bluuebunny/crossref_metadata_2025 huggingface dataset:
Knowledge, abilities, cognitive characteristics and behavioral competences of engineers with high capacity for engineering systems thinking (CEST)
Authors: Frank Moti
Published: February 2006

A major high‐order thinking skill that enables engineers to successfully perform systems engineering tasks is Engineering Systems Thinking. To successfully perform their tasks, systems engineers need a systems view or, in other words, a high capacity for engineering systems thinking (CEST). This paper summarizes the findings of three studies aimed at identifying the knowledge, abilities, cognitive characteristics (thinking skills) and personal traits (behavioral competences) of systems engineers with high capacity for engineering systems thinking (or, in other words, successful systems engineers). The findings suggest that successful systems engineers possess interdisciplinary knowledge. They are expert in at least one main field but have general knowledge in additional fields and disciplines. They become familiar with the jargon and professional language of the other disciplines and are able to communicate with people or experts from different fields and disciplines. Overall, 10 cognitive characteristics, 11 abilities, and 10 behavioral competences were identified. In addition, nine additional roles of systems engineering were identified. © 2006 Wiley Periodicals, Inc. Syst Eng 9: 91–103, 2006
Robust Nonorthogonal Analyses Revisited: An Update Based on Trimmed Means
Authors: Keselman H. J. , Kowalchuk Rhonda K. , Lix Lisa M.
Published: February 2006

Three approaches to the analysis of main and interaction effect hypotheses in nonorthogonal designs were compared in a 2 × 2 design for data that was neither normal in form nor equal in variance. The approaches involved either least squares or robust estimators of central tendency and variability and/or a test statistic that either pools or does not pool sources of variance. Specifically, we compared the ANOVA F test which used trimmed means and Winsorized variances, the Welch-James test with the usual least squares estimators for central tendency and variability and the Welch-James test using trimmed means and Winsorized variances. As hypothesized, we found that the latter approach provided excellent Type I error control, whereas the former two did not.
Shrinkage Estimation of Linear Combinations of True Scores
Authors: Longford Nicholas T.
Published: February 2006

This paper is concerned with combining observed scores from sections of tests. It is demonstrated that in the presence of population information a linear combination of true scores can be estimated more efficiently than by the same linear combination of the observed scores. Three criteria for optimality are discussed, but they yield the same solution which can be described and motivated as a multivariate shrinkage estimator.
Multivariate Normal Integrals and cOntingency Tables with Ordered Categories
Authors: Wang Yuchung J.
Published: February 2006

A 1k-dimensional multivariate normal distribution is made discrete by partitioning the k-dimensional Euclidean space with rectangular grids. The collection of probability integrals over the partitioned cubes is a k-dimensional contingency table with ordered categories. It is shown that loglinear model with main effects plus two-way interactions provides an accurate approximation for the k-dimensional table. The complete multivariate normal integral table is computed via the iterative proportional fitting algorithm from bivariate normal integral tables. This approach imposes no restriction on the correlation matrix. Comparisons with other numerical integration algorithms are reported. The approximation suggests association models for discretized multivariate normal distributions and contingency tables with ordered categories.
Minimization of a Class of Matrix Trace Functions by means of Refined Majorization
Authors: Kiers Henk A. L. , ten Berge Jos M. F.
Published: February 2006

A procedure is described for minimizing a class of matrix trace functions. The procedure is a refinement of an earlier procedure for minimizing the class of matrix trace functions using majorization. It contains a recently proposed algorithm by Koschat and Swayne for weighted Procrustes rotation as a special case. A number of trial analyses demonstrate that the refined majorization procedure is more efficient than the earlier majorization-based procedure.
A Comparison of the Classification Capabilities of the 1-Dimensional Kohonen Neural Network with Two Pratitioning and Three Hierarchical Cluster Analysis Algorithms
Authors: Waller Niels G. , Kaiser Heather A. , Illian Janine B. , Manry Mike
Published: February 2006

Neural Network models are commonly used for cluster analysis in engineering, computational neuroscience, and the biological sciences, although they are rarely used in the social sciences. In this study we compare the classification capabilities of the 1-dimensional Kohonen neural network with two partitioning (Hartigan and Späth k-means) and three hierarchical (Ward's, complete linkage, and average linkage) cluster methods in 2,580 data sets with known cluster structure. Overall, the performance of the Kohonen networks was similar to, or better than, the performance of the other methods.
On the Sampling Interpretation of Confidence Intervals and Hypothesis Tests in the Context of Conditional Maximum Likelihood Estimation
Authors: Maris E.
Published: February 2006

