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No excess of events over the standard model expectation is observed.
The upper half of Figure2 displays the three major classes of model types, available information types, as well as model expectation categories.
The error variance of the estimated regression coefficients can be decomposed into the model variance of the errorless regression coefficients and the model expectation of the conditional sampling variance.
When the column sums were kept, significant difference between the observation and the null model expectation would suggest mechanisms other than those determining local species richness (most possibly site/habitat heterogeneity) driving the multi-site species turnover.
As has often been argued in the literature that abiotic gradients between sites (and thus environmental filters) are the primary drivers of species turnover (e.g. Lebrija-Trejos et al. 2010; Soininen 2010), we should expect to see that the observed zeta turnover pattern conforms to the null model expectation with column sums constrained.
When the row sums were kept, significant difference between the observed zeta diversity turnover and the null model expectation would signal mechanisms other than those determining ecological differences (here, species occupancies; i.e. row sums) driving the multi-site species turnover in the community.
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Generally non-significant deviations from the model expectations are expected for chi-square-based statistics, and within range (± 2.5) for residual fit statistics.
Where the observed pattern of responses do not deviate too much from that expected by the model, the scale is said to satisfy Rasch model expectations.
Two items (item SSE_2 and item SSE_7) did not perform as expected and were removed to achieve better fit to the Rasch model expectations.
Fig. 2 Path model (expectations of future performance).
The original MFM failed to meet the model expectations in each domain.
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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