Nagelkerke's R^2 as estimator of goodness of fit (Pragati Rao )


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&#39;s R^2 should be = used. I am using the following formula to calculate nagelkerke&#39;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 EQQJgAiCBEAEQQIggiABEEGQAIggSABEECQAIggSABEECYAIggRABEECIIIgARBBkACIIEgARBAk ACKMHKTW2tlLAGCrkYMEQCGCBEAEQQIggiABEEGQAIggSABEECQAIggSABEECYAIIwTJT2QAGED5 IKkRwBhqB6m11ns/exUAfEHtIKkRwDBqBwnGs/cQetf3X3rxe79/xwsvjTDyeja4uzteGuBfyvDm 1+xOr9a337+L6TCSL4Q/Zy9gXyJELb1PrR1xyfhrYDYuae/Fl37/x3xmSxs8SFDOh9es9dLsfUH0 /s9652MQJCjsd35c9ahLkKCYZYTkh5GMECQHRQxPhLiCEYIEo9r7pjuIIkiQ6JYiHeJSBAmC2BJx ZYIEKXyfChcnSHA+AzqYBAnOJUUwEyQ4hxTBHUGCEzgugt/8+gk4mhrBQ3ZIcBxjOlghSHAQGyNY Z2QHR1AjeEmQYHdqBFsIEuxLjWAjQYIdqRFsJ0iwFzWCPxEk2IUawV8JEnyfGsEbBAmACIIEX2Z7 BO+J/kkNbf71mdPUH/0Xf/kEOJgawdtyg9RaWzbm7s0tTwCgECM7+BrbI/iEIMF3qBF8aJAgLQ+T YG9ebrCH3DOkl3rvc4eWj5fc9cDX3V5Td/sh2yP4XOEgTRsaI0J8Xe9qBLsYZGQHR5If2EPhIC3H ce755iy2R/AtuSO7u2OhuTdze+7OkI5fIagRfFFukKYnmVn+oQ4BDKPwyA7OZXsE3yVIAEQQJAAi CBK8w7wOvk6QAIggSPBntkewB0ECIIIgwd/YHsFOBAmACIIEf2B7BPsRJAAiCBJsZXsEuxIkACII EmxiewR7EyQAIggSABEECYAIggSvOUCCAwgSABEECV6wPYJj/Jy9gDWttflxf3RJePkEAKrIDVJr bdmYuze3PAE+Z3sEhzGyAyCCIAEQIXdk91Lv3RkSuzKvgyMVDtKWMyTFAqiicJC2ECHeZnsEB3OG BEAEQQIgQu7I7tk9C/NZkZsa2I95HRwvN0jTk8Ys/1CEAIZhZAf3bI/gFIIEQARBAiCCIAEQQZAA iCBI8B/uaICzCBIAEQQJgAiCBP8yr4MTCRIAEQQJgAiCBP8wr4NzCRIAEQQJgAiCBNNkXgcBBAmA CIIEQARBAvM6iCBIAEQQJAAi/Jy9gDWttflx/zVSWf7ts+fAS+Z1ECI3SK21ZWDu3pz+m5/ffwtA LUZ2AEQYIUi2RwADGCFIAAwg9wxpo/Xt0fptEQDkKB+kdSIEUEXtkZ3TIz7knm/IUTtIAAwjd2TX e394AmRXBDCkkS/u0sU68zqIYmQHQARBAiCCIHFR5nWQRpAAiCBIAEQQJAAiCBJX5AAJAgkSABEE CYAIgsTlmNdBJkECIIIgARBBkACIIEhciwMkiCVIAEQQJAAiCBIAEQSJC3GABMkECYAIggRAhJ+z F7CmtTY/7o9GLS+fAEAVuUFqrS0bc/fmlicAUMg4Izs1AihtnCABUFruyG6j+RjJDol17vmGcLWD tDw3eniG5K4HgCpqB+llY0QIoApnSABEECQuwQES5Msd2fXeH54AzWdFz54AQEW5QZqeNGb5hyIE