Computational speed - MCMCglmm/lmer

Hi all--

I use (g)lmer and MCMCglmm on a weekly basis, and I am wondering about 
options for speeding up their computations.  This is primarily an issue 
with MCMCglmm, given the many necessary MCMC iterations to get to 
convergence on some problems.  But, even with glmer(), I have runs that 
get into 20-30 minutes.

First, let me be very clear that this is in no way a criticism of Doug's 
and Jarrod's work (package developers for lme4 and MCMCglmm, 
respectively).  Their code has probably brought models/data into range 
that would not have been possible.

Second, I have included link to data and script below, along with some 
timings on my computer: Mac Book Pro, 2.5GHz, with 4GB RAM.  Here's 
sessionInfo from my runs:

 > sessionInfo()
R version 2.11.1 (2010-05-31)
i386-apple-darwin9.8.0

locale:
[1] en_US.UTF-8/en_US.UTF-8/C/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base

other attached packages:
[1] MCMCglmm_2.05      corpcor_1.5.6      ape_2.5-3
[4] coda_0.13-5        tensorA_0.35       lme4_0.999375-34
[7] Matrix_0.999375-41 lattice_0.19-7

loaded via a namespace (and not attached):
[1] gee_4.13-14   grid_2.11.1   nlme_3.1-96   stats4_2.11.1 tools_2.11.1

Specific questions:

1. Would be curious to know timings on other people's set-ups.  Jarrod 
and I had an exchange one time where he was gracious enough to run a 
zero-inflated model where I was concerned about convergence.  He ran a 
model with 1.3M iterations, which I think would take a number of days, 
if not a week on my computer.  This was part of what got me thinking 
about this.  Thus, my first interest is whether there is an "optimal" 
hardware/OS configuration, or does it matter?

Some things I see in R-help archives:

2. 32 vs. 64-bit: Seems like this is mostly an issue of data/model size 
and whether you need to access more than 4GB of RAM.  AFAICS, 64-bit 
processors are not necessarily faster.

3. "Optimized" BLAS: There's a bit of discussion about optimized BLAS 
(basis linear algebra... something).  However, these discussions note 
that there is no generally superior BLAS.  Not sure whether specific 
BLAS might be optimized for GLMM computations.

4. Parallel computing: With multi-core computers, looks like there are 
some avenues for splitting intensive computations across processors.

Finally, I'm asking here b/c I run into these issues with GLMM (and 
zero-inflated mixed models), though most of the discussion I've seen 
thus far about computation speed has been on R-help.

The data below are self-reported drinks (alcohol) from college students 
for up to the last 90 days.  Distribution of counts is zero-inflated.  I 
run a Poisson GLMM with glmer, over-dispersed Poisson GLMM with 
MCMCglmm, and then zero-inflated OD Poisson with MCMCglmm and provide 
timings for my set-up.

Okay, any and all thoughts welcomed.

thanks, Dave

### thinking through computational speed with lmer and MCMCglmm
#
### read drinking data
drink.df <- read.table(file = 
"http://depts.washington.edu/cshrb/newweb/stats%20documents/tlfb.txt",
						header = TRUE, sep = "\t")
str(drink.df) # 57K rows

### id is id variable (shocking)
### gender and weekday are 0/1 indicator variables
### drinks has number of drinks consumed

### distribution of outcome
table(drink.df$drinks)
plot(table(drink.df$drinks), lwd=2) # zero-inflated

### how many people?
length(unique(drink.df$id)) # 990
sort(table(drink.df$id))

### NOTE: most people have max of 90, which they should
###			two folks with 180 and 435 (prob data errors)
###			long negative tail down from 90
#
### NOTE: for this purpose, not worrying about the 180/435

### speed tests
#
### fit random intercept and random slope for weekday
### fixed effects for gender and weekday and interaction
#
### Poisson GLMM with glmer()
library(lme4)

system.time(
drk.glmer <- glmer(drinks ~ weekday*gender + (weekday | id),
					data = drink.df, family = poisson,
					verbose = TRUE)
)
summary(drk.glmer)

### timing
#
###    user  system elapsed
###  36.326   9.013  45.316

### over-dispersed Poisson GLMM with MCMCglmm()
library(MCMCglmm)

prior <- list(R = list(V = 1, n = 1),
				G = list(G1 = list(V = diag(2), n = 2)))
system.time(
drk.mcmc <- MCMCglmm(drinks ~ weekday*gender,
					random = ~ us(1 + weekday):id,
					data = drink.df, family = "poisson",
					prior = prior)
)
summary(drk.mcmc) # NOTE: using summary.MCMCglmm in v 2.05 of package

### timing
#
###        user   system  elapsed
### 	1034.317  165.128 1203.536

### zero-inflated, over-dispersed Poisson GLMM with MCMCglmm()
#
### NOTE: haven't run the following yet, other than a quick "toy run" to
###			sure that it is set up correctly.
### NOTE: this only has random intercept in each portion of the model

prior2 <- list(R = list(V = diag(2), n = 1, fix = 2),
				G = list(G1 = list(V = 1, n = 1),
						  G2 = list(V = 1, n = 1)))
system.time(
drk.zimcmc <- MCMCglmm(drinks ~ -1 + trait*weekday*gender,
					random = ~ idh(at.level(trait, 1)):id + idh(at.level(trait, 2)):id,
					rcov = ~ idh(trait):units,
					data = drink.df, family = "zipoisson",
					prior = prior2)
)
summary(drk.zimcmc)

### timing
#
###    	 user   system  elapsed
###    2105.366  544.881 2640.030