Skip to content

Specifying random effects for multiple covariates via lmer

11 messages · Andy Bush, Douglas Bates, Bush, Andrew J +4 more

Original
Douglas Bates
#
On 9/5/07, Andy Bush <ajbush at bellsouth.net> wrote:
Maybe I am missing the point but wouldn't the model you are
considering be written as

lmer(LFEV1 ~ Age + loght + InitAge + logbht + (loght + Age|id), data =
fev, na.action = na.omit, method = "REML")

That provides correlated random effects for the intercept, the
coefficient for loght and the coefficient for Age at each level of the
id factor.
Andy Bush
# 
Thank you for taking the time to try to help me, Douglas. I had already
formulated the suggested model as model m3 shown below.  Please note that id
is defined as "ordered" and all other variables are defined as "numeric".
Here are the models I've tried:

m1=lmer(LFEV1~Age+loght+InitAge+logbht+(1+Age|id),data=fev,
       na.action=na.omit,
       method="REML")
m2=lmer(LFEV1~Age+loght+InitAge+logbht+
       (1+loght|id),data=fev,
       na.action=na.omit,
       method="REML")
m3=lmer(LFEV1~Age+loght+InitAge+logbht+
       (Age+loght|id),
       data=fev,
       na.action=na.omit,
       method="REML")

lmer handles models m1 and m2 with no difficulty (and the results agree
quite closely with SAS Proc Mixed returns). However, lmer generates the
following warning messages for m3 and lead me to wonder if I'd mispecified
the model:

1: Estimated variance-covariance for factor 'id' is singular
 in: `LMEoptimize<-`(`*tmp*`, value = list(maxIter = 200L, tolerance =
1.49011611938477e-08,  
2: nlminb returned message false convergence (8)
 in: `LMEoptimize<-`(`*tmp*`, value = list(maxIter = 200L, tolerance =
1.49011611938477e-08,  

Please note that when I run this model through SAS Proc Mixed, I get quite
different results for the random effects without apparent convergence
problems.

Following is the lmer summary of random effects for m3:

Linear mixed-effects model fit by REML 
Formula: LFEV1 ~ Age + loght + InitAge + logbht + (Age + loght | id) 
   Data: fev 
   AIC   BIC logLik MLdeviance REMLdeviance
 -4511 -4449   2266      -4570        -4533
Random effects:
 Groups   Name Variance   Std.Dev.  Corr        
 id            3.1748e-03 0.0563455             
               7.4210e-06 0.0027241 0.064       
               9.4341e-03 0.0971292 0.064 1.000 
 Residual      3.9789e-03 0.0630788             
number of obs: 1993, groups: id, 299

In retrospect, I wonder if I should attempt to add an override for default
convergence control values in lmer for m3. 

I'll be glad to email you the dataset and programs directly if you'd like.

Respectfully,
Andy

-----Original Message-----
From: dmbates at gmail.com [mailto:dmbates at gmail.com] On Behalf Of Douglas
Bates
Sent: Wednesday, September 05, 2007 9:22 PM
To: ajbush at bellsouth.net
Cc: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] Specifying random effects for multiple covariates
via lmer
On 9/5/07, Andy Bush <ajbush at bellsouth.net> wrote:
separately:
Maybe I am missing the point but wouldn't the model you are
considering be written as

lmer(LFEV1 ~ Age + loght + InitAge + logbht + (loght + Age|id), data =
fev, na.action = na.omit, method = "REML")

That provides correlated random effects for the intercept, the
coefficient for loght and the coefficient for Age at each level of the
id factor.
Douglas Bates
#
On 9/6/07, Andy Bush <ajbush at bellsouth.net> wrote:
Thanks for checking further on this.  I would appreciate it if you
could email the data.  One  way to do this so that it retains all the
attributes is to create an R Data save file

save(fev, file = "fev.rda")

and email that file.  The representation in such a file is independent
of the hardware and operating system.

By the way, when you get such results it is a good idea to rerun the
model fitting process with the "verbose" option set.  In the currently
released version of the lme4 package this is done with the rather
wordy argument specification

control = list(msVerbose = 1)

In the development version of the lme4 package this specification
still works or it can be shortened to

verbose = 1
Notice that one of the correlations is effectively 1.00.  This
indicates a singular variance-covariance matrix for the random
effects.  The maximum likelihood estimates or the REML estimates can
correspond to a singular matrix.  In this case none of the variances
are zero, it is a variance of a linear combination of the random
effects that has been driven to zero.   SAS PROC MIXED doesn't handle
this situation well.
Typically that doesn't improve the situation.  If the REML estimates
are singular no amount of tweaking of the optimization procedure will
improve the situation.
I appreciate the offer and look forward to examining the data and models.
Bush, Andrew J
# 
Dear Douglas,

In frustration, I invoked lmer2 this morning and I'm pleased to be able
to tell you that lmer2 copes well and quickly with the model having a
random intercept and two random covariate slopes.  I have not been able
to get lmer to converge for the model on the same data.

Andy

-----Original Message-----
From: dmbates at gmail.com [mailto:dmbates at gmail.com] On Behalf Of Douglas
Bates
Sent: Wednesday, September 05, 2007 9:22 PM
To: ajbush at bellsouth.net
Cc: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] Specifying random effects for multiple
covariates via lmer
On 9/5/07, Andy Bush <ajbush at bellsouth.net> wrote:
(pp
(1)
and
difficulty
for
try to
separately:
id),data=fev,
id),data=fev,
Maybe I am missing the point but wouldn't the model you are
considering be written as

lmer(LFEV1 ~ Age + loght + InitAge + logbht + (loght + Age|id), data =
fev, na.action = na.omit, method = "REML")

That provides correlated random effects for the intercept, the
coefficient for loght and the coefficient for Age at each level of the
id factor.
Douglas Bates
#
On 9/6/07, Bush, Andrew J <abush at utmem.edu> wrote:
Thanks for the information.

