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4.3 Exploratory Factor Analysis (EFA) and Confirmatory Factor
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a data reduction technique. This data reduction technique should be followed by factor analysis techniques (Yong and Pearce, 2013), for example, CFA, to confirm the findings.
After choosing the suitable extracting technique, a rotation method should be chosen; factor rotation leads to clearer loading,
and unrotated factors result in unclear and vague structure. Two main categories exist for factor rotation orthogonal and oblique rotation methods. The orthogonal rotation involves two types Quartimax and Varimax rotation. In Quartimax rotation, the number of items needed to explain variables is minimised. In a Varimax rotation, the rotation aims to detect higher loading items on each component and minimise the small loading (Yong and Pearce, 2013), (Hair, et al., 2010).
In this research, the Varimax orthogonal rotation was chosen based on two reasons. First, the orthogonal is the most widely used rotation method, and second, the Quartimax are seen as less effective than Varimax since the latter helps achieve a more simplified structure (Hair et al., 2010, p. 92).
The EFA test requires checking a few tests before studying the rotated factor matrix; those tests aim to check the suitability of the data for analysis. The basic terms that will be mentioned in the EFA analysis are presented next:
KMO: Kaiser-Meyer-Olkin measure of sampling adequacy, the KMO cut point is >
0.5 (Yong and Pearce, 2013)
Bartlett test of sphericity: "Statistical test for overall significance of all correlation within a correlation matrix" (Hair et al., 2010, p. 90). A Bartlett test should be significant in order to consider the data suitable for the EFA test (p < 0.05).
Communality: "Total amount of variance an item shares with all other items included in the analysis", usually a commonality less than (0.20) is considered bad, and the
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item with such communality value should be eliminated (Hair et al., 2010, p. 90;
Yong and Pearce, 2013).
Total variance explained: Provide a hint that the variable extracted are valuable and represented; the total variance explained should be around 60% for each scale, and sometimes lower values can be accepted in social science since the gathered information can have lower precision (Hair et al., 2010, p. 108).
Factor loading: According to (Garson, 2012), in EFA, item loading should show a higher loading on the construct (the one that the item theoretically measures) than loading in other constructs. In any case, the factor loading should not be less than (0.30) to be considered significant. Nonetheless, according to (Hair, et al., 2010, p.
116), the significance of the loading should be determined depending on the sample size; in our case, with a sample size of (431) respondents, the loading should be (0.35-0.4).
Cross loading: Cross loading means that one item shows significant loading on more than one construct; this might create a problem in discriminant validity and lead to multicollinearity between the dimensions. Cross-loading is not acceptable for an absolute value of difference less than (0.20) (Garson, 2012), or as recommended by (Samuels, 2017), "Items should not cross-load too highly between factors measured by the ratio of loadings being greater than 75%" (p. 1). It is an item loaded on two constructs with differences in the loading less than 0.20 or with a ratio higher than 75% means that the item should be removed.
4.3.2 Confirmatory Factor Analysis (CFA)
Confirmatory factor analysis is a method that is used to approve, construct validity, and examine factorial validity. Factorial validity refers to whether the constructs or sub-construct
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are related (Harrington, 2009); it is an extension of the content validity (an empirical extension) and is usually used when a specific construct compromises several dimensions.
In factorial validation, the items that are thought to measure a specific dimension (variable) should be more highly related to one another than those measuring other dimensions (Bolarinwa, 2009). CFA test is done to check the observed items (questionnaire items) loading into the latent variable (dimension or variable), as a general rule that the higher the loading, the better, and any item standardised factor loading below (0.50) are unsuitable (Harrington, 2009).
A few requirements should be checked before conducting the CFA test, including no missing data, Normality, outliers, and adequate sample size (as a rule of thumb > 100). Those requirements are met in this research. Additionally, in order to evaluate the model fit, several indices can be checked, namely: Absolute fit indices such as the model chi-square; this index evaluates the model fitness within the population. Usually, this value is evaluated by dividing the chi-square value over the degree of freedom (DF); the value should be < (5) (Harrington, 2009)
Parsimony Correction Indices are measured by the root mean square error of approximation (RMSEA) tests. RMSEA refers to the degree to which the model fits rationally within the population; this value usually should be < (0.08), while other strict criteria require this value to be (<0.05) (Harrington, 2009). The Comparative Fit Indices (CFI) assess the model's fit when compared to a more restricted model, and the CFI value should be close to one. The goodness of fit (GFI) value should be close to one (Harrington, 2009; Hair et al., 2010).
Nevertheless, not all the indices should be evaluated to confirm model fit. Hair et al. stated that multiple fit indices should be used to assess any model goodness of fit, namely, c2 and its associated degree of freedom (df), one absolute fit index (RMSEA or GFI), one
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incremental fit index (CFI or TLI), one goodness of fit index (GFI, CFI, TLI,) and one badness of fit index (RMSEA) (Hair, et al., 2010). Additionally, (Hair, et al., 2010) stated that no strict thresholds should be applied to all research cases. For instance, large sample analysis should be treated similarly to small sample analysis. Accordingly, they provided a guide table that demonstrates the cut points for the modification indices depending upon the sample size (N) and the number of observed variables (m); for this research, N= (401)
>(250), where m=(47>30), CFI, TLI >(0.90) and RMSEA < (0.07) as can be seen from Figure (13) (Adopted from (Hair, et al., 2010).
FIGURE 13MODEL FIT INDICES
In conclusion, the following thresholds are followed for assessing the models of this research the values were decided upon (Hair, et al., 2010) and (Harrington, 2009): 2 / df < (5), RMSEA < (0.07), CFI > (0.90), TLI > (0.90), GFI > (0.90).
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