Some properties of two measures of multivariate association

Two kinds of measures of multivariate association, based on Wilks' and the Bartlett-Nanda-Pillai trace criterionV, respectively, are compared in terms of properties of the univariateR ² which they generalize. A unified set of derivations of the properties is provided which are self-contained and not restricted to decompositions in canonical variates. One conclusion is that asymmetric index based on allows generalization of the multiplicative decomposition ofR ² in terms of squared partial correlations, but not the additive decomposition in terms of squared semipartial correlations, while the reverse is true for anasymmetric index based onV.We are indebted to Jos M. F. ten Berge for some fruitful discussions.     

Application of model-selection criteria to some problems in multivariate analysis

A review of model-selection criteria is presented, with a view toward showing their similarities. It is suggested that some problems treated by sequences of hypothesis tests may be more expeditiously treated by the application of model-selection criteria. Consideration is given to application of model-selection criteria to some problems of multivariate analysis, especially the clustering of variables, factor analysis and, more generally, describing a complex of variables.     

Pseudo maximum likelihood estimation and a test for misspecification in mean and covariance structure models

Using the theory of pseudo maximum likelihood estimation the asymptotic covariance matrix of maximum likelihood estimates for mean and covariance structure models is given for the case where the variables are not multivariate normal. This asymptotic covariance matrix is consistently estimated without the computation of the empirical fourth order moment matrix. Using quasi-maximum likelihood theory a Hausman misspecification test is developed. This test is sensitive to misspecification caused by errors that are correlated with the independent variables. This misspecification cannot be detected by the test statistics currently used in covariance structure analysis.For helpful comments on a previous draft of the paper we are indebted to Kenneth A. Bollen, Ulrich L. Küsters, Michael E. Sobel and the anonymous reviewers of Psychometrika. For partial research support, the first author wishes to thank the Department of Sociology at the University of Arizona, where he was a visiting professor during the fall semester 1987.     

Object knowledge and the emergence of language

Infants' spontaneous play with objects was examined for evidence of developments in object knowledge in relation to the emergence of words and the single-word period in language development. Subjects were 7 girls and 7 boys, from different ethnic and economic backgrounds, who were studied longitudinally from 9 months to 26 months of age. Two types of displacements of objects in relation to one another were identified in the children's play: separations and constructions. The development of constructions was associated with the emergence of words, and constructions increased with age while separations decreased. The development of specific constructions, which account for knowledge of the particular properties of objects, was more strongly associated with a vocabulary spurt at the end of the single-word period than with chronological age. Despite the wide variation in the infants' ages when developments in language and play were reached, relations between achievements in the two domains were consistent among them, as confirmed with the Friedman test, p<.001. The results are discussed in terms of the cognitive developments required for play with objects and saying words.     

Object decision test (BORB): normative data for the adult Quebec population and performance in Alzheimer’s disease and the semantic variant of primary progressive aphasia

Object decision (OD) test is one subtest of the Birmingham Object Recognition Battery (BORB). It is useful for differential diagnosis among several neurodegenerative diseases. However, normative data provided with this battery count on very few subjects and do not control for the effect of age, which limits interpretability. The purpose of Study 1 was to provide normative data for the OD test of the BORB (version A—hard). The objectives of Study 2 were to establish the diagnostic validity of this task and predictive validity of the normative data in the case of the semantic variant of primary progressive aphasia (svPPA) and Alzheimer’s disease (AD).Based on multiple linear regressions, equations to calculate Z-scores corrected for age were provided for 130 participants aged from 47 to 89 years. Performance of 20 healthy participants was compared to that of 14 individuals with svPPA and 18 with AD. After controlling for confounders, participants with svPPA had a lower total score than controls and AD participants. AD participants had a poorer performance than controls only when chimeric objects were considered. Among those with a deficit on the total score of the test, 94% (17/18, including 12 with svPPA) were correctly identified as having a pathological condition (svPPA or AD). This test could help refine differential diagnosis between svPPA and AD patients, especially before the deficits of episodic memory show up.     

