[R-sig-ME] LMM with Big data using binary DV

[Malcolm Fairbrother]

Dear AC (and perhaps Doug),

>>> 2. Are there any clever work arounds (e.g., random sampling of subset of
>>> data, etc) that would allow me to use only R packages to run this dataset
>>> (assuming I need to use another program due to the size of the dataset)?

You may be well aware of this, but one way of substantially speeding up the estimation of models with binary data is to use "cbind", though the feasibility of this depends on the nature of the model (number of predictors and number of unique values for each predictor variable). The kind of code you need for this is below. You'll see that the fixed effects estimates, standard errors, and random effects variances turn out the same.

> If you would have an opportunity to run that model fit or a comparable
> on lme4Eigen::glmer we would appreciate information about speed,
> accuracy and memory usage.

> As a fallback, we would appreciate the code that you used to simulate
> the response.  We could generate something ourselves, of course, but
> it is easier to compare when you copy someone else's simulation.

I've compared the speed of lme4 versus lme4Eigen, on a simulated dataset with 100,000 observations, using a 2GHz MacBook. Based on a handful of simulations, there doesn't appear to be much difference between the two packages in terms of speed (sometimes one is faster, sometimes the other). I have reported the results of one simulation here. The two packages generate identical results for this dataset.

Cheers,
Malcolm


N <- 100000
grps <- 100
dat <- data.frame(x1 = sample(1:10, N, replace=T), x2 = sample(18:23, N, replace=T), grp=rep(1:grps, each=N/grps))
dat$y <- rbinom(N, prob = plogis(-5 + 0.1*dat$x1 + 0.2*dat$x2 + rnorm(grps)[dat$grp]), size = 1)
failures <- by(dat, list(dat$x1, dat$x2, dat$grp), function(x) sum(x$y==0))
successes <- by(dat, list(dat$x1, dat$x2, dat$grp), function(x) sum(x$y==1))
dat2 <- expand.grid(x1=sort(unique(dat$x1)), x2=sort(unique(dat$x2)), grp=sort(unique(dat$grp)))
dat2$failures <- as.vector(failures)
dat2$successes <- as.vector(successes)
library(lme4)
system.time(glmer(y ~ x1 + x2 + (1 | grp), dat, family=binomial))
#   user  system elapsed 
# 22.918   0.660  24.441
system.time(glmer(cbind(successes, failures) ~ x1 + x2 + (1 | grp), dat2, family=binomial))
#   user  system elapsed 
#  1.833   0.017   1.855 
detach("package:lme4")
library(lme4Eigen)
system.time(glmer(y ~ x1 + x2 + (1 | grp), dat, family=binomial))
#   user  system elapsed 
# 24.824   1.811  26.773 
system.time(glmer(cbind(successes, failures) ~ x1 + x2 + (1 | grp), dat2, family=binomial))
#   user  system elapsed 
#  1.687   0.039   1.723



> Date: Thu, 9 Feb 2012 14:13:24 -0600
> From: Douglas Bates <bates at stat.wisc.edu>
> To: Joshua Wiley <jwiley.psych at gmail.com>
> Cc: AC Del Re <acdelre at stanford.edu>, r-sig-mixed-models at r-project.org
> Subject: Re: [R-sig-ME] LMM with Big data using binary DV
> 
> On Wed, Feb 8, 2012 at 8:28 PM, Joshua Wiley <jwiley.psych at gmail.com> wrote:
>> Hi AC,
>> 
>> My personal preference would be glmer from the lme4 package. ?I prefer
>> the Laplace approximation for the likelihood over the quasilikelihood
>> in glmmPQL. ?To give some exemplary numbers, I simulated a dataset
>> with 2 million observations nested within 200 groups (10,000
>> observations per group). ?I then ran an random intercepts model using:
>> 
>> system.time(m <- glmer(Y ~ X + W + (1 | G), family = "binomial"))
>> 
>> where the matrices/vectors are of sizes: Y = [2 million, 1]; X = [2
>> million, 6]; W = [2 million, 3]; G = [2 million, 1]
>> 
>> This took around 481 seconds to fit on a 1.6ghz dual core laptop.
>> With the OS and R running, my system used ~ 6GB of RAM for the model
>> and went up to ~7GB to show the summary (copies of the data are
>> made---changed in the upcoming version of lme4).
>> 
>> So as long as you have plenty of memory, you should have no trouble
>> modelling your data using glmer(). ?To initially make sure all your
>> code works, I might use a subset of your data (say 10k), once you are
>> convinced you have the model you want, run it on the full data.
> 
> If you would have an opportunity to run that model fit or a comparable
> on lme4Eigen::glmer we would appreciate information about speed,
> accuracy and memory usage.
> 
> In lme4Eigen::glmer there are different levels of precision in the
> approximation to the deviance being optimizer.  These are controlled
> by the nAGQ argument to the function.  The default, nAGQ=1, uses the
> Laplace approximation.  The special value nAGQ=0 also uses the Laplace
> approximation but profiles out the fixed-effects parameters.  This
> profiling is not exact but usually gets you close to the optimum that
> you would get from nAGQ=1, but much, much faster.  In a model like
> this you can also use nAGQ>1 and <= 25.  On the model fits we have
> tried we don't see a lot of difference in timing between, say, nAGQ=9
> and nAGQ=25 but on a model fit like this you might.
> 
> As a fallback, we would appreciate the code that you used to simulate
> the response.  We could generate something ourselves, of course, but
> it is easier to compare when you copy someone else's simulation.
>> On Wed, Feb 8, 2012 at 5:28 PM, AC Del Re <acdelre at stanford.edu> wrote:
>>> Hi,
>>> 
>>> I have a huge dataset (2.5 million patients nested within ?> 100
>>> facilities) and would like to examine variability across facilities in
>>> program utilization (0=n, 1=y; utilization rates are low in general), along
>>> with patient and facility predictors of utilization.
>>> 
>>> I have 3 questions:
>>> 
>>> 1. What program and/or package(s) do you recommend for running LMMs with
>>> big data (even if they are not R packages)?
>>> 
>>> 2. Are there any clever work arounds (e.g., random sampling of subset of
>>> data, etc) that would allow me to use only R packages to run this dataset
>>> (assuming I need to use another program due to the size of the dataset)?
>>> 
>>> 3. What type of LMM is recommended with a binary DV similar to the one I am
>>> wanting to examine? I know of two potential options (family=binomial option
>>> in lmer and the glmmPQL in the MASS package) but am not sure which is more
>>> appropriate or what other R packages and functions are available for this
>>> purpose?
>>> 
>>> Thank you,
>>> 
>>> AC