Nagelkerke's R^2 as estimator of goodness of fit

[Pragati Rao <pragatir@xxxxxxxxx>]

Dear all,

After many suggestions how to fit the data (for the question GLM vs Cubic Smoothing Spline) and reading the articles suggested by members, I am now using maximum likelihood for logistic regression to fit the data. As I remember reading, the usual R^2 is not a good way to comment on goodness of fit for logistic regression. So Nagelkerke's R^2 should be used. I am using the following formula to calculate nagelkerke's R^2.

R^2=[1- (L0/L)^(2/n)]/ [1-L0^(2/n)]

1. I wanted to know whether L0 is the likelihood of observed data if the estimator predicted constant probability irrespective of input (vot, f2 etc)?

 2. I have attached two figures where this method was used to estimate the fit . For figure VOT_hin_sub9 the nagelkerke R^2 value is 0.9676 and for the figure VOT_hin_sub15, it is 0.465.I wanted to know if the goodness of fit is reflected accurately in values of R^2?

Any suggestions/comments are welcome.

Regards,

Pragati Rao
Research Officer,
All India Institute of Speech and Hearing,
Mysore, India.

Attachment: VOT_hin_sub9.png
Description: PNG image

Attachment: VOT_hin_sub15.png
Description: PNG image