Correspondence analysis of incomplete contingency tables

Correspondence analysis can be described as a technique which decomposes the departure from independence in a two-way contingency table. In this paper a form of correspondence analysis is proposed which decomposes the departure from the quasi-independence model. This form seems to be a good alternative to ordinary correspondence analysis in cases where the use of the latter is either impossible or not recommended, for example, in case of missing data or structural zeros. It is shown that Nora's reconstitution of order zero, a procedure well-known in the French literature, is formally identical to our correspondence analysis of incomplete tables. Therefore, reconstitution of order zero can also be interpreted as providing a decomposition of the residuals from the quasi-independence model. Furthermore, correspondence analysis of incomplete tables can be performed using existing programs for ordinary correspondence analysis.     

Comparing item characteristic curves

Test items are often evaluated and compared by contrasting the shapes of their item characteristics curves (ICC's) or surfaces. The current paper develops and applies three general (i.e., nonparametric) comparisons of the shapes of two item characteristic surfaces: (i) proportional latent odds, (ii) uniform relative difficulty, and (iii) item sensitivity. Two items may be compared in these ways while making no assumption about the shapes of item characteristic surfaces for other items, and no assumption about the dimensionality of the latent variable. Also studied is a method for comparing the relative shapes of two item characteristic curves in two examinee populations.The author is grateful to Paul Holland, Robert Mislevy, Tue Tjur, Rebecca Zwick, the editor and reviewers for valuable comments on the subject of this paper, to Mari A. Pearlman for advice on the pairing of items in the examples, and to Dorothy Thayer for assistance with computing.     

An alternating least squares algorithm for fitting the two- and three-way dedicom model and the idioscal model

The DEDICOM model is a model for representing asymmetric relations among a set of objects by means of a set of coordinates for the objects on a limited number of dimensions. The present paper offers an alternating least squares algorithm for fitting the DEDICOM model. The model can be generalized to represent any number of sets of relations among the same set of objects. An algorithm for fitting this three-way DEDICOM model is provided as well. Based on the algorithm for the three-way DEDICOM model an algorithm is developed for fitting the IDIOSCAL model in the least squares sense.The author is obliged to Jos ten Berge and Richard Harshman.     

Convergence properties of an iterative procedure of ipsatizing and standardizing a data matrix,with applications to parafac/candecomp preprocessing

Centering a matrix row-wise and rescaling it column-wise to a unit sum of squares requires an iterative procedure. It is shown that this procedure converges to a stable solution. This solution need not be centered row-wise if the limiting point of the interations is a matrix of rank one. The results of the present paper bear directly on several types of preprocessing methods in Parafac/Candecomp.     

Measures of observer agreement when binomial data are collected in free operant situations

This paper examines a model and defines reasonable assumptions underlying different measures of observer agreement for categorical data collected in free operant situations. It is assumed that two or more observers classify operant behaviors of subjects into occurrences and nonoccurrences by recognition by validated response classes (categories) such that the rates of false positives and observer biases are acceptably low. Thus errors are mostly omissions, i.e., failing to observe events that occur. Four alternative cases are derived, together with formulas for calculating significance tests, variances, and standard errors, three of which do not depend on knowledge of the proportion of time points at which the event does not occur.We wish to acknowledge NICHD Grant HD-10570, The Neuropharmacology of Developmental Disorders, George Breese, Ph.D., and C. T. Gualtieri, M.D., Principal Investigators; NIEHS Grant ES-01104; USPHS Grant HD-03110; and MCH Project 916 to the Division for Disorders of Development and Learning.     

Statistics as psychometrics

In this paper, modern statistics is considered as a branch of psychometrics and the question of how the central problems of statistics can be resolved using psychometric methods is investigated. Theories and methods developed in the fields of test theory, scaling, and factor analysis are related to the principle problems of modern statistical theory and method. Topics surveyed include assessment of probabilities, assessment of utilities, assessment of exchangeability, preposterior analysis, adversary analysis, multiple comparisons, the selection of predictor variables, and full-rank ANOVA. Reference is made to some literature from the field of cognitive psychology to indicate some of the difficulties encountered in probability and utility assessment. Some methods for resolving these difficulties using the Computer-Assisted Data Analysis (CADA) Monitor are described, as is some recent experimental work on utility assessment.1980 Psychometric Society presidential address.I am indebted to Paul Slovic and David Libby for valuable consultation on the issues discussed in this paper and to Nancy Turner and Laura Novick for assistance in preparation.Research reported herein was supported under contract number N00014-77-C-0428 from the Office of Naval Research to The University of Iowa, Melvin R. Novick, principal investigator. Opinions expressed herein reflect those of the author and not those of sponsoring agencies.     

On more powerful tests of judge agreement with a known standard

To establish the existence of his abilities, a judge is given the task of classifying each ofN=rs subjects into one ofr known categories, each containings of the subjects. An incomplete design is proposed whereby the judge is presented withb groups, each one containingn=rs/b<r subjects. Then different categories corresponding to members of the group are known. Using the total number of correct classifications, this method of grouping is compared to that in which the group size is equal to the number of categories. The incomplete grouping is shown to yield a more powerful test for discriminating between the null hypothesis that the judge is guessing the classifications and the alternative hypothesis that he has some definite abilities. The incomplete design is found to be most effective (powerful) when the number of subjects in a group is limited to two or three.The author is grateful for the suggestions of the referees and the editor, which greatly improved the paper.     

关于幼儿嗅、味、动、触摸感觉道记忆的研究

记忆在幼儿心理的发展过程中,具有极为重要的作用。幼儿知识的掌握,语言的学习,技巧的培养,以至个性的形成,都与记忆活动密切联系。国内外关于幼儿记忆的研究,主要限于有意与无意识记,机械与意义识记,形象与语词记忆等方面,很少从不同感觉道输入信息来进行比较。有的实验虽然涉及到不同感觉道的记忆,但被试者都是7岁以上的儿童,如斯梅德利(Smedley)和三岛、横尾等人的研究。为了全面了解幼儿的记忆发展水平,我们设计了关于幼儿不同感觉道记忆的实验研究,试图通过对幼儿各个感觉道输入信息来全面测查幼儿的视觉、听觉、味觉、嗅觉、动觉和触摸党的记忆水平,了解其发展规律及特点,以便为幼儿记忆的理论研究提供实验数据,为幼儿教育提供心理学依据。     

Psychometric properties and reference data for Danish versions of Free and Cued Selective Reminding Test,Category Cued Memory Test and Logical Memory

Memory assessment is a key element in neuropsychological testing. Gold standard evaluation is based on updated normative data, but in many small countries (e.g. in Scandinavia) such data are sparse. In Denmark, reference data exist for non‐verbal memory tests and list‐learning tests but there is no normative data for memory tests which capture narrative recall and cued recall. In a nation‐wide study, Free and Cued Selective Reminding Test (FCSRT ), WMS ‐III Logical Memory (LM ) and a newly developed test Category Cued Memory Test (CCMT ‐48) were applied in 131 cognitively intact persons (aged 60–96 years). Regression‐based reference data for Danish versions of FCSRT , CCMT ‐48 and LM adjusted for age, education and gender are provided. Gender and age‐group had a significant impact on the expected scores, whereas the effect of education had a limited effect on expected scores. Test performances were significantly correlated in the range 0.21–0.51. Based on these findings and previous results it may be relevant to assess both free recall, cued recall and recognition to tap the earliest changes associated with neurodegeneration, and this study therefore provides an important supplement to existing Danish normative data. Future studies should investigate the discriminative validity of the tests and the clinical utility of the presented reference data.