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 (In another question ("GLMM: relationship between AIC, R squared and overdispersion?"), it became clear that using study areas as random effect was not useful nor correct).
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):
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 , and here are the results (only models of AICc lower than 2 represented):
 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)