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Subject:

hierarchical models: better models for variance parameters, faster convergence, plots for understanding model fit, and plots for model checking

From:

Andrew Gelman <[log in to unmask]>

Reply-To:

Andrew Gelman <[log in to unmask]>

Date:

Fri, 6 Jan 2006 11:16:39 -0500

Content-Type:

text/plain

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Parts/Attachments

text/plain (106 lines)

Here are a few quick suggestions regarding Wayne Thogmartin's questions 
about fitting, understanding, and checking complex multilevel models.

Andrew

1.  Those inverse-gamma prior distributions can create problems; uniform 
prior dists on the sd's would be better; see here:
http://www.stat.columbia.edu/~gelman/research/published/taumain.pdf

2.  If you have a lot of variance parameters, I suggest modeling them 
hierarchically using the half-Cauchy family; see Section 6 of the 
above-referenced paper.

3.  If convergence is still slow after the above 2 steps, try parameter 
expansion (see pp.597-598 in Appendix C of Bayesian Data analysis); the 
appendix is also here:
http://www.stat.columbia.edu/~gelman/bugsR/software.pdf

4.  To understand the model fit, I recommend plots of data (or estimated 
coefficients) and fitted curve, at each level of the model.  For 
example, see Figures 1 and 2 of this paper:
http://www.stat.columbia.edu/~gelman/research/published/multi2.pdf
or Figures 2 and 3 of this paper:
http://www.stat.columbia.edu/~gelman/research/published/parkgelmanbafumi.pdf

5.  You can check model fit by simulating replicated datasets and 
comparing to the actual data.  Graphical comparisons are usually best, 
in my experience.  See Chapter 6 of BDA, and p.598 of the aforementioned 
appendix for an example in Bugs.

Sorry for referring only to my own stuff.  These are topics that I've 
thought a lot about, and naturally I find my own writing on the topic 
easiest to understand!  Good luck.

Wayne E Thogmartin wrote:

>
> I would appreciate if interested folks might comment on the attached 
> code which attempts to model factors associated with the 
> discrimination between four land cover states.  The global model has a 
> slew of random effects which makes convergence difficult.  The 
> attached code is more quickly able to converge, but still has some 
> mixing problems.  I'm wondering if I might make the code more 
> efficient.  I would also appreciate thoughts on approaches to 
> interpretation; currently, I examine the results to identify patterns 
> in the random effects (i.e., where some groups differ in interesting 
> ways from the main).  I'm also a bit unsure how I might assess model 
> fit.  Any thoughts would be appreciated.
>
> Regards
> Wayne Thogmartin
>
>
>
>
>
> Wayne E. Thogmartin, PhD
> USGS Upper Midwest Environmental Sciences Center
> 2630 Fanta Reed Road
> La Crosse, WI 54603
> 608-781-6309 (off)
> 608-783-6066 (fax)
> [log in to unmask]
> http://www.umesc.er.usgs.gov/terrestrial/migratory_birds/bird_conservation.html
>
> The contents of this message are mine personally and do not reflect 
> any portion of the US government.
>
> "A recurrent theme in the history of science is that novel claims 
> conjoined with a paucity of data inevitably attract the attention of 
> statisticians, much in the manner that offal attracts flies."  W.M. 
> Schaffer 


-- 
Andrew Gelman
Professor, Department of Statistics
Professor, Department of Political Science
[log in to unmask]
www.stat.columbia.edu/~gelman

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