[R-sig-ME] Ordered logistic regression with random effects (clmm2)

[Ronny Steen]

Dear all,


I try to do a ordered logistic regression with random effects. I have tried
clmm2 from package 'ordinal'  and manage to run the test, but can not
figure out how to get det predictions and confidence intervals.


We have a small "cafeteria experiment" to check if a bird has dietary
preferences, indicated by free-choice feeding from boxes with food of
different qualities.


More details about the setup:

We have offered Jays three choices of acorns (ordered quality) to see if
they have preferences. Unfortunately we do not have control of their
identity, but we have monitored 5 different places (which is included as
random effect). In the experiment we have video recorded behaviour and
we offered the Jays with 3 boxes with acorns (one box with 5 *intact *acorns,
one with 5 acorns with *holes* and one with 5 *damaged* acorns).  Hence
intact acorns is of highest quality, below is acorns with holes ("infected"
by insect larvae) and lowest is damaged acorns (eaten at by a rodent). Our
hypothesis is that the Jay should prefer the intact acorns since they will
last longer for storage.


The data:


> head(Jay)
  State  Choice Place Intact_count Hole_count Damaged_count
1     0 Damaged    B1            5          5             2
2     0 Damaged    B1            5          5             1
3     2  Intact    B1            5          5             0
4     2  Intact    B1            4          5             0
5     2  Intact    B1            3          5             0
6     2  Intact    B1            2          5             0

> str(Jay)
'data.frame': 318 obs. of  6 variables:
 $ State        : Ord.factor w/ 3 levels "0"<"1"<"2": 1 1 3 3 3 3 3 2 2 2
...
 $ Choice       : Factor w/ 3 levels "Damaged","Holes",..: 1 1 3 3 3 3 3 2
2 2 ...
 $ Place        : Factor w/ 5 levels "B1","E1","E2",..: 1 1 1 1 1 1 1 1 1 1
...
 $ Intact_count : int  5 5 5 4 3 2 1 0 0 0 ...
 $ Hole_count   : int  5 5 5 5 5 5 5 5 4 3 ...
 $ Damaged_count: int  2 1 0 0 0 0 0 0 0 0 ...

State is the ordered Choice (Damaged = 0, Hole = 1 and Intact = 2), Place
is the random effect.  Intact_count, Hole_count and Damaged_count is
numeric and gives the information about how many acorns that are in each
box. At the beginning of the day it was 5 acorns in each box, and less as
the Jay collected acorns.


The best model seems to be:
fm3 <- clmm2(State~ Intact_count*Hole_count, random=Place, data=Jay,
             Hess=TRUE, nAGQ=10)


> (fm3)
Cumulative Link Mixed Model fitted with the adaptive Gauss-Hermite
quadrature approximation with 10 quadrature points

Call:
clmm2(location = State ~ Intact_count * Hole_count, random = Place,
    data = Jay, Hess = TRUE, nAGQ = 10)

Random effects:
               Var      Std.Dev
Place 9.486096e-09 9.739659e-05

Location coefficients:
           Intact_count              Hole_count Intact_count:Hole_count
              1.6015787               0.8237153              -0.3237785

No Scale coefficients

Threshold coefficients:
     0|1      1|2
1.458473 3.826715

log-likelihood: -258.4659
AIC: 528.9318


I would like to get predicted probabilities with confidence intervals. What
is the probability of choosing a intact vs. holes vs. damaged. How does
this vary with Intact_count, Hole_count (e.g. Intact_count = 1, 3 or 5,
Hole_count = 1, 3, 5)?


Best regards,

Ron

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