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Cheung and Rensvold (1998, 1999) suggested that if the proportion of non-invariant items of a scale is small, the comparison of factor means can still be meaningful even if full measurement invariance does not hold, as the non-invariant items will not heavily affect the comparison [ 55, 56].
If the assumption of measurement invariance does not hold, to what extent do country-specific measurement models differ?
Given a significant difference between these models, the more constrained model is rejected and the investigation of measurement invariance does not proceed further.
The differential item functioning (DIF) is a form of violation of measurement invariance, in other words, DIF represents a situation where the measurement invariance does not hold [ 7].
However, given that partial measurement invariance does not by default lead to biased observed scores,[ 38, 84] nor do statistically significant criteria necessarily translate into meaningful differences[ 38] I also investigated whether item-level bias affected 1992 item-set alcohol abuse estimates.
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As can be seen in Table 2 the CFAs did not support measurement invariance for either gender or age.
Acquiring evidence of measurement invariance is vital for assuring that the measures do not act differently across gender groups (Scherer and Siddiq 2015b).
First, Martin et al. did not explicitly use the term measurement invariance in their report.
Before doing that, we addressed the issue of measurement invariance that is critical in order to appraise between-group differences as meaningful [ 42].
However, differences between models did not indicate improved parsimony for the strict measurement invariance model with and without constrained means (CFI change >.01,.943 vs..955; TLI,.936 vs..948; RMSEA,.039 vs..036).
The CFI difference between the strong and the weak measurement invariance models was less than.01 (.968 vs..970), and the TLI (.952 vs..951) and RMSEA (.034 vs..034) did not differ.
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