MAwjO8ZnXgclCBIAEQQJgAiCBEAEQWJwDpCgCkECIIIgARBBkACIIEiMzAESFCJIAEQQJAAiCBIA EQSJYTlAgloECYAIggRABEECIIIgMSYHSFCOIAEQQZAAiCBIAEQQJAAi/Jy9gDWttflxf3RCvXzC s+cAUEJukFpry8DcvTkTIYAxGNkBEKFwkJ7tmcA3IUFFuSO7LV4eMgFQRe0gvTxkUqwLun3ObZKg nMJB2hIYEbosn3kop/AZEjyjRlBR4SDdfRMSAKXljux67w9PgOazomdPAKCike+cdl/4BbmXAeoq PLIDYCSCBEAEQQIggiAxDgdIUJogARBBkACIIEgARBAkBuEACaoTJAAiCBIAEQQJgAiCxAgcIMEA BAmACIIEQARBAiCCIAEQQZAAiCBIAEQQJMpzzzeMQZAAiPBz9gLWtNbmx331a+DW2voTAAiXG6S7 xqwkZ9ktAIoysqM2B0gwjPJBMqwDGEP5IAEwhtwzpC1ebo+23xYBwLlqB+klERqbAyQYSeGR3W33 01qbH5y9IgDeV3iHtPGmcABKyA1S7/3hCZD2AAxp5Iu7dI3NARIMpvAZEgAjESQAIggSJZnXwXgE CYAIggRABEECIIIgUY8DJBiSIAEQQZAAiCBIFGNeB6MSJAAiCBIAEQQJgAiCBEAEQQIggiABEEGQ qMQ93zAwQQIggiABEEGQAIjwc/YC1rTW5sf90dHByycwEgdIMLbcILXWlo25e3PLEwAopPDITn4A RlI4SFyKeR0ML3dkt9F8jGTDBFBa+SDNHXp4huSuB4AqygdpnQiNwbwOrsAZEgARCgdpOY4DoLrc kV3v/eEJ0HxW9OwJDMa8Di4iN0jTk8Ys/1CEAIZReGQHwEgEiWjmdXAdggRABEECIIIgARBBkACI IEgARBAkACIIErnc8w2XIkgARBAkQtkewdUIEgARBAmACIJEIvM6uCBBAiCCIAEQQZCIY14H1yRI AEQQJAAiCBJZzOvgsn7OXsCa1tr8uD+6Sr18AgBV5AaptbZszN2bW54AQCGFR3byMx7zOriywkEC YCSCRArbI7i43DOkP3l2gOSuB4AqRgjSyu0MIgRQRfmRnZvrAMZQO0hqBDCM3JFd7/3hCdAcodvf OiUagzsagNwgTU8CM/+h/ACMpPbIDoBhCBLnM68DJkECIIQgcTLbI+BGkACIIEicyfYImAkSABEE idPYHgFLggRABEHiHLZHwB1BAiCCIAEQQZAAiCBInMABEvCbIAEQQZA4mu0R8JAgARBBkDiU7RHw jCBxHDUCVggSABF+zl7Amtba/Lg//9K6tbbyt4SwPQLW5QbpLjPPqrOMFgB11R7Z2RtVYXsEvFQ7 SGpUghoBW9QOEnUZtQJ3cs+QvmLjbREc7PZpsXMClgYPkgid7mF1elcj4J6RHTtaqY4aAXcEib3Y AwF/kjuy670/PAFyqzfAkEa+uEvXiWyPgL8ysuP71Ah4gyDxZWoEvEeQ+CY1At4mSABEECS+xvYI +IQg8R1qBHxIkPgCNQI+J0h8So2Ar8j9SQ3ku/0kDTUCvsIOiY+oEfAtgsSbTOqA7zKy489M6oA9 CBJ/Y2ME7ESQ2MrGCNiVILGJjRGwN0HiBRsj4BiCxFNSBBxJkHhAioDjCRL/unVokiLgDIKEDgER agepzZfSaequpn+kQ0CUwkFqrS0jdPcmvy3yPU06BIQpHCTW3eVnUiAgmyDV9rs6M/kBahGkHW38 6QYrUXlpv+r40QzAwcYOUv/kWv8VWxbwxnV/73/X7f1rEnCksYN08m0O+13Qe9+3Fnu/f4Df/IK+ He16Qd+7FmoEHEyQAIhQeGTXe/eNsQDDKBykSYQABmJkB0AEQQIggiABEEGQAIggSABEuHSQ2uk/ WegDpRc/FV+/xZ/F4sd26SABkEOQAIggSABEECQAIpz8Cxp25QgR4E7yNX/kIAFQiJEdABEECYAI ggRABEECIELtX9D3htb+cx9Hxd85W3HNN0U/+A/XafFHWr5yqiz+7i7f21KrLP4s1wrS3Uvk9/Ux /yVScc03RT/4D9dp8UdavnJqLf5ubbUWf4oLjex8+k9U94NfdNk3pRfPBV0oSP5znsgHn/cU/VKm 6LJPd62RHVzQPPJyiTyS46I3CBJsVfTL3uXtALXWX27BS46L3jBykHxhyBe5prCdl8p7Rg6S1wTf okbHu31BOX9Z6VNwBRe6qQHeU/dSWPoH3veFqdrXl6U/8ieq+j/tbUW/N3Op4ppvKn7wf19Zan2H o2+MPcsYH/mDXS5IAGQysgMggiABEEGQAIggSABEECQAIggSABEECYAIggRABEECIIIgARBBkACI IEgARBAkACIIEgARBAmACIIEQARBAiCCIAEQQZAAiCBIAEQQJAAiCBIAEQQJgAiCBEAEQQIggiAB EEGQAIggSABEECQAIvwfP75Xkn7a3UIAAAAASUVORK5CYII= --14dae9340621197cda04bfac60d5 Content-Type: image/png; name="VOT_hin_sub15.png" Content-Disposition: attachment; filename="VOT_hin_sub15.png" Content-Transfer-Encoding: base64 X-Attachment-Id: f_h21ok2jx2 iVBORw0KGgoAAAANSUhEUgAAAjAAAAGkCAIAAACgjIjwAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA B3RJTUUH3AUKCh4DTqryUwAAACJ0RVh0Q3JlYXRpb24gVGltZQAxMC1NYXktMjAxMiAxNjowMDow MqXz/pgAAAAkdEVYdFNvZnR3YXJlAE1BVExBQiwgVGhlIE1hdGh3b3JrcywgSW5jLrrEUs8AAAxk SURBVHic7d3bctu4FkVRIuX//2WeB/VRGF1piSTWBseofrDTKgXFyJzGRXab53kCgN7+9B4AAEyT IAEQQpAAiCBIAEQQJAAiCBIAEQQJgAiCBEAEQQIggiABEEGQAIggSABEECQAIggSABEECYAIggRA BEECIIIgARBBkACIIEgARBAkACIIEgARBAmACIIEQARBAiCCIAEQQZAAiCBIAEQQJAAiCBIAEQQJ gAgjB6m11nsIAKw1cpAAKESQAIggSABEECQAIggSABEECYAIggRABEECIIIgARBBkACIIEgARBAk ACIIEgARBAmACIIEQIQRguT3HgEMoHyQ1AhgDLWD1Fqb57n3KADYQO0gqRHAMGoHCbqwTvzM3lfG lR/b4EFqC73HwiAuLyUvqHt7XxlXfng/vQewL2t6bG6ep9Ymr6x7e18ZV354g8+QYA/uic/sfWVc +bEJEgARBAmACCMEyUYRwABGCBIAAxAkACIIEgARBAmACIIEQARBAiCCIAEQQZAAiCBIAEQQJAAi CBIAEQQJgAiCBEAEQQIggiABEOGn9wAAeK+1bZ4n+ffHCRJwdlvd63eVHJKtCBIwgm+icoZ7fQmC BERbWRpRGYAgAf29qI7SnIcgAYd62B7VYRIkYFf3+dEenhEkYDPywzcECfjKMkLywzcECfg1EWIP ggSsIkLsTZCAV64dEiH2JkjAAzrE8QQJ+EuH6EiQAB0igiDBqV1SpEMkECQ4KSkiTXSQ2uKc6fzo 