bluuebunny/crossref_metadata_2025 huggingface dataset:
A Distance-Based Variety of Nonlinear Multivariate Data Analysis, Including Weights for Objects and Variables
Authors: Commandeur Jacques J. F. , Groenen Patrick J. F. , Meulman Jacqueline J.
Published: January 2006

In the distance approach to nonlinear multivariate data analysis the focus is on the optimal representation of the relationships between the objects in the analysis. In this paper two methods are presented for including weights in distance-based nonlinear multivariate data analysis. In the first method, weights are assigned to the objects while the second method is concerned with differential weighting of groups of variables. When each analysis variable defines a group the latter method becomes a variable weighting method. For objects the weights are assumed to be given; for groups of variables they may be given, or estimated. These weighting schemes can also be combined and have several important applications. For example, they make it possible to perform efficient analyses of large data sets, to use the distance-based variety of nonlinear multivariate data analysis as an addition to loglinear analysis of multiway contingency tables, and to do stability studies of the solutions by applying the bootstrap on the objects or the variables in the analysis. These and other applications are discussed, and an efficient algorithm is proposed to minimize the corresponding loss function.
The Analysis of Three-Way Contingency Tables by Three-Mode Association Models
Authors: Anderson Carolyn J.
Published: January 2006

The RC(M) association model (Goodman, 1979, 1985, 1986, 1991) is useful for analyzing the relationship between the variables of a 2-way cross-classification. The models presented here are generalizations of the RC(M) association model for 3-way tables. The family of models proposed here, “3-mode association” models, use Tucker's 3-mode components model (Tucker, 1964, 1966; Kroonenberg, 1983) to represent either the three factor interaction or the combined effects of two and three factor interactions. An example from a study in developmental psychology (Kramer & Gottman, 1992) is provided to illustrate the usefulness of the proposed models.
The Tunneling Method for Global Optimization in Multidimensional Scaling
Authors: Groenen Patrick J. F. , Heiser Willem J.
Published: January 2006

This paper focuses on the problem of local minima of the STRESS function. It turns out that unidimensional scaling is particularly prone to local minima, whereas full dimensional scaling with Euclidean distances has a local minimum that is global. For intermediate dimensionality with Euclidean distances it depends on the dissimilarities how severe the local minimum problem is. For city-block distances in any dimensionality many different local minima are found. A simulation experiment is presented that indicates under what conditions local minima can be expected. We introduce the tunneling method for global minimization, and adjust it for multidimensional scaling with general Minkowski distances. The tunneling method alternates a local search step, in which a local minimum is sought, with a tunneling step in which a different configuration is sought with the same STRESS as the previous local minimum. In this manner successively better local minima are obtained, and experimentation so far shows that the last one is often a global minimum.
Repeated Challenge Studies: A Comparison of Union-Intersection Testing with Linear Modeling
Authors: Levine Richard A. , Ohman Pamela A.
Published: January 2006

Challenge studies are often implemented for assessing whether a subject is sensitive to a certain agent or allergen. In particular, researchers test groups of subjects to determine if there really exists a causal relationship between some agent of interest and a response. To answer such a question, we need to detect the presence of the phenomenon in just one individual. Typically, however, there are a large number of unknown risk factors associated with the response and a potentially small population prevalence. Hence, standard statistical techniques, by averaging the treatment effect across the group, may miss a significant response of a single individual and lead to inconclusive results. We develop an alternative approach based on union-intersection testing that will allow a practitioner to correctly examine observations on an individual apart from the other subjects and test the hypothesis of interest: Does the phenomenon exist in the population? More specifically, we show how this technique adjusts for the multiple number of tests encountered when analyzing data for each individual subject separately. Furthermore, we demonstrate power calculations for the determination of sample size prior to performing the study. The performance of the union-intersection approach in comparison to linear models and semiparametric techniques is considered through sample size calculations and simulations. The union-intersection testing methodology out performs the Kolmogorov tests. However, the nested linear model performs as well if not better than the union-intersection tests. To illustrate the ideas presented in the paper, we provide an application in which we analyze psychological data collected by way of a challenge study design.
Influence Analysis of Structural Equation Models with Polytomous Variables
Authors: Poon Wai-Yin , Wang Shu-Jia , Lee Sik-Yum
Published: January 2006

The estimation of model parameters in structural equation models with polytomous variables can be handled by several computationally efficient procedures. However, sensitivity or influence analysis of the model is not well studied. We demonstrate that the existing influence analysis methods for contingency tables or for normal theory structural equation models cannot be applied directly to structural equation models with polytomous variables; and we develop appropriate procedures based on the local influence approach of Cook (1986). The proposed procedures are computationally efficient, the necessary bits of the proposed diagnostic measures are readily available following an usual fit of the model. We consider the influence of an individual cell frequency with respect to three cases: when all parameters in an unstructured model are of interest, when the unstructured polychoric correlations are of interest, and when the structural parameters are of interest. We also consider the sensitivity of the parameters estimates. Two examples based on real data are presented for illustration.
The Bias Function of the Maximum Likelihood Estimate of Ability for the Dichotomous Response Level
Authors: Samejima Fumiko
Published: January 2006

