for calculating the χ^2 value for that model. Hoelter’s recommendation was that
where CN is ≥200 then the sample size is large enough to for χ^2 to be calculated
satisfactorily. Garson (2011b) notes that a CN of less than 75 is considered
insufficient to accept a model by chi-square.
Fit measure Desired Acceptable
χ^2 p ≥ 0.05 With 12 to 30 observed variables, significant pcan result even with good fit (Hair et al. 2006: 753)-values
RMSEA < 0.06 < 0.08
pclose > 0.05 > 0.05
CFI > 0.96 > 0.95
SRMR < 0.09 < 0.10
Hoelter’s CN > 200 > 75 but preferably closer to 200
Figure 7-3 Summary of acceptable threshold levels
In summary, the selection of these particular fit indices for use in this research:
(a) is based on a review of the available fit indices and taking into consideration
their appropriateness for the characteristics of the models in this research; (b)
follows the recommendations of Hooper et al. (2008) and Kline (2005); and (c)
reflects Hair et al.’s (2006: 805) recommendation to use at least one absolute and
one incremental fit index in addition to the model chi-square. Figure 7 - 3
summarises the acceptable threshold levels for this research.
7.2.7 Testing the measurement model (CFA 1:1)
The measurement model for Model 1 was specified as illustrated in Figure 7 - 2 and
the estimates calculated using AMOS version 18. Maximum Likelihood (ML)
estimation was used and missing values were replaced using AMOS’s model-based
imputation function. Table 7 - 1 shows the results from the initially-specified (CFA
1:1) model.
An examination of the model results reveals that the model does not demonstrate
a particularly good fit (a significant chi-square; RMSEA > 0.06; and CFI <0.95)
although the SRMR is within Hu and Bentler’s (1999) guideline of <0.08.