6+btA4AbVueIlRuk1tqyMTefrnkAcKM1HSJXbpCADVmgI58gweCkiCr+9B7ANto3v74Ykmz1Wm7t v//mWY3W2vVG4i71VuEZ0jzP1w4tP15y6oFaLi/Y73d67BV9YKuLf/yTD6NwkKYVjREhaplnNepm k4vf5cmHUTtIMJ5v7lm2i76066Xz7/JW4SAtz3k7883JSREDyA3SzbbQfXtu9pCOHyGEsBbEGEae WJg2cQZqxDByZ0jAa5bpGIwgQT1SxJAECYqxRseoBvlJDXASasTABAnKUCPGJkhQgxoxPHtIkM4R Bk5CkCCaiRHnYckOcqkRpyJIEEqNOBtBgkRqxAkJEsRRI85JkCCLGnFaTtlBCse7OTkzJAiiRpyZ IEEEK3UgSNCfGsEkSNCdGsGFIEFPagRXggTdqBEsCRL0oUZwQ5CgAzWCe4IEQARBgqOZHsFDggSH UiN4RpDgOGoELwgSHESN4DVBgiOoEbwlSLA7NYI1BAmACIIE+zI9gpWif2Nsu/wGzWmapml+9DX9 9gHQlxrBerlBaq0tG3Pz6ZoHQF9qBL9iyQ52oUbwW4IEQITcJbu35nm2h0Qm0yP4QOEgrdlDUiyO p0bwmcJBWkOEOJgawcfsIQEQQZBgM6ZH8I3cJbtnZxaue0UONRBFjeBLuUGanjRm+YciBDAMS3aw AdMj+J4gwbfUCDYhSPAVNYKtCBJ8To1gQ4IEQARBgg+ZHsG2BAmACIIEnzA9gs0JEvyaGsEeBAmA CIIEv2N6BDsRJPgFNYL9CBKspUawK0ECIIIgwSqmR7A3QQIggiDBe6ZHcABBAiCCIMEbpkdwDEGC V9QIDiNI8JQawZEECYAIggSPmR7BwQQJHlAjOJ4gARBBkOCW6RF0IUgARBAk+IfpEfQiSABEECT4 y/QIOhIk+I8aQV+CBECEn94DeKW1dv14vvvedfl/nz0GVjI9gu5yg9RaWwbm5tPp3/zc/19YT40g gSU7zk6NIMQIQTI9AhjACEGCG3fbi0ABuXtIK72eHr0+FsGQLv/mKxfirNdBjvJBek2ETmieZQZK qr1kZ/eIh1a+KHQLotQOEnxMjSBN7pLdPM8Pd4DMivieGkGg3CBNT3aAln+oTADDsGTH6ZgeQSZB 4lzUCGIJEgARBIkTMT2CZIIEQARBAiCCIHEW1usgnCBxCmoE+QSJ8akRlCBIAEQQJAZnegRVCBIj UyMoRJAAiCBIDMv0CGoRJMakRlCOIAEQQZAAiCBIDMh6HVQkSIxGjaAoQWIoagR1CRIAEQSJcZge QWmCxCDUCKoTJEagRjAAQQIggiABEEGQKM96HYxBkKhNjWAYggRABEGiMNMjGIkgUZUawWAEiZLU CMbz03sAr7TWrh/Pj24/bx8AQBW5QWqtLRtz8+maBzAq0yMY0jhLdmp0EmoEoxonSACUlrtkt9J1 G8kM6QxMj77nGhKrdpCW+0YP95CceoClyxeEJpGpdpDeNkaERuI2+r15dhnJZQ+JGtxGt+IyEkuQ KECN4Axyl+zmeX64A3TdK3r2AAajRnASI7+Z1FtlB6BGcB6W7ACIIEgARBAkclmvg1MRJEKpEZyN IJFIjeCEBIk4agTnJEhkUSM4LUEiiBrBmQkSKdQITk6QAIggSABEECQiWK8DBIn+1AiYBInu1Ai4 ECR6UiPgSpDoRo2AJUGiDzUCbggSABEEiQ5Mj4B7P70HwLm0Nk2TGgEPCBLHMTECXrBkx0HUCHhN kDiCGgFvCRK7UyNgDUECIIIgsS/TI2Alp+zYixPewK8IErswMQJ+y5Id21Mj4AOCxMbUCPiMILEl