Comparison of factor extraction and rotation methods in exploratory factor analysis

Abstract

Exploratory Factor Analysis (EFA) is a technique to explore the underlying factors of a large set of observed variables which cannot be measured directly. In general there are seven types of factor extraction methods. For a meaningful interpretation of occurred factor model, the extraction method usually followed by either Orthogonal rotation or Oblique rotation method. However it has not been recommended a particular method of EFA for a given set of data. Further most of the researchers are misusing Principal Component Analysis (PCA) with Exploratory Factor Analysis. Therefore, this study was carried out to investigate a possibility of recommending a particular method for a given set of data using a data set comprising seven variables on crimes. Data were analysed using the statistical software SPSS. To illustrate the contrast of PCA and EFA, analysis was begun with Principle Component. For the comparison of different types of extraction methods under EFA, variables were extracted using Maximum Likelihood Factoring, Principle Axis Factoring and General Least Squares followed by all the Orthogonal rotation methods separately. The steps of the analysis in EFA were quite same with all the extraction methods, however the final result and the effect of the prior assumptions make difference. It is very important to confirm that KMO statistic to be greater than 0.6, prior to carry out EFA for the adequacy of sample size in order to derive valid statistical inferences. If the variables having multivariate normal distribution it is recommended to conduct Maximum Likelihood or General Least Squares. For the non normal distributions, Principle axis factoring is recommended. However it is recommended to compare the results from each method irrespective of the distribution of data set. Among Orthogonal rotations Varimax rotation is recommended as it provides simple factor loadings to interpret. Quartimax generally does not provide simple factor loadings as in Varimax. It is not recommended to carry out ail possible combinations of factor extraction methods and rotation methods to any set of data, as same results will not be produced by each combination. The recommendation given for the particular data set was confirmed using Jackknife validation method.