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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Nagelkerke's R^2 as estimator of goodness of fit*From*: Pragati Rao <pragatir@xxxxxxxxx>*Date*: Thu, 10 May 2012 16:19:34 +0530*Approved-by*: pragatir@xxxxxxxxx*Delivery-date*: Thu May 10 06:51:47 2012*List-archive*: <http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>*List-help*: <http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>, <mailto:LISTSERV@LISTS.MCGILL.CA?body=INFO AUDITORY>*List-owner*: <mailto:AUDITORY-request@LISTS.MCGILL.CA>*List-subscribe*: <mailto:AUDITORY-subscribe-request@LISTS.MCGILL.CA>*List-unsubscribe*: <mailto:AUDITORY-unsubscribe-request@LISTS.MCGILL.CA>*Reply-to*: Pragati Rao <pragatir@xxxxxxxxx>*Sender*: AUDITORY - Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

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**

**Attachment:
VOT_hin_sub15.png**

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