lmer model construction

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]]

-- 

*___________________________________________________________________________Jeremy
M. Chacon, Ph.D.*

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

	[[alternative HTML version deleted]]