Rotation to simple loadings using component loss functions: The orthogonal case

Component loss functions (CLFs) are used to generalize the quartimax criterion for orthogonal rotation in factor analysis. These replace the fourth powers of the factor loadings by an arbitrary function of the second powers. Criteria of this form were introduced by a number of authors, primarily Katz and Rohlf (1974) and Rozeboom (1991), but there has been essentially no follow-up to this work. A method so simple, natural, and general deserves to be investigated more completely. A number of theoretical results are derived including the fact that any method using a concave CLF will recover perfect simple structure whenever it exists, and there are methods that will recover Thurstone simple structure whenever it exists. Specific CLFs are identified and it is shown how to compare these using standardized plots. Numerical examples are used to illustrate and compare CLF and other methods. Sorted absolute loading plots are introduced to aid in comparing results and setting parameters for methods that require them.The author is very indebted to a reviewer for pointing him to the generalized hyperplane count literature and to all the reviewers for valuable comments and suggestions.     

Exploratory second-order analyses for components and factors

Abstract: Exploratory methods using second‐order components and second‐order common factors were proposed. The second‐order components were obtained from the resolution of the correlation matrix of obliquely rotated first‐order principal components. The standard errors of the estimates of the second‐order component loadings were derived from an augmented information matrix with restrictions for the loadings and associated parameters. The second‐order factor analysis proposed was similar to the classical method in that the factor correlations among the first‐order factors were further resolved by the exploratory method of factor analysis. However, in this paper the second‐order factor loadings were estimated by the generalized least squares using the asymptotic variance‐covariance matrix for the first‐order factor correlations. The asymptotic standard errors for the estimates of the second‐order factor loadings were also derived. A numerical example was presented with simulated results.     

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.     

Organizing Components into Combinations: How Stage Transition Works

This paper investigates the nature of transition between stages. The Model of Hierarchical Complexity of tasks leads to a quantal notion of stage, and therefore delineates the nature of stage transition. Piaget's dialectical model of stage change was extended and precisely specified. Transition behavior was shown to consist of alternations in previous-stage behavior. As transition proceeded, the alternations increased in rate until the previous stage behaviors were “smashed” together. Once the smashed-together pieces became coordinated, new-stage behavior could be said to have formed. Because stage transition is quantal, individuals can only change performance by whole stage. We reviewed theories of the specific means by which new-stage behavior may be acquired and the emotions and personalities associated with steps in transition. Contemporary challenges in the society increasingly call for transition to postformal and postconventional responses on the part of both individuals and institutions as the examples illustrate.     

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.     

采用理想点方法检验生活取向测验及其修订版的单维性

该文从项目反应过程出发,认为可能是由于原有的维度分析方法将生活取向测验（LOT）及其修订版（LOT-R）这两个测验的项目反应理想点过程错误地限定为优势过程,导致两个测验违背单维性的结论;进而采用主成分分析的未旋转成分负荷散点图和对应分析的维度分数散点图,并结合项目相关矩阵法验证LOT和LOT-R的维度。结果显示LOT-R的单维性得到了验证,LOT由于包含两个测量应对的项目而导致违背单维性。最后作者提出应该与理想点过程相一致的心理计量学模型对LOT-R的数据进行分析。     

阅读障碍检测的“差异模型”与“成分模型”比较分析

阅读障碍检测的“差异模型”因其操作性强的特点备受研究者喜爱且已成为该领域研究中广为采用的检测模型,然而研究表明“差异模型”在理论与实践方面存在诸多弊端;鉴于此,一些研究者提出了基于阅读成分理论、以干预为导向、科学合理、简便易施的“成分模型”,从而避免了单一采用“差异模型”进行阅读障碍检测。研究表明“成分模型”在汉语阅读障碍检测和亚类型鉴定中同样具有可行性和有效性,因此尝试采用“成分模型”实施阅读障碍检测可以避免汉语阅读障碍检测方面存在的混杂现象,进而促使我国阅读障碍检测及亚类型鉴定朝向更加科学化、规范化方向迈进     

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.

Effects of temperature and prior residence on territorial aggression in the convict cichlid Cichlasoma nigrofasciatum

Aggression in the convict cichlid Cichlasoma nigrofasciatum was measured under two different environmental parameters after introduction of a conspecific intruder. Measurements were made after 24-hr and 48-hr teritorial residence times at both 26°C and 30°C. Eight fish established territories in individual tanks each containing one terra cotta pot. Intruders contained in a glass cylinder were introduced into the territories. An opaque divider separating the resident from the intruder was removed after a 15-min acclimation period. At 26°C, we observed a significant difference in the mean number of bites of the cichlids of 24-hr and 48-hr residency durations, whereas, at 30°C, such a difference did not exist. Statistical analysis showed that cichlids exhibited more aggression at 30°C than at 26°C. Increased aggression levels at the higher temperature may be related to the fact that cichlids establish territories and spawn at about 30°C.     

Component Integrity of Teacher Intervention Management Behavior Using a Student Self-Monitoring Treatment: An Experimental Analysis

This investigation was undertaken to determine the effects of differing levels of treatment integrity resulting from implementation of varying numbers of intervention components. The self-monitoring program was conducted over 4 weeks and targeted positive and negative classroom behaviors. The independent variable included three levels: 100% integrity, that included reward and graphing of behavior; 83.3% integrity, that included the reward component; and 66.7% integrity, that employed self-monitoring with recording only. Participants included 49 elementary school students, mean age of 10.4 years, 36.7% female, 93.9% Anglo. Results of treatment on teacher and student ratings from the Social Skills Rating System, teacher ratings from the Abbreviated Symptom Questionnaire, ratings of the child-specific target behaviors, and student frequency counts of target behaviors were analyzed using Multivariate Analyses of Variance. The changes in rating measures from pre-test to post-test did not significantly differ between groups. Students in the two more inclusive treatment programs recorded more positive behaviors.