Expertise and gambling: Using Type 2 signal detection theory to investigate differences between regular gamblers and nongamblers

This paper presents an experimental investigation into how individuals make decisions under uncertainty when faced with different payout structures in the context of gambling. Type 2 signal detection theory was utilized to compare sensitivity to bias manipulations between regular nonproblem gamblers and nongamblers in a novel probability-based gambling task. The results indicated that both regular gamblers and nongamblers responded to the changes of rewards for correct responses (Experiment 1) and penalties for errors (Experiment 2) in setting their gambling criteria, but that regular gamblers were more sensitive to these manipulations of bias. Regular gamblers also set gambling criteria that were more optimal. The results are discussed in terms of an expertise-transference hypothesis.     

Acquisition of arbitrary conditional discriminations by young normally developing children

Three experiments investigated conditions designed to facilitate acquisition of arbitrary conditional discriminations in 3- to 6-year-old normally developing children. In Experiment 1, 6 subjects failed to master the arbitrary match-to-sample task under conditions of differential reinforcement alone, but 7 subjects did so when instructions or instructions and sample naming were added. In Experiment 2, sample naming introduced in a blocked-trial arrangement resulted in acquisition, but only when the sample name was a nonsense syllable provided by the experimenter (5 of 7 subjects) and not when the sample name was generated by the subject (0 of 5 subjects). Experiment 3 demonstrated the effectiveness of a training sequence involving thematically related stimuli as an intermediate step facilitating the transition from identity to novel arbitrary relations. The difficulties in mastering arbitrary conditional discriminations shown here imply that further analyses with young children will be particularly important in efforts to investigate the development of theoretically important stimulus relations.     

Frege,Boolos, and Logical Objects

In this paper, the authors discuss Frege's theory of logical objects (extensions, numbers, truth-values) and the recent attempts to rehabilitate it. We show that the eta relation George Boolos deployed on Frege's behalf is similar, if not identical, to the encoding mode of predication that underlies the theory of abstract objects. Whereas Boolos accepted unrestricted Comprehension for Properties and used the eta relation to assert the existence of logical objects under certain highly restricted conditions, the theory of abstract objects uses unrestricted Comprehension for Logical Objects and banishes encoding (eta) formulas from Comprehension for Properties. The relative mathematical and philosophical strengths of the two theories are discussed. Along the way, new results in the theory of abstract objects are described, involving: (a) the theory of extensions, (b) the theory of directions and shapes, and (c) the theory of truth values.     

Cognitive development in object manipulation by infant chimpanzees

This study focuses on the development of spontaneous object manipulation in three infant chimpanzees during their first 2 years of life. The three infants were raised by their biological mothers who lived among a group of chimpanzees. A human tester conducted a series of cognitive tests in a triadic situation where mothers collaborated with the researcher during the testing of the infants. Four tasks were presented, taken from normative studies of cognitive development of Japanese infants: inserting objects into corresponding holes in a box, seriating nesting cups, inserting variously shaped objects into corresponding holes in a template, and stacking up wooden blocks. The mothers had already acquired skills to perform these manipulation tasks. The infants were free to observe the mothers' manipulative behavior from immediately after birth. We focused on object–object combinations that were made spontaneously by the infant chimpanzees, without providing food reinforcement for any specific behavior that the infants performed. The three main findings can be summarized as follows. First, there was precocious appearance of object–object combination in infant chimpanzees: the age of onset (8–11 months) was comparable to that in humans (around 10 months old).Second, object–object combinations in chimpanzees remained at a low frequency between 11 and 16 months, then increased dramatically at the age of approximately 1.5 years. At the same time, the accuracy of these object–object combinations also increased. Third, chimpanzee infants showed inserting behavior frequently and from an early age but they did not exhibit stacking behavior during their first 2 years of life, in clear contrast to human data.