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



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