Enhancing Interpretability in Factor Analysis by Means of Mathematical Optimization

Abstract

Exploratory Factor Analysis (EFA) is a widely used statistical technique to discover the structure of latent unobserved variables, called factors, from a set of observed variables. EFA exploits the property of rotation invariance of the factor model to enhance factors’ interpretability by building a sparse loading matrix. In this paper, we propose an optimization-based procedure to give meaning to the factors arising in EFA by means of an additional set of variables, called explanatory variables, which may include in particular the set of observed variables. A goodness-of-fit criterion is introduced which quantifies the quality of the interpretation given this way. Our methodology also exploits the rotational invariance of EFA to obtain the best orthogonal rotation of the factors, in terms of the goodness-of-fit, but making them match to some of the explanatory variables, thus going beyond traditional rotation methods. Therefore, our approach allows the analyst to interpret the factors not only in terms of the observed variables, but in terms of a broader set of variables. Our experimental results demonstrate how our approach enhances interpretability in EFA, first in an empirical dataset, concerning volumes of reservoirs in California, and second in a synthetic data example.     

国师之师——南林寺慧静社会关系研究

南林寺慧静是南朝宋代的涅槃名家之一、梁代国师慧约之恩师,以"律行总持"著称。一直以来,南林寺慧静少为学界所关注,有关其社会关系的诸多问题有待研究。本文结合史料,从师承、同门、弟子和外护等方面,对南林寺慧静的社会关系进行初步探讨,指出南林寺慧静是法业的高足、佛陀跋陀罗的再传弟子,可谓佛陀跋陀罗法系的律行传承者;慧静不像同门昙斌那样被统治者敕令回京弘法,而是游化于浙东的山寺;慧约早年跟随慧静的山居生活经历,对其一生有深远的影响,其成就与慧静律行精严、俭素苦行的身教是分不开的;颜延之、何尚之和颜竣等外护对慧静的弘法活动有一定影响。     

BOOK REVIEWS:

Both the Piagetian theory of the learning process and a psycholinguistic interpretation of the reading process are integrated in and reflected by the reading program that is presented in this paper. Because of this, a brief interpretation of the reading process and of Piaget's theory is necessary to understand and appreciate the reading program. Each component of the program will be explained and interpreted from Piagetian perspectives. Finally, evaluative data attesting to the success of the program will be presented.     

Book reviews

Bloom, A. H. The Linguistic Shaping of Thought : A Study of the Impact of Language on Thinking in China and the West. Hillsdale, N.J.: Erlbaum. 1981. Pp. 106. £9.95. ISBN 0 89859 089 2.

Fodor, J. A. Representations : Philosophical Essays in the Foundations of Cognitive Science. Brghton: Harvester. 1981. Pp. 343. £22.50. ISBN 0 85527 977 X.

Sanford, A. J. and Garrod, S. C. Understanding Written Language: Explorations in Comprehension Beyond the Sentence. Chichester: John Wiley & Sons. 1981. Pp. xiv + 224. £ 11.30. ISBN 0 471 27842 4.

Springer, S. P. and Deutsch, G. Left Brain, Right Brain. San Francisco: W. H. Freeman & Co. 1981. Pp. 243. £4.95 (paperback). ISBN 0 7167 1270 9.

Crystal, D. Introduction to Language Pathology. London : Edward Arnold. 1980. Pp. 214. ISBN 0 7131 62759. £5.50.

Hulme, C. Reading Retardation and Multi-Sensory Teaching. London : Routledge & Kegan Paul. 1981. £12.50. Pp. 200. ISBN 0 7100 0761 2.

Liben, I,. S., Patterson, A. R. and Newcombe, N. (Eds). Spatial Representation and Behaviour Across the Life Span. New York: Academic Press. 1981. Pp. 404. ISBN 0 12 447980 4. £17.80.

Coltman, D. Jean Piaget: Experiments in Contradiction. Chicago: University of Chicago Press. 1980. Pp. 310. ISBN 0 226 66779 0. £13.20.

Hofer, M. A. The Roots of Human Behavior. San Francisco: Freeman. 1981. Pp. xiii + 331. Paperback £6.70. ISBN 0 7167 1278 4.     

Persuasive communications to change actions: an analysis of behavioral and cognitive impact in HIV prevention.

This meta-analysis examined the validity of various theoretical assumptions about cognitive and behavioral change following a communication recommending condom use. The synthesis comprised 82 treatment and 29 control groups included in 46 longitudinal reports with measures of perceived severity and susceptibility, attitudes and expectancies, norms, perceptions of control, intentions, knowledge, behavioral skills, or condom use. Results indicated that across the sample of studies, communications taught recipients about facts related to HIV and also induced favorable attitudes and expectancies, greater control perceptions, and stronger intentions to use condoms in the future. Moreover, messages that presented attitudinal information and modeled behavioral skills led to increased condom use. Results are discussed in the context of theories of human behavior and change and in reference to HIV-prevention interventions.     

El enigma de los «Big five»: ¿realidad o representación?

Resumen

A partir de la revisión de Sánchez Bernardos sobre el enfoque léxico y los cinco grandes factores de personalidad se hacen algunos comentarios y especulaciones. Se aborda la polémica cuestión de si los cinco grandes son estructuras cognitivo-semánticas o reflejan realidades empíricas.     

16PF问卷网络与纸笔施测方式的比较

为检验网络测试与纸笔测试方式是否具有同等的信效度,16PF问卷被用于对两个样本分别进行网络(n=213)和纸笔(n=2801)施测;并从网络测试样本中随机抽取47人,随后进行纸笔重测。在α系数、测题同质性和次级因素结构三项检验中,各个人格因素的表现各有优劣,未得出统一的结论,但可以确定网络测试的信效度较纸笔测试没有明显下降。配对t检验的结果显示,两种施测方式下同一批被试的结果在部分因素上有显著性差异,不能将纸笔测试获得的常模直接用于网络测试。     

Parent-report measure of Theory of Mind: Adaptation to Polish of the Children’s Social Understanding Scale

The main aim of the study was to investigate whether the Children’s Social Understanding Scale (CSUS), a parent report technique, is a valid and reliable measure of Theory of Mind (ToM) abilities in Polish-speaking children. Additionally, the role of language abilities in ToM development was explored. A group of 225 parents of approximately 3.5-year-old Polish children was tested using the Polish version of the CSUS. Their children were tested with a word comprehension test and five behavioural ToM tasks. Satisfactory psychometric properties of the Polish CSUS were observed and positive correlations between the CSUS and behavioural ToM tasks were found. A two-factor structure was found in the CSUS: Mental State Talk (MST) and Mental State Comprehension. The MST factor was significantly related to word comprehension. The utility of the Polish version of the CSUS for future cross-cultural research with this population is discussed.