Samejima has recently given an approximation for the bias function for the maximum likelihood estimate of the latent trait in the general case where item responses are discrete, generalizing Lord's bias function in the three-parameter logistic model for the dichotomous response level. In the present paper, observations are made about the behavior of this bias function for the dichotomous response level in general, and also with respect to several widely used mathematical models. Some empirical examples are given.
A Simple Gauss-Newton Procedure for Covariance Structure Analysis with High-Level Computer Languages
Authors: Cudeck Robert , Klebe Kelli J. , Henly Susan J.
Published: January 2006

An implementation of the Gauss-Newton algorithm for the analysis of covariance structures that is specifically adapted for high-level computer languages is reviewed. With this procedure one need only describe the structural form of the population covariance matrix, and provide a sample covariance matrix and initial values for the parameters. The gradient and approximate Hessian, which vary from model to model, are computed numerically. Using this approach, the entire method can be operationalized in a comparatively small program. A large class of models can be estimated, including many that utilize functional relationships among the parameters that are not possible in most available computer programs. Some examples are provided to illustrate how the algorithm can be used.
A Thurstonian Pairwise Choice Model with Univariate and Multivariate Spline Transformations
Authors: De Soete Geert , Winsberg Suzanne
Published: January 2006

A probabilistic choice model is developed for paired comparisons data about psychophysical stimuli. The model is based on Thurstone's Law of Comparative Judgment Case V and assumes that each stimulus is measured on a small number of physical variables. The utility of a stimulus is related to its values on the physical variables either by means of an additive univariate spline model or by means of multivariate spline model. In the additive univariate spline model, a separate univariate spline transformation is estimated for each physical dimension and the utility of a stimulus is assumed to be an additive combination of these transformed values. In the multivariate spline model, the utility of a stimulus is assumed to be a general multivariate spline function in the physical variables. The use of B splines for estimating the transformation functions is discussed and it is shown how B splines can be generalized to the multivariate case by using as basis functions tensor products of the univariate basis functions. A maximum likelihood estimation procedure for the Thurstone Case V model with spline transformation is described and applied for illustrative purposes to various artificial and real data sets. Finally, the model is extended using a latent class approach to the case where there are unreplicated paired comparisons data from a relatively large number of subjects drawn from a heterogeneous population. An EM algorithm for estimating the parameters in this extended model is outlined and illustrated on some real data.
Grice-Representability of Response Time Distribution Families
Authors: Dzhafarov Ehtibar N.
Published: January 2006

Any family of simple response time distributions that correspond to different values of stimulation variables can be modeled by a deterministic stimulation-dependent process that terminates when it crosses a randomly preset criterion. The criterion distribution function is stimulation-independent and can be chosen arbitrarily, provided it is continuous and strictly increasing. Any family of N-alternative choice response time distributions can be modeled by N such process-criterion pairs, with response choice and response time being determined by the process that reaches its criterion first. The joint distribution of the N criteria can be chosen arbitrarily, provided it satisfies certain unrestrictive conditions. In particular, the criteria can be chosen to be stochastically independent. This modeling scheme, therefore, is a descriptive theoretical language rather than an empirically falsifiable model. The only role of the criteria in this theoretical language is to numerically calibrate the ordinal-scale axes for the deterministic response processes.
Constrained DEDICOM
Authors: Kiers Henk A. L. , Takane Yoshio
Published: January 2006

The DEDICOM method for the analysis of asymmetric data tables gives representations that are identified only up to a nonsingular transformation. To identify solutions it is proposed to impose subspace constraints on the stimulus coefficients. Most attention is paid to the case where different subspace constraints are imposed on different dimensions. The procedures are discussed both for the case where the complete table is fitted, and for cases where only offdiagonal elements are fitted. The case where the data table is skew-symmetric is treated separately as well.
A Generalized Majorization Method for Least Squares Multidimensional Scaling of Pseudodistances that may be Negative
Authors: Heiser Willem J.
Published: January 2006

The usual convergence proof of the SMACOF algorithm model for least squares multidimensional scaling critically depends on the assumption of nonnegativity of the quantities to be fitted, called the pseudodistances. When this assumption is violated, erratic convergence behavior is known to occur. Three types of circumstances in which some of the pseudodistances may become negative are outlined: nonmetric multidimensional scaling with normalization on the variance, metric multidimensional scaling including an additive constant, and multidimensional scaling under the city-block distance model. A generalization of the SMACOF method is proposed to resolve the difficulty that is based on the same rationale frequently involved in robust fitting with least absolute residuals.
Assessing Statistical Accuracy in Ability Estimation: A Bootstrap Approach
Authors: Liou Michelle , Yu Lien-Chi
Published: January 2006

