Correlational reasoning in an everyday context

In the context of everyday reasoning, individuals inferring a causal relation between an antecedent (A) and event (E) rarely have available as evidence for their inferences frequencies of all the four possible occurences, AE, A$\text{E}$, $\text{A}$E, and $\text{AE}$. The present study investigated the willingness of subjects in fourth, seventh, and tenth grades, and college to infer such a relation under the more typical condition of incomplete frequency data. There was some improvement with age, but even college subjects were remarkably willing to infer a relationship based on minimal data, notably the presence of cases in the AE cell. No subjects indicated the need for information regarding the remaining cells. Subsequent presentations of datafor the A$\text{E}$ cell did not substantially alter subjects' willingness to infer a relation, nor did subsequent presentation of data for the remaining two cells, despite the fact that complete frequency data indicated independence of A and E. A comparison group of subjects presented with all four cells at once showed somewhat more frequent application of quantitative reasoning strategies, but their willingness to infer a relationship between A and E was not notably less than that of subjects to whom the data were presented sequentially.     

A preferential matching problem

A matching method proposed by Dr. C. E. Stuart is presented in some detail and the essentials for a test of significance are derived. This method differs from the older matching methods in that partial credit is allowed for a near miss. A slight variation of the method permits the matching of one item withM sets ofn traits.     

Component analysis in cross-sectional and longitudinal data

An extension of component analysis to longitudinal or cross-sectional data is presented. In this method, components are derived under the restriction of invariant and/or stationary compositing weights. Optimal compositing weights are found numerically. The method can be generalized to allow differential weighting of the observed variables in deriving the component solution. Some choices of weightings are discussed. An illustration of the method using real data is presented.Preparation of this article was supported in part by PSC-CUNY Grant #665365 to Roger E. Millsap and by National Institute of Aging Grant NIA-AG03164-03 to William Meredith. The authors thank John Nesselroade for permitting the use of the data presented in the article.     

The analysis of variance and pairwise scaling

Variance analyses are presented for two data layouts—each corresponding to the class of all ordered pairs from a single finite set. The analysis of the dominance layout is in terms of a fixed effects linear model which includes parameters representing the scale values of the elements of the set, response bias, and pairwise interactions. A parallel parametrization is carried out for the composition layout for which corresponding point estimates and hypothesis tests are given. A joint treatment of concurrently observed dominance and composition layouts is suggested and illustrative data are presented.This research was supported in part by National Institutes of Health Grant MH-04439-06. The author would like to express his appreciation to Richard Beatty of the University of Toronto, James Baker and William Carroll of Oregon Research Institute, and J. E. Keith Smith of the University of Michigan, for their helpful comments concerning aspects of this work. Computing assistance was obtained from the Health Sciences Computing Facility, UCLA, sponsored by NIH Grant FR-3.     

Asymptotic standard errors of irt observed-score equating methods

A method of the IRT observed-score equating using chain equating through a third test without equating coefficients is presented with the assumption of the three-parameter logistic model. The asymptotic standard errors of the equated scores by this method are obtained using the results given by M. Liou and P.E. Cheng. The asymptotic standard errors of the IRT observed-score equating method using a synthetic examinee group with equating coefficients, which is a currently used method, are also provided. Numerical examples show that the standard errors by these observed-score equating methods are similar to those by the corresponding true score equating methods except in the range of low scores.The author is indebted to Michael J. Kolen for access to the real data used in this article and anonymous reviewers for their corrections and suggestions on this work.     

