# Furthermore, Normed indices of fit Chi-square (?2) p

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)

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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).

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