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To find out how the violation of equal factor loadings affects the power to detect genetic effects in the sum-score model, we simulated data according to a unidimensional measurement model, comprising 6 or 12 items.
Third, we found that when the condition of equal factor loadings is violated (Figure 4b), the power to detect genetic effects on sum-scores is decreased compared to the true latent factor model, which accommodates unequal factor loadings.
For 12 items, the effect of the violation of equal factor loadings was more pronounced, with the power of the sum-score model being 39 78% of the power of the true latent factor model.
The finding of equal factor variances across groups is important for at least two reasons.
However, partial metric invariance (L3) was reached after relaxing the constraint of equal factor loadings for some items.
Given configural invariance, more rigorous tests are conducted concerning first the hypothesis of equal factor loadings across groups, or metric invariance [ 23, 27, 29].
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Following Marsh and Grayson [ 59], the longitudinal stability of the latent factor and of the residual of each item was investigated after the assessment of equal scale factors (i.e. after measurement invariance was completely assessed).
On the base of distribution of factors of safety of all dam monoliths, an idea called "the design of equal safety" is suggested, which says that all monoliths should have nearly equal factors of safety as far as possible.
Residual invariance is therefore not as important to the evaluation of measurement invariance as the test of equal form and factor loadings.
The items within each dimension were confirmed by a cross-validation analysis, whereby questionnaires were randomly allocated into two subgroups of equal size and factor analysis repeated on each subgroup.
Reviews of MI studies have shown that lack of MI is a common finding: In a review of cross-cultural MI, Chen [ 3] found that 74% of reviewed studies showed non-equal factor loadings in at least one item.
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