Can being scared cause tummy aches? Naive theories, ambiguous evidence, and preschoolers' causal inferences

Causal learning requires integrating constraints provided by domain-specific theories with domain-general statistical learning. In order to investigate the interaction between these factors, the authors presented preschoolers with stories pitting their existing theories against statistical evidence. Each child heard 2 stories in which 2 candidate causes co-occurred with an effect. Evidence was presented in the form: AB?E; CA?E; AD?E; and so forth. In 1 story, all variables came from the same domain; in the other, the recurring candidate cause, A, came from a different domain (A was a psychological cause of a biological effect). After receiving this statistical evidence, children were asked to identify the cause of the effect on a new trial. Consistent with the predictions of a Bayesian model, all children were more likely to identify A as the cause within domains than across domains. Whereas 3.5-year-olds learned only from the within-domain evidence, 4- and 5-year-olds learned from the cross-domain evidence and were able to transfer their new expectations about psychosomatic causality to a novel task.     

On the statistical treatment of residuals in factor analysis

A method for estimation in factor analysis is presented. The method is based on the assumption that the residual (specific and error) variances are proportional to the reciprocal values of the diagonal elements of the inverted covariance (correlation) matrix. The estimation is performed by a modification of Whittle's least squares technique. The method is independent of the unit of scoring in the tests. Applications are given in the form of nine reanalyses of data of various kinds found in earlier literature.The writer wishes to thank Prof. H. Wold, Dr. E. Lyttkens, and Dr. P. Whittle for valuable comments and suggestions.     

Redundancy analysis an alternative for canonical correlation analysis

A component method is presented maximizing Stewart and Love's redundancy index. Relationships with multiple correlation and principal component analysis are pointed out and a rotational procedure for obtaining bi-orthogonal variates is given. An elaborate example comparing canonical correlation analysis and redundancy analysis on artificial data is presented.A Fortran IV program for the method of redundancy analysis described in this paper can be obtained from the author upon request.     

ROOTCLUS: Searching for “ROOT CLUSters” in Three-Way Proximity Data

In the context of three-way proximity data, an INDCLUS-type model is presented to address the issue of subject heterogeneity regarding the perception of object pairwise similarity. A model, termed ROOTCLUS, is presented that allows for the detection of a subset of objects whose similarities are described in terms of non-overlapping clusters (ROOT CLUSters) common across all subjects. For the other objects, Individual partitions, which are subject specific, are allowed where clusters are linked one-to-one to the Root clusters. A sound ALS-type algorithm to fit the model to data is presented. The novel method is evaluated in an extensive simulation study and illustrated with empirical data sets.

     

Hierarchical classes: Model and data analysis

A discrete, categorical model and a corresponding data-analysis method are presented for two-way two-mode (objects × attributes) data arrays with 0, 1 entries. The model contains the following two basic components: a set-theoretical formulation of the relations among objects and attributes; a Boolean decomposition of the matrix. The set-theoretical formulation defines a subset of the possible decompositions as consistent with it. A general method for graphically representing the set-theoretical decomposition is described. The data-analysis algorithm, dubbed HICLAS, aims at recovering the underlying structure in a data matrix by minimizing the discrepancies between the data and the recovered structure. HICLAS is evaluated with a simulation study and two empirical applications.This research was supported in part by a grant from the Belgian NSF (NFWO) to Paul De Boeck and in part by NSF Grant BNS-83-01027 to Seymour Rosenberg. We thank Iven Van Mechelen for clarifying several aspects of the Boolean algebraic formulation of the model and Phipps Arabie for his comments on an earlier draft.     

A multinomial model for short-term priming in word identification.

A simple multinomial model for short-term priming in perceptual word identification is presented. In the experiments to which the model is applied, prime words are presented just prior to a flashed target word, and subjects must decide which of 2 alternative words matches the target. The model assumes that on some proportion of trials, confusion among the words leads to the decision being based on 1 of the prime words instead of the target. In addition, it is assumed that subjects sometimes discount a prime that matches 1 of the test alternatives and so choose the alternative that does not match. With these assumptions, the model fits the data from 5 experiments (including 4 used to develop the model known as ROUSE [responding optimally with unknown sources of evidence]; D. E. Huber, R. Shiffrin, K. Lyle, & K. Ruys, 2001). The multinomial model fits the data about as well as the ROUSE model and so should lead to further development and critical testing of both models.     