In the context of conditional maximum likelihood (CML) estimation, confidence intervals can be interpreted in three different ways, depending on the sampling distribution under which these confidence intervals contain the true parameter value with a certain probability. These sampling distributions are (a) the distribution of the data given the incidental parameters, (b) the marginal distribution of the data (i.e., with the incidental parameters integrated out), and (c) the conditional distribution of the data given the sufficient statistics for the incidental parameters. Results on the asymptotic distribution of CML estimates under sampling scheme (c) can be used to construct asymptotic confidence intervals using only the CML estimates. This is not possible for the results on the asymptotic distribution under sampling schemes (a) and (b). However, it is shown that the conditional asymptotic confidence intervals are also valid under the other two sampling schemes.
Correlation Coefficients for more than one Scale Type: An Alternative to the Janson and Vegelius Approach
Authors: Zegers Frits E. , Ten Berge Jos M. F.
Published: February 2006

Janson and Vegelius have recently suggested a family of correlations for variables of mixed scale types, including nominal scales. The resulting correlations are E- coefficients, which means that they are unity if the variables involved are identical up to permissible transformations, and that they can be considered as inner products in a Euclidian space. Some of the coefficients of the correlation family suggested by Janson and Vegelius are generalized squared product-moment correlations and some are not. In the present paper, a family of correlations for variables of mixed scale types is advocated all members of which are generalized squared product-moment correlations. Some practical advantages of the latter family are explained.
A Taxonomy of Item Response Models
Authors: Thissen David , Steinberg Lynne
Published: February 2006

A number of models for categorical item response data have been proposed in recent years. The models appear to be quite different. However, they may usefully be organized as members of only three distinct classes, within which the models are distinguished only by assumptions and constraints on their parameters. “Difference models” are appropriate for ordered responses, “divide-by-total” models may be used for either ordered or nominal responses, and “left-side added” models are used for multiple-choice responses with guessing. The details of the taxonomy and the models are described in this paper.
A Note on the Identification of Restricted Factor Loading Matrices
Authors: Bekker Paul A.
Published: February 2006

It is shown that problems of rotational equivalence of restricted factor loading matrices in orthogonal factor analysis are equivalent to problems of identification in simultaneous equations systems with covariance restrictions. A necessary (under a regularity assumption) and sufficient condition for local uniqueness is given and a counterexample is provided to a theorem by J. Algina concerning necessary and sufficient conditions for global uniqueness.
Local vs. Global Covert Visual Attention: Are Two States Necessary? Comment on Liechty et al., 2003
Authors: Reichle Erik D. , Nelson Jessica R.
Published: February 2006

Liechty, Pieters, and Wedel (2003) report an eye-tracking experiment that is taken to support the distinction between two states of covert visual attention: local versus global. We discuss several logical problems with this dichotomy and their experiment, and then provide an alternate account of their data using a model, E-Z Reader, that requires only a single attention state.
Evidence for Covert Attention Switching from Eye-Movements. Reply to Commentaries on Liechty et al., 2003
Authors: Wedel Michel , Pieters Rik , Liechty John
Published: February 2006

We argue that our research objectives in Liechty, Pieters, and Wedel (2003) are to provide generalizable insights into covert visual attention to complex, multimodal stimuli in their natural context, through inverse inference from eye-movement data. We discuss the most important issues raised by Feng (2003) and Reichle and Nelson (2003), in particular the task definition, inclusion of ad features, object-based versus space-based attention and the evidence for the where and what streams.
Orthomax Rotation and Perfect Simple Structure
Authors: Bernaards Coen A. , Jennrich Robert I.
Published: February 2006

A loading matrix has perfect simple structure if each row has at most one nonzero element. It is shown that if there is an orthogonal rotation of an initial loading matrix that has perfect simple structure, then orthomax rotation with 0 ≤γ ≤ 1 of the initial loading matrix will produce the perfect simple structure. In particular, varimax and quartimax will produce rotations with perfect simple structure whenever they exist.
Higher-Order Latent Trait Models for Cognitive Diagnosis
Authors: de la Torre Jimmy , Douglas Jeffrey A.
Published: February 2006

Higher-order latent traits are proposed for specifying the joint distribution of binary attributes in models for cognitive diagnosis. This approach results in a parsimonious model for the joint distribution of a high-dimensional attribute vector that is natural in many situations when specific cognitive information is sought but a less informative item response model would be a reasonable alternative. This approach stems from viewing the attributes as the specific knowledge required for examination performance, and modeling these attributes as arising from a broadly-defined latent trait resembling the ϑ of item response models. In this way a relatively simple model for the joint distribution of the attributes results, which is based on a plausible model for the relationship between general aptitude and specific knowledge. Markov chain Monte Carlo algorithms for parameter estimation are given for selected response distributions, and simulation results are presented to examine the performance of the algorithm as well as the sensitivity of classification to model misspecification. An analysis of fraction subtraction data is provided as an example.
A Conjunctive Parallelogram Model for Pick any/n Data
Authors: Leenen Iwin , Van Mechelen Iven
Published: February 2006

