As mentioned in Chapter 4, factor analysis is used to check construct validity, and contains exploratory analysis and confirmatory analysis. For the main survey, a confirmatory factor analysis was used to test the convergent and discriminant validity of the measures. AMOS 24.0 was used to conduct the CFA. Several fit indices were employed to assess the fit of the model. Since CFA is a special case of SEM, the selection of indices and the corresponding criteria of the CFA used to test the fit of the model are similar to SEM.
There are two kinds of fit indices which should be used for reporting the results of SEM. According to Lin (2005), absolute fit can assess the degree to which the covariance implied by the proposed model matches the observed covariance. The indices of incremental fit are used to assess the degree to which the proposed model is superior to an alternative model. More specifically, absolute fit indices typically gauge ‘badness of fit’, while indices of incremental fit gauge ‘goodness of fit’. Although there is no consensus about the best index to use when reporting structural equational models, the most widely reported absolute fit indices contains 2, 2/𝑑𝑓, GFI, AGFI, SRMR and RMSEA, while
the most commonly used incremental fit indices include NFI, NNFI and CFI. Table 5-10 demonstrates the indices and the recommended criteria for the most frequently reported indices in previous research.
The index 2 will not be used in this study, although it appears to be the most
popular index, due to its high sensitivity to sample size. According to Ghazali (2011), when the sample size increases, the 2 statistic tends toward statistical
significance, increasing the possibility of model rejection, irrespective of whether the model is true or false (a type II error). Instead, the degree of freedom was considered when using the chi-square to make the value meaningful. In addition, the values of GFI and AGFI were not considered to reject the model in this study, since they are strongly affected by sample size
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and so may appear to be good, even for incorrectly specified models (Kenny, 2010). Therefore, the main fit indices which will be reported in this thesis and used for model assessment are: 2/𝑑𝑓, SRMR, RMSEA, NFI, NNFI and CFI.
The other two indices, GFI and AGFI, are reported as a reference.
Table 5-10 Recommended Criteria of Various Fit Indices Used for Model Assessments Index Description Recommended Value of the Index Referen ce Absolute fit indices 2 A calculation used to determine how closely the observed data fit the expected data. p>0.05 Hu et al. (1992) 2/𝑑𝑓 Used to investigate whether distributions of categorical variables differ from one another.
<5 (acceptable) <3 (Good fit)
Goodness-of-fit Index (GFI)
Indexes the relative amount of the observed variances and covariance accounted for by a model. >0.90 Lin (2005) Adjusted goodness of fit index (AGFI)
Corrects the GFI, which is affected by the number of indicators of each latent variable. >0.90 Standardized root mean squared residual (SRMR) Estimates the average size of residuals between fitted and sample covariance matrix. It is very sensitive to model mis- specification but less sensitive to sample size. <0.10 Root means square error approximation (RMSEA)
Illustrates the degree to which the model fits the population covariance matrix, taking into consideration the number of degrees of freedom. Unlike other
<0.10 (Acceptable fit) <0.08 (Adequate fit) <0.05 Lin (2005)
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At this stage, when the initial proposed measurement model appears to not be the best fitting model, the model needs to be re-specified, based on the modification indices (Kline, 2005). However, if there is a lack of theoretical basis when a path to the model was deleted or added empirically, then model trimming or building should be considered. Once the model is re-specified, the same CFA procedures can be conducted again to determine the best fitting model and check the construct validity. The next section will test the
fit statistics, it is able to generate a 90 percent confidence interval, which provides information about precision of the estimate of fit. Adequately sensitive to model mis- specification. (Good fit) Incremental fit indices
Normed fit index (NFI)
Analyses the discrepancy between the chi-square value of the hypothesized model and the chi- square value of the null model.
>0.90 Ghazali (2011)
Non-normed fit index (NNFI)
Compares the lack of fit of a target model to the lack of fit of a baseline model, usually the independent model. Usually TLI/NNFI is used to estimate the relative improvement per degree of freedom of the target model over a baseline model. Not recommended for small samples (<150). >0.90 Ghazali (2011) Comparative fit index (CFI)
Indexes the relative reduction in lack of fit as estimated by the non-central 2 of a targeted model versus a baseline model. >0.90 Bentler (1995)
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measurement model of all latent scales. Fit indices will be considered to determine the fit of the model.