A bayesian procedure for mastery decisions based on multivariate normal test data

A Bayesian framework for making mastery/nonmastery decisions based on multivariate test data is described in this study. Overall, mastery is granted (or denied) if the posterior expected loss associated with such action is smaller than the one incurred by the denial (or grant) of mastery. An explicit form for the cutting contour which separates mastery and nonmastery states in the test score space is given for multivariate normal test scores and for a constant loss ratio. For multiple cutting scores in the true ability space, the test score cutting contour will resemble the boundary defined by multiple test cutting scores when the test reliabilities are reasonably close to unity. For tests with low reliabilities, decisions may very well be based simply on a suitably chosen composite score.This work was performed pursuant to Grant NIE-G-78-0087 with the National Institute of Education, Department of Health, Education, and Welfare, Huynh Huynh, Principal Investigator. Points of view or opinions stated do not necessarily reflect NIE positions or policy and no official endorsement should be inferred. The assistance of Joseph C. Saunders is gratefully acknowledged. The author is indebted to an anonymous referee who pointed out several computational errors in the earlier versions of the paper.     

Mixtures of conditional mean- and covariance-structure models

Models and parameters of finite mixtures of multivariate normal densities conditional on regressor variables are specified and estimated. We consider mixtures of multivariate normals where the expected value for each component depends on possibly nonnormal regressor variables. The expected values and covariance matrices of the mixture components are parameterized using conditional mean- and covariance-structures. We discuss the construction of the likelihood function, estimation of the mixture model with regressors using three different EM algorithms, estimation of the asymptotic covariance matrix of parameters and testing for the number of mixture components. In addition to simulation studies, data on food preferences are analyzed.The authors are grateful to Donald B. Rubin and Michael E. Sobel for critical reading of a first draft of this paper and to three anonymous reviewers ofPsychometrika for their helpful comments and suggestions. The research of the first and the third author was supported by a grant from the Deutsche Forschungsgemeinschaft.     

A simple multivariate probabilistic model for preferential and triadic choices

Multidimensional probabilistic models of behavior following similarity and choice judgements have proven to be useful in representing multidimensional percepts in Euclidean and non-Euclidean spaces. With few exceptions, these models are generally computationally intense because they often require numerical work with multiple integrals. This paper focuses attention on a particularly general triad and preferential choice model previously requiring the numerical evaluation of a 2n-fold integral, wheren is the number of elements in the vectors representing the psychological magnitudes. Transforming this model to an indefinite quadratic form leads to a single integral. The significance of this form to multidimensional scaling and computational efficiency is discussed.The authors would like to thank Jean-Claude Falmagne and Norman Johnson for suggestions and advice concerning quadratic forms.     

Multivariate analysis with linearizable regressions

We study the class of multivariate distributions in which all bivariate regressions can be linearized by separate transformation of each of the variables. This class seems more realistic than the multivariate normal or the elliptical distributions, and at the same time its study allows us to combine the results from multivariate analysis with optimal scaling and classical multivariate analysis. In particular a two-stage procedure which first scales the variables optimally, and then fits a simultaneous equations model, is studied in detail and is shown to have some desirable properties.     

Sequential social network data

A new method is proposed for the statistical analysis of dyadic social interaction data measured over time. The data to be studied are assumed to be realizations of a social network of a fixed set of actors interacting on a single relation. The method is based on loglinear models for the probabilities for various dyad (or actor pair) states and generalizes the statistical methods proposed by Holland and Leinhardt (1981), Fienberg, Meyer, & Wasserman (1985), and Wasserman (1987) for social network data. Two statistical models are described: the first is an associative approach that allows for the study of how the network has changed over time; the second is a predictive approach that permits the researcher to model one time point as a function of previous time points. These approaches are briefly contrasted with earlier methods for the sequential analysis of social networks and are illustrated with an example of longitudinal sociometric data.Research support provided by National Science Foundation Grant #SES84-08626 to the University of Illinois at Urbana-Champaign and by a predoctoral traineeship awarded to the second author by the Quantitative Methods Program of the Department of Psychology, University of Illinois at Urbana-Champaign, funded by ADAHMA, National Research Service Award #MH14257. We thank the editor and three anonymous referees for helpful comments.This paper is based on research presented at the 1986 Annual Meeting of the Psychometric Society, Toronto, Ontario, June, 1986.     