This paper proposes a multidimensional generalization of Coombs' (1964) parallelogram model for “pick any/n” data, which result from each of a number of subjects having selected a number of objects (s)he likes most from a prespecified set of n objects. In the model, persons and objects are represented in a low dimensional space defined by a set of ordinal variables with a prespecified number of categories; objects are represented as points and persons as intervals on each dimension. A conjunctive combination rule is assumed implying that a person selects an object if and only if the object is within the subject's interval on each dimension. An algorithm for fitting the model to a data set is presented and evaluated in a simulation study. The model is illustrated with data on preferences regarding holiday trips.
Structural Equation Modeling with Heavy Tailed Distributions
Authors: Yuan Ke-Hai , Bentler Peter M. , Chan Wai
Published: February 2006

Data in social and behavioral sciences typically possess heavy tails. Structural equation modeling is commonly used in analyzing interrelations among variables of such data. Classical methods for structural equation modeling fit a proposed model to the sample covariance matrix, which can lead to very inefficient parameter estimates. By fitting a structural model to a robust covariance matrix for data with heavy tails, one generally gets more efficient parameter estimates. Because many robust procedures are available, we propose using the empirical efficiency of a set of invariant parameter estimates in identifying an optimal robust procedure. Within the class of elliptical distributions, analytical results show that the robust procedure leading to the most efficient parameter estimates also yields a most powerful test statistic. Examples illustrate the merit of the proposed procedure. The relevance of this procedure to data analysis in a broader context is noted.
On the Asymptotic Distributions of Two Statistics for Two-Level Covariance Structure Models within the Class of Elliptical Distributions
Authors: Yuan Ke-Hai , Bentler Peter M.
Published: February 2006

Since data in social and behavioral sciences are often hierarchically organized, special statistical procedures for covariance structure models have been developed to reflect such hierarchical structures. Most of these developments are based on a multivariate normality distribution assumption, which may not be realistic for practical data. It is of interest to know whether normal theory-based inference can still be valid with violations of the distribution condition. Various interesting results have been obtained for conventional covariance structure analysis based on the class of elliptical distributions. This paper shows that similar results still hold for 2-level covariance structure models. Specifically, when both the level-1 (within cluster) and level-2 (between cluster) random components follow the same elliptical distribution, the rescaled statistic recently developed by Yuan and Bentler asymptotically follows a chi-square distribution. When level-1 and level-2 have different elliptical distributions, an additional rescaled statistic can be constructed that also asymptotically follows a chi-square distribution. Our results provide a rationale for applying these rescaled statistics to general non-normal distributions, and also provide insight into issues related to level-1 and level-2 sample sizes.
Derivative Free Gradient Projection Algorithms for Rotation
Authors: Jennrich Robert I.
Published: February 2006

A simple modification substantially simplifies the use of the gradient projection (GP) rotation algorithms of Jennrich (2001, 2002). These algorithms require subroutines to compute the value and gradient of any specific rotation criterion of interest. The gradient can be difficult to derive and program. It is shown that using numerical gradients gives almost precisely the same results as using exact gradients. The resulting algorithm is very easy to use because the only problem specific code required is that needed to define the rotation criterion. The computing time is increased when using numerical gradients, but it is still very modest for most purposes. While used extensively elsewhere, numerical derivatives seem to be underutilized in statistics.
Model Based Clustering of Large Data Sets: Tracing the Development of Spelling Ability
Authors: Hoijtink Herbert , Notenboom Annelise
Published: February 2006

There are two main theories with respect to the development of spelling ability: the stage model and the model of overlapping waves. In this paper exploratory model based clustering will be used to analyze the responses of more than 3500 pupils to subsets of 245 items. To evaluate the two theories, the resulting clusters will be ordered along a developmental dimension using an external criterion. Solutions for three statistical problems will be given: (1) an algorithm that can handle large data sets and only renders non-degenerate clusters; (2) a goodness of fit test that is not affected by the fact that the number of possible response vectors by far out-weights the number of observed response vectors; and (3) a new technique, data expunction, that can be used to evaluate goodness-of-fit tests if the missing data mechanism is known.
Random Effects Diagonal Metric Multidimensional Scaling Models
Authors: Clarkson Douglas B. , Gonzalez Richard
Published: February 2006

By assuming a distribution for the subject weights in a diagonal metric (INDSCAL) multidimensional scaling model, the subject weights become random effects. Including random effects in multidimensional scaling models offers several advantages over traditional diagonal metric models such as those fitted by the INDSCAL, ALSCAL, and other multidimensional scaling programs. Unlike traditional models, the number of parameters does not increase with the number of subjects, and, because the distribution of the subject weights is modeled, the construction of linear models of the subject weights and the testing of those models is immediate. Here we define a random effects diagonal metric multidimensional scaling model, give computational algorithms, describe our experiences with these algorithms, and provide an example illustrating the use of the model and algorithms.
On Maximizing Item Information and Matching Difficulty with Ability
Authors: Bickel Peter , Buyske Steven , Chang Huahua , Ying Zhiliang
Published: February 2006

