[R-sig-ME] lmer model construction

[Jeremy Chacon]

Dear Thierry,

Thanks for your help. You are correct, my LRT was incorrectly dropping more
than one term--I've fixed that now.  And good to hear I setup the nested
part of the model correctly.

My more general question is how do I know whether terms such as main
effects are important? I understand there is disagreement about whether to
assign p-values to terms in a mixed model due to the degrees of freedom not
being fully known, but I would still like some measure of how important a
term is.

Is a good way to keep doing likelihood-ratio tests all the way down to a
single-intercept model? Or is there another, perhaps better way to
interpret importance in the results of a mixed model?

Thanks again,

Jeremy

On Wed, Oct 7, 2015 at 5:10 AM, Thierry Onkelinx <thierry.onkelinx at inbo.be>
wrote:

> 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 at 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*
>>
>>         [[alternative HTML version deleted]]
>>
>> _______________________________________________
>> R-sig-mixed-models at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>
>
>


-- 

*___________________________________________________________________________Jeremy
M. Chacon, Ph.D.*

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

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