I expect to remove the confusion between lmer and lmer2 in the near
future.  The development version of the lme4 package has an lmer
function that is close to the current lmer2 in design.  It should
exhibit the same convergence behavior and be slightly faster on models
fit to large data sets than is the current lmer2.

This version has been in development for longer than I had expected.
I still have a few "infelicities" to resolve in the Laplace method for
generalized linear mixed models before I make test versions available.

I would be interested in the data set if you would be willing to
provide it.  I could perhaps incorporate it in the lme4 package so
others would have access to it.
5 days later
Martin Maechler
# 

        
DB> On 9/6/07, Bush, Andrew J <abush at utmem.edu> wrote:

        
>> Dear Douglas,

    >> In frustration, I invoked lmer2 this morning and I'm pleased to be able
    >> to tell you that lmer2 copes well and quickly with the model having a
    >> random intercept and two random covariate slopes.  I have not been able
    >> to get lmer to converge for the model on the same data.

    DB> Thanks for the information.

    DB> I expect to remove the confusion between lmer and lmer2 in the near
    DB> future.  The development version of the lme4 package has an lmer
    DB> function that is close to the current lmer2 in design.  It should
    DB> exhibit the same convergence behavior and be slightly faster on models
    DB> fit to large data sets than is the current lmer2.

    DB> This version has been in development for longer than I had expected.
    DB> I still have a few "infelicities" to resolve in the Laplace method for
    DB> generalized linear mixed models before I make test versions available.

    DB> I would be interested in the data set if you would be willing to
    DB> provide it.  I could perhaps incorporate it in the lme4 package so
    DB> others would have access to it.

Yes, indeed.  
The example might be particularly interesting as test case, not
only because some software implementations "converge" with
singular covariance matrix, but also because it
differs from other examples in having "many" fixed effects and
just one level random effects.

Martin

    >> -----Original Message-----
    >> From: dmbates at gmail.com [mailto:dmbates at gmail.com] On Behalf Of Douglas
    >> Bates
    >> Sent: Wednesday, September 05, 2007 9:22 PM
    >> To: ajbush at bellsouth.net
    >> Cc: r-sig-mixed-models at r-project.org
    >> Subject: Re: [R-sig-ME] Specifying random effects for multiple
    >> covariates via lmer
    >>

        
>> On 9/5/07, Andy Bush <ajbush at bellsouth.net> wrote:

        
>> > While working through the text "Applied Longitudinal Analysis" by
    >> > Fitzmaurice, Laird and Ware, I encountered a fairly simple case study
    >> (pp
    >> > 210-7) in which a longitudinal model specifies three random effects:
    >> (1)
    >> > random intercepts for id, (2) random slopes for covariate1 (Age | id),
    >> and
    >> > (3) random slopes for covariate2 (log(ht) | id).  I've had no
    >> difficulty
    >> > formulating lmer models with correlated random intercepts and slopes
    >> for
    >> > either of the covariates individually but have not succeeded when I
    >> try to
    >> > compose a model with correlated random intercepts and slopes for two
    >> > covariates.
    >> 
    >> > Following is code that works well with the individual covariates
    >> separately:
    >> 
    >> > m1=lmer(LFEV1~Age + loght + InitAge + logbht + (1 + Age |
    >> id),data=fev,
    >> >        na.action=na.omit, method="REML")
    >> 
    >> > m2=lmer(LFEV1~Age + loght + InitAge + logbht+(1 + loght |
    >> id),data=fev,
    >> >        na.action=na.omit, method="REML")
    >> 
    >> Maybe I am missing the point but wouldn't the model you are
    >> considering be written as
    >> 
    >> lmer(LFEV1 ~ Age + loght + InitAge + logbht + (loght + Age|id), data =
    >> fev, na.action = na.omit, method = "REML")
    >> 
    >> That provides correlated random effects for the intercept, the
    >> coefficient for loght and the coefficient for Age at each level of the
    >> id factor.
    >> 

    DB> _______________________________________________
    DB> R-sig-mixed-models at r-project.org mailing list
    DB> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

  
  


  


      

    

    

      
      

        


  

        

      Henric Nilsson (Public)
    

    

      
      #
    

  


  

      
Quoting Martin Maechler <maechler at stat.math.ethz.ch>:

            

      
      
      
    

        
The data set in question, and, I belive, most others from Fitzmaurice,  
Laird and Ware's (2004) book on longitudinal data analysis, is  
available along with accompanying SAS programs at

http://biosun1.harvard.edu/~fitzmaur/ala/

In particular, the data used above is here

http://biosun1.harvard.edu/~fitzmaur/ala/fev1.txt

and the SAS code is here

http://biosun1.harvard.edu/~fitzmaur/ala/prog8_8.html


HTH,
Henric

            

      
      
      
    

        

      
      
    

  
  


  


      

    

    

      
      

        
      

    

    

      
      

        
      

    

    

      
      

        


  

        

      Andrew Robinson
    

    

      
      #
    

  


  

      
On Thu, Sep 13, 2007 at 09:51:17AM +0200, Henric Nilsson (Private) wrote:

            

      
      
      
    

        
Which, I would like to add is a great book.  As part of a review for
Statistics in Medicine I asked Fitzmaurice to count the occurrences of
"For example," and "In other words," ... it was 300 and 400 times,
respectively.

I heartily recommend it as an introductory text to the area.

Andrew