Factors Analysis

Principal Component Analysis (PCA) and Factor Analysis (FA) are used when the researcher is interested in decreasing the number of variables in order to fit a framework or a structure. The variables with high correlation among them and are largely independent, are combined into factors or groups. FA and PCA are usually applied for measuring the instruments that are not directly observable in real life (Gaur and Gaur, 2006). PCA and FA are essentially techniques that are applied for data reduction. In PCA, all variances in the variables were duly analysed. However, in FA, only the shared variance is analysed (Kerr et al., 2002).

3.11.5.1 Exploratory and Confirmatory Analysis

In the exploratory factor analysis (EFA), scholars are interested in exploring the underlying or hidden dimensions that leads to correlations among the collected variables. However, in the confirmatory factor analysis (CFA), the researchers are interested in testing whether the correlation between variables is in line with the hypothesized framework; this hypothesis is based on previous researches or theories (Gaur et al., 2006). Therefore, EFA deals with theory building and CFA with theory testing. In this research, the framework is result of a literature review, theory and a model that is why confirmatory factor analysis is applied for hypothesis testing.

86

3.11.5.2 Sampling Adequacy in FA

Kaiser-Meyer-Oklin (KMO) and Bartlett‘s test are two tests that determine whether the samples are suitable for FA and factor reduction. KMO test reveals whether the variances of the variables are affected by the variance of hidden variables. In other words, the variances of hidden variables influences the total variance (HabibporGetabi et al., 2006). The measurements of KMO test are between zero and one. The measures less than 0.5 show that these data are unsuitable for FA. The measure between 0.5 and 0.69 implies that the data should be improved, and a measures more than 0.7 implies the fact that the data are suitable for factor analysis or reduction. The measures that are closer to one are more suitable for FA.

Bartlett‘s test of sphericity helps scholars realize the relationship between variables and factors, and reveals the existing structure between them. In fact, Bartlett‘s test reveals the relational matrix, a matrix with zero main diagonal. Kline (1994) suggested three to five variables to measure a factor. Therefore, the number of variables is three times more than the number of factors. The factors with three or less variables are weak, while factors with five variables are more suitable. The sample size follows the rule of ―more is better‖. Some experts have expressed the opinion that the sample size should not be less than 100 samples (George et al., 2003). Factor loading shows the relationship between variables and factors. Therefore, factor loading changes between -1 and +1. More factor loadings show more relation between variables and a factor. Tabachnick et al. (2007) suggested 0.32 as a minimum value of factor loading. Chong (2013) and Wang et al. (2011) have mentioned factor loading greater than 0.5 is more significant

87 for statistical model. In this research the items with less than 0.5 loading were omitted from the model.

3.11.5.3 Factors Determination

Researchers explore the number of factors based on the relationships between items and factors. In the exploratory factor analysis, the results of factor analysis show the number of factors (Rawen, 1997). Different methods use for determination of factors:

3.11.5.3.1 Prior Criterion

In this case, researcher has an initial model that shows relationships between items and factors based on literature review. Prior criterion helps to select the number of principal components that will explain a maximal amount of variance. Scholars attempt to prove the existing relationship or improve the model. For instance, experts are interested to know whether system quality, information quality, service quality, product quality, delivery quality have relationship with customer satisfaction and trust in e- Commerce (Habibpor and Safari, 2008).

3.11.5.3.2 The Variance of Factors by Variables

It is a simple method for the determination of factors. Cumulative variance of variables on the factor shows the number of factors. Therefore, the variables are acceptable, which have more variance affect certain factors. The measure of acceptable variance is different in variant science. For instance, the acceptable variance for medical science is %60, while for social science, it is %90 (Mansorfar, 2005).

88

3.11.5.3.3 Kaiser Method

This method is called Guttman-Kaiser. The factors are acceptable, with their Eigenvalues being more than 1. This method is mostly utilized in the FA (Rawen, 1997). Therefore, all factors with Eigenvalue of less than 1 will be deleted. In contrast, Tucker and MacCallum (1997) believed that sometimes, factors with Eigenvalues of less than (close to) 1 can be regarded as main factors.

3.11.5.3.4 Screen Test

The screen graph shows the Eigenvalue of the factors, and the factors with Eigenvalues of more than 1 are acceptable. The selection of factors continues unless the specific variance is less than common variance.

There is a variation in the collection of data. Scholars are interested in identifying the source of the variation, due to the fact that when we have a single source, there is systematic variance. Also, there might be other sources of variations. The variance of a variable encompasses common, specific and error variance.

Common variance: Variance of a variable that is shared with common factors. Specific variance: The others variance have no effect on it.

Error variance: In simple words, variation due to errors can be part of error variance. In this research, the independent variables are extracted from literature review and interview with experts. Then based on their effects and notions a classification of variables was presented. This classification shows the effects of technological, organizational and customer factors on e-Satisfaction, e-trust and e-Loyalty. Indeed, the researchers are aware of the construct and are attempting to enhance the structure. In the next chapter, the results of factor reduction will be discussed with more details.

89