This is the next step after Model Estimation. In this step it is determined that how well the data fits the proposed model or to what extent the theoretical model is supported by the collected sample of data. Some common testing indices, which indicate the fitness of model, are used. These include the parameter estimates with statistical significance level and standard errors, the residuals, and the model fit indices.
Normally, to assess the fit of the individual parameters in a model, the first step is to determine the viability of their estimated values, statistical significance level, and their accompanied standard errors (S.E.) (Jöreskog and Sörbom, 2001; Bentler, 2005). Hoyle (1995) recommended that the critical ratio (C.R. or Z score, calculated by the parameter estimate / S.E. of the parameter estimate) is significant at p0.05 are considered insignificant paths to the model (accept H0, but still 5% of the time a Type II error would be committed) (Wu, 2009; Walker and Maddan, 2012). Also, the estimated values should demonstrate the correct sign, within an expected range, and be consistent with the underlying theory (Schumacker and Lomax, 2004; Byrne, 2010).
An examination of the Standardised Residual Covariance Matrix (from AMOS output to review the discrepancy between each of the residual) is carried out, since this too could give the evidence of the model fit to the hypothesised model (Wu, 2009). As recommended by Rong (2009) and Jöreskog (1993), standardised residuals (fitting errors) within the range of ±2.58 indicate a good model fit, and on the same pattern, when the residuals fall outside this range signals that the associated estimated values (i.e., path relations) are not fully accounted for in the model. These are result of the misspecifications of relationships between different parameters (paths/variables) in the model (Schumacker and Lomax, 2004).
Once again, the model fit indices are required to be assessed (Anderson and Gerbing, 1988; Cousins and Lawson, 2007). In case, the indices show the model fit is good, the sample data should fit the hypothesised path model (Wu, 2009; Byrne, 2010). AMOS yields the following common fit indices to indicate the specified data to model fit (Table 5.16).
Model Fitness Statistics Fitness Indices
Normed indices of fit
Chi-square (?2) p > .05
Goodness-of-Fit (GFI) > 0.9
Adjusted Goodness-of-Fit (AGFI) > 0.9
Root-Mean-Square Residual (RMR) < 0.05
Standardised RMR (SRMR) ? 0.05
RMR of approximation (RMSEA) ? 0.05
Expected Cross-Validation Index (ECVI) 0.9
Relative Fit Index (RFI) > 0.9
Incremental Fit Index (IFI) > 0.9
Tucker-Lewis Index (TLI) > 0.9
Comparative Fit Index(CFI) > 0.9
Parsimony-based indices of fit
Parsimony-Adjusted CFI (PCFI) > 0.5
Parsimony-Adjusted NFI (PNFI) > 0.5
Critical N (CN) > 200
Normed Chi-Square (NC, CMIN/DF) 1 < NC < 3
Table 5.16 The common model fitness indices in AMOS (Schumacker and Lomax, 2004, p87; Wu, 2009; Byrne, 2010)
To have a better fitting for the sample data, a model modification is applied to the initial hypothesised SEM model. Chou and Bentler (1990) and MacCallum et al. (1992) concluded that the model modification could generate more than one model, at times it could end up with a large number of models, which fit a data set well. Thus, a theory-driven (vs. data-driven) model modification need to be performed. The model modification is made of the following three common processes: (1) remove the insignificant parameters (paths) to form a better fitting model (Byrne, 2010); (2) remove the variables which have standardised residual values that fall outside ±2.58 (Wu, 2009); and (3) include new parameters (paths) if they reach the significant level (p