[R-sig-ME] lmer model construction

[Jeremy Chacon]

Hello all,

I would appreciate any advice on how to construct and analyze my model.

I have conducted a study where I put bacterial colonies onto petri dishes.
The colonies were randomly spread across the petri dishes, and the number
of colonies varied slightly across each petri dish. Some petri dishes
received one bacterial species, some petri dishes received another species.
Additionally, half of the petri dishes contained one type of growth media,
and the other half contained a different media.

So my experimental design is basically a two-factor design:

2 levels of species X 2 levels of media.

The design is balanced.

The complicated part is that my response of interest is how the proximity
of one bacterial colony to its neighbors affects the size of the bacterial
colony, and importantly, how this relationship is affected by the bacterial
species, growth media, and their interaction.

In other words, I have a nested design where my measurements of interest
(bacterial colonies) are nested with the truly independent replicates
(petri dishes), which is why I intend to use a mixed model.

So the data look like this:

results =

species    media    colonySize    proximityToNeighbor    petriDishID
  A        A        12            4                      1
  A        A        38            42                     1
  A        B        18            50                     2

etc, with one observation per colony, and typically about 100 colonies per
petri dish.

I am trying to correctly construct the model using lme4. I would appreciate
suggestion on my model. Also, I would appreciate suggestions on
interpretations.

My current thought: use a random intercept for each petri dish:

m1 = lmer(colonySize ~ proximityToNeighbor * species * media + (1 |
petriDishID), data = results)

but this does not describe the nesting of each colony within a petri dish
(at least as far as I understand). Do I need to do this?

In terms of interpretation, I have been (1) looking at plots to get a feel
for effect size and then (2) getting significance values by doing a
predictor removal model comparison, like below:

m1 = lmer(colonySize ~ proximityToNeighbor * species * media + (1 |
petriDishID), data = results)

m2 = lmer(colonySize ~ proximityToNeighbor * species + media + (1 |
petriDishID), data = results)

anova(m1, m2, test = "F")


When I do this, I get a tiny p-value, which (along with plots) suggests to
me that the interaction between species and media in their effect on
proximityToNeighbor's effect on colonySize is important. Does this sound
correct? Any better ways to do this?

Thanks very much!

Jeremy


-- 

*___________________________________________________________________________Jeremy
M. Chacon, Ph.D.*

*Post-Doctoral Associate, Harcombe Lab*
*University of Minnesota*
*Ecology, Evolution and Behavior*

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