Abstract
Factor analysis identifies unobserved variables that explain patterns of correlations within a set of observed variables. It is often used to identify a small number of factors that explain most of the variance embedded in a larger number of variables. Thus, factor analysis is about data reduction. It can also be used to generate hypotheses regarding the composition of factors. Furthermore, factor analysis is often used to screen variables for subsequent analysis (e.g., to identify collinearity prior to performing a linear regression analysis as discussed in Chap. 7).
Learning Objectives
After reading this chapter, you should understand:
– The principles of exploratory and confirmatory factor analysis.
– The difference between principal components analysis and principal axis factoring.
– Key terms such as s, communality, factor loadings and factor scores.
– How to determine whether data are suitable for carrying out an exploratory factor analysis.
– How to interpret SPSS factor analysis output.
– The principles of and how to carry it out in SPSS.
– The basic idea behind
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- 1.
This number is calculated as kċ(k−1)/2, with k being the number of items to compare.
- 2.
Note that this changes when factors are rotated in a oblique way. We will discuss factor rotation later in this chapter.
- 3.
Note that variables should not be perfectly correlated (the correlation is −1 or 1), as this might lead to problems in the analysis.
- 4.
Note that in Fig. 8.3, we consider a special case as the five variables are scaled down into a two-dimensional space. Actually, in this set-up, it would be possible to explain all five variables by means of the two factors. However, in real-life, the five variables span a five-dimensional vector space.
- 5.
Researchers often argue along the lines of measurement error when distinguishing between principal components analysis and principal axis factoring (e.g., Hair et al. 2010). However, as this distinction does not really have implications for market research studies, we omitted this argument.
- 6.
Note that there are further approaches to determine the number of factors such as the parallel analysis or the minimum average partial test which we discuss in the Web Appendix ( Web Appendix → Chapter. 8).
- 7.
Alternative procedures include the Bartlett method and the Anderson–Rubin method, which are designed to overcome potential problems associated with the regression technique. However, these problems are of rather theoretical nature and of little importance to market research practice.
- 8.
In some cases, path analysis can also be used in an exploratory way, especially when using PLS path modeling. Asparouhov and Muthén (2009) provide a rather technical discussion of this subject in the context of covariance-based structural equation modeling. However, please note that using structural equation modeling in an exploratory way is still an exception.
- 9.
In
the Web Appendix (→Chapter 8), we illustrate the use of the parallel analysis and the minimum average partial test for determining the number of factors using this dataset.
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Mooi, E., Sarstedt, M. (2010). Factor Analysis. In: A Concise Guide to Market Research. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12541-6_8
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