Estimation of stimulus-response curves by bayesian least squares

Bayesian least squares techniques are adapted to estimation of stimulus-response curves, rather broadly conceived. Illustrative examples deal with estimation of person characteristic curves and item characteristic curves in the context of mental testing, and estimation of a stimulus-response curve using data from a psychophysical experiment.The present paper is a version of an invited address of the same title, presented to the meetings of The Psychometric Society in Monterey, California on June 8, 1979, expanded by adding Example 1.The writer gratefully acknowledges the benefit of conversations with Don Pierce, and with John Shih, whose related work on density estimation pointed up an error in the original version of Section 2. He acknowledges, gratefully, support by the National Science Foundation through Grants MCS 76-02166A01 and MCS 78-01932. And he wishes to express his gratitude for the cordial hospitality and gracious cooperation offered by Professor Donald M. MacKay and the staff of the Department of Communication, University of Keele, during spring and summer, 1976; in particular, by Professor Dennis P. Andrews and Keichi Uchikawa, who kindly furnished data, a small portion of which is used in the illustrative example, Example 2.     

Maximum marginal likelihood estimation for semiparametric item analysis

The item characteristic curve (ICC), defining the relation between ability and the probability of choosing a particular option for a test item, can be estimated by using polynomial regression splines. These provide a more flexible family of functions than is given by the three-parameter logistic family. The estimation of spline ICCs is described by maximizing the marginal likelihood formed by integrating ability over a beta prior distribution. Some simulation results compare this approach with the joint estimation of ability and item parameters.IRCAMThe research reported in this paper was supported by Grants APA320 and A4035 from the Natural Sciences and Engineering Research Council of Canada. It was also supported by Contract No. F41689-82-C-10020 from the Air Force Human Resources Laboratory to Educational Testing Service. The author wishes to thank M. Abrahamowicz for his assistance and R. Darrell Bock for providing the parameters for the items used in the simulations.     

Fitting longitudinal reduced-rank regression models by alternating least squares

An alternating least squares method for iteratively fitting the longitudinal reduced-rank regression model is proposed. The method uses ordinary least squares and majorization substeps to estimate the unknown parameters in the system and measurement equations of the model. In an example with cross-sectional data, it is shown how the results conform closely to results from eigenanalysis. Optimal scaling of nominal and ordinal variables is added in a third substep, and illustrated with two examples involving cross-sectional and longitudinal data.Financial support by the Institute for Traffic Safety Research (SWOV) in Leidschendam, The Netherlands is gratefully acknowledged.     

On the optimality of the simultaneous redundancy transformations

The objective of this paper is to introduce and motivate additional properties and interpretations for the redundancy variables. It is shown that these variables can be derived by application of certain invariance arguments and without reference to the index of redundancy. In addition, an optimality property for the variables is presented which is important whenever one restricts attention in a study to a subset of the redundancy variables. This optimality property pertains to the subset rather than to the individual variables.This paper is based in part on the author's doctoral dissertation, Department of Statistics, Princeton, University. Research was conducted under the supervision of Lawrence S. Mayer.     

On rotating to smooth functions

Tucker has outlined an application of principal components analysis to a set of learning curves, for the purpose of identifying meaningful dimensions of individual differences in learning tasks. Since the principal components are defined in terms of a statistical criterion (maximum variance accounted for) rather than a substantive one, it is typically desirable to rotate the components to a more interpretable orientation. Simple structure is not a particularly appealing consideration for such a rotation; it is more reasonable to believe that any meaningful factor should form a (locally) smooth curve when the component loadings are plotted against trial number. Accordingly, this paper develops a procedure for transforming an arbitrary set of component reference curves to a new set which are mutually orthogonal and, subject to orthogonality, are as smooth as possible in a well defined (least squares) sense. Potential applications to learning data, electrophysiological responses, and growth data are indicated.Portions of this research were supported by the National Research Council of Canada, Grant A8615 to the second author. We thank Jagdeth Sheth for supplying his raw data.     

