I am working on a nlme model that has multiple fixed effects (linear and
nonlinear) with a nonlinear (asymptotic) random effect.
asymporig<-function(x,th1,th2)th1*(1-exp(-exp(th2)*x))
asymporigb<-function(x,th1b,th2b)th1b*(1-exp(-exp(th2b)*x))
mod.vol.nlme<-nlme(fa20~(ah*habdiv+ads*ds+ads2*ds2+at*trout)+asymporig(da.p,th1,th2)+
asymporigb(vol,th1b,th2b),
fixed=ah+ads+ads2+at+th1+th2+th1b+th2b~1,
random=pdBlocked(list(th1~1,th2~1)),
start=c(ah=.5524,ads=.8,ads2=-.1,at=-1,th1=2.542,th2=-7.117,th1b=2,th2b=-7),
data=pca1.grouped,verbose=T)
I am looking at potential multicollinearity among the fixed effects, in
particular I am concerned about multicollinearity between da.p (drainage area)
and vol (volume). How do I interpret the correlation reported in the summary
command for th1 and th1b, which are the asymptotes for fa20~da.p and fa20~vol.
It is -.50, but how is the correlation calculated?
I have run the above model with out vol and the coefficients for the remaining
variables are very similar (within the approx. 95% conf. interv.) to the
coefficients in the above model and vol and da.p are significant, both
suggesting multicollinearity is not severe?? I am interested in which variables
influence fa20 (richness) not necessarily the model with the smallest residual
sd.
I do have Pinheiro and Bates, but do not find much reference to this type of
information. Thanks for any suggestions or help.
Dan
####summary
#################
Nonlinear mixed-effects model fit by maximum likelihood
Model: fa20 ~ (ah * habdiv + ads * ds + ads2 * ds2 + at * trout) +
asymporig(da.p, th1, th2) + asymporigb(vol, th1b, th2b)
Data: pca1.grouped
AIC BIC logLik
3151.665 3248.518 -1555.832
Random effects:
Composite Structure: Blocked
Block 1: th1
Formula: th1 ~ 1 | bas
th1
StdDev: 0.8125094
Block 2: th2
Formula: th2 ~ 1 | bas
th2 Residual
StdDev: 0.9468531 1.028757
Variance function:
Structure: Different standard deviations per stratum
Formula: ~1 | bas
Parameter estimates:
LS CD MS DM RN LM UM RD
1.0000000 0.7884995 1.2107482 1.4159803 1.0463657 1.3982966 1.2195945 1.1978807
MN SC
1.3858409 1.2006228
Fixed effects: ah + ads + ads2 + at + th1 + th2 + th1b + th2b ~ 1
Value Std.Error DF t-value p-value
ah 0.597032 0.1330044 920 4.488812 0
ads 1.283297 0.0874561 920 14.673614 0
ads2 -0.125186 0.0130289 920 -9.608281 0
at -0.731506 0.1394553 920 -5.245451 0
th1 2.363269 0.3385592 920 6.980373 0
th2 -3.910520 0.3575392 920 -10.937318 0
th1b 1.402536 0.2188125 920 6.409764 0
th2b -6.765038 0.2931669 920 -23.075723 0
Correlation:
ah ads ads2 at th1 th2 th1b
ads -0.595
ads2 0.571 -0.974
at -0.092 -0.104 0.104
th1 0.010 -0.153 0.147 -0.020
th2 -0.012 -0.139 0.105 -0.015 -0.071
th1b 0.043 -0.110 0.070 0.084 -0.500 0.163
th2b -0.038 -0.032 -0.030 -0.016 -0.017 -0.225 -0.056
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-3.73841391 -0.63008005 0.03189713 0.68903314 3.90583424
Number of Observations: 937
Number of Groups: 10
