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The previous section dealt with validation of the measurement model, which related the variables to the constructs. The next step is testing all the hypotheses proposed. This research uses SEM to test the various hypotheses, i.e. how the constructs are related to each other. This structural or path model is used to test the hypothesised relationships. The full SEM model is the final step in model building. The full SEM 157

model comprises both the measurement and the structural models. As mentioned earlier, the measurement model relates variables to the constructs while the structural model relates constructs to each other.

To test whether the full SEM model developed reflects underlying theory, a number of model fit measures have been suggested in the literature. These fit indices are normally grouped into three, namely, absolute fit indices, incremental fit indices and parsimony fit indices (Hooper, Coughlan and Mullen 2008).

4.7.3.1 Absolute Fit Indices

Absolute fit indices provide the most fundamental indication of how well an a priori model fits the data. These fit indices are also used to determine which model has a superior fit when competing models that are built based on the data collected. The most commonly used fit indices in this category are the Chi-squared test, GFI, AGFI, RMSEA and the SRMR.

Model Chi-square (χ²): According to Hu and Bentler (1999), the chi-square value “assesses the magnitude of discrepancy between the sample and fitted covariances matrices”. An insignificant result at the 0.05 threshold would represent a good model fit. However, a number of limitations of the chi-square metric have subsequently been identified in literature. The main limitations are that the chi-square test assumes multivariate normality and rejects models where large sample sizes are used. An alternative that has been suggested is the use of the relative/normed chi-square, χ²/df.

Tabachnick and Fidell (2006) recommend good model fit if the χ²/df value is less than 2.0.

Goodness-of-Fit (GFI): Created as an alternative to the chi-square test, the ‘goodness-of-fit’ (GFI) calculates the proportion of variance accounted for by estimated population covariance. The GFI too, like the chi-square, has some drawbacks. GFI shows a downward bias when the degrees of freedom are large compared to the sample size. The GFI has also been shown to increase with the number of parameters in the model. The GFI is therefore a sensitive index and its popularity has decreased. There have also been calls in the literature that use of GFI should be discouraged (Sharma, Mukherjee, Kumar and Dillon 2005).

Adjusted Goodness-of-Fit (AGFI): Tabachnick and Fidell (2006) note that the ‘adjusted goodness-of-fit’ (AGFI) statistic adjusts the GFI, based on the degrees of freedom. However, the AGFI also increases with sample size and, as a result, neither it nor the GFI are relied on as stand-alone indices (Hooper, Coughlan and Mullen 2008).

Root Mean Square Error of Approximation (RMSEA): The RMSEA indicates how well the model fits the population covariance matrix. Diamantopoulos and Siguaw (2000) view the RMSEA as “one of the most informative fit indices” and the reason why RMSEA is such a key statistic in SEM is because of its sensitivity to the number of estimated parameters. A very good fit is said to be achieved if the RMSEA value is below 0.06 (Hu and Bentler 1999).

Standardised Root Mean Square Residual (SRMR): The ‘root mean square residual’ (RMR) and the ‘standardised root mean square residual’ (SRMR) are “the square root of the difference between the residuals of the sample covariance matrix and the hypothesised covariance model” (Hooper et al. 2008). The SRMR is the preferred option in the literature. Regarding the acceptable range of the SRMR, Iacobucci (2010) recommends a range of around 0.9.

4.7.3.2 Incremental Fit Indices

Incremental fit indices are also known as comparative or relative fit indices. Incremental fit indices are a group of indices which compare chi-square value to a baseline model, and not in its raw form (Hooper et al. 2008). In other words, an incremental fit index, in contrast to an absolute fit index, measures proportionate improvements in fit of the target model with a nested baseline model (Singh 2009).

Incremental Fit Index (IFI): ‘Incremental fit index’ (IFI) is also known as ‘Bollen’s IFI’ or ‘Delta2’. IFI is defined as the difference between the chi-square of the null and default model divided by the difference between the chi-square of the null model and degrees of freedom for the default model. An IFI of 0.9 or more is generally acceptable. One of the reasons why IFI is a commonly reported statistic is because it is independent of sample size.

Normed Fit Index (NFI): Also known as the ‘Bentler-Bonett’, or simply ‘Delta1’, the ‘normed fit index’ (NFI) reflects the proportion by which the model developed improves fit when compared to the null model. One of the weaknesses of the NFI is

that the fit may be underestimated for small samples, usually less than 200. This research is not affected by this problem as the sample size is greater than 200. However, there is a problem in the parsimony of NFI. The more parameters the model has, the greater is the NFI coefficient. To overcome this problem the non- normed fit index is preferred by contemporary researchers.

Non-Normed Fit Index (NNFI): The ‘non-normed fit index’ (NNFI) is also called the ‘Tucker Lewis index’ (TLI) or ‘RHO2’. The advantage of TLI is that it has been found to be relatively independent of sample size. Hu and Bentler (1999) suggest an NNFI value of 0.95 or greater as very good.

Comparative Fit Index (CFI): Also known as the ‘Bentler comparative fit index’, the CFI compares existing model fit with that of the null model. The CFI and RMSEA are said to be the two measures least affected by sample size (Fan, Wang and Thompson 1999). This is one of the reasons why CFI and RMSEA are widely reported in studies involving SEM. By convention, a CFI value of greater than 0.9 is considered acceptable. A CFI value of 0.9 indicates that 90% of covariation of data is able to be reproduced by the given model.

4.7.3.3 Parsimony Fit Indices

The function of parsimony indices is to penalise for lack of parsimony so that a better fit is not indicated for a theoretical model that is not rigorous. This is based on the rationale that all things being equal, a more complex model will generally fit better than those which are less complex. The ‘parsimony goodness-of-fit index’ (PGI) and 161

the ‘parsimonious normed fit index’ (PNFI) are the two parsimony fit indices commonly used. These were developed by Mulaik, James, Alstine, Bennett, Lind and Stilwell (1989). However, these measures are not reported in studies, as there are no suggested threshold levels recommended for theses indices (Hooper et al. 2008). This research will not therefore report parsimony fit indices.

Based on the review of the fit indices as provided above, this research will report the important absolute and relative/incremental fit measures. Specifically, this research will report the following measures – χ², df, χ²/df, GFI, AGFI, RMSEA, SRMR, NFI, IFI, NNFI and CFI. Table 4.4 provides a summary of the recommended values of the important fit indices, based mainly on the recent work of Iacobucci (2010).

Table 4.4 Recommended SEM Fit Indices

Fit Measure Recommended Value

Relative/Normed Chi-square (χ²/df) < 3.0

Root Mean Square Error of Approximation (RMSEA) < 0.06 Standardised Root Mean Square Residual (SRMR) < 1.0

Normed Fit Index (NFI) > 0.90

Incremental Fit Index (IFI) > 0.90

Non-Normed Fit Index / Tucker Lewis Index (NNFI/TLI) > 0.90

Comparative Fit Index (CFI) > 0.90