An important assumption in IRT model-based adaptive testing is that matching difficulty levels of test items with an examinee's ability makes a test more efficient. According to Lord, “An examinee is measured most effectively when the test items are neither too difficult nor too easy for him”. This assumption is examined and challenged through a class of one-parameter IRT models including those of Rasch and the normal ogive. It is found that for a specific model, the validity of the fundamental assumption is closely related to the so-called van Zwet tail ordering of symmetric distributions. In this connection, the cosine distribution serves as the borderline between those satisfying the assumption and those violating the assumption. Graphic and numerical illustrations are presented to demonstrate the theoretic results.
On a Metric, Unidimensional Unfolding Model for Attitudinal and Developmental Data
Authors: Davison Mark L.
Published: February 2006

If stimulus responses are linearly related to squared distances between stimulus scale values and person scores along a latent continuum, (a) the stimulus × stimulus correlation matrix will display a simplex-like pattern, (b) the signs of first-order partial correlations can be specified in an empirically testable manner, and (c) the variables will have a semicircular, two-factor structure. Along the semicircle, variables will be ordered by their positions on the latent dimension. The above results suggest procedures for examining the appropriateness of the model and procedures for ordering the stimuli. Applications to developmental and attitudinal data are discussed.
A Generalization of Coefficient Alpha
Authors: Raju Nambury S.
Published: February 2006

It is well known that coefficient alpha can be used to estimate the reliability of a test even when the test is split into several parts. It is also known that alpha can severely underestimate test reliability when the several parts have an unequal number of items. A gernalization of alpha, βk, is proposed to correct this defect. Several properties of βk are also presented.
An Empirical Comparison of Methods of Communality Estimation
Authors: Medland Francis F.
Published: February 2006

This paper shows the formulation of nine methods of estimating the unknown communalities. Each of these methods has been used on experimental data and the results tabulated for comparison. The results show that the most accurate approximations are obtained from the Centroid No . 1 and the Graphical methods.
On the Estimation of Polychoric Correlations and their Asymptotic Covariance Matrix
Authors: Jöreskog Karl G.
Published: February 2006

A general theory for parametric inference in contingency tables is outlined. Estimation of polychoric correlations is seen as a special case of this theory. The asymptotic covariance matrix of the estimated polychoric correlations is derived for the case when the thresholds are estimated from the univariate marginals and the polychoric correlations are estimated from the bivariate marginals for given thresholds. Computational aspects are also discussed.
Bayesian Analysis of Order-Statistics Models for Ranking Data
Authors: Yu Philip L. H.
Published: February 2006

In this paper, a class of probability models for ranking data, the order-statistics models, is investigated. We extend the usual normal order-statistics model into one where the underlying random variables follow a multivariate normal distribution. Bayesian approach and the Gibbs sampling technique are used for parameter estimation. In addition, methods to assess the adequacy of model fit are introduced. Robustness of the model is studied by considering a multivariate-t distribution. The proposed method is applied to analyze the presidential election data of the American Psychological Association (APA).
The Weighted Oblimin Rotation
Authors: Lorenzo-Seva Urbano
Published: February 2006

Cureton & Mulaik (1975) proposed the Weighted Varimax rotation so that Varimax (Kaiser, 1958) could reach simple solutions when the complexities of the variables in the solution are larger than one. In the present paper the weighting procedure proposed by Cureton & Mulaik (1975) is applied to Direct Oblimin (Clarkson & Jennrich, 1988), and the rotation method obtained is called Weighted Oblimin. It has been tested on artificial complex data and real data, and the results seem to indicate that, even though Direct Oblimin rotation fails when applied to complex data, Weighted Oblimin gives good results if a variable with complexity one can be found for each factor in the pattern. Although the weighting procedure proposed by Cureton & Mulaik is based on Landahl's (1938) expression for orthogonal factors, Weighted Oblimin seems to be adequate even with highly oblique factors. The new rotation method was compared to other rotation methods based on the same weighting procedure and, whenever a variable with complexity one could be found for each factor in the pattern, Weighted Oblimin gave the best results. When rotating a simple empirical loading matrix, Weighted Oblimin seemed to slightly increase the performance of Direct Oblimin.
Minimax D-Optimal Designs for Item Response Theory Models
Authors: Berger Martijn P. F. , Joy King C. Y. , Wong Weng Kee
Published: February 2006

Various different item response theory (IRT) models can be used in educational and psychological measurement to analyze test data. One of the major drawbacks of these models is that efficient parameter estimation can only be achieved with very large data sets. Therefore, it is often worthwhile to search for designs of the test data that in some way will optimize the parameter estimates. The results from the statistical theory on optimal design can be applied for efficient estimation of the parameters.