Given known item parameters, the bootstrap method can be used to determine the statistical accuracy of ability estimates in item response theory. Through a Monte Carlo study, the method is evaluated as a way of approximating the standard error and confidence limits for the maximum likelihood estimate of the ability parameter, and compared to the use of the theoretical standard error and confidence limits developed by Lord. At least for short tests, the bootstrap method yielded better estimates than the corresponding theoretical values.
Comparing the Predictive Powers of Alternative Multiple Regression Models
Authors: Hagerty Michael R. , Srinivasan V.
Published: January 2006

Mean squared error of prediction is used as the criterion for determining which of two multiple regression models (not necessarily nested) is more predictive. We show that an unrestricted (or true) model with t parameters should be chosen over a restricted (or misspecified) model with m parameters if (Pt2−Pm2)>(1−Pt2)(t−m)/n, where Pt2 and Pm2 are the population coefficients of determination of the unrestricted and restricted models, respectively, and n is the sample size. The left-hand side of the above inequality represents the squared bias in prediction by using the restricted model, and the right-hand side gives the reduction in variance of prediction error by using the restricted model. Thus, model choice amounts to the classical statistical tradeoff of bias against variance. In practical applications, we recommend that P2 be estimated by adjusted R2. Our recommendation is equivalent to performing the F-test for model comparison, and using a critical value of 2−(m/n); that is, if F>2−(m/n), the unrestricted model is recommended; otherwise, the restricted model is recommended.
On the Sampling Theory Roundations of Item Response Theory Models
Authors: Holland Paul W.
Published: January 2006

Item response theory (IT) models are now in common use for the analysis of dichotomous item responses. This paper examines the sampling theory foundations for statistical inference in these models. The discussion includes: some history on the “stochastic subject” versus the random sampling interpretations of the probability in IRT models; the relationship between three versions of maximum likelihood estimation for IRT models; estimating θ versus estimating θ-predictors; IRT models and loglinear models; the identifiability of IRT models; and the role of robustness and Bayesian statistics from the sampling theory perspective.
Social Networks with Two Sets of Actors
Authors: Iacobucci Dawn , Wasserman Stanley
Published: January 2006

Traditional network research analyzes relational ties within a single group of actors: the models presented in this paper involve relational ties exist beteen two distinct sets of actors. Statistical models for traditional networks in which relations are measured within a group simplify when modeling unidirectional relations measured between groups. The traditional paradigm results in a one-mode socionatrix; the network paradigm considered in this paper results in a two-mode socionatrix; A statistical model is presented, illustrated on a sample data set, and compared to its traditional counterpart. Extensions are discussed, including those that model multivariate relations simultaneously, and those that allow for the inclustion of attributes of the individuals in the group.
When can we Trust the F-Approximation of the Box-Test?
Authors: Foerster Friedrich , Stemmler Gerhard
Published: January 2006

Consider a multivariate context with p variates and k independent samples, each of size n. To test equality of the k population covariance matrices, the likelihood ratio test is commonly employed. Box's F-approximation to the null distribution of the test statistic can be used to compute p-values, if sample sizes are not too small. It is suggested to regard the F-approximation as accurate if the sample sizes n are greater than or equal to 1+0.0613p2 + 2.7265p -1.4182p0.5 + 0.235p1.4* In (k), for 5≤ p ≤30, k ≤20.
Robust Multidimensional Scaling
Authors: Spence Ian , Lewandowsky Stephan
Published: January 2006

A method for multidimensional scaling that is highly resistant to the effects of outliers is described. To illustrate the efficacy of the procedure, some Monte Carlo simulation results are presented. The method is shown to perform well when outliers are present, even in relatively large numbers, and also to perform comparably to other approaches when no outliers are present.
A Mixture Model for Distributions of Correlation Coefficients
Authors: Thomas Hoben
Published: January 2006

An old problem in personnel psychology is to characterize distributions of test validity correlation coefficients. The proposed model views histograms of correlation coefficients as observations from a mixture distribution which, for a fixed sample size n, is a conditional mixture distribution h(r|n) = Σjλjh(r; ρj, n), where R is the correlation coefficient, ρj are population correlation coefficients and λj are the mixing weights. The associated marginal distribution of R is regarded as the parent distribution underlying histograms of empirical correlation coefficients. Maximum likelihood estimates of the parameters ρj and λj can be obtained with an EM algorithm solution and tests for the number of components t are achieved after the (one-component) density of R is replaced with a tractable modeling density h(r; ρj, n). Two illustrative examples are provided.
Local Homogeneity in Latent Trait Models. A Characterization of the Homogeneous Monotone IRT Model
Authors: Ellis Jules L. , van den Wollenberg Arnold L.
Published: January 2006

