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In comparing between types of tasks, we notice that the more challenging open-ended tasks benefit significantly more than constrained item types by the use of DNN-HMMs.
Besides item PF8 and I1 (as seen in model 1), in model 2 we also constrained item A1 to 0.05, because of a negative residual variance.
In the second dimension, one constrained item had low discrimination, whereas for another, the discrimination exceeded the assumed common value.
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The t-values for the weighted mean squares in the first dimension indicate that one of the constrained items discriminated too strongly in the first dimension and that two others did not discriminate sufficiently (t = 2.6).
Metric and Scalar models incrementally constrain item factor loadings and response category thresholds between groups.
If metric invariance was indicated we then tested for scalar invariance by also constraining item intercepts to be equal [ 24- 26].
Strong invariance (model three) involved constraining item intercepts to equality across groups (or time) to evaluate potential for systematic bias in responses from one group to another (or from one time point to another).
This analysis provides reassurance that the promotion of the items to interval measurement assumptions did not deviate from the pattern of factor coefficients compared with a less constrained distributional item profile.
Second, a grammatically appropriate two-word description (which may be true or false) is selected from a set constrained to the item or category in question: for example, a human trait ("read books"), a non-living-object trait ("don't breathe") or a specific trait ("design buildings", "aren't sharp", "is jazz").
Likelihood ratio tests between fitted nested IRT models were performed comparing the Rasch model (all item discriminations constrained to one), the one-parameter model (1PL; item discriminations are the same but freely estimated), and the two-parameter model (2PL).
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).
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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