Interpreting model averaging results in R

I am trying to understand and know what to report from my analysis of some data using model averaging in R.

I am using the following script to analyse the effect of method of measurement over a given variable:
Here is the dataset:
https://www.dropbox.com/s/u9un273gzw9o30u/VMT4.csv?dl=0

Model to be fitted:

LM.1 <- gls(VMTf ~ turn+sex+method, na.action="na.fail", method = "ML",VMT4)

dredge full model

require(MuMIn)
d=dredge(LM.1)
print(d)
coefficients(d)

Obtain summary information of all models to get parameter estimates

summary(model.avg(d))

I know that either all models can be averaged (full model averaging) or just a subset of them (conditional averaging). Now, I would like to know: when is better to use full or conditional averaging to make inferences. What should I report of all this for a scientific article? What means exactly the Z value and associated p for a model averaging situation?

To make it easier to visualize my questions. Here is the result table,

> summary(model.avg(d))# now, there are effects

Call:
model.avg(object = d)

Component model call: 
gls(model = VMT ~ <8 unique rhs>, data = VMT4, method = ML, na.action = 
 na.fail)

Component models: 
       df  logLik   AICc delta weight
1       4 -247.10 502.52  0.00   0.34
12      5 -246.17 502.83  0.31   0.29
13      5 -246.52 503.52  1.01   0.20
123     6 -245.60 503.88  1.36   0.17
(Null)  2 -258.62 521.33 18.81   0.00
3       3 -258.38 522.95 20.43   0.00
2       3 -258.60 523.39 20.88   0.00
23      4 -258.36 525.05 22.53   0.00

Term codes: 
method    sex   turn 
     1      2      3 

Model-averaged coefficients:  
(full average) 
                       Estimate Std. Error Adjusted SE z value Pr(>|z|)    
(Intercept)            42.63521    0.37170     0.37447 113.856  < 2e-16 ***
methodlight chamber    -1.05276    0.36098     0.36440   2.889  0.00386 ** 
methodthermal gradient -1.80567    0.36103     0.36445   4.955    7e-07 ***
sex2                    0.19023    0.29403     0.29548   0.644  0.51970    
turn                    0.05005    0.10083     0.10141   0.494  0.62165    

(conditional average) 
                       Estimate Std. Error Adjusted SE z value Pr(>|z|)    
(Intercept)             42.6352     0.3717      0.3745 113.856  < 2e-16 ***
methodlight chamber     -1.0528     0.3609      0.3643   2.890  0.00386 ** 
methodthermal gradient  -1.8058     0.3608      0.3642   4.958  7.1e-07 ***
sex2                     0.4144     0.3089      0.3119   1.328  0.18402    
turn                     0.1337     0.1264      0.1276   1.047  0.29492    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Relative variable importance: 
                     method sex  turn
Importance:          1.00   0.46 0.37
N containing models:    4      4    4

Answer

See Grueber et al. 2011, “Multimodel inference in ecology and evolution: challenges and solutions” Evolutionary Biology 24:699-711.

It really depends on goals as to whether you want to use full or conditional data. In my field we would use criteria, such as AICC to determine which models are most supported, then use those as your conditional subset. This information would then be reported. For example, your first four models are all within 2 AIC units of each other, so they all would be included in your subset. The others are way out there (higher AIC) so including information from them would actually reduce the quality of your beta estimates.

Attribution
Source : Link , Question Author : Agus Camacho , Answer Author : AUDeer

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