A major problem in finding an optimal design for IRT models is that the designs are only optimal for a given set of parameters, that is, they are locally optimal. Locally optimal designs can be constructed with a sequential design procedure. In this paper minimax designs are proposed for IRT models to overcome the problem of local optimality. Minimax designs are compared to sequentially constructed designs for the two parameter logistic model and the results show that minimax design can be nearly as efficient as sequentially constructed designs.
On Measurement Properties of Continuation Ratio Models
Authors: Hemker Bas T. , Andries van der Ark L. , Sijtsma Klaas
Published: February 2006

Three classes of polytomous IRT models are distinguished. These classes are the adjacent category models, the cumulative probability models, and the continuation ratio models. So far, the latter class has received relatively little attention. The class of continuation ratio models includes logistic models, such as the sequential model (Tutz, 1990), and nonlogistic models, such as the acceleration model (Samejima, 1995) and the nonparametric sequential model (Hemker, 1996). Four measurement properties are discussed. These are monotone likelihood ratio of the total score, stochastic ordering of the latent trait by the total score, stochastic ordering of the total score by the latent trait, and invariant item ordering. These properties have been investigated previously for the adjacent category models and the cumulative probability models, and for the continuation ratio models this is done here. It is shown that stochastic ordering of the total score by the latent trait is implied by all continuation ratio models, while monotone likelihood ratio of the total score and stochastic ordering on the latent trait by the total score are not implied by any of the continuation ratio models. Only the sequential rating scale model implies the property of invariant item ordering. Also, we present a Venn-diagram showing the relationships between all known polytomous IRT models from all three classes.
Asymptotic Identifiability of Nonparametric Item Response Models
Authors: Douglas Jeffrey A.
Published: February 2006

The identifiability of item response models with nonparametrically specified item characteristic curves is considered. Strict identifiability is achieved, with a fixed latent trait distribution, when only a single set of item characteristic curves can possibly generate the manifest distribution of the item responses. When item characteristic curves belong to a very general class, this property cannot be achieved. However, for assessments with many items, it is shown that all models for the manifest distribution have item characteristic curves that are very near one another and pointwise differences between them converge to zero at all values of the latent trait as the number of items increases. An upper bound for the rate at which this convergence takes place is given. The main result provides theoretical support to the practice of nonparametric item response modeling, by showing that models for long assessments have the property of asymptotic identifiability.
Regression Among Factor Scores
Authors: Skrondal Anders , Laake Petter
Published: February 2006

Structural equation models with latent variables are sometimes estimated using an intuitive three-step approach, here denoted factor score regression. Consider a structural equation model composed of an explanatory latent variable and a response latent variable related by a structural parameter of scientific interest. In this simple example estimation of the structural parameter proceeds as follows: First, common factor models areseparately estimated for each latent variable. Second, factor scores areseparately assigned to each latent variable, based on the estimates. Third, ordinary linear regression analysis is performed among the factor scores producing an estimate for the structural parameter. We investigate the asymptotic and finite sample performance of different factor score regression methods for structural equation models with latent variables. It is demonstrated that the conventional approach to factor score regression performs very badly. Revised factor score regression, using Regression factor scores for the explanatory latent variables and Bartlett scores for the response latent variables, produces consistent estimators for all parameters.
On the Precision of a Euclidean Structure
Authors: Best Alvin M. , Young Forrest W. , Hall Robert G.
Published: February 2006

This paper is concerned with the development of a measure of the precision of a multidimensional euclidean structure. The measure is a precision index for each point in the structure, assuming that all the other points are precisely located. The measure is defined and two numerical methods are presented for its calculation. A small Monte Carlo study of the measure's behavior is performed and findings discussed.
A Maximum Likelihood Approach to the “Test of Inclusion”
Authors: Owston Ronald D.
Published: February 2006

The method of scoring is used to obtain maximum likelihood estimates of the parameters in the White and Clark learning hierarchy validation model. From the estimate of the proportion of the population possessing only the superordinate skill in a pair of hierarchical skills, and its variance, the hypothesis of inclusion is tested. An illustrative example of the procedure is given.
Ramifications of a Population Model for κ as a Coefficient of Reliability
Authors: Kraemer Helena Chmura
Published: February 2006

Coefficient κ is generally defined in terms of procedures of computation rather than in terms of a population. Here a population definition is proposed. On this basis, the interpretation of κ as a measure of diagnostic reliability in characterizing an individual, and the effect of reliability, as measured by κ, on estimation bias, precision, and test power are examined. Factors influencing the magnitude of κ are identified. Strategies to improve reliability are proposed, including that of combining multiple unreliable diagnoses.
An Application of Order Restricted Inference Methodology to a Problem in Psychiatry
Authors: Robertson Tim , Warrack Giles
Published: February 2006