Correctness of Kruskal's algorithms for monotone regression with ties

Kruskal has proposed two modifications of monotone regression that can be applied if there are ties in nonmetric scaling data. In this note we prove Kruskal's conjecture that his algorithms give the optimal least squares solution of these modified monotone regression problems. We also propose another (third) approach for dealing with ties.Comments by Dr. J. B. Kruskal have been most helpful.     

Fitting and testing carroll's weighted unfolding model for preferences

A quadratic programming algorithm is presented for fitting Carroll's weighted unfolding model for preferences to known multidimensional scale values. The algorithm can be applied directly to pairwise preferences; it permits nonnegativity constraints on subject weights; and it provides a means of testing various preference model hypotheses. While basically metric, it can be combined with Kruskal's monotone regression to fit ordinal data. Monte Carlo results show that (a) adequacy of true preference recovery depends on the number of data points and the amount of error, and (b) the proportion of data variance accounted for by the model sometimes only approximately reflects true recovery.This study is based on a doctoral dissertation submitted to the University of Illinois at Urbana-Champaign. The author wishes to thank the members of his dissertation committee—Lawrence E. Jones, Chairman, Charles Lewis, Stephen Golding, Ledyard Tucker, and Nancy Wiggins—for their helpful comments.     

Word Order Variation is Partially Constrained by Syntactic Complexity

Previous work suggests that when speakers linearize syntactic structures, they place longer and more complex dependents further away from the head word to which they belong than shorter and simpler dependents, and that they do so with increasing rigidity the longer expressions get, for example, longer objects tend to be placed further away from their verb, and with less variation. Current theories of sentence processing furthermore make competing predictions on whether longer expressions are preferentially placed as early or as late as possible. Here we test these predictions using hierarchical distributional regression models that allow estimates of word order and word order variation at the level of individual dependencies in corpora from 71 languages, while controlling for confounding effects from the type of dependency (e.g., subject vs. object), and the type of clause (main vs. subordinate) involved as well as from trends that are characteristic of individual languages, language families, and language contact areas. Our results show the expected correlations of length with position and variation only for two out of six dependency types (obliques and nominal modifiers) and no difference between clause types. These findings challenge received theories of across-the-board effects of complexity on word order and word order variation and call for theoretical models that relativize effects to specific kinds of syntactic structures and dependencies.     

贝叶斯统计方法的应用与现状

贝叶斯统计方法是心理学数据分析的热门方法。研究全面论述贝叶斯方法在心理学领域的应用与方向。现阶段贝叶斯方法以模拟研究为主,应用方向为心理学研究常用的项目反应理论、认知诊断、计算机自适应、结构方程模型。同时,评述发现贝叶斯方法正逐步被国内心理学研究者所接受。最后,文章讨论了当下贝叶斯统计在心理学研究中应用的局限性及可能的原因,建议统计学者开发界面友好的贝叶斯软件,并在心理学课程中加入贝叶斯知识。     

Regression II. Development through regression

As shown in our previous paper (‘Regression I. Experimental approaches to regression’, JAP, 65, 2, 345-65), the common mechanism of regression can be described as reversible dedifferentiation, which is understood as a relative increase of the proportion of low-differentiated (older) systems in actualized experience. Experimental data show that regression following disease (chronic tension headache) is followed by adaptation and an increase in system differentiation in that experience domain which contains systems responsible for that adaptation. The results of mathematical modelling support the idea that reversible dedifferentiation can be one of the mechanisms for increasing the effectiveness of adaptation through learning. Reversible dedifferentiation, which is phenomenologically described as regression, is a general mechanism for restructuring the organism-environment interactions in situations where behaviours that were effective in the past become ineffective. Reversible dedifferentiation has evolved as a component of adaptation when new behaviours are formed and large-scale modifications in the existing behaviours are required in the face of changes in the external and/or internal environment. Thus, the authors believe that this article provides evidence for Jung’s view that regression is not only a ‘return’ to past forms of thinking, affects and behaviour, but that regressive processes provide a significant impetus for psychological growth and development.