[R-sig-ME] lmer model construction

Wed Oct 7 16:08:06 CEST 2015

I guess the first step is to try to decide on some reasonably precise definition of what it means for a variable to be "important." I think this is a fundamental problem plaguing most discussions of "variable importance." Are you just talking about getting an indication of the strength of association between a predictor and the response variable--like an effect size? In that case I would recommend just looking at and interpreting the slope and its standard error and using your scientific judgment. Standardized effect size is kind of a fraught issue in linear mixed models.

Jake

> Date: Wed, 7 Oct 2015 08:55:18 -0500
> From: chaco001 at umn.edu
> To: thierry.onkelinx at inbo.be
> CC: r-sig-mixed-models at r-project.org
> Subject: Re: [R-sig-ME] lmer model construction
> 
> 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*
> 
> 	[[alternative HTML version deleted]]
> 
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

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