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Figure 3 shows the performance on the old/new recognition test in terms of correct decisions for studied items and false alarms for non-studied items (error bars denote 95% within-subjects confidence intervals [44]).
However, as modification indices suggested shared content among some PHQ-9 and GAD-7 items, and fit indices improved when relevant items' error terms were correlated, the PHQ-9 and GAD-7 items may possess overlaps in item content.
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In addition, item error variances and error covariances between related items were set to vary freely.
Finally, model 8 shared the factorial structure of model 7, but within-factor item error terms were correlated.
Therefore the item error invariant model was more appropriate.
This was implemented by subtracting raw one-item error variance from raw three-item error variance, and recalculating precision accordingly, i.e. precision difference = 1/√ SDVWM 3)– SDVWM(1/√ SDVWM 3
Form, slope, intercept, item error, and covariance invariance were all still supported (see Table 5, revised five-item models).
In the fourth model, in addition to constraining the factor loading slopes and intercepts, the item error variances were constrained across the groups (called item error or strict factorial invariance).
If this restricted model were supported, it would indicate that both groups not only have the same slopes and intercepts, but also the same item error variances.
Additional tests were performed that enabled statistical comparison of item error variances and the factor covariance to be identical across gender.
Specifically, when using pairwise deletion, the three health worry items (death, health, and children's health) exhibited neither intercept invariance nor item error invariance across the long- and short-term survivor groups.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com