MuMIn package, Inquiry on summary output _ Conditional or Full average models?

Dear Laura,

Grueber et al. (2011) discusses the distinctions and the rationale for
making this choice (p 705-706), citing Burnham & Anderson (2002) and
Nakagawa and Freckleton (2011).


Burnham KP, and DR Anderson (2002). Model Selection and Multimodel
Inference: a Practical Information-Theoretic Approach. 2nd edition.
Springer, New York.

Grueber CE, S Nakagawa, RJ Laws, and IG Jamieson (2011). Multimodel
inference in ecology and evolution: challenges and solutions. Journal of
Evolutionary Biology 24:699-711.

Nakagawa S, and RP Freckleton (2011). Model averaging, missing data and
multiple imputation: a case study for behavioural ecology. Behavioral
Ecology and Sociobiology 65:103-116.





On 2/14/2016 10:02 AM, Laura Riggi wrote:

Dear all,

I have a question regarding the output for model averaging in R with
MuMin package. In the summary for model averaging two models of coefficient
calculations come out: the "full average" and the "conditional (or subset)
average" model (example of output below).

As explained on the MuMin package pdf:
"The 'subset' (or 'conditional') average only averages over the models
where the parameter appears. An alternative, the 'full' average assumes
that a variable is included in every model, but in some models the
corresponding coefficient (and its respective variance) is set to zero.
Unlike the 'subset average', it does not have a tendency of biasing the
value away from zero. The 'full' average is a type of shrinkage estimator
and for variables with a weak relationship to the response they are smaller
than 'subset' estimators."

However, I cannot find information online concerning the theory behind
these different outputs. I am not sure what is the point of having a
"conditional" model as it seems to go against the idea of doing a model
averaging analysis.
Do you know of articles / books that discuss this? When should we use one
or the other?
Any advice would be appreciated.

summary(model.avg(dd, subset = delta < 2))

Call:
model.avg.model.selection(object = dd, subset = delta < 2)

Component model call:
lme.formula(fixed = log(Parasitoi_S1.S2 + 1) ~ <8 unique rhs>, data =
data, random = ~1 | Field.x/Site.x, method
      = ML, na.action = na.fail)

Component models:
       df  logLik   AICc delta weight
1345   8 -161.74 340.52  0.00   0.22
345    7 -162.97 340.74  0.22   0.19
12345  9 -161.26 341.82  1.31   0.11
13456  9 -161.36 342.03  1.51   0.10
2345   8 -162.53 342.10  1.58   0.10
3456   8 -162.54 342.11  1.60   0.10
35     6 -164.76 342.12  1.60   0.10
145    7 -163.84 342.47  1.96   0.08

Term codes:
                    L         OSR2012_X500         OSR2013_X500
 Weed.cover            Wood_X500 Weed.cover:Wood_X500
                    1                    2                    3
          4                    5                    6

Model-averaged coefficients:
(full average)
                        Estimate Std. Error Adjusted SE z value Pr(>|z|)
(Intercept)           2.5693356  0.5295081   0.5337822   4.813  1.5e-06
***
L                    -0.0005893  0.0007720   0.0007756   0.760    0.447
OSR2013_X500         -3.7932641  2.1558940   2.3307509   1.627    0.104
Weed.cover            0.1331237  0.0915813   0.0922877   1.442    0.149
Wood_X500            -5.5516524  3.2502461   3.5300659   1.573    0.116
OSR2012_X500          0.4326628  1.3007077   1.3966718   0.310    0.757
Weed.cover:Wood_X500  0.1922066  0.6215019   0.6255589   0.307    0.759

(conditional average)
                        Estimate Std. Error Adjusted SE z value Pr(>|z|)
(Intercept)           2.5693356  0.5295081   0.5337822   4.813  1.5e-06
***
L                    -0.0011489  0.0007205   0.0007279   1.578   0.1145
OSR2013_X500         -4.1301091  1.9155698   2.1268744   1.942   0.0522 .
Weed.cover            0.1474601  0.0847131   0.0855581   1.724   0.0848 .
Wood_X500            -5.5516524  3.2502461   3.5300659   1.573   0.1158
OSR2012_X500          2.0508163  2.1681256   2.4346913   0.842   0.3996
Weed.cover:Wood_X500  0.9639767  1.0923693   1.1039224   0.873   0.3825
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Relative variable importance:
                      Wood_X500 OSR2013_X500 Weed.cover L    OSR2012_X500
Weed.cover:Wood_X500
Importance:          1.00      0.92         0.90       0.51 0.21
 0.20
N containing models:    8         7            7          4    2
  2

Thank you for your help.
Kind Regards,
Laura


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