Bayesian estimation of item response curves

Item response curves for a set of binary responses are studied from a Bayesian viewpoint of estimating the item parameters. For the two-parameter logistic model with normally distributed ability, restricted bivariate beta priors are used to illustrate the computation of the posterior mode via the EM algorithm. The procedure is illustrated by data from a mathematics test.This work was supported under Contract No. N00014-85-K-0113, NR 150-535, from Personnel and Training Research Programs, Psychological Sciences Division, Office of Naval Research. The authors wish to thank Mark D. Reckase for providing the ACT data used in the illustration and Michael J. Soltys for computational assistance. They also wish to thank the editor and four anonymous reviewers for many valuable suggestions.     

Exact conditional tests for cross-classifications: Approximation of attained significance levels

A procedure is proposed for approximating attained significance levels of exact conditional tests. The procedure utilizes a sampling from the null distribution of tables having the same marginal frequencies as the observed table. Application of the approximation through a computer subroutine yields precise approximations for practically any table dimensions and sample size.     

Estimation of covariance structure models with parameters subject to functional restraints

This paper demonstrates the feasibility of using the penalty function method to estimate parameters that are subject to a set of functional constraints in covariance structure analysis. Both types of inequality and equality constraints are studied. The approaches of maximum likelihood and generalized least squares estimation are considered. A modified Scoring algorithm and a modified Gauss-Newton algorithm are implemented to produce the appropriate constrained estimates. The methodology is illustrated by its applications to Heywood cases in confirmatory factor analysis, quasi-Weiner simplex model, and multitrait-multimethod matrix analysis.The author is indebted to several anonymous reviewers for creative suggestions for improvement of this paper. Computer funding is provided by the Computer Services Centre, The Chinese University of Hong Kong.     

II. Genotype-environment interaction in the schizophrenia spectrum: qualitative observations

Previous reports from the Finnish Adoptive Family Study of Schizophrenia have documented significant interplay between genetics (G) and family rearing (E), leading to adoptee outcomes of schizophrenia spectrum disorders. Quantitative evidence for this interplay is significantly enhanced when both high genetic liability and severe environmental dysfunction are present. However, when either genetic liability is low or the rearing environment is healthy, the adoptees appear to be resiliently protected against a pathologic outcome. Nevertheless, exceptions to this pattern do occur. Six qualitative vignettes, together with quantitative measures and categorical diagnoses from the same families, illustrate how multiple methods partially confirm one another and also suggest where further exploration of gene-environment interaction is needed.     

Genetic Evaluation and Counseling of Couples with Recurrent Miscarriage: Recommendations of the National Society of Genetic Counselors

The objective of this document is to provide recommendations for genetic evaluation and counseling of couples with recurrent miscarriage (RM). The recommendations are the opinions of the multidisciplinary Inherited Pregnancy Loss Working Group (IPLWG), with expertise in genetic counseling, medical genetics, maternal fetal medicine, internal medicine, infectious disease, cytogenetics, and coagulation disorders. The IPLWG defines RM as three or more clinically recognized consecutive or non-consecutive pregnancy losses occurring prior to fetal viability (<24 weeks gestation). These recommendations are provided to assist genetic counselors and other health care providers in clinical decision-making, as well as to promote consistency of patient care, guide the allocation of medical resources, and increase awareness of the psychosocial and cultural issues experienced by couples with RM. The IPLWG was convened with support from the March of Dimes Western Washington State Chapter and the University of Washington Division of Medical Genetics. The recommendations are U.S. Preventive Task Force Class III, and are based on clinical experiences, review of pertinent English-language published articles, and reports of expert committees. This document reviews the suspected causes of RM, provides indications for genetic evaluation and testing, addresses psychosocial and cultural considerations, and provides professional and patient resources. These recommendations should not be construed as dictating an exclusive course of medical management, nor does the use of such recommendations guarantee a particular outcome. The professional judgment of a health care provider, familiar with the circumstances of a specific case, should always supersede these recommendations.     

Choice model analysis of the “pick any/n” type of binary data

In the “pick any/n” method, subjects are asked to choose any number of items from a list of n items according to some criterion. This kind of data can be analyzed as a special case of either multiple-choice data or successive categories data where the number of response categories is limited to two. An item response model was proposed for the latter case, which is a combination of an unfolding model and a choice model. The marginal maximum-likelihood estimation method was developed for parameter estimation to avoid incidental parameters, and an expectation-maximization algorithm used for numerical optimization. Two examples of analysis are given to illustrate the proposed method, which we call MAXSC.     

Marginal maximum likelihood estimation for a psychometric model of discontinuous development

Item response theory models posit latent variables to account for regularities in students' performances on test items. Wilson's “Saltus” model extends the ideas of IRT to development that occurs in stages, where expected changes can be discontinuous, show different patterns for different types of items, or even exhibit reversals in probabilities of success on certain tasks. Examples include Piagetian stages of psychological development and Siegler's rule-based learning. This paper derives marginal maximum likelihood (MML) estimation equations for the structural parameters of the Saltus model and suggests a computing approximation based on the EM algorithm. For individual examinees, empirical Bayes probabilities of learning-stage are given, along with proficiency parameter estimates conditional on stage membership. The MML solution is illustrated with simulated data and an example from the domain of mixed number subtraction. The authors' names appear in alphabetical order. We would like to thank Karen Draney for computer programming, Kikumi Tatsuoka for allowing us to use the mixed-number subtraction data, and Eric Bradlow, Chan Dayton, Kikumi Tatsuoka, and four anonymous referees for helpful suggestions. The first author's work was supported by Contract No. N00014-88-K-0304, R&T 4421552, from the Cognitive Sciences Program, Cognitive and Neural Sciences Division, Office of Naval Research, and by the Program Research Planning Council of Educational Testing Service. The second author's work was supported by a National Academy of Education Spencer Fellowship and by a Junior Faculty Research Grant from the Committee on Research, University of California at Berkeley. A copy of the Saltus computer program can be obtained from the second author.     

A maximum likelihood approach to test validation with missing and censored dependent variables

A maximum likelihood approach is described for estimating the validity of a test (x) as a predictor of a criterion variable (y) when there are both missing and censoredy scores present in the data set. The missing data are due to selection on a latent variable (y _s ) which may be conditionally related toy givenx. Thus, the missing data may not be missing random. The censoring process in due to the presence of a floor or ceiling effect. The maximum likelihood estimates are constructed using the EM algorithm. The entire analysis is demonstrated in terms of hypothetical data sets.