Having now developed Model 5b, it is worthwhile comparing this with the earlier
Model 5 (version SEM 5:1, with the WV construct and its [non-significant]
WV→EPA path). The rationale for this comparison is described by Kline (2005:
323) who urges researchers to consider alternative models that explain the same
theory in a different way. Kline goes on to note that, where the overall fits of
these competing models are similar, then researchers must specify their reasons
for why a particular model is preferred.
Models 5 and 5b are compared using their model fit diagnostics in Table 7 - 31.
Fit measure SEM 5:1 estimated on
209 casesSEM 5b:2 estimated on
213 cases (no WV factor)
χ^2 (d.f.; p) 160.472 (143; 0.151) 116.829 (98; 0.094)
RMSEA
(upper; lower; pclose)- 024
(0.042; 0.000; 0.995)
0.030
(0.049; 0.000; 0.959)
CFI 0.992 0.991
SRMR 0.0553 0.0559
Hoelter’s Critical N 223 222
ECVI 1.223 0.910Table 7-31 Comparison of Models 5 and 5b
The findings from this comparison are that:
both models have a good fit to the data as indicated by the chi square measure
both demonstrate good fit based on the RMSEA, CFI and SRMR measures
there is a negligible (0.001) difference in the values for CFI
there is slightly more unexplained variance in Model 5b as indicated by the
higher RMSEA and SRMR values (although these differences are very small)
there is a negligible (1) difference in the values for Hoelter’s Critical N
The final comparison criteria, the Expected Cross-Validation Index (ECVI) has not
yet been introduced. The ECVI was developed by Browne and Cudeck (1989) to
assess “...in a single sample, the likelihood that the model cross-validates across
similar-sized samples from the same population” (Byrne 2010: 82). There is no
specific range of acceptable values, rather, models exhibiting smaller ECVI values
have the greatest potential for replication. According to the ECVI values
described in Table 7 - 31 , Model 5b has the greatest potential for cross-validation
in an independent sample.