**Invariance
under a constant scaling factor. **In this case, **A
**is in the group G1 where

(146)

In essence, a model is invariant under a constant
factor if multiplying **S**
by a non-zero constant will not change the fact that a model fits **S**. Most covariance structures
of any practical interest are at least invariant under a constant scaling
factor. Some of the non-centrality based fit indices developed by Steiger
(1989, 1990) require that the model fitted be invariant under a constant
scaling factor (ICSF).

**Invariance under changes of scale. **In
this case **A **is in the group G2,
where

(147)

where Diag (**t**)
is a diagonal matrix with diagonal elements given by the *p *components
of the vector **t**.