Furthermore, the model fit indices were assessed. Some important fit indices (see Table

5.16 in Section 5.3.3) are listed in Table 7.5 for the hypothesised path model (a). These include Chi-square (?2), the goodness of fit index (GFI), comparative fit index (CFI), incremental fit index (IFI), normed fit index (NFI), root mean square error of approximation (RMSEA) and the standardised root means square residual (SRMR).

Model Fitness Statistics Fitness Indices Estimated Indices Model Fit

Normed indices of fit

Chi-square (?2) p > .05 98.394, D.f .= 17 (p 0.9 0.947 Yes

AGFI > 0.9 0.859 No

RMR < 0.05 0.289 No

SRMR ? 0.05 0.077 No

RMSEA ? 0.05 0.114 No

ECVI 0.9 0.817 No

RFI > 0.9 0.613 No

IFI > 0.9 0.844 No

TLI > 0.9 0.657 No

CFI > 0.9 0.838 No

Parsimony-based indices of fit

PCFI > 0.5 0.396 No

PNFI > 0.5 0.386 No

CN > 200 126 No

NC (CMIN/DF) 1 < NC < 3 5.788 No

Table 7.5 The selected common model fit indices for the hypothesised path model (a) (Note: good model fit indices shown in bold)

From Table 7.5 the model fit indices show a relatively poor model fit, since only one of the common indices (GFI) indicates good model fit. Other important indices (e.g., NFI, RFI, RMSEA etc.) were all below the usual acceptable level of fit. Accordingly, this particular set of model fit indices indicated that the data-to-model fit was only approaching a reasonable level. This indicated that modifications were necessary to improve fit.

7.1.5 Model modification for model (a)

Next, a theory-driven (vs. data-driven) model modification was performed (see Section 5.3.3). Figure 7.3 illustrates the modified path model (a).