(unobserved) factor must be assigned a scale (or metric) in order that estimates
of effects can be calculated.
The latter issue is dealt with by constraining the unstandardised coefficient
(loading) of one indicator per latent factor to 1, as illustrated in Figure 7 - 2. This
type of constraint is referred to as a unit loading identification (ULI) constraint; an
alternative method (not used here) exists, wherein the variance of the latent
factor is constrained to 1 , this being referred to as a unit variance identification
(UVI) constraint. Also for scaling purposes, a unit loading identification (ULI)
constraint (value = 1) is applied to each indicator’s unstandardised residual path
coefficient (the connecting line between each indicator and its error term) - again,
these constraints can be seen in Figure 7 - 2. A more detailed discussion of model
identification can be found in Kline (2005: 170-171).
The former issue, that of identifying a unique solution for each parameter to be
estimated can be addressed by using the following guidelines from Hair et al.
(2006: 785; 792):
the four indicator rule stating that for a single factor CFA model, 4 indicators
are required for the model to be identified;
the three indicator rule which “is satisfied when all factors in a congeneric
(indicators load onto only one factor) model have at least three significant
indicators” and;
the two indicator rule which “states that a congeneric factor model with two
significant items per factor will be identified as long as each factor also has a
significant relationship with some other factor”.
Regarding the ‘two indicator rule’ it should be noted that while factors with only
two items can be successfully integrated into SEM models following the criteria
above, (i) two indicator factors can be subject to estimation problems at later
stages of the SEM process (Hair et al. 2006 : 786) and (ii) researchers should be
aware of the issue of interpretational confounding where some of the substantive
meaning of the factor is accounted for by the nature of the other latent factors in
the model and not just by that factor’s own indicators (see e.g. Burt 1976).
The specification of four and five indicators (respectively) for the latent factors in
Model 1 exceeds these recommendations and concurs with Rigdon’s (1995: 376)
advice to initially specify models with sufficient parameters to allow for the
deletion of parameters during model modification.