[R-sig-ME] lmer model construction

[Thierry Onkelinx]

Dear Jeremy,

Adding a random effect for petridish takes the nested design into account.

P * S * M expands to P + S + M + P:S + P:M + S:M + P:S:M. So it includes
the threeway interaction. I'm not sure if you want that.
P * S + M expands to P + S + M + P:S. Hence the difference with P * S * M
is P:M + P:S:M. So a LRT between P * S * M and P * S + M tests the combined
effect of P:M and P:S:M.

Best regards,

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey

2015-10-06 21:06 GMT+02:00 Jeremy Chacon <chaco001 op umn.edu>:

> 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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>
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