Using data which reflects upon the genetic makeup of patients, Cadoret, Woolson and Winokur (1977) test two theories regarding the genetic makeup of patients suffering from unipolar affective disorder. This hypothesis test is a good example of a problem in order restricted inference. Using some recently developed techniques in order restricted inference we analyze these data and compare the analyses.
Correspondence Analysis used Complementary to Loglinear Analysis
Authors: van der Heijden Peter G. M. , de Leeuw Jan
Published: February 2006

Loglinear analysis and correspondence analysis provide us with two different methods for the decomposition of contingency tables. In this paper we will show that there are cases in which these two techniques can be used complementary to each other. More specifically, we will show that often correspondence analysis can be viewed as providing a decomposition of the difference between two matrices, each following a specific loglinear model. Therefore, in these cases the correspondence analysis solution can be interpreted in terms of the difference between these loglinear models. A generalization of correspondence analysis, recently proposed by Escofier, will also be discussed. With this decomposition, which includes classical correspondence analysis as a special case, it is possible to use correspondence analysis complementary to loglinear analysis in more instances than those described for classical correspondence analysis. In this context correspondence analysis is used for the decomposition of the residuals of specific restricted loglinear models.
Iterative Least Squares Estimates of Communality: Initial Estimate Need not Affect Stabilized Value
Authors: Widaman Keith F. , Herringer Lawrence G.
Published: February 2006

A common criticism of iterative least squares estimates of communality is that method of initial estimation may influence stabilized values. As little systematic research on this topic has been performed, the criticism appears to be based on cumulated experience with empirical data sets. In the present paper, two studies are reported in which four types of initial estimate (unities, squared multiple correlations, highest r, and zeroes) and four levels of convergence criterion were employed using four widely available computer packages (BMDP, SAS, SPSS, and SOUPAC). The results suggest that initial estimates have no effect on stabilized communality estimates when a stringent criterion for convergence is used, whereas initial estimates appear to affect stabilized values employing rather gross convergence criteria. There were no differences among the four computer packages for matrices without Heywood cases.
External Analysis with Three-Mode Principal Component Models
Authors: van der Kloot Willem A. , Kroonenberg Pieter M.
Published: February 2006

Through external analysis of two-mode data one attempts to map the elements of one mode (e.g., attributes) as vectors in a fixed space of the elements of the other mode (e.g., stimuli). This type of analysis is extended to three-mode data, for instance, when the ratings are made by more individuals. It is described how alternating least squares algorithms for three-mode principal component analysis (PCA) are adapted to enable external analysis, and it is demonstrated that these techniques are useful for exploring differences in the individuals' mappings of the attribute vectors in the fixed stimulus space. Conditions are described under which individual differences may be ignored. External three-mode PCA is illustrated with data from a person perception experiment, designed after two studies by Rosenberg and his associates whose results were used as external information.
Statistical Consistency and Hypothesis Testing for Nonmetric Multidimensional Scaling
Authors: Brady Henry E.
Published: February 2006

The properties of nonmetric multidimensional scaling (NMDS) are explored by specifying statistical models, proving statistical consistency, and developing hypothesis testing procedures. Statistical models with errors in the dependent and independent variables are described for quantitative and qualitative data. For these models, statistical consistency often depends crucially upon how error enters the model and how data are collected and summarized (e.g., by means, medians, or rank statistics). A maximum likelihood estimator for NMDS is developed, and its relationship to the standard Shepard-Kruskal estimation method is described. This maximum likelihood framework is used to develop a method for testing the overall fit of the model.
The Relative Error Magnitude in Three Measures of Change
Authors: Zimmerman Donald W. , Williams Richard H.
Published: February 2006

Formulas for the standard error of measurement of three measures of change—simple difference scores, residualized difference scores, and the measure introduced by Tucker, Damarin, and Messick—are derived. Equating these formulas by pairs yields additional explicit formulas which provide a practical guide for determining the relative error of the three measures in any pretest-posttest design. The functional relationship between the standard error of measurement and the correlation between pretest and posttest observed scores remains essentially the same for each of the three measures despite variations in other test parameters (reliability coefficients, standard deviations), even when pretest and posttest errors of measurement are correlated.
A Rasch Model for Partial Credit Scoring
Authors: Masters Geoff N.
Published: February 2006

A unidimensional latent trait model for responses scored in two or more ordered categories is developed. This “Partial Credit” model is a member of the family of latent trait models which share the property of parameter separability and so permit “specifically objective” comparisons of persons and items. The model can be viewed as an extension of Andrich's Rating Scale model to situations in which ordered response alternatives are free to vary in number and structure from item to item. The difference between the parameters in this model and the “category boundaries” in Samejima's Graded Response model is demonstrated. An unconditional maximum likelihood procedure for estimating the model parameters is developed.
Efficient Estimation and Local Identification in Latent Class Analysis
Authors: McHugh Richard B.
Published: February 2006

