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I have computed the Nagelkerke Pseudo-R-Squared for the proportional odds model with two variables. I report ORs with p-values and confidence intervals and would like to quantify the strength of the association too. The idea is to calculate the effect size according Cohen (1992) https://journals.sagepub.com/doi/10.1111/1467-8721.ep10768783 He suggests to calculate the effect size for multiple and multiple partial correlation (for linear models) with the formula $$ f^2=\frac{R^2}{1-R^2} $$ My question is if this method of determination of the effect size would be also make sense for the Nagelkerke pseudo-R-squared? (It is also scaled as the R-squared for linear regression models from 0 to 1).

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