Chapter 4 – Research Methodology
4.3 Data Analyses Procedures
4.3.2 Exploratory Factor Analysis Procedures
Due to the exploratory nature of this study, an EFA was performed to obtain a robust and reliable factor structure. EFA is the most common approach in marketing research (see: Andaleeb & Conway, 2006; Bindu, Chandrasekharan, & Sai, 2008; Clemes et al., 2010; Dagger et al., 2007; Lu et al., 2009; Stewart, 1981; Swaid & Wigand, 2009).
EFA is often used in the early stages of research to gather information by providing a data summarization perspective, which offers a better understanding of the factors and therefore would be an appropriate analysis to undertake before SEM (Hair et al., 2010; Kline, 2005; Pallant, 2007; Schumacker & Lomax, 2004).
The two types of factor rotation methods used in the computations for EFA are Oblique and Orthogonal rotation. The objective of factor rotation is to make the factor structure more interpretable when the dimensions are rotated (Aaker et al., 2005). VARIMAX, QUARTIMAX and EQUIMAX are the three major orthogonal rotations; however, VARIMAX is the most popular factor rotation method and is frequently applied in marketing research (see: Ady, 2009; Bindu et al., 2008; Kim, Lee, et al., 2006; Noone, 2008; Shu, 2010; Swaid & Wigand, 2009). Principal Component Analysis (PCA) and the VARIMAX rotation were specifically used in this study to extract the factors for all 56 items. The VARIMAX factor rotation was used because it simplifies the columns in a factor matrix (Hair et al., 2010); an OBLIMIN factor rotation (oblique rotation) was also undertaken here. Oblique rotations and orthogonal rotations often result in similar solutions, but the output of an oblique rotation is more difficult to interpret (Hair et al., 2010; Meyers, Gamst, & Guarino, 2006; Tabachnick & Fidell, 2007). Thus, the final factorial structure was based on the VARIMAX rotation results because the output of an oblique rotation is more difficult to interpret (Tabachnick & Fidell, 2007).
4.3.2.1Performing Exploratory Factor Analysis – Tests and Interpretation 4.3.2.1.1Factor Loadings
Factor loadings were used as the criterion for item reduction in the EFA performed for this study. Hair et al. (2010) suggest that factor loadings in the range 0.30 to 0.40 meet the minimal level for interpretation of structure; factor loadings of 0.50 or greater are considered practically significant and factor loadings exceeding 0.70 are considered indicative of a well-defined structure. In this study, following the recommendation of Hair et al. (2010), items loading below 0.50, item cross loadings, and item misclassifications were removed from the item pool.
4.3.2.1.2Tests for Determining Appropriateness of Exploratory Factor Analysis
In order to perform a factor analysis, several investigations need to be conducted to ensure that the data matrix has sufficient correlations to justify the application of factor
analysis (Pallant, 2007). The investigations include: (1) examining the correlation matrix; (2) inspection of the anti-image correlation matrix; (3) assessing the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy; and (4) assessing the Bartlett’s Test of Sphericity. The explanations of each investigation are as follows:
1. Examination of the correlation matrix is a simple method to determine the appropriateness of factor analysis (Hair et al., 2010). Pallant (2007) suggests factor analysis is appropriate when there are substantial numbers of correlations greater than 0.30 in a data matrix, indicating that the items share common factors and are, therefore, suitable for factor analysis (Chinna, 2009; Pallant, 2007). Otherwise, the data matrix is considered to be inappropriate for factor analysis.
2. The anti-image correlation matrix is the negative value of the partial correlation (Hair et al., 2010). For good factoring, most of the off-diagonal elements are assumed to be small in the diagonal of the anti-image correlation matrix (Tabachnick & Fidell, 2007). However, if the anti-image matrix has many non- zeros, or a larger number of partial off-diagonal entries, the correlation matrix may not be suitable for factor analysis (Stewart, 1981).
3. KMO provides a measure to determine whether the variables belong together (Stewart, 1981). KMO interpretations are: if the value is less than 0.50 it is unacceptable; 0.50 or above is miserable; 0.60 or above is mediocre; 0.70 or above is middling; 0.80 or above is meritorious; and 0.90 or above is marvelous (Kaiser & Rice, 1974). By convention, to indicate appropriateness, KMO values should be above 0.50 (Chinna, 2009).
4. Bartlett’s Test of Sphericity is a statistical test for the presence of correlations among the variables and, therefore, provides statistical evidence that the correlation matrix has significant correlations among at least some of the variables (Hair et al., 2010).
4.3.2.1.3Interpretation of Factors
Three commonly used criteria to determine the number of factors and the criteria for ceasing extraction are: (1) Eigenvalues or the latent root criterion; (2) percentage of variance criterion; and (3) scree test criterion (Janssens et al., 2008; Pallant, 2007; Stewart, 1981). Eigenvalues are the most commonly used technique for selecting the number of
factors (Hair et al., 2010). Pallant (2007) suggests that any factors with Eigenvalues greater than one should be considered significant, otherwise the factors should be ignored.
Beside Eigenvalues, the percentage of variance criterion was also checked. The purpose of this criterion is to ensure practical significance for the derived factors by ensuring that they explain at least a specified amount of total variance (Hair et al., 2010). Hair et al. (2010) suggest that, in the social sciences, it is common to consider a solution that accounts for 60% or less (in some circumstances) of the total variance as satisfactory.
In addition to Eigenvalues and the percentage of variance criterion, the last criterion, the scree test criterion, was also checked. The scree test criterion, according to Hair et al. (2010), is derived by plotting the latent roots against the number of factors in their order of extraction. The shape of the resulting curve is used to assess the cut-off point. The procedure is explained by Stewart (1981, p. 58), as follows:
A straight edge is laid across the bottom portion of the roots to see where they form an approximate straight line. The point where the factors curve above the straight line gives the number of factors, the last factor being the one whose eigenvalues immediately precede the straight line.
Once the final factors were established, Cronbach alphas were calculated for the remaining items to ensure scale reliability (see Subsections 4.1.5.2). The last step was to label or name the final factors following Hair et al. (2010, p. 149) who recommend that “variables with higher loadings are considered more important and have greater influence on the name or label selected to represent a factor’s conceptual meaning.”
Once the final factor was identified SEM was conducted following the EFA (Anderson & Gerbing, 1988a; Bagozzi & Yi, 1988; Churchill, 1979). As noted by Kline (2005), EFA is a standard statistical technique for evaluating a measurement model. However, to test the efficacy of the research model, SEM should be employed. In fact, numerous recent studies on service quality have employed EFA to develop a model and scale and used SEM to develop a comprehensive factor structure model (Bindu et al., 2008; Dagger et al., 2007; Fassnacht & Koese, 2006; González & Brea, 2005; Lu et al., 2009; Olorunniwo et al., 2006; Swaid & Wigand, 2009).