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2018 | OriginalPaper | Chapter

8. Principal Component and Factor Analysis

Authors : Erik Mooi, Marko Sarstedt, Irma Mooi-Reci

Published in: Market Research

Publisher: Springer Singapore

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Abstract

We first provide comprehensive and advanced access to principal component analysis, factor analysis, and reliability analysis. Based on a discussion of the different types of factor analytic procedures (exploratory factor analysis, confirmatory factor analysis, and structural equation modeling), we introduce the steps involved in a principal component analysis and a reliability analysis, offering guidelines for executing them in Stata. Specifically, we cover the requirements for running an analysis, modern options for extracting the factors and deciding on their number, as well as for interpreting and judging the quality of the results. Based on a step-by-step description of Stata’s menu options and code, we present an in-depth discussion of each element of the Stata output. Interpretation of output can be difficult, which we make much easier by means of various illustrations and applications, using a detailed case study to quickly make sense of the results. We conclude with suggestions for further readings on the use, application, and interpretation of factor analytic procedures.

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previous chapter Regression Analysis

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Other methods for carrying out factor analyses include, for example, unweighted least squares, generalized least squares, or maximum likelihood. However, these are statistically complex and inexperienced users should not consider them.

Related discussions have been raised in structural equation modeling, where researchers have heatedly discussed the strengths and limitations of factor-based and component-based approaches (e.g., Sarstedt et al. 2016, Hair et al. 2017a, b).

Note that this changes when oblique rotation is used. We will discuss factor rotation later in this chapter.

Note that factor rotation primarily applies to factor analysis rather than PCA—see Preacher and MacCallum (2003) for details. However, our illustration draws on the factor, pcf command, which uses the factor analysis algorithm to compute PCA results for which rotation applies.

When the gamma is set to 1, this is a special case, because the value of 1 represents orthogonality. The result of setting gamma to 1 is effectively a varimax rotation.

Note that this is not the case when using factor analysis if the standard deviations are different from one (DiStefano et al. 2009).

Note that we omitted the error terms for clarity’s sake.

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Title: Principal Component and Factor Analysis
Authors: Erik Mooi
Marko Sarstedt
Irma Mooi-Reci
Publisher: Springer Singapore
Book: Market Research
Print ISBN: 978-981-10-5217-0

Electronic ISBN: 978-981-10-5218-7

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-981-10-5218-7_8