The stochastic subject formulation of latent trait models contends that, within a given subject, the event of obtaining a certain response pattern may be probabilistic. Ordinary latent trait models do not imply that these within-subject probabilities are identical to the conditional probabilities specified by the model. The latter condition is called local homogeneity. It is shown that local homogeneity is equivalent to subpopulation invariance of the model. In case of the monotone IRT model, local homogeneity implies absence of item bias, absence of item specific traits, and the possibility to join overlapping subtests. The following characterization theorem is proved: the homogeneous monotone IRT model holds for a finite or countable item pool if and only if the pool is experimentally independent and pairwise nonnegative association holds in every positive subpopulation.
Additive and Multiplicative Models for Gamma Distributed Random Variables, and their Application as Psychometric Models for Response Times
Authors: Maris Eric
Published: January 2006

A class of models for gamma distributed random variables is presented. These models are shown to be more flexible than the classical linear models with respect to the structure that can be imposed on the expected value. In particular, both additive, multiplicative, and combined additive-multiplicative models can be formulated. As a special case, a class of psychometric models for reaction times is presented, together with their psychological interpretation. By means of a comparison with existing models, this class of models is shown to offer some possibilities that are not available in existing methods. Parameter estimation by means of maximum likelihood (ML) is shown to have some attractive properties, since the models belong to the exponential family. Then, the results of a simulation study of the bias in the ML estimates are presented. Finally, the application of these models is illustrated by an analysis of the data from a mental rotation experiment. This analysis is preceded by an evaluation of the appropriateness of the gamma distribution for these data.
Tscale: A New Multidimensional Scaling Procedure Based on Tversky's Contrast Model
Authors: DeSarbo Wayne S. , Johnson Michael D. , Manrai Ajay K. , Manrai Lalita A. , Edwards Elizabeth A.
Published: January 2006

Tversky's contrast model of proximity was initially formulated to account for the observed violations of the metric axioms often found in empirical proximity data. This set-theoretic approach models the similarity/dissimilarity between any two stimuli as a linear (or ratio) combination of measures of the common and distinctive features of the two stimuli. This paper proposes a new spatial multidimensional scaling (MDS) procedure called TSCALE based on Tversky's linear contrast model for the analysis of generally asymmetric three-way, two-mode proximity data. We first review the basic structure of Tversky's conceptual contrast model. A brief discussion of alternative MDS procedures to accommodate asymmetric proximity data is also provided. The technical details of the TSCALE procedure are given, as well as the program options that allow for the estimation of a number of different model specifications. The nonlinear estimation framework is discussed, as are the results of a modest Monte Carlo analysis. Two consumer psychology applications are provided: one involving perceptions of fast-food restaurants and the other regarding perceptions of various competitive brands of cola softdrinks. Finally, other applications and directions for future research are mentioned.
Examining Differential Item Functioning Due to Item Difficulty and Alternative Attractiveness
Authors: Westers Paul , Kelderman Henk
Published: January 2006

A method for analyzing test item responses is proposed to examine differential item functioning (DIF) in multiple-choice items through a combination of the usual notion of DIF, for correct/incorrect responses and information about DIF contained in each of the alternatives. The proposed method uses incomplete latent class models to examine whether DIF is caused by the attractiveness of the alternatives, difficulty of the item, or both. DIF with respect to either known or unknown subgroups can be tested by a likelihood ratio test that is asymptotically distributed as a chi-square random variable.
Ultrametric Hierarchical Clustering Algorithms
Authors: Milligan Glenn W.
Published: January 2006

Johnson has shown that the single linkage and the complete linkage hierarchical clustering algorithms induce a metric on the data known as the ultrametric. Through the use of the Lance and Williams recurrence formula, Johnson's proof is extended to four other common clustering algorithms. It is also noted that two additional methods produce hierarchical structures which can violate the ultrametric inequality.
An Examination of Indexes for Determining the Number of Clusters in Binary Data Sets
Authors: Dimitriadou Evgenia , Dolničar Sara , Weingessel Andreas
Published: January 2006

The problem of choosing the correct number of clusters is as old as cluster analysis itself. A number of authors have suggested various indexes to facilitate this crucial decision. One of the most extensive comparative studies of indexes was conducted by Milligan and Cooper (1985). The present piece of work pursues the same goal under different conditions. In contrast to Milligan and Cooper's work, the emphasis here is on high-dimensional empirical binary data. Binary artificial data sets are constructed to reflect features typically encountered in real-world data situations in the field of marketing research. The simulation includes 162 binary data sets that are clustered by two different algorithms and lead to recommendations on the number of clusters for each index under consideration. Index results are evaluated and their performance is compared and analyzed.
On the Construction of all Factors of the Model for Factor Analysis
Authors: Krijnen Wim P.
Published: January 2006

