Hi everyone,
How to I import Bugs graphics into latex
Phenyo.
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Phenyo E. Lekone, PhD.
Doctor of Mathematical Statistics
Mailing Address:
Department of Mathematics,
University of Botswana
Private Bag 00704
Gaborone, Botswana
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-----Original Message-----
From: (The BUGS software mailing list) [mailto:[log in to unmask]] On Behalf Of David Spiegelhalter
Sent: 02 February 2007 14:39
To: [log in to unmask]
Subject: [BUGS] Deviance increases with additional explanatory variable
the recent discussion on this phenomenon has been enlightening (to me at
least, as I had not appreciated how easily this could happen).
I have added an extra FAQ on
http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/dicpage.shtml#q17
which shows Dbar can easily be made to increase by fitting a covariate
with no explanatory power.
*
If Dbar measures 'lack of fit', why can it increase when I add a
covariate?*
Suppose Yi is assumed to be N(0,1) under model 1, and consider a
covariate xi with mean 0 and which is uncorrelated with Y. Then it is
straightforward to show that fitting a more complex model 2: Yi ~ N(b
xi,1) leads to Dbar increasing by 1. The crucial idea is that Dbar
should perhaps not really be considered a measure of fit (in spite of
the title of Spiegelhalter et al (2002)!). Fit might better be measured
by Dhat. As emphasised by van der Linde (2005)
<http://www.blackwell-synergy.com/links/doi/10.1111/j.1467-9574.2005.00278.x/abs/>
(also available from here
<http://www.math.uni-bremen.de/%7Eavdl/download/papers/varsel2.pdf> ),
Dbar is more a measure of model 'adequacy', and already incorporates a
degree of penalty for complexity.
David Spiegelhalter
Joachim Büschken wrote:
> Hello Bugs List:
>
> recently, I posted this email:
>
> I am running a hierarchical logistic regression in Winbugs and have
> this problem: When I add a specific explanatory variable to the
> model, the deviance more than doubles, which implies that adding this
> variable reduces the fit of the model. This does not happen when I run
> the same model (without the random effect, i.e. "non-hierarchical") in
> SPSS.
>
> I received a number of very helpful comments (many thanks to all who
> responded!) which I copied below:
>
> "In your case, I wonder if the explanatory variable explains the
> hierarchy? I don't know the specifics of your situation, but let's
> say your random effect was gender and your explanatory variable was
> hair length. There might be very good correspondence between gender
> and hair length such that you do not require both in the model. One
> or the other would be sufficient. Might this describe your case?"
>
> This may happen. I checked by running a correlation between my theta
> vector (random effect) and the explanatory variable. The correlation
> is 0.11 and insignificant. Thus, I do not think that this is the
> problem here. However, how do we prevent this from happening (adding a
> random effect which correlates with an explanatory variable in the model)?
>
> "David Lindely in a discussion (JRSSB) of Aitkens' paper showed that
> the posterior mean of Log L can have very bad behavior because it
> counts the data twice: once in log L and once in the posterior
> distribution."
> Not being a statistician, I cannot really comment on that.
>
> "One problem is that adding a variable also increases the size of your
> parameter space a lot in HB models. If you had the same prior
> variances for each beta for the two models, then the prior in the
> second model is much flatter/smaller than the prior in the first
> model. In fact, the rate of "flattness" decreases exponentialy with #
> of dimensions. In a situation were there are a large number of
> parameters to observations, the flattening of the "hat" will lead to a
> flattening of the posterior distribution, which means small values of
> the logL get relatively greater weight in the deviance. So your
> E(LogL) can decrease even though the additional covariate is
> good. Model selection using deviance, or even better, Bayes factors or
> posterior probs of models, can get tricky for large model spaces and
> flat likelhoods. In addition to being hard to compute, seemingly
> small changes in the prior can have a big impact on these measures.
> Asymptotically where the likelihood dominates the prior, everything
> works well.
>
> I find this last point rather troubling. If this can happen, how do we
> evaluate the fit of a hierarchical model if LogL is "bad"?
>
> Cheers
> Joachim
>
> Dr. Joachim Büschken,
> Professor of Marketing
>
> Catholic University of Eichstätt-Ingolstadt, Germany
>
> [log in to unmask] <mailto:[log in to unmask]> or [log in to unmask]
> <mailto:[log in to unmask]>
>
>
> Phone: (49) 841.937.1976
> Fax: (49) 841.937.2976
>
>
>
>
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For help with crashes and error messages, first mail [log in to unmask]
To mail the BUGS list, mail to [log in to unmask]
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Please do not mail attachments to the list.
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