indicators. Researchers must keep in mind, however, that statistics alone should
not drive model modification (see e.g. Boomsma 2000: 474-476 for a discussion
on how modifications should be defensible primarily from a theoretical
perspective) and Hair et al. do remind us (2006: 777) that even as factor loadings
fall below 0.7 they can still be considered as being important components in the
model. Kline (2005: 186) notes that an indicator may have a standardised
loading as low as 0.2 before it can be considered to ‘substantially fail’ to load on
its factor.
Average variance extracted This is a summary indicator of convergence
insofar as it describes the proportion of variation in the indicator variables -
averaged across all of the indicators - accounted for by the latent factor. Fornell
and Larker (1981: 47) recommend that latent factors should have an AVE of ≥0.5
on the basis that if the AVE is less than 0.5, then the variance owing to
measurement error is greater than the variance explained by the construct, and
the validity of the individual indicators, as well as the latent factor, is
questionable.
Construct reliability relates to the amount of variance in the factor indicators
that is actually accounted for by the factor (and not measurement or random
error). Coefficient alpha, developed by Cronbach (1951), is a commonly used
estimate for item reliability (also referred to as internal consistency); however, its
suitability for use in SEM applications has been criticised on the basis of its over-
and, more commonly, under-estimating of reliability (Raykov 1998; Hair et al.
2006: 777). Accordingly, some effort has been made by SEM researchers to
develop alternative measures (see, e.g. Fornell and Larcker 1981; Bacon et al.
1995; Raykov 1997, 1998). This work utilises the method of construct reliability
developed by Fornell and Larker (1981, see below) and recommended by Hair et
al. (2006: 777) and Garson (2011b). Kline (2005: 59) notes that there is no
‘gold standard’ for reliability scores and provides the following guidelines:
reliability coefficients of around 0.90 are considered excellent, around 0.80 are
very good and around 0.70 are adequate.
Measures employed for AVE and construct reliability Neither AVE or CR are
available as outputs in AMOS, accordingly, these were calculated separately in
Microsoft Excel using the methods developed by Fornell and Larker (1981).
Fornell and Larker’s method for calculating AVE goes beyond that recommended
by Hair et al. (2006: 777) in that it measures “the amount of variance that is