A construction method is given for all factors that satisfy the assumptions of the model for factor analysis, including partially determined factors where certain error variances are zero. Various criteria for the seriousness of indeterminacy are related. It is shown that Green's (1976) conjecture holds: For a linear factor predictor the mean squared error of prediction is constant over all possible factors. A simple and general geometric interpretation of factor indeterminacy is given on the basis of the distance between multiple factors. It is illustrated that variable elimination can have a large effect on the seriousness of factor indeterminacy. A simulation study reveals that if the mean square error of factor prediction equals .5, then two thirds of the persons are “correctly” selected by the best linear factor predictor.
Remarks on the Identifiability of Thurstonian Paired Comparison Models Under Multiple Judgment
Authors: Tsai Rung-Ching
Published: January 2006

It is well-known that the representations of the Thurstonian models for difference judgment data are not unique. It has been shown that equivalence classes can be formed to provide a more meaningful partition of the covariance structures of the Thurstonian ranking models. In this paper, we examine the equivalence relations between Thurstonian covariance structure models for paired comparison data obtained under multiple judgment and discuss their implications on the general identification constraints and methods to check for parameter identifiability in restricted models.
The Many Null Distributions of Person Fit Indices
Authors: Molenaar Ivo W. , Hoijtink Herbert
Published: January 2006

This paper deals with the situation of an investigator who has collected the scores of n persons to a set of k dichotomous items, and wants to investigate whether the answers of all respondents are compatible with the one parameter logistic test model of Rasch. Contrary to the standard analysis of the Rasch model, where all persons are kept in the analysis and badly fitting items may be removed, this paper studies the alternative model in which a small minority of persons has an answer strategy not described by the Rasch model. Such persons are called anomalous or aberrant. From the response vectors consisting of k symbols each equal to 0 or 1, it is desired to classify each respondent as either anomalous or as conforming to the model. As this model is probabilistic, such a classification will possibly involve false positives and false negatives. Both for the Rasch model and for other item response models, the literature contains several proposals for a person fit index, which expresses for each individual the plausibility that his/her behavior follows the model. The present paper argues that such indices can only provide a satisfactory solution to the classification problem if their statistical distribution is known under the null hypothesis that all persons answer according to the model. This distribution, however, turns out to be rather different for different values of the person's latent trait value. This value will be called “ability parameter”, although our results are equally valid for Rasch scales measuring other attributes.

As the true ability parameter is unknown, one can only use its estimate in order to obtain an estimated person fit value and an estimated null hypothesis distribution. The paper describes three specifications for the latter: assuming that the true ability equals its estimate, integrating across the ability distribution assumed for the population, and conditioning on the total score, which is in the Rasch model the sufficient statistic for the ability parameter.

Classification rules for aberrance will be worked out for each of the three specifications. Depending on test length, item parameters and desired accuracy, they are based on the exact distribution, its Monte Carlo estimate and a new and promising approximation based on the moments of the person fit statistic. Results for the likelihood person fit statistic are given in detail, the methods could also be applied to other fit statistics. A comparison of the three specifications results in the recommendation to condition on the total score, as this avoids some problems of interpretation that affect the other two specifications.
Majorization as a Tool for Optimizing a Class of Matrix Functions
Authors: Kiers Henk A. L.
Published: January 2006

The problem of minimizing a general matrix, trace function, possibly subject to certain constraints, is approached by means of majorizing this function by one having a simple quadratic shape and whose minimum is easily found. It is shown that the parameter set that minimizes the majorizing function also decreases the matrix trace function, which in turn provides a monotonically convergent algorithm for minimizing the matrix trace function iteratively. Three algorithms based on majorization for solving certain least squares problems are shown to be special cases. In addition, by means of several examples, it is noted how algorithms may be provided for a wide class of statistical optimization tasks for which no satisfactory algorithms seem available.
Effect Analysis and Causation in Linear Structural Equation Models
Authors: Sobel Michael E.
Published: January 2006

This paper considers total and direct effects in linear structural equation models. Adopting a causal perspective that is implicit in much of the literature on the subject, the paper concludes that in many instances the effects do not admit the interpretations imparted in the literature. Drawing a distinction between concomitants and factors, the paper concludes that a concomitant has neither total nor direct effects on other variables. When a variable is a factor and one or more intervening variables are concomitants, the notion of a direct effect is not causally meaningful. Even when the notion of a direct effect is meaningful, the usual estimate of this quantity may be inappropriate. The total effect is usually interpreted as an equilibrium multiplier. In the case where there are simultaneity relations among the dependent variables in tghe model, the results in the literature for the total effects of dependent variables on other dependent variables are not equilibrium multipliers, and thus, the usual interpretation is incorrect. To remedy some of these deficiencies, a new effect, the total effect of a factor X on an outcome Y, holding a set of variables F constant, is defined. When defined, the total and direct effects are a special case of this new effect, and the total effect of a dependent variable on a dependent variable is an equilibrium multiplier.
Bayesian Modeling of Measurement Error in Predictor Variables Using Item Response Theory
Authors: Fox Jean-Paul , Glas Cees A. W.
Published: January 2006

