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First, a model was estimated in which all loadings and inter-
cepts were freely estimated across universities. For identification
purposes, latent means were constrained to zero, and latent var-
iances were constrained to one. Latent factors were also allowed
to freely covary with one another. This baseline model was then
compared to subsequent nested models.
To test whether participants were using the same range of scale points, we equated
loadings across sites (while also freeing all but one of the latent
variances, which was fixed for identification). Then we equated
intercepts across sites to test whether the origin, or zero point, of
items was the same across sites (again, we did this while freeing
all but one latent mean, which remained fixed to zero for identifi-
cation). If these invariance tests are satisfied, we can conclude
that the measurement of traits was invariant across sites and pro-
ceed with comparing latent variances and covariances, as well
as latent means. Comparison of the latent means allows a global
test of whether there are differences between sites in the mean
level of traits.
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