[R-sig-ME] how to interpret non-linear mixed effect model results

[Seth Bigelow]

Lara, 

Since no one else has replied I will take your question as an opportunity
for advancing my own learning -- it has motivated me to work through the
'Soybean' example in Pinheiro & Bates, which seems to have the same number
of covariates and parameters as your problem. In looking at your output, it
appears that nlme is mistakenly trying to fit a series of linear, quadratic,
and cubic polynomials to a species by parameter interaction. I don't think
this is what is wanted, is it? At least, the output is very different from
that provided by the final Soybean model (p. 294, model fm4Soy.nlme), which
is reasonably interpretable. I could not hazard any guesses about solutions
to the problem without seeing your input code & some kind of dataset

--Seth  



-----Original Message-----
From: r-sig-mixed-models-bounces at r-project.org
[mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of Lara
Reichmann
Sent: Thursday, April 25, 2013 9:34 AM
To: <r-sig-mixed-models at r-project.org>
Subject: [R-sig-ME] how to interpret non-linear mixed effect model results

Dear list,

I used the nlme function to analyze the effect of Fertilization (2 levels)
and Species (4 levels) on leaf CO2 uptake for 31 different plants under
different light conditions (PARi). CO2 uptake follows an exponential model
with parameters A, B and C. First, I looked at the between-plant variation
to choose the appropriate structure of the random effects, where A and B
resulted highly correlated, thus I only used A and C to create the random
effect structure. Then, a plot of the predicted random effects against
covariates showed a  possible interaction between Fertilization and Species
for the parameter A, but not clear for C. 
I finally run a model with Species and Fertilization as fixed effects, but I
need help to interpret the results, i.e. whether the parameters A and C
differ among Species and Fertilization. I think that the table shows a
Fertilization effect on A, and a significant species effect but in quadratic
combination of the levels? Is this the correct interpretation? How do I
proceed from here to find out which plant species are different form the
rest in the parameters A and C? I copied the contrasts that R creates below
the nlme result. 

I imagine this is pretty straight forward but I am fairly new with
non-linear mixed models and the possibilities in R.

Thanks!
Lara


Nonlinear mixed-effects model fit by maximum likelihood
  Model: Photo ~ A * (1 - exp(-C * PARi/A)) - B
 Data: lightresponse 
       AIC      BIC   logLik
  1018.412 1097.743 -488.206

Random effects:
 Formula: list(A ~ 1, C ~ 1)
 Level: Subject2
 Structure: General positive-definite, Log-Cholesky parametrization
              StdDev      Corr  
A.(Intercept) 6.862964403 A.(In)
C.(Intercept) 0.009835824 0.026 
Residual      0.760129991       

Fixed effects: list(A + C ~ Species * Fert, B ~ 1) 
                       Value Std.Error  DF   t-value p-value
A.(Intercept)      24.799122  1.279099 276 19.387956  0.0000
A.Species.L        -2.715205  2.510509 276 -1.081536  0.2804
A.Species.Q        -5.082033  2.553854 276 -1.989946  0.0476
A.Species.C        -1.480629  2.596444 276 -0.570253  0.5690
A.Fert.L            9.502754  1.805936 276  5.261954  0.0000
A.Species.L:Fert.L  0.027821  3.550408 276  0.007836  0.9938
A.Species.Q:Fert.L -5.784219  3.611704 276 -1.601521  0.1104
A.Species.C:Fert.L -4.650500  3.671944 276 -1.266495  0.2064
C.(Intercept)       0.067437  0.002208 276 30.548919  0.0000
C.Species.L        -0.008292  0.003958 276 -2.094717  0.0371
C.Species.Q        -0.006519  0.004061 276 -1.605485  0.1095
C.Species.C         0.002977  0.004160 276  0.715493  0.4749
C.Fert.L           -0.000825  0.002886 276 -0.285688  0.7753
C.Species.L:Fert.L -0.013529  0.005600 276 -2.415831  0.0163
C.Species.Q:Fert.L  0.004215  0.005744 276  0.733708  0.4637
C.Species.C:Fert.L  0.009809  0.005887 276  1.666258  0.0968
B     


contrasts(lightresponse$Species)
             .L   .Q         .C
[1,] -0.6708204  0.5 -0.2236068
[2,] -0.2236068 -0.5  0.6708204
[3,]  0.2236068 -0.5 -0.6708204
[4,]  0.6708204  0.5  0.2236068

 contrasts(lightresponse$Fert)
             .L
[1,] -0.7071068
[2,]  0.7071068
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