NQI+JkhsRo2Ab0QfamiXc1rTNE3T/OhWt3zAs8dwDDUCvpQbpNbaMjA3n16JUHeOdwObyA0SJZgY AVspvIf0bM7EYdQI2FDtGdLbTSb282WNxAy4UTtIbzeZFGsP328aXZ5Bk4ClwkFaExgR2tZW5xfm WY2AW4WDxMG2TYgaATdqH2roPYQTMaEB9pY7Q5rn+eEO0HWv6NkD2Ja3GQHHGPnktHPhX5Ii4Ei5 MyQ6kiLgeILELdtFQBeCxF8mRkBHgsQ0SREQQJDOToqAEIJ0XlIERBGk07m+d0uKgCiCdCKmREAy QRqfKRFQgiANS4eAWgRpQJbmgIoEaRDLH30uRUBFglSbdTlgGIJUj8kQMCRBKuDmNxGKEDAkQUqk QMAJCVIEBQIQpEPdhOdKgQAEaXvPqjMJD8BzgvRrL3pzoToAHzh1kN6m5SG9AdjD2EGaXydHWgBy jB2kNmsOQBF/eg8AAKZJkAAIIUgARBAkACIIEgARBAmACIIEQARBAiBC9Btj2+IHLbx+i2tr3gML UFtukG4a8yI57bOfSQdAEkt2AEQoHySLdQBjKB8kAMaQu4e0xtvp0fpjEQD0VTtIb4kQQBWFl+wu s5/W2vWD3iMC4HOFZ0grD4UDUEJukOZ5frgDpD0AQxr55i5dAIUU3kMCYCSCBEAEQQIggiABEEGQ AIggSABEECQAIggSABEECYAIggRABEECIIIgARBBkACIIEgARBAkACIIEgARBAmACIIEQARBAiCC IAEQQZAAiCBIAEQQJAAiCBIAEQQJgAiCBEAEQQIggiABEEGQAIggSABEECQAIggSABF+eg/gldba 9eN5nj94AABV5AaptbZszM2nax4AQCGFl+zkB2AkhYMEwEjKB6n9X+CEabHDVezJD3h+gBu5e0gr XTv0sEkdTz1c/ubWpj3+2l2f/IDnB7hXPkivdZw2zfOON/Rdn/yA5we4V37JLtmuN/S9a6FGwMEK B6nZ5QAYSO6S3TzPD3eArntFzx4AQEWJh9O2knn0DoCHCi/ZATASQQIggiABEEGQAIggSABEECQA IggSABEECYAIggRABEECIIIgARDh1EEq/fPCSw9+Kj5+g+/F4Md26iABkEOQAIggSABEECQAIoz8 K+xsIQLcSL7njxwkAAqxZAdABEECIIIgARBBkACI8NN7AEdr7Z9zHMuTeFXOd1Qc80XRi/9wnAZ/ pOUrp8rgb075XoZaZfC9nCtINy+R+/tj/kuk4pgvil78h+M0+CMtXzm1Bn8ztlqD7+JES3b++Tuq e/GLDvui9OA5oRMFyRdnRy4+nyn6rUzRYXd3riU7OKHrkpdb5JFsF31AkGCtot/2Lo8D1Bp/uQEv 2S76wMhB8o0hG3JPYT0vlc+MHCSvCbaiRse7fEN5/bbSP8EZnOhQA3ym7q2w9A+8nxemat9flr7y HVX9SvtY0fdmLlUc80XFi39/Z6n1DkdvjO1ljCt/sNMFCYBMluwAiCBIAEQQJAAiCBIAEQQJgAiC BEAEQQIggiABEEGQAIggSABEECQAIggSABEECYAIggRABEECIIIgARBBkACIIEgARBAkACIIEgAR BAmACIIEQARBAiCCIAEQQZAAiCBIAEQQJAAiCBIAEQQJgAj/A9qXUOrDjbq1AAAAAElFTkSuQmCC --14dae9340621197cda04bfac60d5--


This message came from the mail archive
/var/www/postings/2012/
maintained by:
DAn Ellis <dpwe@ee.columbia.edu>
Electrical Engineering Dept., Columbia University