The effects on the predictive variance of a new subject’s score for a new test

Abstract: It is often required to predict the scores or their variations under interest. Ishii and Watanabe (2001) investigated, in the context of psychological measurement, the Bayesian predictive distribution of a new subject’s scores for tests and subjects’ scores for a new test. In this paper, the Bayesian posterior predictive distribution of a new subject’s scores for a new parallel test were considered. And the effects of the number of subjects, the number of the tests, and the test reliability were investigated. Then, it was found that, under assumptions that (co)variance parameters are known, the predictive variance of a new subject’s score for a new test was equal to the predictive variances of the new subject’s scores for the existent tests. It was also found that the effect of the number of subjects was relatively large and the effect of the number of tests was relatively small, when a new subject’s scores for existent tests were not observed.     

Statistical inference of minimum rank factor analysis

For any given number of factors, Minimum Rank Factor Analysis yields optimal communalities for an observed covariance matrix in the sense that the unexplained common variance with that number of factors is minimized, subject to the constraint that both the diagonal matrix of unique variances and the observed covariance matrix minus that diagonal matrix are positive semidefinite. As a result, it becomes possible to distinguish the explained common variance from the total common variance. The percentage of explained common variance is similar in meaning to the percentage of explained observed variance in Principal Component Analysis, but typically the former is much closer to 100 than the latter. So far, no statistical theory of MRFA has been developed. The present paper is a first start. It yields closed-form expressions for the asymptotic bias of the explained common variance, or, more precisely, of the unexplained common variance, under the assumption of multivariate normality. Also, the asymptotic variance of this bias is derived, and also the asymptotic covariance matrix of the unique variances that define a MRFA solution. The presented asymptotic statistical inference is based on a recently developed perturbation theory of semidefinite programming. A numerical example is also offered to demonstrate the accuracy of the expressions.This work was supported, in part, by grant DMS-0073770 from the National Science Foundation.     

The Distance from Psychological Research to Real Life

Considering our experiences in everyday life, the result of research based on sample assumed to be derived from a “population” cannot afford individual predictions. That is because the variabilities within individuals which play an important role in actual psychological processes are erased from the data in samples-based studies. In this article, we begin the discussion with how the intra-individual variance contributes to individual prediction. As case study works on the basis of variability within each individual, it explores the intrinsic mechanism of development and emphasize the connection between person and environment. The question of how to generalize from case studies requires that the researcher to selectively consider some of the variance and construction of a hypothetical model that shows how different features of oppositions (Yin and Yang) are integrated into an abstract whole that is applicable to all individual cases.

概化理论方差分量估计的跨分布分析

方差分量估计是进行概化理论分析的关键。采用MonteCarlo模拟技术,探讨心理与教育测量数据分布对概化理论各种方法估计方差分量的影响。数据分布包括正态、二项和多项分布,估计方法包括Traditional、Jackknife、Bootstrap和MCMC方法。结果表明:(1)Traditional方法估计正态分布和多项分布数据的方差分量相对较好,估计二项分布数据需要校正,Jackknife方法准确地估计了三种分布数据的方差分量,校正的Bootstrap方法和有先验信息的MCMC方法(MCMCinf)估计三种分布数据的方差分量结果较好;(2)心理与教育测量数据分布对四种方法估计概化理论方差分量有影响,数据分布制约着各种方差分量估计方法性能的发挥,需要加以区分地使用。     

Strengths-Based Assessment of Children with SED: Consistency of Reporting by Teachers and Parents

Parents and teachers rated the strengths of a group of 20 children diagnosed as having serious emotional disturbance. The degree of consistency between different informants' reports was examined to determine whether certain items and scales on the Behavioral and Emotional Rating Scale (BERS) were more appropriately answered by different sources or in different situations, and whether there were method effects associated with each group. A repeated measures ANOVA and correlations between the informants on each subscale demonstrated significant convergent and discriminant validity as well as possible assessment biases. Results also supported the need for developing separate norms for different informants.     

Determining the number of components from the matrix of partial correlations

A common problem for both principal component analysis and image component analysis is determining how many components to retain. A number of solutions have been proposed, none of which is totally satisfactory. An alternative solution which employs a matrix of partial correlations is considered. No components are extracted after the average squared partial correlation reaches a minimum. This approach gives an exact stopping point, has a direct operational interpretation, and can be applied to any type of component analysis. The method is most appropriate when component analysis is employed as an alternative to, or a first-stage solution for, factor analysis.     

A model for repeat paired comparison preference tests

A model is proposed that describes subject behavior on repeat paired comparison preference tests. The model extends prior work in this area in that it explicitly allows for abstentions and permits the derivation of individual true scores for discrimination ability as well as conditional estimates of proportionate preference. With these results, the properties of a paired comparison test can be thoroughly explored. An empirical example is presented, and test design issues are considered. In particular, repeat paired comparison preference tests are shown to be inherently less efficient discrimination tests than are pick 1 of 2 tests.     

Repeated measurements analysis of variance when the correlations have a certain pattern

Consider a repeated measurements study in which a single observation is taken at each oft(t > 2) equally spaced time points for each ofn subjects. This paper uses a result of Box to find the appropriate multiplicative correction term for the degrees of freedom in the analysis of variance table for the case when there is equal variability per time point, and when the correlation between observationsu time units apart is equal to ^u . For large values oft, the multiplicative correction has a lower bound approximately equal to 2.5/(t – 1).Dr. Fleiss is also with the Biometrics Research Unit of the New York State Psychiatric Institute. This work was supported in part by grant DE 04068 from the National Institute of Dental Research.     

Robust techniques for testing heterogeneity of variance effects in factorial designs

Several ways of using the traditional analysis of variance to test heterogeneity of spread in factorial designs with equal or unequaln are compared using both theoretical and Monte Carlo results. Two types of spread variables, (1) the jackknife pseudovalues ofs ² and (2) the absolute deviations from the cell median, are shown to be robust and relatively powerful. These variables seem to be generally superior to the Z-variance and Box-Scheffé procedures.This research was sponsored by Public Health Service Training Grant MH-08258 from the National Institute of Mental Health. The author thanks Mark I. Appelbaum, Elliot M. Cramer, and Scott E. Maxwell for their helpful criticisms of this paper. An earlier version of this work was presented at the Annual Meeting of the Psychometric Society, Murray Hill, New Jersey, April, 1976.     

On Bayesian estimation in unrestricted factor analysis

It is shown that the common and unique variance estimates produced by Martin & McDonald's Bayesian estimation procedure for the unrestricted common factor model have a predictable sum which is always greater than the maximum likelihood estimate of the total variance. This fact is used to justify a suggested simple alternative method of specifying the Bayesian parameters required by the procedure.