It is shown that measurement error in predictor variables can be modeled using item response theory (IRT). The predictor variables, that may be defined at any level of an hierarchical regression model, are treated as latent variables. The normal ogive model is used to describe the relation between the latent variables and dichotomous observed variables, which may be responses to tests or questionnaires. It will be shown that the multilevel model with measurement error in the observed predictor variables can be estimated in a Bayesian framework using Gibbs sampling. In this article, handling measurement error via the normal ogive model is compared with alternative approaches using the classical true score model. Examples using real data are given.
Discrepancy Risk Model Selection Test Theory for Comparing Possibly Misspecified or Nonnested Models
Authors: Golden R. M.
Published: January 2006

A new model selection statistical test is proposed for testing the null hypothesis that two probability models equally effectively fit the underlying data generating process (DGP). The new model selection test, called the Discrepancy Risk Model Selection Test (DRMST), extends previous work (see Vuong, 1989) on this problem in four distinct ways. First, generalized goodness-of-fit measures (which include log-likelihood functions) can be used. Second, unlike the classical likelihood ratio test, the models are not required to be fully nested where the nesting concept is defined for generalized goodness-of-fit measures. The DRMST also differs from the likelihood ratio test by not requiring that either competing model provides a completely accurate representation of the DGP. And, fourth, the DRMST may be used to compare competing time-series models using correlated observations as well as data consisting of independent and identically distributed observations.
Using Response Times to Detect Aberrant Responses in Computerized Adaptive Testing
Authors: van der Linden Wim J. , van Krimpen-Stoop Edith M. L. A.
Published: January 2006

A lognormal model for response times is used to check response times for aberrances in examinee behavior on computerized adaptive tests. Both classical procedures and Bayesian posterior predictive checks are presented. For a fixed examinee, responses and response times are independent; checks based on response times offer thus information independent of the results of checks on response patterns. Empirical examples of the use of classical and Bayesian checks for detecting two different types of aberrances in response times are presented. The detection rates for the Bayesian checks outperformed those for the classical checks, but at the cost of higher false-alarm rates. A guideline for the choice between the two types of checks is offered.
A Two-Stage Logistic Regression Model for Analyzing Inter-Rater Agreement
Authors: Lipsitz Stuart R. , Parzen Michael , Fitzmaurice Garrett M. , Klar Neil
Published: January 2006

Studies of agreement commonly occur in psychiatric research. For example, researchers are often interested in the agreement among radiologists in their review of brain scans of elderly patients with dementia or in the agreement among multiple informant reports of psychopathology in children. In this paper, we consider the agreement between two raters when rating a dichotomous outcome (e.g., presence or absence of psychopathology). In particular, we consider logistic regression models that allow agreement to depend on both rater- and subject-level covariates. Logistic regression has been proposed as a simple method for identifying covariates that are predictive of agreement (Coughlin et al., 1992). However, this approach is problematic since it does not take account of agreement due to chance alone. As a result, a spurious association between the probability (or odds) of agreement and a covariate could arise due entirely to chance agreement. That is, if the prevalence of the dichotomous outcome varies among subgroups of the population, then covariates that identify the subgroups may appear to be predictive of agreement. In this paper we propose a modification to the standard logistic regression model in order to take proper account of chance agreement. An attractive feature of the proposed method is that it can be easily implemented using existing statistical software for logistic regression. The proposed method is motivated by data from the Connecticut Child Study (Zahner et al., 1992) on the agreement among parent and teacher reports of psychopathology in children. In this study, parents and teachers provide dichotomous assessments of a child's psychopathology and it is of interest to examine whether agreement among the parent and teacher reports is related to the age and gender of the child and to the time elapsed between parent and teacher assessments of the child.
Limited Information Estimation and Testing of Thurstonian Models for Paired Comparison Data Under Multiple Judgment Sampling
Authors: Maydeu-Olivares Albert
Published: January 2006

We relate Thurstonian models for paired comparisons data to Thurstonian models for ranking data, which assign zero probabilities to all intransitive patterns. We also propose an intermediate model for paired comparisons data that assigns nonzero probabilities to all transitive patterns and to some but not all intransitive patterns.

