Subject: Nagelkerke's R^2 as estimator of goodness of fit From: Pragati Rao <pragatir@xxxxxxxx> Date: Thu, 10 May 2012 16:19:34 +0530 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>--14dae9340621197cda04bfac60d5 Content-Type: multipart/alternative; boundary=14dae9340621197cd704bfac60d3 --14dae9340621197cd704bfac60d3 Content-Type: text/plain; charset=ISO-8859-1 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. --14dae9340621197cd704bfac60d3 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Dear all,<br><br>After many suggestions how to fit the data (for the questi= on GLM vs Cubic Smoothing Spline) and reading the articles suggested by mem= bers, 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.<b= r> <br>R^2=3D[1- (L0/L)^(2/n)]/ [1-L0^(2/n)]<br><br>1. I wanted to know whethe= r L0 is the likelihood of observed data if the estimator predicted constant= probability irrespective of input (vot, f2 etc)?<br><br>=A02. I have attac= hed 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 ac= curately in values of R^2?<br> <br>Any suggestions/comments are welcome.<br><br>Regards,<br><br>Pragati Ra= o<br>Research Officer,<br> All India Institute of Speech and Hearing,<br>Mysore, India.<br> --14dae9340621197cd704bfac60d3-- --14dae9340621197cda04bfac60d5 Content-Type: image/png; name="VOT_hin_sub9.png" Content-Disposition: attachment; filename="VOT_hin_sub9.png" Content-Transfer-Encoding: base64 X-Attachment-Id: f_h21ok2jm0 iVBORw0KGgoAAAANSUhEUgAAAjAAAAGkCAIAAACgjIjwAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA B3RJTUUH3AUKCiE2QMccTAAAACJ0RVh0Q3JlYXRpb24gVGltZQAxMC1NYXktMjAxMiAxNjowMzo1 NCNSAAYAAAAkdEVYdFNvZnR3YXJlAE1BVExBQiwgVGhlIE1hdGh3b3JrcywgSW5jLrrEUs8AAAxO SURBVHic7d3RcqO4FoZRdCrv/8o6F55iGMfGxDbwb7HWldPtSqkTN1+0RZLWe58A4Gz/O3sBADBN ggRACEECIIIgARBBkACIIEgARBAkACIIEgARBAmACIIEQARBAiCCIAEQQZAAiCBIAEQQJAAiCBIA 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