Greetings, and apologies for cross-posting.
FYI, a paper on heteroscedasticity in multilevel/hierarchical modeling is
available for downloading in PostScript format from
http://www.bath.ac.uk/~masdd
(near the top of the page; the file is 404K in size and prints 21 pages).
The citation and abstract are as follows.
Browne WJ, Draper D, Goldstein H, Rasbash J (2000). Bayesian and likelihood
methods for fitting multilevel models with complex level-1 variation.
Submitted.
Abstract
In multilevel modeling it is common practice to assume constant variance at
level 1 across individuals. In this paper we consider situations where the
level-1 variance depends on predictor variables. We examine two cases using
a dataset from educational research; in the first case the variance at
level 1 of a test score depends on a continuous "intake score" predictor,
and in the second case the variance is assumed to differ according to
gender. We contrast two maximum-likelihood methods based on iterative
generalized least squares with two MCMC methods based on adaptive hybrid
versions of the Metropolis-Hastings (MH) algorithm, and we use two
simulation experiments to compare these four methods. We find that all four
approaches have good repeated-sampling behavior in the classes of models we
simulate. We conclude by contrasting raw- and log-scale formulations of the
level-1 variance function, and we find that adaptive MH sampling is
considerably more efficient than adaptive rejection sampling when the
heteroscedasticity is modeled polynomially on the log scale.
Comments on this paper would be welcome.
Best wishes, David Draper
============================================================================
Professor David Draper
Head of Statistics Group web http://www.bath.ac.uk/~masdd
Department of email [log in to unmask]
Mathematical Sciences phone UK (01225) 826 222, nonUK +44 1225 826 222
University of Bath fax UK (01225) 826 492, nonUK +44 1225 826 492
Claverton Down
Bath BA2 7AY England
Interesting quotes, number 19 in a series:
One more example of that oxymoron "military intelligence":
This is the transcript of an actual radio conversation between a US Naval
ship and Canadian authorities off the coast of Newfoundland in October
1995. Radio conversation released by the Chief of Naval Operations 10-10-95.
US SHIP: Please divert your course 0.5 degrees to the South to avoid a
collision.
CND REPLY: Recommend you divert YOUR course 15 degrees to the South to
avoid a collision.
US SHIP: This is the Captain of a US Navy Ship. I say again, divert YOUR
course.
CND REPLY: No. I say again, divert YOUR course!
US SHIP: THIS IS THE AIRCRAFT CARRIER USS MISSOURI. WE ARE A LARGE WARSHIP
OF THE US NAVY. DIVERT YOUR COURSE N O W !!!!!
CND REPLY: This is a lighthouse. Your call.
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