There is a close correspondence between the multidimensional normal ogive model employed in educational testing and Thurstone's model for paired comparisons data under multiple judgment sampling with minimal identification restrictions. Alike the normal ogive model, Thurstonian models have two formulations, a factor analytic and an IRT formulation. We use the factor analytic formulation to estimate this model from the first and second order marginals of the contingency table using estimators proposed by Muthén. We also propose a statistic to assess the fit of these models to the first and second order marginals of the contingency table. This is important, as a model may reproduce well the estimated thresholds and tetrachoric correlations, yet fail to reproduce the marginals of the contingency table if the assumption of multivariate normality is incorrect.

A simulation study is performed to investigate the performance of three alternative limited information estimators which differ in the procedure used in their final stage: unweighted least squares (ULS), diagonally weighted least squares (DWLS), and full weighted least squares (WLS). Both the ULS and DWLS show a good performance with medium size problems and small samples, with a slight better performance of the ULS estimator.
Fuzzy Partition Models for Fitting a Set of Partitions
Authors: Gordon A. D. , Vichi M.
Published: January 2006

Methodology is described for fitting a fuzzy consensus partition to a set of partitions of the same set of objects. Three models defining median partitions are described: two of them are obtained from a least-squares fit of a set of membership functions, and the third (proposed by Pittau and Vichi) is acquired from a least-squares fit of a set of joint membership functions. The models are illustrated by application to both a set of hard partitions and a set of fuzzy partitions and comparisons are made between them and an alternative approach to obtaining a consensus fuzzy partition proposed by Sato and Sato; a discussion is given of some interesting differences in the results.
A Simple General Procedure for Orthogonal Rotation
Authors: Jennrich Robert I.
Published: January 2006

A very general algorithm for orthogonal rotation is identified. It is shown that when an algorithm parameter α is sufficiently large the algorithm converges monotonically to a stationary point of the rotation criterion from any starting value. Because a sufficiently largeα is in general hard to find, a modification that does not require it is introduced. Without this requirement the modified algorithm is not only very general, but also very simple. Its implementation involves little more than computing the gradient of the rotation criterion. While the modified algorithm converges monotonically from any starting value, it is not guaranteed to converge to a stationary point. It, however, does so in all of our examples. While motivated by the rotation problem in factor analysis, the algorithms discussed may be used to optimize almost any function of a not necessarily square column-wise orthonormal matrix. A number of these more general applications are considered. Empirical examples show that the modified algorithm can be reasonably fast, but its purpose is to save an investigator's effort rather than that of his or her computer. This makes it more appropriate as a research tool than as an algorithm for established methods.
Generalized Constrained Multiple Correspondence Analysis
Authors: Hwang Heungsun , Takane Yoshio
Published: January 2006

A comprehensive approach for imposing both row and column constraints on multivariate discrete data is proposed that may be called generalized constrained multiple correspondence analysis (GCMCA). In this method each set of discrete data is first decomposed into several submatrices according to its row and column constraints, and then multiple correspondence analysis (MCA) is applied to the decomposed submatrices to explore relationships among them. This method subsumes existing constrained and unconstrained MCA methods as special cases and also generalizes various kinds of linearly constrained correspondence analysis methods. An example is given to illustrate the proposed method.
Concise Formulas for the Standard Errors of Component Loading Estimates
Authors: Ogasawara Haruhiko
Published: January 2006

Concise formulas for the asymptotic standard errors of component loading estimates were derived. The formulas cover the cases of principal component analysis for unstandardized and standardized variables with orthogonal and oblique rotations. The formulas can be used under any distributions for observed variables as long as the asymptotic covariance matrix for sample covariances/correlations is available. The estimated standard errors in numerical examples were shown to be equivalent to those by the methods using information matrices.
Reliability and Expected Loss: A Unifying Principle
Authors: Cooil Bruce , Rust Roland T.
Published: January 2006

We provide a unified, theoretical basis on which measures of data reliability may be derived or evaluated, for both quantitative and qualitative data. This approach evaluates reliability as the “proportional reduction in loss” (PRL) that is attained in a sample by an optimal estimator. The resulting measure is between 0 and 1, linearly related to expected loss, and provides a direct way of contrasting the measured reliability in the sample with the least reliable and most reliable data-generating cases. The PRL measure is a generalization of many of the commonly-used reliability measures.

