[R-sig-ME] GLMM- relationship between AICc weight and random effects?

[Teresa Oliveira]

Dear list members,

I am developing GLMM's in order to assess habitat selection (using GLMMs'
coeficients to construct Resource selection functions). I have (telemetry)
data from 5 study areas, and each area has a different number of
individuals monitored.

To develop GLMM's, the dependend variable is binary (1-used locations;
0-available locations), and I have a initial set of 14 continuous variables
(8 land cover variables; 2 distance variables, to artificial areas and
water sources; 4 topographic variables): a buffer was placed around each
location and the area of each land cover within that buffer was accounted
for; distances were measured from each point to the nearest feature, and
topographic variables were obtained using DEM rasters. I tested for
correlation using Spearman's Rank, so not all 14 were used in the GLMMs.
All variables were transformed using z-score.

As random effect, I used individual ID. I thought at the beggining to use
study area as a random effect but I only had 5 levels and there was almost
no variance when that random effect was used.

I constructed a GLMM with 9 variables (not correlated) and a random effect,
then used "dredge()" function and "model.avg(dredge)" to sort models by AIC
values. This was the result (only models of AICc lower than 2 represented):

[1]Call:
model.avg(object = dredge.m1.1)

Component model call:
glmer(formula = Used ~ <512 unique rhs>, data = All_SA_Used_RP_Area_z,
family =
     binomial(link = "logit"))

Component models:
          df   logLik    AICc  delta weight
123578     8 -4309.94 8635.89   0.00   0.14
1235789    9 -4309.22 8636.44   0.55   0.10
123789     8 -4310.52 8637.04   1.14   0.08
1235678    9 -4309.75 8637.50   1.61   0.06
12378      7 -4311.78 8637.57   1.67   0.06
1234578    9 -4309.79 8637.58   1.69   0.06

Variables 1 and 2 represent the distance variables; from 3 to 8 land cover
variables, and 9 is a topographic variable. Weights seem to be very low,
even if I average all those models as it seems to be common when delta
values are low. Even with this weights, I constructed GLMMs for each of the
combinations, and the results were simmilar for all 6 combinations. Here
are the results for the first one (GLMM + overdispersion + r-squared):

Random effects:
 Groups    Name        Variance Std.Dev.
 ID.CODE_1 (Intercept) 13.02    3.608
Number of obs: 32670, groups:  ID.CODE_1, 55

Fixed effects:
            Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.54891    0.51174  -1.073 0.283433
3       -0.22232    0.04059  -5.478 4.31e-08 ***
5       -0.05433    0.02837  -1.915 0.055460 .
7       -0.13108    0.02825  -4.640 3.49e-06 ***
8       -0.15864    0.08670  -1.830 0.067287 .
1         0.28438    0.02853   9.968  < 2e-16 ***
2         0.11531    0.03021   3.817 0.000135 ***
Residual deviance: 0.256
r.squaredGLMM():
       R2m        R2c
0.01063077 0.80039950
This is what I get from this analysis:

1) Variance and SD of the random effect seems fine (definitely better than
the "0" I got when using Study Areas as random effect);

2) Estimate values make sense from what I know of the species and the
knowledge I have of the study areas;

3) Overdispersion values seem good, and R-squared values don't seem very
good (at least when considering only fixed effects) but, as I read in
several places, AIC and r-squared are not always in agreement.

4) Weight values seem very low. Does it mean the models are not good?

Then what I did was construct a GLM ("glm()"), so no random effect was
used. I used the same set of variables used in [1], and here are the
results (only models of AICc lower than 2 represented):

[2] Call:
model.avg(object = dredge.glm_m1.1)

Component model call:
glm(formula = Used ~ <512 unique rhs>, family = binomial(link = "logit"),
data =
     All_SA_Used_RP_Area_z)

Component models:
          df   logLik     AICc   delta weight
12345678   9 -9251.85 18521.70    0.00   0.52
123456789 10 -9251.77 18523.54    1.84   0.21
1345678    8 -9253.84 18523.69    1.99   0.19

In this case, weight values are higher.

Does this mean that it is better not to use a random effect? (I am not sure
I can compare GLMM with GLM results, correct me if I am doing wrong
assumptions)

Thank you very much in advance for your time and help. I hope I made myself
clear enough so you can understand what I am asking!

Best regards,
Teresa

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