I have a quick question concerning concurvity in a generalized additive mixed effects model. There are wonderful aids for identifying concurvity for GAMs not containing random effects. However, I have not seen explanations concerning high concurvity between fixed effect smooths for example s(x,bs="ts") and random effect smooths for example s(subject,bs="re"). This same question was asked before with no response concurvity in presence of random smooths.
My analysis is as follows. I have repeated measures of "res" for each area. Res is a continuous value and modeled with a gaussian distribution. I have a continuous environmental variable specific to the area in which res was recorded (z) and a continuous temperature value during the recording of res (temp). I am interested in the combined effects of temp and x on res. I therefore set up a gam as follows.
mod1<-gam(res~ s(z) + s(temp))
Because I have repeated measures I would like to included the area as a random effect. Therefore having the following model structure.
mod2<-gam(res~ s(z) + s(temp) + s(area,bs="re"))
The pairwise concurvity values between the environmental variable associated with the area (z) and the random effect (area) are near 1 in the worst case scenario. I have a few questions.
- Given that it is between a fixed and random effect, Is the high concurvity between z and area problematic?
- If the presented concurvity is problematic, what could be an alternative approach?
concurvity(mod2)
para s(temp) s(z) s(area)
worst 1 0.030865482 0.9430052 1.0000000
observed 1 0.004766551 0.9399573 0.2296209
estimate 1 0.017776578 0.9058069 0.1510413
concurvity(mod2,full=F)
$worst
para s(temp) s(z) s(area)
para 1.0000000000 0.0002903174 0.0004151957 1.00000000
s(temp) 0.0002903174 1.0000000000 0.0080636515 0.02601184
s(z) 0.0004151957 0.0080636515 1.0000000000 0.94272513
s(area) 1.0000000000 0.0260118411 0.9427251271 1.00000000
$observed
para s(temp) s(z) s(area)
para 1.0000000000 2.617954e-05 3.194895e-05 4.488602e-05
s(temp) 0.0002903174 1.000000e+00 7.446183e-03 1.857687e-03
s(z) 0.0004151957 1.440157e-03 1.000000e+00 2.292680e-01
s(area) 1.0000000000 2.433589e-03 9.397200e-01 1.000000e+00
$estimate
para s(temp) s(z) s(area)
para 1.0000000000 2.150218e-05 2.491193e-05 0.025074805
s(temp) 0.0002903174 1.000000e+00 5.792759e-03 0.001217245
s(z) 0.0004151957 4.562905e-03 1.000000e+00 0.125040009
s(area) 1.0000000000 1.492578e-02 9.054246e-01 1.000000000
https://jroy042.github.io/nonlinear/week3.html and https://eric-pedersen.github.io/mgcv-esa-workshop/slides/02-model_checking.html#/.
