random effect variance per treatment group in lmer

 
Simon, Andrew:

Thanks for the replies.
I am not interested in stratifying the variance of the innermost
residuals,
but rather the variance of the random effects, viz., b_ij (drug i,
patient j) 
is a random variable w/ variance depending on i.  

Possible solution suggested offline for previously supplied pseudo data:

fm.cov =  lmer(z ~ drug + time + (drug|Patient), data = dat.new ) 
OR,
fm.no.cov  =  lmer(z ~ drug + time + (0 + drug|Patient), data = dat.new
) 

Formally, consider:

Case 1:
Y_ijk = mu + alpha_i + b_ij + theta_k + espilon_ijk 
alpha = fixed effect for group, theta = fixed effect for time, 
b = random effect per patient; b_ij ~ N(0, tau_i)  ## variance of random
effect depends on treatment

Case 2: 
Y_ijk = mu + alpha_i + Indicator_treat_i * b_treatment_ij + 
		Indicator_placebo_i * b_placebo_ij + theta_k +
espilon_ijk

Indicator_treat_i = 1 if i is in treatment group, 0 otherwise 
Indicator_placebo_i = 1 if i is in placebo group, 0 otherwise

where b_treatment_ij and b_placebo_ij are different random effects
terms, with
different variances; only one will apply per patient equation as per the
indicator 
variables.  The cumbersome notation allows for a covariance since we now
have "two" random effects. (although it seem nonsensical to want such a 
covariance)

Does fm.no.cov estimates Case 1 model and fm.cov estimates Case 2 model?

Cheers,
Dave








-----Original Message-----
From: Simon Blomberg [mailto:s.blomberg1 at uq.edu.au] 
Sent: Wednesday, July 11, 2007 1:58 AM
To: Andrew Robinson
Cc: Afshartous, David; r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] random effect variance per treatment group in
lmer

I think he is asking to stratify the variance of the innermost
residuals, or at least it's not clear. In lme that can be accomplished
with weights=varFixed(~1|Patient).

To stratify at different levels of nesting, say the data is this:
 dat <- data.frame(inner=rep(1:10, each=5), outer=rep(1:2, each=25),
x=rnorm(50))

Then this call to lme does the job:

 fit <- lme(x ~ 1, random=list(outer=~1, inner=~1), data=dat,
weights=varComb(varIdent(form=~1|outer), varIdent(form=~1|inner)))

edited output:

Combination of variance functions: 
 Structure: Different standard deviations per stratum
 Formula: ~1 | outer
 Parameter estimates:
        1         2 
1.0000000 0.5170794
 Structure: Different standard deviations per stratum
 Formula: ~1 | inner
 Parameter estimates:
        1         2         3         4         5         6         7
8
1.0000000 0.3127693 0.4475444 0.7323698 0.3647991 0.5962917 1.4127508
1.7664527 
        9        10 
0.9475334 0.3666155 

Cheers,

Simon.

weights=varOn Wed, 2007-07-11 at 15:04 +1000, Andrew Robinson wrote:

Hi David,

as far as I am aware, there is no option for stratifying the variance 
of random effects in either lme or lmer.  One can stratify the 
variance of the innermost residuals in lme, but that is different than

what you are asking for.

Cheers,

Andrew


On Tue, Jul 10, 2007 at 10:23:21AM -0400, Afshartous, David wrote:

All,
I didn't receive a response to the query below sent to the general 
R-help mailing list so figured I'd try this mailing list.  Apologies

in advance if this is an overly simplistic question for this list; I

just started w/ lmer after not using lme for awhile.
Cheers,
Dave

for

the intercept has a different variance per treatment group?  
Thus, in the model equation, we'd have say b_ij represent the random

effect for patient j in treatment group i, with variance depending 
on i, i.e,
var(b_ij) = tau_i.
 
Didn't see this in the docs or Pinherio & Bates (section 5.2 is 
specific for modelling within group errors).  Sample repeated 
measures code below is for a single random effect variance, where 
the random effect corresponds to patient.
cheers,
dave
 
 
z <- rnorm(24, mean=0, sd=1)
time <- factor(paste("Time-", rep(1:6, 4), sep="")) Patient <- 
rep(1:4, each = 6) drug <- factor(rep(c("D", "P"), each = 6, times =

2)) ## P = placebo, D = Drug dat.new <- data.frame(time, drug, z, 
Patient) fm =  lmer(z ~ drug + time + (1 | Patient), data = dat.new 
)

--
Simon Blomberg, BSc (Hons), PhD, MAppStat. 
Lecturer and Consultant Statistician
Faculty of Biological and Chemical Sciences The University of Queensland
St. Lucia Queensland 4072 Australia Room 320 Goddard Building (8)
T: +61 7 3365 2506
email: S.Blomberg1_at_uq.edu.au

Policies:
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2.  Your deadline is your problem.

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