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Cox, Stephen

2005-Dec-05 23:03 UTC

[R] lmer and glmmPQL

I have been looking into both of these approaches to conducting a GLMM,
and want to make sure I understand model specification in each.  In
particular - after looking at Bates' Rnews article and searching through
the help archives, I am unclear on the specification of nested factors
in lmer.  Do the following statements specify the same mode within each
approach?

m1 = glmmPQL(RICH ~ ZONE, family = poisson, data, random = ~ YEAR | SITE
/ QUADRAT)
m2 = lmer(RICH ~ ZONE +(YEAR|SITE)+ (YEAR|QUADRAT), family = poisson,
data)

As a follow up - what would be the most appropriate model formula (using
glmmPQL syntax) to specify both a nested facor and repeated
observations?  Specifically, I am dealing with experimental data with
three factors.  ZONE is a fixed effect.  Three sites (SITE) are nested
within each ZONE.  Multiple quadrats within each SITE are measured
across multiple years.  I want to represent the nesting of SITE within
ZONE and allow for repeated observations within each QUADRAT over time
(the YEAR | QUADRAT random effect).  -- I am assuming that glmmPQL is
the best option at this point because of recent discussion on Rhelp
about issues associated with the Matrix package used in lmer (i.e., the
anova results do not seem to match parameter tests).

Any information would be very much appreciated!

Regards

Stephen

Douglas Bates

2005-Dec-07 14:27 UTC

head link

[R] lmer and glmmPQL

On 12/5/05, Cox, Stephen <stephen.cox at ttu.edu>
wrote:> I have been looking into both of these approaches to conducting a GLMM,
> and want to make sure I understand model specification in each.  In
> particular - after looking at Bates' Rnews article and searching
through
> the help archives, I am unclear on the specification of nested factors
> in lmer.  Do the following statements specify the same mode within each
> approach?
>
> m1 = glmmPQL(RICH ~ ZONE, family = poisson, data, random = ~ YEAR | SITE
> / QUADRAT)
> m2 = lmer(RICH ~ ZONE +(YEAR|SITE)+ (YEAR|QUADRAT), family = poisson,
> data)
If you want to ensure that QUADRAT is nested within SITE then use the
interaction operator explicitly

m2 <- lmer(RICH ~ ZONE +(YEAR|SITE)+ (YEAR|SITE:QUADRAT), family poisson,
data)

For the grouping factors nested versus non-nested depends on the
coding.  If QUADRAT has a distinct level for each SITE:QUADRAT
combination then the nesting will automatically be detected.  However,
if the nesting is implicit (that is, if levels of QUADRAT are repeated
at different SITES) then it is necessary to use the interaction
operator.  There is no harm in using the interaction operator when the
nesting is explicit.>
> As a follow up - what would be the most appropriate model formula (using
> glmmPQL syntax) to specify both a nested facor and repeated
> observations?  Specifically, I am dealing with experimental data with
> three factors.  ZONE is a fixed effect.  Three sites (SITE) are nested
> within each ZONE.  Multiple quadrats within each SITE are measured
> across multiple years.  I want to represent the nesting of SITE within
> ZONE and allow for repeated observations within each QUADRAT over time
> (the YEAR | QUADRAT random effect).  -- I am assuming that glmmPQL is
> the best option at this point because of recent discussion on Rhelp
> about issues associated with the Matrix package used in lmer (i.e., the
> anova results do not seem to match parameter tests).
>
I believe the anova problems only occur with a binomial response. 
They are caused by my failure to use the prior.weights appropriately. 
For a Poisson model this should not be a problem.
> Any information would be very much appreciated!
>
> Regards
>
> Stephen
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html
>

Cox, Stephen

2005-Dec-07 15:16 UTC

head link

[R] lmer and glmmPQL

Thanks for the reply Doug!

A follow up question and comment ...

1) If I understand correctly, looking at a simple situation in which
SITES are nested in ZONES, the following should be similar.  However,
despite the same F values, the p-value from lmer is 1/2 the other
methods.  Why is this true?
> anova(lmer(RICH ~ ZONE + (1|SITE:ZONE), data))Analysis of Variance Table
     Df Sum Sq Mean Sq  Denom F value  Pr(>F)  
ZONE  4   97.8    24.5 6610.0  2.1046 0.07753 .
> # make the nesting explicit
> data$SinZ = with(data, ZONE:SITE)[drop=TRUE]
> anova(lme(RICH ~ ZONE, data, random = ~1 | SinZ))            numDF denDF   F-value p-value
(Intercept)     1  6600 100.38331  <.0001
ZONE            4    10   2.10459   0.155
> summary(aov(RICH ~ ZONE + Error(SITE:ZONE), data))
Error: SITE:ZONE
          Df Sum Sq Mean Sq F value Pr(>F)
ZONE       4  29669    7417  2.1046  0.155
Residuals 10  35243    3524   


