Date: Sun, 28 Sep 2008 21:55:22 -0300
From: " Paulo In?cio de Knegt L?pez de Prado " <prado at ib.usp.br>
Subject: [R-sig-eco] Are likelihood approaches frequentist?
To: r-sig-ecology at r-project.org
Message-ID: <20080929002804.M94451 at ib.usp.br>
Content-Type: text/plain; charset=iso-8859-1
Dear r-sig-ecology users
Here follow the messages I exchanged with Ben Bolker last week about the
likelihood and frequentist approaches. We both would like to open this
topic
for discussion in the list.
Best wishes
Paulo
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Dear Dr. Bolker,
I am puzzled why some authors treat likelihood approaches as
frequentist, as it seems you did in page 13 of your book 'Ecological
Models
and Data'.
This sounds odd to me because what brought my attention to likelihood
was
Richard Royall's book 'Statistical Evidence'. His framing of a paradigm
based on the likelihood principle, and the clear distinction he makes
between this paradigm and frequentist and Bayesian approaches looks
quite convincing to me.
I agree with him that we use likelihood criteria to identify, among
competing hypotheses, which one attribute the highest probability to a
given dataset. If I understood correctly, this is what Royal calls the
'evidence value' of a data set to a hypothesis 'vis a vis' other
hypotheses. I also like his idea that the role of statistics in science
is just to gauge this evidence value, no less, no more.
This approach differs from the frequentist because the sampling
space is irrelevant, that is, other datasets that might be observed do
not
affect the evidence value of the observed data set. My favourite example
is
the comparison of binomial and negative binomial experiments on coin
tossing, in the sections 1.11 and 1.12 of his book.
I am not an "orthodox likelihoodist"; on the contrary, I agree with the
pragmatic view you express in your book. I'd just like to understand
the key differences among the available statistical tools, in order to
make
a good pragmatic use of them. I'd really appreciate if you can help me
with this.
Best wishes
Paulo
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Very well put. Royall, and Edwards (author of _Likelihood_, Johns
Hopkins 1992) are what I would call "pure", or "hard-core",
or "orthodox", likelihoodists. They are satisfied with a statement
of relative likelihood, and don't feel the need to attach a p-value
to the result in order to have a decision rule for hypothesis rejection.
Far more commonly, however, people impose (? add ?) an additional
layer of frequentist procedure on top of this basic structure, namely
using the likelihood ratio test to assess the statistical significance
of a given observed likelihood ratio and/or to set a cutoff value
for profile confidence intervals. Using the LRT puts the inference
back squarely into the frequentist domain, although the sample space
we are now dealing with (sample space of likelihoods derived from
coin-tossing experiments) is quite different from the one
we started with (sample space of outcomes of coin-tossing experiments).
As far as I can see, Edwards and Royall are almost alone in their
adherence to "pure" likelihood -- most of the rest of us pander
to the desire for p-values (or, less cynically, to the desire
for a probabilistically sound decision rule).
I would also add that different scientists have different
goals (belief, prediction, decision, assessing evidence). I too
think Royall makes a good case for the primacy of
assessing strength-of-evidence, and he gives the clearest
explanation I have seen, but I wouldn't completely
rule out the other frameworks.
Hope that makes sense -- thanks for the kind words!
cheers
Ben Bolker
--
Paulo In?cio de Knegt L?pez de Prado
Depto. de Ecologia - Instituto de Bioci?ncias - USP
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