We show how the quantitative measures from generalizability theory can be derived as PRL measures (including Cronbach's alpha and measures proposed by Winer). For categorical data, we develop a new measure for the general case in which each of N judges assigns a subject to one of K categories and show that it is equivalent to a measure proposed by Perreault and Leigh for the case where N is 2.
The Robustness of Estimates of Total Indirect Effects in Covariance Structure Models Estimated by Maximum Likelihood
Authors: Stone Clement A. , Sobel Michael E.
Published: January 2006

The large sample distribution of total indirect effects in covariance structure models in well known. Using Monte Carlo methods, this study examines the applicability of the large sample theory to maximum likelihood estimates oftotal indirect effects in sample sizes of 50, 100, 200, 400, and 800. Two models are studied. Model 1 is a recursive model with observable variables and Model 2 is a nonrecursive model with latent variables. For the large sample theory to apply, the results suggest that sample sizes of 200 or more and 400 or more are required for models such as Model 1 and Model 2, respectively.
A Minimum-Cost Network-Flow Solution to the Case V Thurstone Scaling Problem
Authors: Lattin James M.
Published: January 2006

This paper presents an approach for determining unidimensional scale estimates that are relatively insensitive to limited inconsistencies in paired comparisons data. The solution procedure, shown to be a minimum-cost network-flow problem, is presented in conjunction with a sensitivity diagnostic that assesses the influence of a single pairwise comparison on traditional Thurstone (ordinary least squares) scale estimates. When the diagnostic indicates some source of distortion in the data, the network technique appears to be more successful than Thurstone scaling in preserving the interval scale properties of the estimates.
The Effect of Uncertainty of Item Parameter Estimation on Ability Estimates
Authors: Tsutakawa Robert K. , Johnson Jane C.
Published: January 2006

The conventional method of measuring ability, which is based on items with assumed true parameter values obtained from a pretest, is compared to a Bayesian method that deals with the uncertainties of such items. Computational expressions are presented for approximating the posterior mean and variance of ability under the three-parameter logistic (3PL) model. A 1987 American College Testing Program (ACT) math test is used to demonstrate that the standard practice of using maximum likelihood or empirical Bayes techniques may seriously underestimate the uncertainty in estimated ability when the pretest sample is only moderately large.
New Lower and Upper Bounds for Communality in Factor Analysis
Authors: Yanai Haruo , Ichikawa Masanori
Published: January 2006

We derive several relationships between communalities and the eigenvalues for a p × p correlation matrix Σ under the usual factor analysis model. For suitable choices of j, λj(Σ), where λj(Σ) is the j-th largest eigenvalue of Σ, provides either a lower or an upper bound to the communalities for some of the variables. We show that for at least one variable, 1 - λp (Σ) improves on the use of squared mulitiple correlation coefficient as a lower bound.
Geographic variation in density‐dependent dynamics impacts the synchronizing effect of dispersal and regional stochasticity
Authors: Liebhold Andrew M. , Johnson Derek M. , Bjørnstad Ottar N.
Published: January 2006

Explanations for the ubiquitous presence of spatially synchronous population dynamics have assumed that density‐dependent processes governing the dynamics of local populations are identical among disjunct populations, and low levels of dispersal or small amounts of regionalized stochasticity (“Moran effect”) can act to synchronize populations. In this study we used historical spatially referenced data on gypsy moth (Lymantria dispar) outbreaks to document that density‐dependent processes can vary substantially across geographical landscapes. This variation may be due in part to geographical variation in habitat (e.g., variation in forest composition). We then used a second‐order log‐linear stochastic model to explore how inter‐population variation in density‐dependent processes affects synchronization via either synchronous stochastic forcing or dispersal. We found that geographical variation in direct density‐dependence (first order) greatly diminishes synchrony caused by stochasticity but only slightly decreases synchronization via dispersal. Variation in delayed density‐dependence (second order) diluted synchrony caused by regional stochasticity to a lesser extent than first‐order variation, but it did not have any influence on synchrony caused by dispersal. In general, synchronization caused by dispersal was primarily dependent upon the instability of populations and only weakly, if at all, affected by similarities in density‐dependence among populations. We conclude that studies of synchrony should carefully consider both the nature of the synchronizing agents and the pattern of local density‐dependent processes, including how these vary geographically.
Community structure and stability analysis for intraguild interactions among host, parasitoid, and predator
Authors: Nakazawa T , Yamamura N
Published: January 2006

Intraguild predation (IGP) occurs when one species preys on a competitor species that shares a common resource. Modifying a prey–predator model with prey infection, we propose a model of IG interactions among host, parasitoid, and predator, in which the predator eats parasitized and unparasitized hosts, and the adult parasitoid density is explicitly expressed. Parameter dependences of community structure, including stability of the system, were analytically obtained. Depending on interaction strength (parasitization and predation on unparasitized and parasitized hosts), the model provides six types of community structure: (1) only the host exists, (2) the host and predator coexist stably, (3) the host and parasitoid coexist stably, (4) the host–parasitoid population dynamics are unstable, (5) the three species coexist stably, and (6) the population dynamics of the three species are unstable. In contrast to a traditional prey–predator model with prey infection, which predicts that population dynamics are always locally stable, our model predicts that they are unstable when the parasitization rate is high.