On Jan 7, 2011, at 8:26 AM, sovo0...@gmail.com wrote:
On Thu, 6 Jan 2011, David Winsemius wrote:
On Jan 6, 2011, at 11:23 AM, Sören Vogel wrote:
Thanks for your replies. I am no mathematician or statistician by
far,
however, it appears to me that the actual value of any of the two
LLs
is indeed important when it comes to calculation of
Pseudo-R-Squared-s. If Rnagel devides by (some transformation of)
the
actiual value of llnull then any calculation of Rnagel should
differ.
How come? Or is my function wrong? And if my function is right, how
can I calculate a R-Squared independent from the software used?
You have two models in that function, the null one with ".~ 1" and
the origianl one and you are getting a ratio on the likelihood
scale (which is a difference on the log-likelihood or deviance
scale).
If this is the case, calculating 'fit' indices for those models must
end up in different fit indices depending on software:
n <- 143
ll1 <- 135.02
ll2 <- 129.8
# Rcs
(Rcs <- 1 - exp( (ll2 - ll1) / n ))
# Rnagel
Rcs / (1 - exp(-ll1/n))
ll3 <- 204.2904
ll4 <- 199.0659
# Rcs
(Rcs <- 1 - exp( (ll4 - ll3) / n ))
# Rnagel
Rcs / (1 - exp(-ll3/n))
The Rcs' are equal, however, the Rnagel's are not. Of course, this
is no question, but I am rather confused. When publishing results I
am required to use fit indices and editors would complain that they
differ.
It is well known that editors are sometimes confused about statistics,
and if an editor is insistent on publishing indices that are in fact
arbitrary then that is a problem. I would hope that the editor were
open to education. (And often there is a statistical associate editor
who will be more likely to have a solid grounding and to whom one can
appeal in situations of initial obstinancy.) Perhaps you will be
doing the world of science a favor by suggesting that said editor
first review a first-year calculus text regarding the fact that
indefinite integrals are only calculated up to a arbitrary constant
and that one can only use the results in a practical setting by
specifying the limits of integration. So it is with likelihoods. They
are only meaningful when comparing two nested models. Sometimes the
software obscures this fact, but it remains a statistical _fact_.
Whether you code is correct (and whether the Nagelkerke "R^2" remain
invariant with respect to such transformations) I cannot say. (I
suspect that it would be, but I have never liked the NagelR2 as a
measure, and didn't really like R^2 as a measure in linear regression
for that matter, either.) I focus on fitting functions to trends,
examining predictions, and assessing confidence intervals for
parameter estimates. The notion that model fit is well-summarized in a
single number blinds one to other critical issues such as the
linearity and monotonicity assumptions implicit in much of regression
(mal-)practice.
So, if someone who is more enamored of (or even more knowledgeably
scornful of) the Nagelkerke R^2 measure wants to take over here, I
will read what they say with interest and appreciation.
Sören
David Winsemius, MD
West Hartford, CT
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