# 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>

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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.

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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>

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