2) I think the anova problems with lmer may also apply to poisson.
Compare the following (which includes a covariate).  Based on the
parameter estimates, the covariate should be significant.  However, its
anova p-value is .998:
> lmer(RICH ~ ZONE + lANPP + (1|SITE:ZONE), family = poisson, data)Generalized linear mixed model fit using PQL 
Formula: RICH ~ ZONE + lANPP + (1 | SITE:ZONE) 
   Data: data 
 Family: poisson(log link)
      AIC      BIC    logLik deviance
 9700.252 9754.628 -4842.126 9684.252
Random effects:
     Groups        Name    Variance    Std.Dev. 
  SITE:ZONE (Intercept)    0.069493     0.26361 
# of obs: 6615, groups: SITE:ZONE, 15

Estimated scale (compare to 1)  1.183970 

Fixed effects:
              Estimate Std. Error z value Pr(>|z|)    
(Intercept)  1.5169605  0.1533564  9.8917  < 2e-16 ***
ZONE2        0.4034169  0.2156956  1.8703  0.06144 .  
ZONE3       -0.1772011  0.2158736 -0.8209  0.41173    
ZONE4       -0.2368290  0.2158431 -1.0972  0.27254    
ZONE5       -0.1011186  0.2158114 -0.4686  0.63939    
lANPP        0.2201926  0.0081857 26.8995  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
'.' 0.1 ' ' 1
> anova(lmer(RICH ~ ZONE + lANPP + (1|SITE:ZONE), family = poisson,data))
Analysis of Variance Table
      Df    Sum Sq   Mean Sq Denom   F value Pr(>F)
ZONE   4 2.809e-05 7.022e-06  6609 4.298e-06 1.0000
lANPP  1 5.229e-06 5.229e-06  6609 3.200e-06 0.9986

Thanks again for any insight you may be able to provide!!



 
> -----Original Message-----
> From: Douglas Bates [mailto:dmbates at gmail.com] 
> Sent: Wednesday, December 07, 2005 8:28 AM
> To: Cox, Stephen
> Cc: r-help at stat.math.ethz.ch
> Subject: Re: [R] lmer and glmmPQL
> 
> On 12/5/05, Cox, Stephen <stephen.cox at ttu.edu> wrote:
> > I have been looking into both of these approaches to conducting a 
> > GLMM, and want to make sure I understand model 
> specification in each.  
> > In particular - after looking at Bates' Rnews article and
searching
> > through the help archives, I am unclear on the 
> specification of nested 
> > factors in lmer.  Do the following statements specify the same mode 
> > within each approach?
> >
> > m1 = glmmPQL(RICH ~ ZONE, family = poisson, data, random = ~ YEAR | 
> > SITE / QUADRAT)
> > m2 = lmer(RICH ~ ZONE +(YEAR|SITE)+ (YEAR|QUADRAT), family 
> = poisson,
> > data)
> 
> If you want to ensure that QUADRAT is nested within SITE then 
> use the interaction operator explicitly
> 
> m2 <- lmer(RICH ~ ZONE +(YEAR|SITE)+ (YEAR|SITE:QUADRAT), 
> family = poisson, data)
> 
> For the grouping factors nested versus non-nested depends on 
> the coding.  If QUADRAT has a distinct level for each 
> SITE:QUADRAT combination then the nesting will automatically 
> be detected.  However, if the nesting is implicit (that is, 
> if levels of QUADRAT are repeated at different SITES) then it 
> is necessary to use the interaction operator.  There is no 
> harm in using the interaction operator when the nesting is explicit.
> >
> > As a follow up - what would be the most appropriate model formula 
> > (using glmmPQL syntax) to specify both a nested facor and repeated 
> > observations?  Specifically, I am dealing with experimental 
> data with 
> > three factors.  ZONE is a fixed effect.  Three sites (SITE) 
> are nested 
> > within each ZONE.  Multiple quadrats within each SITE are measured 
> > across multiple years.  I want to represent the nesting of 
> SITE within 
> > ZONE and allow for repeated observations within each 
> QUADRAT over time 
> > (the YEAR | QUADRAT random effect).  -- I am assuming that 
> glmmPQL is 
> > the best option at this point because of recent discussion on Rhelp 
> > about issues associated with the Matrix package used in lmer (i.e., 
> > the anova results do not seem to match parameter tests).
> >
> 
> I believe the anova problems only occur with a binomial response. 
> They are caused by my failure to use the prior.weights appropriately. 
> For a Poisson model this should not be a problem.
> 
> > Any information would be very much appreciated!
> >
> > Regards
> >
> > Stephen
> >
> > ______________________________________________
> > R-help at stat.math.ethz.ch mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide! 
> > http://www.R-project.org/posting-guide.html
> >
> 
>

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