Dear all,
I have a very big sample with very few positive cases - so I decided to run a Firth Logistic Regression in SPSS. However, the program does not provide the squared R. Do you know a method to calculate them?
The program provides Last Log-likelihood Change, Maximum Last Beta Change, Coefficient, Std. Error, Chi-Square & Sig.
Thanks a lot,
Best regards,
Lorena
Hello Lorena,
Formally, there is no R-squared value in logistic regression, since you're not really partitioning observed score variance. That's why the usual measures (e.g., Cox & Snell, Nagelkerke, McFadden) are called "pseudo-R-square" estimates. As such, their utility is pretty much limited to comparing alternate models on the same data (higher is better for a given estimator).
Here is a good link explaining a host of pseudo R-squared estimators and their individual foibles: https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-what-are-pseudo-r-squareds/
However, if you absolutely, positively have to have these, here are the keys:
Cox & Snell = 1 - [L(null model) / L (full model)]^(2/N)
Where L = Likelihood of model (if SPSS output gives -2LL, you'll have to divide by -2, then exponentiate the result, e.g., e^LL).
null model = base, no IVs included
full model = model with all relevant IVs included
N = Number of cases
Nagelkerke = Cox & Snell value / [1 - L(null model)^(2/N)]
McFadden = 1 - [LL(full model) / LL(null model)]
Good luck with your work.
HI,
I agree with David's answer (perfectly explained), but I would like to add that you should consider reporting the results of information criteria like AIC or BIC (or variants thereof). In contrast to R^2 (and this is also true for typical linear models), information criteria do not only improve, but may also get worse. Therefore, in case of nested models, they clearly indicate if the addition of extra parameters truely improves the model or just inflates R^2, which cannot get smaller. So, if in your case the full model would be better than the null model, AIC and BIC would be smaller, if not, you only added complexity but no additional "information". This approach is very common for generalized linear models and hierarchical linear models. To assess the contribution of each predictor, you can report and interpret Odds Ratio. Hope it helps.
Rainer
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