Easy bayes estimation for rasch-type models

A Bayes estimation procedure is introduced that allows the nature and strength of prior beliefs to be easily specified and modal posterior estimates to be obtained as easily as maximum likelihood estimates. The procedure is based on constructing posterior distributions that are formally identical to likelihoods, but are based on sampled data as well as artificial data reflecting prior information. Improvements in performance of modal Bayes procedures relative to maximum likelihood estimation are illustrated for Rasch-type models. Improvements range from modest to dramatic, depending on the model and the number of items being considered.This research was supported by ORN Contact #00014-86-K0087. We wish to thank Sheng-Hui Chu and Dzung-Ji Lii for providing intelligent and energetic programming support for this article. We also thank one of the reviewers for pointing out several interesting and useful perspectives.     

Canonical/redundancy factoring analysis

The interrelationships between two sets of measurements made on the same subjects can be studied by canonical correlation. Originally developed by Hotelling [1936], the canonical correlation is the maximum correlation betweenlinear functions (canonical factors) of the two sets of variables. An alternative statistic to investigate the interrelationships between two sets of variables is the redundancy measure, developed by Stewart and Love [1968]. Van Den Wollenberg [1977] has developed a method of extracting factors which maximize redundancy, as opposed to canonical correlation.A component method is presented which maximizes user specified convex combinations of canonical correlation and the two nonsymmetric redundancy measures presented by Stewart and Love. Monte Carlo work comparing canonical correlation analysis, redundancy analysis, and various canonical/redundancy factoring analyses on the Van Den Wollenberg data is presented. An empirical example is also provided.Wayne S. DeSarbo is a Member of Technical Staff at Bell Laboratories in the Mathematics and Statistics Research Group at Murray Hill, N.J. I wish to express my appreciation to J. Kettenring, J. Kruskal, C. Mallows, and R. Gnanadesikan for their valuable technical assistance and/or for comments on an earlier draft of this paper. I also wish to thank the editor and reviewers of this paper for their insightful remarks.     

Spatial,non-spatial and hybrid models for scaling

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.1976 Psychometric Society Presidential Address.While people too numerous to list here have contributed ideas, inspiration, and other help, I particularly wish to acknowledge the contributions of Sandra Pruzansky, without whom this paper could not have been written. I would also like to acknowledge the past contributions of my long-time colleague Jih-Jie Chang, without whose help I probably would not have beenasked to write it.     

Testing the conditional independence and monotonicity assumptions of item response theory

When item characteristic curves are nondecreasing functions of a latent variable, the conditional or local independence of item responses given the latent variable implies nonnegative conditional covariances between all monotone increasing functions of a set of item responses given any function of the remaining item responses. This general result provides a basis for testing the conditional independence assumption without first specifying a parametric form for the nondecreasing item characteristic curves. The proposed tests are simple, have known asymptotic null distributions, and possess certain optimal properties. In an example, the conditional independence hypothesis is rejected for all possible forms of monotone item characteristic curves.The author acknowledges Paul W. Holland for valuable conversations on the subject of this paper; Henry Braun and Fred Lord for comments at a presentation on this subject which led to improvements in the paper; Carl H. Haag for permission to use the data in §4; Bruce Kaplan for assistance with computing; and two referees for helpful suggestions. Requests for reprints should be sent to Paul R. Rosenbaum     

Cuban Mothers' Schemas of ADHD: Development, Characteristics, and Help Seeking Behavior

Parents play a crucial role in the diagnosis and treatment of Attention-Deficit Hyperactivity Disorder (ADHD), one of the most prevalent developmental disorders of young children We report the findings of a qualitative study of Cuban-American mothers of 7 to 10 year old children with ADHD. Results suggest that mothers lacked a cultural model for ADHD and held a cultural model of normal child development which hampered their development of a schema of ADHD. Development of ADHD schemas were motivated by perplexity at their children's behavior and by the high value mothers ascribed to academic achievement. Although the schemas developed by the mothers were labeled as ADHD, their behavioral characterizations of their children, their attributions for the condition and for its causes, and their management strategies were not always in agreement with those of the biomedical model for the condition. However, once mothers classified their children's behavior as atypical, they actively sought assistance from the professional sector.     

An efficient algorithm for joint correspondence analysis

Joint correspondence analysis is a technique for constructing reduced-dimensional representations of pairwise relationships among categorical variables. The technique was proposed by Greenacre as an alternative to multiple correspondence analysis. Joint correspondence analysis differs from multiple correspondence analysis in that it focuses solely on between-variable relationships. Greenacre described one alternating least-squares algorithm for conducting joint correspondence analysis. Another alternating least-squares algorithm is described in this article. The algorithm is guaranteed to converge, and does so in fewer iterations than does the algorithm proposed by Greenacre. A modification of the algorithm for handling Heywood cases is described. The algorithm is illustrated on two data sets.     

‘Attentional Bias’ in correlation judgments? Smedslund (1963) revisited

Smedslund (1963) reports one of the first studies that investigated human judgments of correlation. Smedslund's conclusion, that people reason about correlation mostly from a consideration of the number of times two variables co-occur, has become textbook wisdom (e.g. Baron's "attentional bias", 1994). Yet the data reported in Smedslund's paper fall short of endorsing such a conclusion. After reviewing the original paper, we present the method with which we replicated Smedslund's main experiment. In Experiment 1 subjects were presented with symptom-disease correlation data through a simulated medical diagnosis task. Subjects clearly discriminated between data sets which shared an equal number of symptom-disease co-occurrences but which otherwise showed different levels of correlation. Subjects' diagnoses showed a propensity to predict the disease in the presence of the symptom, and symptom-disease co-occurrences were overestimated in two of the five data sets presented to the subjects. Experiment 2 used a novel abstract scenario with a symmetric predictor variable. Judgments again indicated good discrimination, and biases in prediction responses and case recall were eliminated. In both experiments, judgments of zero correlation were a function of the outcome base rate. We evaluate and contrast the extent to which Cheng's (1997) model of causal induction and two associative models, Rescorla and Wagner (1972) and Pearce (1987) can anticipate the observed pattern in the mean judgments.     

The Products of the Imagination: Psychoanalytic Theory and Postmodern Literary Criticism

This article considers some of the affinities between postmodern literary theory and the psychoanalytic theories concerned with intersubjective phenomena. Postmodern literary theory is described briefly, and it is argued that one of its major concerns is the nature of, and the political and cultural influences on, subjectivity and identity. Despite that, postmodernism generally, and literary postmodernism in particular, can be said to lack a theory of the psychological and interpersonal dimensions of the experience of self. This article contends that the more relational schools of psychoanalytic theory can provide an example of the construction of selfhood that is of importance to contemporary and postmodern literary criticism. The academy has, to a considerable extent identified psychoanalysis with the work of Jacques Lacan, but since the 1980s the work of such theorists as Jane Flax and Jessica Benjamin, building on the work of Nancy Chodorow, have increasingly opened up the possibilities of relational and object relations theory for literary studies. The relational psychoanalytic theories operate in the same epistemological universe as postmodern literary criticism, congruent with the postmodern idea of truth as constructed and relational, and selfhood as shifting, contingent, and always-in-process. Particular attention is paid to the work of Wilfred Bion, whose understanding of self provides an account both of the failure of meaning, and of the development of mind. Some examples of a relational approach to literary analysis are provided.