: January 2006

To date, two new defects in the pentose phosphate pathway have been identified in patients with abnormalities in their polyol profiles. Some of them presented with neurological symptoms of so far unknown aetiology. The pathophysiological role of polyols, e.g. in the brain, is relatively unknown. We tested the neurotoxicity of polyols using a ‘neurochip’ model. After exposure of cortical rat neurons to D‐arabitol and ribitol in increasing concentrations up to 10 mmol/L, the electrophysiological activity was measured. No acute effect on the spontaneous network activity of cortical neurons was observed. We speculate that polyols have only secondary effects on brain dysfunction.