Analysis of structural equation model with ignorable missing continuous and polytomous data

The main purpose of this article is to develop a Bayesian approach for structural equation models with ignorable missing continuous and polytomous data. Joint Bayesian estimates of thresholds, structural parameters and latent factor scores are obtained simultaneously. The idea of data augmentation is used to solve the computational difficulties involved. In the posterior analysis, in addition to the real missing data, latent variables and latent continuous measurements underlying the polytomous data are treated as hypothetical missing data. An algorithm that embeds the Metropolis-Hastings algorithm within the Gibbs sampler is implemented to produce the Bayesian estimates. A goodness-of-fit statistic for testing the posited model is presented. It is shown that the proposed approach is not sensitive to prior distributions and can handle situations with a large number of missing patterns whose underlying sample sizes may be small. Computational efficiency of the proposed procedure is illustrated by simulation studies and a real example.The work described in this paper was fully supported by a grant from the Research Grants Council of the HKSAR (Project No. CUHK 4088/99H). The authors are greatly indebted to the Editor and anonymous reviewers for valuable comments in improving the paper; and also to D. E. Morisky and J.A. Stein for the use of their AIDS data set.     

Prover9's Simplification Explained Away

This note discusses P. Oppenheimer and E. Zalta's ‘A Computationally-Discovered Simplification of the Ontological Argument’ [this journal, 2011]. I try to explain why the simplification presented there was successful and comment on the technical aspects of the method they applied.     

The influence of sex hormones on functional cerebral asymmetries in postmenopausal women

Studies investigating changes in functional cerebral asymmetries (FCAs) with hormonal fluctuations during the menstrual cycle in young women have led to controversial hypotheses about an influence of estrogen (E) and/or progesterone (P) on FCAs. Based on methodical, but also on principal problems in deriving conclusions about hormone effects from correlational designs, the present study investigated hemispheric asymmetries in postmenopausal women, who received hormone replacement either with E alone (E group, n = 32), an E–P combination (E–P group, n = 29) or no hormone substitution (control group, n = 31). Speed and accuracy of responses to a word- and a face decision task, both presented laterally by means of the visual half field technique, were assessed. The control group showed the typical pattern of hemispheric asymmetry with more correct responses to verbal stimuli presented in the right visual field (RVF) and to face stimuli presented in the left visual field (LVF). A hormone-effect was demonstrable only for the verbal task, in which the E group showed an enhanced performance of the right hemisphere (LVF). The E–P group showed no significant differences to the control group or the E group. The results suggest a role of E in the modulation of FCAs at least with regard to verbal processing.     

Bayesian Inference for Growth Mixture Models with Latent Class Dependent Missing Data

Growth mixture models (GMMs) with nonignorable missing data have drawn increasing attention in research communities but have not been fully studied. The goal of this article is to propose and to evaluate a Bayesian method to estimate the GMMs with latent class dependent missing data. An extended GMM is first presented in which class probabilities depend on some observed explanatory variables and data missingness depends on both the explanatory variables and a latent class variable. A full Bayesian method is then proposed to estimate the model. Through the data augmentation method, conditional posterior distributions for all model parameters and missing data are obtained. A Gibbs sampling procedure is then used to generate Markov chains of model parameters for statistical inference. The application of the model and the method is first demonstrated through the analysis of mathematical ability growth data from the National Longitudinal Survey of Youth 1997 (Bureau of Labor Statistics, U.S. Department of Labor, 1997). A simulation study considering 3 main factors (the sample size, the class probability, and the missing data mechanism) is then conducted and the results show that the proposed Bayesian estimation approach performs very well under the studied conditions. Finally, some implications of this study, including the misspecified missingness mechanism, the sample size, the sensitivity of the model, the number of latent classes, the model comparison, and the future directions of the approach, are discussed.     

