Factor Extraction Method

 COMMON FACTOR ANALYSIS VERSUS COMPONENT ANALYSIS

The selection of one method over the other is based on two criteria:

• (1) the objectives of the factor analysis 
• (2) the amount of prior knowledge about the variance in the variables

Component analysis is used when the objective is to summarize most of the original information (variance) in a minimum number of factors for prediction purposes. 

In contrast, common factor analysis is used primarily to identify underlying factors or dimensions that reflect what the variables share in common. 

The most direct comparison between the two methods is by their use of the explained versus unexplained variance:

• Component analysis, also known as principal components analysis, considers the total variance and derives factors that contain small proportions of unique variance and, in some instances, error variance. 
• Common factor analysis, in contrast, considers only the common or shared variance, assuming that both the unique and error variance are not of interest in defining the structure of the variables. 

(Nguồn: Koch, A. F. (2016))

Component factor analysis is most appropriate when:

• Data reduction is a primary concern, focusing on the minimum number of factors needed to account for the maximum portion of the total variance represented in the original set of variables, and 

• Prior knowledge suggests that specific and error variance represent a relatively small proportion of the total variance

Common factor analysis is most appropriate when:

• The primary objective is to identify the latent dimensions or constructs represented in the original variables, and 

• The researcher has little knowledge about the amount of specific and error variance and therefore wishes to eliminate this variance.

Common factor analysis, with its more restrictive assumptions and use of only the latent dimensions (shared variance), is often viewed as more theoretically based. 

(Nguồn: Krishnan (2011).  )

Although theoretically sound, however, common factor analysis has several problems: 

• First, common factor analysis suffers from factor indeterminacy, which means that for any individual respondent, several different factor scores can be calculated from a single factor model result. No single unique solution is found, as in component analysis, but in most instances the differences are not substantial. 

• The second issue involves the calculation of the estimated communalities used to represent the shared variance. Sometimes the communalities are not estimable or may be invalid (e.g., values greater than 1 or less than 0), requiring the deletion of the variable from the analysis.

Tài liệu tham khảo

• Koch, A. F. (2016). Where is the link between direct, minimally guided and constructivist instruction? A new integrated model of constructivist teaching. EAPRIL 2016, 40. 
• Hair, J.F., Black, W.C., Babin, B.J. and Anderson, R.E. (2010) Multivariate Data Analysis. 7th Edition, Pearson, New York. 
• Krishnan, V. (2011). A comparison of principal components analysis and factor analysis for uncovering the early development instrument (EDI) domains. Unpublished manuscript, Early Child Development Mapping (ECMap) Project, Alberta, University of Alberta, Edmonton, Canada.