and Cudeck (1989, 1993) provide a graduated range of RMSEA interpretations:
≤0.05 indicates close fit; >0.05 and <0.08 indicates reasonable fit; and ≥ 0.10
indicates poor fit. The PCLOSE test provides a p value for a significance test to
support or reject a finding of RMSEA ≤ 0.05. PCLOSE tests the null hypothesis
that the population RMSEA is no greater than 0.05 – accordingly, a PCLOSE value
of ≥0.05 is sought indicating that we cannot reject the null hypothesis and can
conclude that an RMSEA value of less than 0.05 is supported. A further
advantage of the RMSEA is that it is possible to calculate a confidence interval and
associated upper and lower boundaries for the likely RMSEA value (Maccallum et
al. 1996). Lastly, the RMSEA also takes model complexity into account and,
because of this, it can also be regarded as a parsimony-adjusted fit index (Kline
2005: 137). Therefore, if two competing models have the same explanatory
power, the RMSEA will favour the simpler (or most parsimonious) one. For these
reasons, the RMSEA has attracted significant support as ‘one of the most
informative fit indices’ (Diamantopoulos and Siguaw 2000: 85).
CFI (Comparative Fit Index) was developed by (Bentler 1990) and belongs to the
family of comparative (or incremental) fit indices. It is favoured because it takes
account of sample size (i.e. it is among the least affected by variations in sample
size: see e.g. Fan et al. 1999) and performs well with smaller sample sizes
(Tabachnick and Fidell 2007). Values >0.95 are usually sought for CFI (Hooper et
al. 2008) although Hair et al. (2006: 753) provide some useful and nuanced
guidelines where CFI should achieve values of between 0.90 and >0.95 depending
on sample size and the number of observed variables in the model.
The SRMR (standardised root mean residual) belongs within the absolute fit index
category and is based on the difference between the residual covariance matrix
derived from the sample data and the residual covariance matrix predicted by the
theoretical model. A perfectly fitting model will have an SRMR value of 0 and as
the SRMR value rises the model deteriorates – as such, the SRMR is a ‘badness-
of-fit’ measure Hair et al. (2006: 748). Acceptable values for SRMR range from
<0.10 (Kline 2005: 141) to <0.08 (Hu and Bentler 1999). Once again, Hair et al.
(2006: 753) provide guidelines accounting for sample size, model complexity and
the relative performance of the CFI index in combination with SRMR.
Finally, Hoelter’s Critical N (CN) (Hoelter 1983) is focussed not on model fit but
on adequacy of sample size (Byrne 2010: 83). AMOS includes Hoelter’s CN in its
model fit output and the value of this indicates the adequacy of the sample size