An estimating equations approach for the LISCOMP model

Maximum likelihood estimation is computationally infeasible for latent variable models involving multivariate categorical responses, in particular for the LISCOMP model. A three-stage generalized least squares approach introduced by Muthén (1983, 1984) can experience problems of instability, bias, non-convergence, and non-positive definiteness of weight matrices in situations of low prevalence, small sample size and large numbers of observed indicator variables. We propose a quadratic estimating equations approach that only requires specification of the first two moments. By performing simultaneous estimation of parameters, this method does not encounter the problems mentioned above and experiences gains in efficiency. Methods are compared through a numerical study and an application to a study of life-events and neurotic illness.The authors would like to thank Bengt Muthén for many helpful discussions and Scott Henderson for generously providing the Canberra data set. This work was supported in part by grant number GM49909 of the National Institutes of Health.     

A Comprehensive Examination of the Model Underlying Acceptance and Commitment Therapy for Chronic Pain

The therapeutic model underlying Acceptance and Commitment Therapy (ACT) is reasonably well-established as it applies to chronic pain. Several studies have examined measures of single ACT processes, or subsets of processes, and have almost uniformly indicated reliable relations with patient functioning. To date, however, no study has performed a comprehensive examination of the entire ACT model, including all of its component processes, as it relates to functioning. The present study performed this examination in 274 individuals with chronic pain presenting for an assessment appointment. Participants completed a battery of self-report questionnaires, assessing multiple aspects of the ACT model, as well as pain intensity, disability, and emotional distress. Initial exploratory factor analyses examined measures of the ACT model and measures of patient functioning separately with each analysis identifying three factors. Next, the fit of a model including ACT processes on the one hand and patient functioning on the other was examined using Structural Equation Modeling. Overall model fit was acceptable and indicated moderate correlations among the ACT processes themselves, as well as significant relations with pain intensity, emotional distress, and disability. These analyses build on the existing literature by providing, to our knowledge, the most comprehensive evaluation of the ACT theoretical model in chronic pain to date.     

An EM algorithm for fitting two-level structural equation models

Maximum likelihood is an important approach to analysis of two-level structural equation models. Different algorithms for this purpose have been available in the literature. In this paper, we present a new formulation of two-level structural equation models and develop an EM algorithm for fitting this formulation. This new formulation covers a variety of two-level structural equation models. As a result, the proposed EM algorithm is widely applicable in practice. A practical example illustrates the performance of the EM algorithm and the maximum likelihood statistic.We are thankful to the reviewers for their constructive comments that have led to significant improvement on the first version of this paper. Special thanks are due to the reviewer who suggested a comparison with the LISREL program in the saturated means model, and provided its setup and output. This work was supported by National Institute on Drug Abuse grants DA01070, DA00017, and a UNH 2002 Summer Faculty Fellowship.     

概化理论研究及应用前景

1972年,Cronbach和他的同事们提出概化理论之后,概化理论在行为与心理测量领域得到了广泛的应用,较之经典测量理论,它的优势逐渐地显露：(1)测量的多种误差来源可以在同一个分析中分别估计;(2)可以指导决策者选择最优测量方案;(3)提供可靠性系数：概化系数(G系数)和依存性指标(φ系数)用于不同的决策任务;(4)排除了严格平行测验的假设。概化理论以它的精确性和可藏性受到了信度测量领域研究者们的青睐,本文旨在对概化理论的基本框架、产生、发展及应用前景进行详细论述。