Estimators which are efficient in the sense of having minimum asymptotic variance are obtained for the structural parameters of Lazarsfeld's latent class model of latent structure analysis. Sufficient conditions for the local identification of the structural parameters are also presented.
An Empirical Evaluation of Multidimensional Successive Intervals
Authors: Messick Samuel J.
Published: February 2006

The multidimensional method of successive intervals and the method of complete triads are applied to similarity judgments of Munsell colors varying in brightness, saturation, and hue. Both methods yield configurations that correlate highly with the Munsell color structure. This validation of these scaling methods in an area of known dimensionality indicates their applicability for exploration in areas of unknown dimensionality.
Determination of the Number of Independent Parameters of a Score Matrix from the Examination of Rank Orders
Authors: Bennett Joseph F.
Published: February 2006

Two ordinal consequences are drawn from the linear multiple-factor analysis model. First, the number R(s, d) of distinct ways in which s subjects can be ranked by linear functions of d factors is limited by the recursive expression R(s, d) = R(s−, d)+(s−1) R(s−, d−1). Second, every set S of d+2 subjects can be separated into two subsets S* and S − S* such that no linear function of d variables can rank all S* over all S − S*, and vice versa. When these results are applied to the hypothetical data of Thurstone's “box problem,” three independent parameters are found. Relations to Thurstone's suggestion for a non-correlational factor analysis are discussed.
The Typical Rank of Tall Three-Way Arrays
Authors: Ten Berge Jos M. F.
Published: February 2006

The rank of a three-way array refers to the smallest number of rank-one arrays (outer products of three vectors) that generate the array as their sum. It is also the number of components required for a full decomposition of a three-way array by CANDECOMP/PARAFAC. The typical rank of a three-way array refers to the rank a three-way array has almost surely. The present paper deals with typical rank, and generalizes existing results on the typical rank of I × J × K arrays with K = 2 to a particular class of arrays with K ≥ 2. It is shown that the typical rank is I when the array is tall in the sense that JK − J < I < JK. In addition, typical rank results are given for the case where I equals JK − J.
Criterion-Related Construct Validity
Authors: Rosenbaum Paul R.
Published: February 2006

Established results on latent variable models are applied to the study of the validity of a psychological test. When the test predicts a criterion by measuring a unidimensional latent construct, not only must the total score predict the criterion, but the joint distribution of criterion scores and item responses must exhibit a certain pattern. The presence of this population pattern may be tested with sample data using the stratified Wilcoxon rank sum test. Often, criterion information is available only for selected examinees, for instance, those who are admitted or hired. Three cases are discussed: (i) selection at random, (ii) selection based on the current test, and (iii) selection based on other measures of the latent construct. Discriminant validity is also discussed.
Item Bias Detection using Loglinear IRT
Authors: Kelderman Henk
Published: February 2006

A method is proposed for the detection of item bias with respect to observed or unobserved subgroups. The method uses quasi-loglinear models for the incomplete subgroup × test score × Item 1 × ... × item k contingency table. If subgroup membership is unknown the models are Haberman's incomplete-latent-class models.

The (conditional) Rasch model is formulated as a quasi-loglinear model. The parameters in this loglinear model, that correspond to the main effects of the item responses, are the conditional estimates of the parameters in the Rasch model. Item bias can then be tested by comparing the quasi-loglinear-Rasch model with models that contain parameters for the interaction of item responses and the subgroups.
Ordinal Network Representation: Representing Proximities by Graphs
Authors: Klauer Karl Christoph
Published: February 2006

Ordinal network representations are graph-theoretic representations of proximity data. They seek to provide parsimonious representations of the ordinal (nonmetric) information in observed proximity data by means of the minimum-path-length distance of a connected and weighted graph. In contrast to traditional tree-based graph-theoretic approaches, ordinal network representation is not limited to but includes the representation by trees. Asymmetry in the proximity data and violations of zero-minimality are allowed for. The paper explores fundamental representation and uniqueness results and discusses a method of constructing ordinal network representations. A simple strategy for handling the problem of errors in the data is described and illustrated.
Selective Influence Through Conditional Independence
Authors: Dzhafarov Ehtibar N.
Published: February 2006

Let each of several (generally interdependent) random vectors, taken separately, be influenced by a particular set of external factors. Under what kind of the joint dependence of these vectors on the union of these factor sets can one say that each vector is selectively influenced by “its own” factor set? The answer proposed and elaborated in this paper is: One can say this if and only if one can find a factor-independent random vector given whose value the vectors in question are conditionally independent, with their conditional distributions selectively influenced by the corresponding factor sets. Equivalently, the random vectors should be representable as deterministic functions of “their” factor sets and of some mutually independent and factor-independent random variables, some of which may be shared by several of the functions.
Global Optimality of the Successive Maxbet Algorithm
Authors: Hanafi Mohamed , ten Berge Jos M. F.
Published: February 2006

