Testing for DIF in a model with single peaked item characteristic curves: The parella model

The PARELLA model is a probabilistic parallelogram model that can be used for the measurement of latent attitudes or latent preferences. The data analyzed are the dichotomous responses of persons to items, with a one (zero) indicating agreement (disagreement) with the content of the item. The model provides a unidimensional representation of persons and items. The response probabilities are a function of the distance between person and item: the smaller the distance, the larger the probability that a person will agree with the content of the item. This paper discusses how the approach to differential item functioning presented by Thissen, Steinberg, and Wainer can be implemented for the PARELLA model. Requests for the PARELLA software should be sent to Iec Progamma PO Box 841, 9700 AV Groningen, The Netherlands.     

儿童最初词汇的获得及其过程

本文追踪研究了两名儿童获得最初词汇的过程。结果表明:在儿童最初语音发展过程中,所发出的音节日益丰富、分化,产生了连续音节,随意性和指向性逐渐增强。儿童获得最初词汇的过程,是连续音节逐渐被有指向的词取代的过程。根据连续音节和有指向的词的比例及沟通作用的变化,儿童获得最初词汇的过程可分为各具特点的三个阶段。两名儿童的最初词汇在其词类构成和功能意义上具有很高的一致性。结合两名儿童之间的个别差异,本文还初步探讨影响儿童获得最初词汇的因素——言语中枢和言语器官的发展、认知的发展,并探讨它们之间可能存在的相互关系。     

Does the Conners' Continuous Performance Test Aid in ADHD Diagnosis?

The performance of clinic-referred children aged 6–11 (N = 100) was examined using the Conners' Continuous Performance Test (CPT) and measures of auditory attention (Auditory Continuous Performance Test; ACPT), phonological awareness, visual processing speed, and visual-motor competence. The Conners' CPT overall index was unrelated to measures of visual processing speed or visual-motor competence. Although the Conners' CPT converged with the ACPT, the latter demonstrated age and order effects. Significant variance in Conners' CPT parameters was predicted by phonological awareness measures, suggesting that Reading Disordered (RD) children could be false positives on the Conners' CPT. The Conners' CPT overall index, phonological awareness, and visual-motor measures were submitted to a 2×2 MANCOVA (ADHD vs. RD, covarying for age and socieoeconomic status): a main effect for RD status was found. Children with ADHD did not have higher Conners' CPT scores than did clinical controls; however, children with Reading Disorders did. Phonological measures distinguished RD children from ADHD children and other clinical controls. ADHD children who failed the Conners' CPT were rated by teachers as more hyperactive. Despite the strengths of the Conners' CPT, its utility for differential diagnosis of ADHD is questioned.     

High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature

Although the Bock–Aitkin likelihood-based estimation method for factor analysis of dichotomous item response data has important advantages over classical analysis of item tetrachoric correlations, a serious limitation of the method is its reliance on fixed-point Gauss-Hermite (G-H) quadrature in the solution of the likelihood equations and likelihood-ratio tests. When the number of latent dimensions is large, computational considerations require that the number of quadrature points per dimension be few. But with large numbers of items, the dispersion of the likelihood, given the response pattern, becomes so small that the likelihood cannot be accurately evaluated with the sparse fixed points in the latent space. In this paper, we demonstrate that substantial improvement in accuracy can be obtained by adapting the quadrature points to the location and dispersion of the likelihood surfaces corresponding to each distinct pattern in the data. In particular, we show that adaptive G-H quadrature, combined with mean and covariance adjustments at each iteration of an EM algorithm, produces an accurate fast-converging solution with as few as two points per dimension. Evaluations of this method with simulated data are shown to yield accurate recovery of the generating factor loadings for models of upto eight dimensions. Unlike an earlier application of adaptive Gibbs sampling to this problem by Meng and Schilling, the simulations also confirm the validity of the present method in calculating likelihood-ratio chi-square statistics for determining the number of factors required in the model. Finally, we apply the method to a sample of real data from a test of teacher qualifications.     

On local influence analysis of full information item factor models

The full information item factor (FIIF) model is very useful for analyzing relations of dichotomous variables. In this article, we present a feasible procedure to assess local influence of minor perturbations for identifying influence aspects of the FIIF model. The development is based on a Q-displacement function which is closely related with the Monte Carlo EM algorithm in the ML estimation. In the E-step of this algorithm, the conditional expectations are approximated by sample means of observations simulated by the Gibbs sampler from the appropriate conditional distributions. It turns out that these observations can be utilized for computing the building blocks of the proposed diagnostic measures. The diagnoses are based on the conformal normal curvature that can be computed easily. A number of interesting perturbation schemes are considered. The methodology is illustrated with two real examples.The research is fully supported by a grant (CUHK 4356/00H) from the Research Grant Council of the Hong Kong Special Administration Region. The authors are thankful to the Editor, Associate Editor, anonymous reviewers, and W.Y. Poon for valuable comments for improving the paper, and to ICPSR and the relevant founding agency for allowing us to use of their data. The assistance of Michael Leung and Esther Tam is gratefully acknowledged.     

Estimating multiple classification latent class models

This paper presents a new class of models for persons-by-items data. The essential new feature of this class is the representation of the persons: every person is represented by its membership tomultiple latent classes, each of which belongs to onelatent classification. The models can be considered as a formalization of the hypothesis that the responses come about in a process that involves the application of a number ofmental operations. Two algorithms for maximum likelihood (ML) and maximum a posteriori (MAP) estimation are described. They both make use of the tractability of the complete data likelihood to maximize the observed data likelihood. Properties of the MAP estimators (i.e., uniqueness and goodness-of-recovery) and the existence of asymptotic standard errors were examined in a simulation study. Then, one of these models is applied to the responses to a set of fraction addition problems. Finally, the models are compared to some related models in the literature.Thanks are to Paul De Boeck for creating the intellectually stimulating atmosphere in which this class of models came about, Iven van Mechelen for theone-sided idea, Kikumi Tatsuoka for the use of her data, and Theodoor Bouw for running part of the simulation study.     

A maximum likelihood approach to the “test of inclusion”

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.This study is based on doctoral dissertation submitted to the University of Ottawa. The author is indebted to Martin Cooper, Marvin Boss and Jean-Paul Dionne for their assistance.     

Estimating the parameters of the latent population distribution

Under consideration is a test battery of binary items. The responses ofn individuals are assumed to follow a Rasch model. It is further assumed that the latent individual parameters are distributed within a given population in accordance with a normal distribution. Methods are then considered for estimating the mean and variance of this latent population distribution. Also considered are methods for checking whether a normal population distribution fits the data. The developed methods are applied to data from an achievement test and from an attitude test.     

A thurstonian pairwise choice model with univariate and multivariate spline transformations

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.The first author is supported as Bevoegdverklaard Navorser of the Belgian Nationaal Fonds voor Wetenschappelijk Onderzoek. The authors are indebted to Ulf Böckenholt and Yoshio Takane for useful comments on an earlier draft of this paper.