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

[Lara Reichmann]

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