The Maxbet method is an alternative to the method of generalized canonical correlation analysis and of Procrustes analysis. Contrary to these methods, it does not maximize the inner products (covariances) between linear composites, but also takes their sums of squares (variances) into account. It is well-known that the Maxbet algorithm, which has been proven to converge monotonically, may converge to local maxima. The present paper discusses an eigenvalue criterion which is sufficient, but not necessary for global optimality. However, in two special cases, the eigenvalue criterion is shown to be necessary and sufficient for global optimality. The first case is when there are only two data sets involved; the second case is when the inner products between all variables involved are positive, regardless of the number of data sets.
Classical Test Theory as a First-Order Item Response Theory: Application to True-Score Prediction from a Possibly Nonparallel Test
Authors: Holland Paul W. , Hoskens Machteld
Published: February 2006

We give an account of Classical Test Theory (CTT) in terms of the more fundamental ideas of Item Response Theory (IRT). This approach views classical test theory as a very general version of IRT, and the commonly used IRT models as detailed elaborations of CTT for special purposes. We then use this approach to CTT to derive some general results regarding the prediction of the true-score of a test from an observed score on that test as well from an observed score on a different test. This leads us to a new view of linking tests that were not developed to be linked to each other. In addition we propose true-score prediction analogues of the Dorans and Holland measures of the population sensitivity of test linking functions. We illustrate the accuracy of the first-order theory using simulated data from the Rasch model, and illustrate the effect of population differences using a set of real data.
Uniqueness Proof for a Family of Models Sharing Features of Tucker's Three-Mode Factor Analysis and PARAFAC/Candecomp
Authors: Harshman Richard A. , Lundy Margaret E.
Published: February 2006

Some existing three-way factor analysis and MDS models incorporate Cattell's “Principle of Parallel Proportional Profiles”. These models can—with appropriate data—empirically determine a unique best fitting axis orientation without the need for a separate factor rotation stage, but they have not been general enough to deal with what Tucker has called “interactions” among dimensions. This article presents a proof of unique axis orientation for a considerably more general parallel profiles model which incorporates interacting dimensions. The model, Xk=AADk HBDk B', does not assume symmetry in the data or in the interactions among factors. A second proof is presented for the symmetrically weighted case (i.e., where ADk=BDk). The generality of these models allows one to impose successive restrictions to obtain several useful special cases, including PARAFAC2 and three-way DEDICOM.
A Short Note on the Estimation of the Asymptotic Covariance Matrix for Polychoric Correlations
Authors: Christoffersson Anders , Gunsjö Anna
Published: February 2006

By using a Taylor expansion of the equations that define the two step estimator for polychoric correlations, the asymptotic covariance matrix for the estimated correlations can be derived in a simple and straightforward way.
Spatial, Non-Spatial and Hybrid Models for Scaling
Authors: Carroll J. Douglas
Published: February 2006

In this paper, hierarchical and non-hierarchical tree structures are proposed as models of similarity data. Trees are viewed as intermediate between multidimensional scaling and simple clustering. Procedures are discussed for fitting both types of trees to data. The concept of multiple tree structures shows great promise for analyzing more complex data. Hybrid models in which multiple trees and other discrete structures are combined with continuous dimensions are discussed. Examples of the use of multiple tree structures and hybrid models are given. Extensions to the analysis of individual differences are suggested.
Regression with Qualitative and Quantitative Variables: An Alternating Least Squares Method with Optimal Scaling Features
Authors: Young Forrest W. , de Leeuw Jan , Takane Yoshio
Published: February 2006

A method is discussed which extends canonical regression analysis to the situation where the variables may be measured at a variety of levels (nominal, ordinal, or interval), and where they may be either continuous or discrete. There is no restriction on the mix of measurement characteristics (i.e., some variables may be discrete-ordinal, others continuous-nominal, and yet others discrete-interval). The method, which is purely descriptive, scales the observations on each variable, within the restriction imposed by the variable's measurement characteristics, so that the canonical correlation is maximal. The alternating least squares algorithm is discussed. Several examples are presented. It is concluded that the method is very robust. Inferential aspects of the method are not discussed.
A Theoretical Study of Two-Stage Testing
Authors: Lord Frederic M.
Published: February 2006

When items cannot be answered correctly by guessing, certain two-stage testing procedures are about as effective over the ability range of interest as the “best” up-and-down procedures studied previously. When answers can be guessed correctly 20 percent of the time, no two-stage procedure is found to match the “best” up-and-down procedures over this ability range. Feet-on-the-desk designs for two-stage procedures may produce poor results.