Hi Dave,

Your random effects specification doesn't make sense.  You say that you have 8 random Species, each of which are observed in a number of random Chambers. So Species and Chamber are crossed. So a preliminary model would look like this:

response ~ CO2 * FT + (1|Chamber) + (1|Spp)

Now, Species are nested under Functional Type, meaning each Species is of one and only one FT (right??), so we cannot estimate a random FT slope across Species. But each species *is* observed under both levels of CO2. So we can modify the Spp random effects thusly:

response ~ CO2 * FT + (1|Chamber) + (CO2|Spp)

I assume that growth Chambers are nested under CO2 level (so that a single Chamber can't have both CO2 levels). So we can't estimate a random CO2 slope across Chambers.  But each Chamber *does* contain Species of both Functional Types, right? So our final model, if I have understood the experimental design correctly, should look like this:

response ~ CO2 * FT + (FT|Chamber) + (CO2|Spp)

Hope this helps,
Jake
> From: marvs@umich.edu
> Date: Mon, 14 Oct 2013 19:55:45 -0400
> To: r-sig-mixed-models@r-project.org
> Subject: [R-sig-ME] Unrealistic fixed effect coefficients
> 
> I am analyzing the growth response of two plant types (vines vs. trees) to different CO2 levels, for a mix of species of each plant type in plant growth chambers. I am fitting a mixed model with lmer using the following fixed and random effects structures:
> 
> response ~ CO2 * FT + (1 + Spp | Chamber)
> 
> CO2 and FT are categorical predictors, each with two levels (elevated/ambient CO2, vine/tree plant Functional Types). Each growth chamber had the same mix of 8 species (Spp), so I would like to include both species and chamber as random effects. With this random effects structure, and please correct me if I am wrong, I believe I am modeling the variation of each species among the growth chambers independent of the CO2 treatment each chamber received. I would like to use this approach since each growth chamber differs slightly in its microsite environment, and want to account for species variation due to microsite (chamber) differences as a random effect.  
> 
> However, the result of the model for most of my response variables (e.g., plant height below) give completely unrealistic fixed effect coefficients (i.e., the plant height is never going to be negative, and the intercept isn't even close to either of the group means from the raw data). Response variables are untransformed and unstandardized. 
> 
> Am I specifying my random effects incorrectly? Or is there another problem I am not seeing/addressing? Thank you. 
> 
> > Linear mixed model fit by REML 
> > Formula: HtChg ~ CO2 * FT + (1 + Spp | Chamber) 
> >    Data: striAseasonal 
> >   AIC  BIC logLik deviance REMLdev
> >  2640 2789  -1279     2571    2558
> > Random effects:
> >  Groups   Name        Variance  Std.Dev. Corr                                             
> >  Chamber  (Intercept)   613.032  24.7595                                                  
> >           SppCLIJAV    6680.902  81.7368  0.747                                           
> >           SppCONN      1046.801  32.3543 -0.987 -0.773                                    
> >           SppCORALL    1479.760  38.4676  0.565  0.619 -0.630                             
> >           SppPHRCO      461.740  21.4881 -0.995 -0.772  0.989 -0.597                      
> >           SppSTIHY    19240.737 138.7110  0.799  0.762 -0.878  0.777 -0.809               
> >           SppTABRO      690.773  26.2826 -0.095 -0.348  0.027  0.144  0.043  0.027        
> >           SppTERAM      211.084  14.5287 -0.752 -0.291  0.679 -0.126  0.699 -0.348  0.136 
> >  Residual                91.938   9.5884                                                  
> > Number of obs: 281, groups: Chamber, 36
> > 
> > Fixed effects:
> >             Estimate Std. Error t value
> > (Intercept)   13.459      1.629   8.260
> > CO2E           3.216      2.276   1.413
> > FTT          -15.751      2.498  -6.305
> > CO2E:FTT      -2.251      3.538  -0.636
> > 
> > Correlation of Fixed Effects:
> >          (Intr) CO2E   FTT   
> > CO2E     -0.716              
> > FTT      -0.518  0.371       
> > CO2E:FTT  0.366 -0.512 -0.706
> 
> 
> 
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