THE EFFECTIVENESS AND TRANSFER VALUE OF TWO METHODS OF CONCEPT LEARNING

WERDELIN, I., BONDESSON, E. & LARSSON, G.-B. The effectiveness and transfer value of two methods of concept learning. Scand. J. Psychol. , 1971, 12, 198–204.–Two methods of learning are compared as to their effectiveness and transfer value, the "direction method", where principles are presented and exemplified, and the "discovery method", where the learner discovers the principles from examples. In an experiment with 12a pupils in grade five it was found that the direction method was superior to the discovery method in these learning situations, that the methods are differently effective with different materials, and that experience with one of the methods may transfer to the ability to learn new materials with either method. The connections between concept, method and previous experience are very complex, however.     

A general approach to nonlinear factor analysis

The method presented attempts to allow for nonlinear, possibly nonmonotonic relations between manifest and latent variates. An attempt is made to provide a workable criterion for choosing between alternative models on the basis of observable data as well as for constructing the appropriate function. An idealized numerical example is given.The author is indebted to Mr. E. J. Burr of the Department of Mathematics, University of New England, and to Dr. J. A. Keats of the University of Queensland, for their advice and criticism.     

Some contributions to maximum likelihood factor analysis

A new computational method for the maximum likelihood solution in factor analysis is presented. This method takes into account the fact that the likelihood function may not have a maximum in a point of the parameter space where all unique variances are positive. Instead, the maximum may be attained on the boundary of the parameter space where one or more of the unique variances are zero. It is demonstrated that suchimproper (Heywood) solutions occur more often than is usually expected. A general procedure to deal with such improper solutions is proposed. The proposed methods are illustrated using two small sets of empirical data, and results obtained from the analyses of many other sets of data are reported. These analyses verify that the new computational method converges rapidly and that the maximum likelihood solution can be determined very accurately. A by-product obtained by the method is a large sample estimate of the variance-covariance matrix of the estimated unique variances. This can be used to set up approximate confidence intervals for communalities and unique variances.The first part of this work was done at the University of Uppsala, Sweden and supported by the Swedish Council for Social Science Research. The second part was done at Educational Testing Service and supported by a grant (NSF-GB-1985) from National Science Foundation to Educational Testing Service.The author is deeply indebted to Dr. D. N. Lawley whose contributions amounted nearly to coauthorship. The author also wishes to thank Mr. G. Gruvaeus for much valuable assistance in constructing the computer program.     

Living With the AIDS Virus: A Representative Case

A human sciences, multilevel, hermeneutic approach was employed to study intensively the relevant life experiences of a 21-year-old male expert consultant who had tested positive for the AIDS virus but who was asymptomatic. The study is presented both as a methodological example of this type of research and as a contribution to understanding an important personal and social issue. Under supervision, the initiating investigator collected anamnestic, behavioral, and projective data, as well as dream reports and spontaneously produced artistic material from the expert consultant. A narrative was produced to describe the study, and the data were integrated in terms of five themes: feeling infected and infectious; facing death and dying; ambivalence; uncertainty; and secrecy. Special features of this method of research are discussed, as is its relevance to the needs and interests of professionals who work with this population.     

Sorting out what's in a word from what's not: Evaluating Clark's Semantic Features Acquisition theory

The Semantic Features Acquisition theory of semantic development which is due to E. Clark (e.g., 1973b) is reviewed and evaluated against the recent experimental literature, with special reference to the acquisition of English antonyms. The review critically examines the three major ontogenetic principles of Clark's theory in light of numerous recent findings, many of which are at variance in some major way with predictions from the theory. In many instances, new data are available which call into question previous findings. A recurrent problem has been that children's comprehension task performance is confounded with their response biases which are specific to the linguistic and nonlinguistic contexts in which the lexical terms are presented. Methodological implications are discussed, with recommendations for employing the logic of converging operations.