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Conducting Exploratory Factor Analysis: A Sample Concise and Practical Method

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Conducting Exploratory Factor Analysis: A Concise and Practical Method

Johnny T. Amora1,2

1De La Salle-College of Saint Benilde

2Philippine Association of Researchers and Statistical Software Users(PARSSU)


 

To uncover the underlying factor structure of the scale, the collected data were subjected to exploratory factor analysis. To test the factorability of the scales, the following were examined: inter-item correlations, Kaiser-Meyer-Olkin(KMO) measure of sampling adequacy, Bartlett’s Test of Sphericity, and communalities.  The inter-item correlation coefficients were examined to ensure that most of them are greater than 0.3 (SPSS, 2000).  Subsequently, the KMO for both multiple and individual variables/items were examined.  The values of KMO vary between 0 and 1, where values closer to 1 are better.  This study used the KMO criterion of greater than 0.5 (Field, 2000).   To ensure that the correlation matrix is not an identity matrix, the Bartlett’s Test of Sphericity was examined. Identity matrix is a matrix in which all of the diagonal elements are 1 and all off diagonal elements are 0. Factor analysis of the data, therefore, is appropriate if Bartlett’s Test of Sphericity is significant (p<.05). 

The principal axis factoring with promax rotation method was used to uncover the factor structure of the scale items.  Principal axis factoring was chosen because it gives the best results for data that are either normally-distributed or significantly non-normal (Costello and Osborne, 2005). The promax rotation method was utilized because the factors are expected to be correlated. To determine the optimum factor solution, the following criteria were utilized: 1) computation of the percentage of variance extracted, and (2) interpretability of the factors (Comrey and Lee, 1992).  The selection of the items to be retained in the final scale was based on the rule of thumb of Tabachnick and Fidell (2001) discussed in Costello and Osborne(2005). Thus, a factor loading with absolute value of greater than .32 was considered sufficiently high to assume a strong relationship between a variable and a factor, while factor loadings of less than .32 in absolute value were regarded as insignificant and the items containing such loadings were removed from the scale.  In addition, items with communalities of less than .40 were not included in the final scale.  Moreover, factors with fewer than three items, even with loadings of greater than .32, were excluded from the final version of the scale. With respect to determining the number of factors, only factors with eigenvalues greater than 1.0 were considered significant.

After the exploratory factor analysis, the reliability coefficients (such as Cronbach’s Alpha and McDonald’s Omega) of the emerging factors were computed.  So that each factor is reliable, the reliability coefficients should be 0.7 or higher (Fornell & Larcker, 1981; Nunnaly, 1978; Nunnally & Bernstein, 1994).

 



References


Comrey, A. L., & Lee, H. B. (1992). A First Course in Factor Analysis (2nd ed.). Lawrence Erlbaum Associates.

Costello, A. B., & Osborne, J. W. (2005). Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis. Practical Assessment, Research, and Evaluation, 10(7), 1-9.

Field, A. P. (2000). Discovering Statistics Using SPSS for Windows: Advanced Techniques for the Beginner. Sage Publications.

Fornell, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18(1), 39-50.

Nunnally, J. C. (1978). Psychometric Theory (2nd ed.). McGraw-Hill.

Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric Theory (3rd ed.). McGraw-Hill.

Tabachnick, B. G., & Fidell, L. S. (2001). Using Multivariate Statistics (4th ed.). Allyn & Bacon.



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