Principal Components Analysis , Exploratory Factor Analysis , and Confirmatory Factor Analysis (original) (raw)
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Common factor analysis and component analysis: are they interchangeable? A word of caution
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In this review, we revisit the debate over the interchangeability of the statistical techniques of common factor analysis and component analysis. The literature shows that both techniques are conceptually distinctive. Additionally, the position that component analysis, in practice, can be used as an effective substitute for common factor analysis has provided mixed results. This paper discusses the risk of mixing up these techniques and concludes with some recommendations for this issue.
Principal Component Analysis versus Factor Analysis
Zeszyty Naukowe WWSI, 2021
The article discusses selected problems related to both principal component analysis (PCA) and factor analysis (FA). In particular, both types of analysis were compared. A vector interpretation for both PCA and FA has also been proposed. The problem of determining the number of principal components in PCA and factors in FA was discussed in detail. A new criterion for determining the number of factors and principal components is discussed, which will allow to present most of the variance of each of the analyzed primary variables. An efficient algorithm for determining the number of factors in FA, which complies with this criterion, was also proposed. This algorithm was adapted to find the number of principal components in PCA. It was also proposed to modify the PCA algorithm using a new method of determining the number of principal components. The obtained results were discussed.
Exploratory factor analysis (EFA) is a complex, multi-step process. The goal of this paper is to collect, in one article, information that will allow researchers and practitioners to understand the various choices available through popular software packages, and to make decisions about " best practices " in exploratory factor analysis. In particular, this paper provides practical information on making decisions regarding (a) extraction, (b) rotation, (c) the number of factors to interpret, and (d) sample size. Exploratory factor analysis (EFA) is a widely utilized and broadly applied statistical technique in the social sciences. In recently published studies, EFA was used for a variety of applications, including developing an instrument for the evaluation of school principals (Lovett, Zeiss, & Heinemann, 2002), assessing the motivation of Puerto Rican high school students (Morris, 2001), and determining what types of services should be offered to college students (Majors & Sedlacek, 2001). A survey of a recent two-year period in PsycINFO yielded over 1700 studies that used some form of EFA. Well over half listed principal components analysis with varimax rotation as the method used for data analysis, and of those researchers who report their criteria for deciding the number of factors to be retained for rotation, a majority use the Kaiser criterion (all factors with eigenvalues greater than one). While this represents the norm in the literature (and often the defaults in popular statistical software packages), it will not always yield the best results for a particular data set. EFA is a complex procedure with few absolute guidelines and many options. In some cases, options vary in terminology across software packages, and in many cases particular options are not well defined. Furthermore, study design, data properties, and the questions to be answered all have a bearing on which procedures will yield the maximum benefit. The goal of this paper is to discuss common practice in studies using exploratory factor analysis, and provide practical information on best practices in the use of EFA. In particular we discuss four issues: 1) component vs. factor extraction, 2) number of factors to retain for rotation, 3) orthogonal vs. oblique rotation, and 4) adequate sample size. BEST PRACTICE Extraction: Principal Components vs. Factor Analysis PCA (principal components analysis) is the default method of extraction in many popular statistical software packages, including SPSS and SAS, which likely contributes to its popularity. However, PCA is
1991
Factor analysis is used frequently by researchers as a data reduction and summarization technique. Many analysts use exploratory factor analysis to search for underlying dimensions in attitudinal studies. Concern arises when novice researchers rely solely on information derived from computer printouts to factor analyze data, dismissing theoretical consideration of concepts underlying this analytical procedure. A primer on principal components exploratory factor analysis is presented, and five decision rules for selecting the number of principal components to retain are discussed: (1) the Kl rule; (2) the Scree test; (3) Bartlett's test; (4) the minimum average partial method; and (5) parallel analysis. A small data set, obtained in an actual exploratory study, was used to illustrate the discussion. The study addressed effects of preemployment tests on attitudes toward a firm formed by individuals outside that firm. In a pilot study, responses of more than 400 graduating seniors to three different preemployment tests were analyzed. In a second study, 249 graduating seniors and master's candidates responded to preemployment test scenarios. Dimensions of applicants' attituc.es were examined through exploratory factor analysis. It is concluded that the results of different decision rules must be used when determining the number of principal components, and that factor analyses should be run with one or two components above and below those suggested with the five methods in order to avoid underextraction or overextraction. Analysts are cautioned to not rely on computer programs and preset default outputs as the "last word.
Exploratory Factor Analysis (EFA) in Quantitative Researches and Practical Considerations
Explanatory factor analysis (EFA) is a multivariate statistical method frequently used in quantitative research and has begun to be used in many fields such as social sciences, health sciences and economics. With EFA, researchers focus on fewer items that explain the structure, instead of considering too many items that may be unimportant and carry out their studies by placing these items into meaningful categories (factors). However, for over sixty years, many researchers have made different recommendations about when and how to use EFA. Differences in these recommendations confuse the use of EFA. The main topics of discussion are sample size, number of items, item extraction methods, factor retention criteria, rotation methods and general applicability of the applied procedures. The abundance of these discussions and opinions in the literature makes it difficult for researchers to decide which procedures to follow in EFA. For this reason, it would be beneficial for researchers to ...
International Journal of Educational Narratives
Background. Exploratory factor analysis can be used as a guideline for constructing instrument homogeneity. Purpose. Factor analysis is the queen of analytical methods because of its strength, flexibility and closeness to the nature of scientific aims and objectives. Method. Roughly speaking, an instrument whose items measure only one trait in general and can determine the indicators of a research variable. To determine the number of indicators based on eigenvalues greater than or equal to one, both in the initial factor analysis and in further analysis. Results. A statement item is declared eligible for inclusion in a factor if the item has a factor load greater than or equal to 0.30 on only one factor. Similarly, an indicator is declared feasible if its factor load is greater than or equal to 0.30. Conclusion. The item that has the highest factor load on a factor contributes the most to that factor, so that item is used as the basis for guidance in naming a factor as the name of t...