Confirmatory factor analysis (CFA), as a part of structural equation modelling, is a means of assessing the measurement model by exploring the relationships between the items and scales (Harrington, 2009). As a preliminary step to SEM analysis, therefore, CFA was used to examine the psychometric properties of the measurement
instruments. Unlike exploratory factor analysis, CFA evaluates all of the items from the questionnaires used in the research model as part of one regression model, thereby analysing them simultaneously.
Confirmatory factor analysis using maximum likelihood estimation was conducted using Analysis of Moment Structure (AMOS) version 22 software. As recommended by Harrington (2009) and Kline (2010), different fit indices were used to examine the model fit. It is generally acknowledged that fit indices can be classified into the three categories: absolute fit indices; parsimony indices; and comparative indices (Brown, 2006). Absolute fit indices, such as the model chi-square (χ2), normed chi-square (that is, the ratio of χ2 to its degree of freedom) and standardised root mean square residual (SRMR), measure how well the proposed model reproduces the observed data (Teo, Ursavas, & Bahcekapili, 2012). Parsimonious indices are similar to the absolute fit indices except that they take the complexity of the model into account. An example of parsimonious indices includes the root mean square error of approximation (RMSEA). Finally, comparative fit indices are used to evaluate a model fit relative to an alternative baseline model (Harrington, 2009; Teo et al., 2012) and include the comparative fit index (CFI) and Tucker-Lewis index (TLI).
The model fit statistics for this study are reported in Table 5.4. Since the Chi-square goodness of fit test is sensitive to sample size (Marsh, Balla, & MacDonald, 1998), the model fit was determined using Comparative Fit Index (CFI), Tucker Lewis Index (TLI), Increment Index of Fit (IFI), Standardised root mean square residual (SRMR) and Root Mean Square Error of Approximations (RMSEA). In essence, CFI and TLI values should be equal to or greater than 0.90 and FMSEA values of greater than 0.5 to indicate good empirical fit (Kline, 2010).
For the 72-item, nine-factor model identified in the EFA (see Table 5.1), the chi- square test was non-significant [χ2 (1884) = 4558.22, p=0.001]; the other fit indices, IFI (0.941), TLI (0.93), CFI (0.94), RMSEA (0.038) and SRMR (0.044), indicated reasonable fit.
Table 5.1 Fit Indices of the proposed research model Model fit indices Model Recommended guidelines References χ2 4558.22 p < 0.001
Non-significant Joreskog & Sorbom, 1993; Klem, 2000; Kline, 2010; McDonald & Ho, 2002; Meeuwisse, Severiens, & Born, 2010
χ2/df 1.90 < 3 Hu & Bentler, 1999; Kline, 2010
TLI .93 ≥ 0.90 Hu & Bentler, 1999; Klem, 2000; McDonald & Ho,
2002;
CFI .94 ≥ 0.90 Bollen, 1989; Byrne, 2010; Hu & Bentler, 1999; Klem, 2000; McDonald & Ho, 2002;
RMSEA .038 < 0.05 Browne & Cudeck, 1993; McDonald & Ho, 2002 SRMR .044 < 0.05 Hu & Bentler, 1999; Klem, 2000; McDonald & Ho,
2002
N =618 students in 15 schools.
Based on Kline’s (2010) recommendation that the χ2 is sensitive to sample size (Schumacker & Lomax, 2004), it was established that the model had acceptable fit to the data (see Table 5.1). Based on these results, each of the scales were considered to be fit for use for SEM purposes.
The measurement model was assessed further to confirm whether the factor structure was valid and reliable for SEM purposes in terms of its construct reliability, convergent validity (reported in Section 5.4.1), and discriminant validity (reported in Section 5.4.2).
5.3.1 Construct reliability and convergent validity
Reliability and convergent validity of the measurement items was assessed by examining the item reliability of each measure, the composite reliability (CR) of each construct, and the average variance extracted (AVE), as proposed by Fornell and Larcker (1981).
The CR was used as measure of item reliability. The interpretation of the composite reliability is similar to that of Cronbach’s alpha (1951), except that it also takes into
account the actual factor loadings rather assuming that each item is equally weighted in the composite load determination (Wang, Wu, & Wang, 2009). The results, reported in Table 5.3, indicate that the CR ranged from 0.89 to 0.93 for different scales, suggesting good reliabilities, as they exceeded the acceptable criterion of 0.60 suggested (Bagozzi & Youjae, 1989; Fornell & Larcker, 1981).
To further examine the convergent validity of the measurement model, the AVE was used. AVE measures the amount of variance captured by the construct in relation to the amount of variance attributable to measure error. The AVE values, reported in Table 5.2, ranged from 0.51 to 0.62 — higher than 0.50, the minimum benchmark recommended by Fornell and Larcker (1981), Hair (1992) and Nunnally and Bernstein (1994). This means that more than one-half of the variance observed in the items was accounted for by their hypothesised factors.
Given these results, all factors in the measurement model were considered to have had adequate reliability and convergent validity.
Table 5.2 Construct reliability, average variance extracted and discriminant validity
Construct CR AVE TS PC SC AD RC RSH MI R WB TS .89 .51 (.71) PC .90 .53 .35** (.73) SC .93 .62 .55** .70** (.79) AD .90 .54 .49** .41** .49** (.73) RC .91 .56 .55** .30** .52** .42** (.75) RSH .89 .51 .54** .39** .50** .46** .51** (.71) MI .91 .56 .38** .44** .45** .45** .38** .50** (.75) R .91 .57 .40** .40** .51** .32** .38** .39** .38** (.75) WB .93 .61 .42** .43** .63** .33** .39** .39** .34** .58** (.78) Note: The bold elements in the main diagonal are the square roots of AVE.
Composite reliability (CR) is computed by (∑λ) 2 / (∑λ) 2 +∑ (1 – λ2); average variance extracted
(AVE) is computed by ∑λ2 / ∑λ2 + ∑ (1 – λ2), where λ = standardised loading. **p <0.01
N =618 students in 15 schools.
5.3.2 Discriminant validity
The discriminant validity of the constructs was assessed to identify the degree to which they differed from each other. As suggested by Barclay, Higgins and
Thompson (1995), the criterion for discriminant validity is that the square root of average variance extracted (AVE) for each construct should be larger than the correlation of that construct with all of the other constructs in the research mode. The results reported in Table 5.2 show that the shared variances between the factors (ranging from 0.51 to 0.62) were lower than the square root of the average variance extracted of the individual factors (ranging from 0.71 to 0.79). These findings support the discriminant validity of the individual constructs.
Overall, the convergent and discriminant validity results of the factor structure and constructs of the WHITS and WERMI were valid and reliable, and therefore considered to be suitable for the purpose of SEM. The results indicated that the factor loadings and constructs of the measurement used were valid and reliable.