Classical Factor Analysis Research Articles

Factor-Analytic Replications of the Estes Attitude Scales

The Elementary Form of the Estes Attitude Scales was administered to 317 children in grades 3-6 who were attending two rural schools in western Virginia and to 49 fourth graders in an urban Pennsylvania elementary school. The Secondary Form of the Estes was administered to 212 rural Virginia adolescents in grades 8-12. Three classical factor analyses were conducted, one for each sample. Results support the factor-analytic integrity of the Estes scales; the findings closely replicate the information reported in the testing manual.

Comparison of Multitrait-Multimethod, Factor, and Smallest Space Analysis on Personality Scale Data

A multitrait-multimethod matrix of four personality constructs, social desirability, neuroticism, extraversion, and masculinity-femininity, measured by three instruments, Comrey Personality Scales, Eysenck Personality Scales, and MMPI, were analyzed by classical factor analysis and smallest space analysis. The results of both procedures showed excellent agreement, giving four clearly defined orthogonal factors as well as four clearly separated regions in space for the personality constructs, confirming the convergent and discriminant validity of the data obtained in a previous study. The results are attributed in part to the special testing instructions designed to minimize faking and social desirability responding.

A psychometric investigation of the Multidimensional Health Locus of Control Questionnaire.

The validity of the alternate forms of the Multidimensional Health Locus of Control scale and the underlying dimensionality of the three test scales were investigated using 70 male and 77 female British university students. A classical item analysis, principal component and image component factor analysis were undertaken. The results indicated that the alternate forms could be considered parallel. However, a sex difference appeared in the factor structure of the test such that the male sample yielded only two factors while the female sample yielded the three scale factors as expected.

Minimum rank and minimum trace of covariance matrices

This paper considers some mathematical aspects of minimum trace factor analysis (MTFA). The uniqueness of an optimal point of MTFA is proved and necessary and sufficient conditions for a point x to be optimal are established. Finally, some results about the connection between MTFA and the classical minimum rank factor analysis will be presented.

Identification of noise in linear data sets by factor analysis

With the use of atomic and nuclear methods to analyze samples for a multitude of elements, very large data sets have been generated. Due to the ease of obtaining these results with computerized systems, the elemental data acquired are not always as thoroughly checked as they should be leading to some, if not many, bad data points. It is advantageous to have some feeling for the trouble spots in a data, set before it is used for further studies. A technique which has the ability to identify bad data points, after the data has been generated, is classical factor analysis. The ability of classical factor analysis to identify two different types of data errors make it ideally suited for scanning large data sets. Since the results, yielded by factor analysis indicate correlations between parameters, one must know something about the nature of the data set and the analytical techniques used to obtain it to confidentially isolate errors.

Multivariate Statistical Analysis of a Regional Subsistence-Settlement Model for Owens Valley

Despite their growing importance in the study of prehistoric human ecology, regional subsistence-settlement models continue to be developed and justified largely on intuitive grounds. This shortcoming can be at least partially overcome by using multivariate statistical techniques to clarify and refine these models. Such an approach is illustrated using classical factor analysis and discriminant analysis to explicate and improve a regional subsistence-settlement model previously developed for Owens Valley, eastern California.

Anwendung von Methoden der Transformationsanalyse als Form konfirmatorischer Faktorenanalyse / Application of methods of transformation analysis as a mode of confirmatory factor analysis

Abstract The solution of two principal problems in factor analysis - number of factors and their rotation - uses transformation analysis based on theoretical considerations. In this respect one can use the classical methods of factor analysis in a more confirmatory way. The application of orthogonal and oblique transformations will be demonstrated by two examples which point to the meaning of transformation analysis for classical and confirmatory factor analysis.

Einführung in die konfirmatorische Faktorenanalyse / Introduction to Confirmatory Factor Analysis

Abstract This paper is an attempt to discuss the principles of confirmatory factor analysis in a fairly simple way and without recourse to mathematical techniques which are either difficult or not well-known among German social scientists. Merely knowledge of the fundamentals of path analysis as well as of classical or exploratory factor analysis is taken for granted. Beside first-order factors, second-order factors are introduced. Assumptions and characteristics of confirmatory and exploratory factor analysis are compared with each other. The comparison does not focus on mathematical details but on „psychology“ and practice of research as well as on substantial or theoretical utility of both approaches. Use of confirmatory factor analysis is especially recommended, if there are multiple, but defective indicators for each theoretically important variable, firstly in order to test the assumption of merely random or unsystematic measurement error, secondly in order to eleminate the effects of such errors by moving from the indicator to the factor level of analysis in testing substantial propositions.

DETECTION OF CORRELATED ERRORS IN LONGITUDINAL DATA

A study of change in ability between two occasions may employ a number of tests believed to measure the ability in question. Either the same battery of tests is used on both occasions, or equivalent forms are used. For a variety of reasons, correlations may exist between certain errors remaining after eliminating variance due to true scores, and hence the classical factor analysis model is not applicable. A procedure for detecting correlations between errors is discussed. A search strategy is proposed since, even if the number of observed variables is small, the number of possible models is very large. A computer program is described, which produces maximum‐likelihood estimates for the parameters in a factor analytic model in which the error variables may be correlated.

The estimation of factor scores and Kalman filtering for discrete parameter stationary processes

We discuss the analogy between the classical factor analysis model and the ‘ state-space ’ representation of a discrete parameter multivariate linear stochastic system. Using the ‘ regression approach ’ to factor analysis the well-known Kalman—Buey linear filter is derived.

On Estimating the Reliability of Composite Indexes Through Factor Analysis

The rationale for Heise and Bohrnstedt's index of reliability, omega, is restated in terms of the models of classical measurement theory and factor analysis. Although omega is the best available internal-consistency estimate of reliability, its value is generally lower than a composite scale's true reliability in the classical measurement model. Under quite foreseeable circumstances, it may be appreciably lower. Some implications for forming indexes through factor analysis are discussed.

Three-mode factor analysis.

Abstract : Three-mode factor analysis is an extension of classical factor analysis for treatment of threeway classification data. It performs a simultaneous factor analysis of all three ways. There are several logical-intuitive interpretations of three-mode factor analysis. The most obvious is in terms of idealized factors. It can be illustrated with sematic differential data. Given a three-way classification set of data like subjects by scales by concepts, arranged in the form of a box, it is possible to reduce this box to a box of idealized subjects by idealized scales by idealized concepts. Each idealized subject is a matrix of scores of the idealized concepts on the idealized scales. Each idealized scale is a matrix of score of the idealized concepts by the idealized subjects and so on. These idealized matrices are sections of the reduced box called the ''inner core matrix.'' Corresponding to the idealized entities we obtain factor-weight-matrices. The factor weights for subjects give a column of weights for each subject, and the score matrix of each subject (scales by concepts) is obtained as a weighted summation of the idealizedsubject matrices; similarly, for concepts and scales. The original scores are reproduced by a triple operation applying consecutively the three sets of weights. Two empirical applications of three-mode factor analysis are reported. (Author)