[R-sig-ME] Nested Random Effects Model using lme4/lmer

[Gustaf Granath]

Hi,
A late reply.

m2 is working because you estimate two variances, one for crop species 
and one for wild. Dont know the experimental set up here but if within 
species variation is not interesting, you may as well average over 
species (mean of the 6(?) replicates) to keep it simple. As you may have 
noticed, the fixed effect estimate will not change. Regarding 
pseudo-replication. This is important for the calculations of DFs. So if 
you use nlme or intend to use t/F-test, you have to make sure that they 
are correct ( F1,30 I guess).

Gustaf

-- 
Gustaf Granath (PhD)
Post doc
McMaster University


> Dear R-sig-mixed-models list,
> I am new to using lmer and was hoping someone could comment on whether the model I am using is properly coded to address my questions and also to answer a specific question about random nested interactions.
> Main questions:  1) Do crops differ in height compared to wild species and 2) is the effect of domestication consistent across different domestication events.
> Data:
> Six individual plants were measured per plant species. Half of the 62 species are crops and the other half are wild plants.
> Each crop species is paired with a close wild relative (PAIR) and thus I have 31 independent domestication events.
>
> Setup:
> - DOMESTICATION as a fixed effect (crop or wild)
> - PAIR as a random effect, I want to know the general consistency of domestication and not the patterns in each pair specifically
> - I need a DOMESTICATION by PAIR interaction term (which would be random) to see if domestication effects change with PAIR
> - I need to avoid pseudo replication and thus I nested SPECIES within PAIR
>
> Mathematical model:
> Height = global mean+ domestication + pair[random] + domestication*pair[random] + species(pair)[random]  + residual error
>
> Working LMER Model??
> m1<- lmer( HEIGHT~ DOMESTICATION + (1  |  PAIR : SPECIES) + (DOMESTICATION | PAIR), data=X1, na.action=na.omit)
>
> I included the term  (1  |  PAIR : SPECIES) to avoid the problem I was having with a previous model (see m2 below).
> Does this model make sense given my design and questions? Have I properly avoided pseudo replication?
>
> Linear mixed model fit by REML
> Formula: HEIGHT ~ DOMESTICATION + (1 | PAIR:SPECIES) + (DOMESTICATION |      PAIR)
>     Data: X1
>    AIC  BIC logLik deviance REMLdev
>   2481 2508  -1233     2472    2467
> Random effects:
>   Groups       Name                     Variance Std.Dev.  Corr
>   PAIR:SPECIES (Intercept)              28.769   5.3637
>   PAIR         (Intercept)              86.789   9.3161
>                DOMESTICATIONWild  13.586   3.6859   0.317
>   Residual                              26.240   5.1225
> Number of obs: 374, groups: PAIR:SPECIES, 62; PAIR, 31
>
> Fixed effects:
>                          Estimate Std. Error t value
> (Intercept)               20.351      1.967  10.346
> DOMESTICATIONWild    1.388      1.605   0.865
>
> Correlation of Fixed Effects:
>              (Intr)
> DOMESTICATI -0.228
>
>
> Problematic LMER model :
> m2<- lmer( HEIGHT~ DOMESTICATION + (DOMESTICATION | PAIR / SPECIES), data=X1, na.action=na.omit)
>
> This is the first model I tried. It has all the effects I want but includes a random effect of SPECIES (nested within PAIR) on the slope (DOMESTICATION) (underlined in output below). I do not understand how this can work given that the data for any given SPECIES is only a single level of DOMESTICATION (all crop or all wild). Am I missing something? Is the m2 approach better than the m1? If so why?
>
> Linear mixed model fit by REML
> Formula: HEIGHT ~ DOMESTICATION + (DOMESTICATION | PAIR/SPECIES)
>     Data: X1
>    AIC  BIC logLik deviance REMLdev
>   2485 2520  -1233     2472    2467
> Random effects:
>   Groups       Name                     Variance Std.Dev.  Corr
>   SPECIES:PAIR (Intercept)              29.923   5.4702
>                DOMESTICATIONWild 19.646   4.4323    -0.381
>   PAIR         (Intercept)              85.633   9.2538
>                DOMESTICATIONWild  10.092   3.1768    0.410
>   Residual                              26.240   5.1225
> Number of obs: 374, groups: SPECIES:PAIR, 62; PAIR, 31
>
> Fixed effects:
>                          Estimate Std. Error t value
> (Intercept)               20.351      1.967  10.346
> DOMESTICATIONWild   1.388      1.605   0.865
>
> Correlation of Fixed Effects:
>              (Intr)
> DOMESTICATI -0.228
>
> thanks for your help
>
> Mart
>
>
> Martin Turcotte, Ph. D.
> Dept. of Biology
> University of Toronto at Mississauga
> 3359 Mississauga Road North, Mississauga,
> Ontario, Canada, L5L 1C6
>
> http://individual.utoronto.ca/martinturcotte