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Unrealistic fixed effect coefficients

1 message · Seth Bigelow

Original
Seth Bigelow
# 
Dave, 

Perhaps you should go back to a simple model and build up from there,
examining residuals at each step as outlined in, e.g., Pinheiro & Bates
Chapter 1, or Simon Wood's GAM book (Chap. 6, Mixed models and GAMMS's is
great). 

My first cut at a simple model for your situation would be to ignore
chambers, specify random effects with species nested within functional
types, and use a likelihood ratio test to compare models with interaction
vs. no interaction of main effects, as in
M1 <- Lmer(response ~ CO2 + FT + (1|FT/spp))
M2 <- Lmer(response ~ CO2*FT +  (1|FT/spp))
anova(M1,M2)

...analogous to the 'machines' example in section 1.3 of Pinheiro & Bates.
Then, if this makes sense and the residual errors make sense, move
(incrementally) to a model that incorporates the chamber effect, using,
e.g., Jake's suggestions. 
-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 Dave Marvin
Sent: Tuesday, October 15, 2013 9:06 AM
To: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] Unrealistic fixed effect coefficients

Thank you for the clarification Jake. 

Your assumptions were correct in that a single Species can only be one
Functional Type (in this experiment at least), and a single Chamber will
only have one CO2 level. The model output with this random effects structure
is below, and gives much more realistic estimates of the fixed effects. 

However, this brings up a second issue (which maybe belongs in a new post?).
The standard errors of the estimated fixed effects are huge -- 3 to 9 times
as large as in the raw data. Is this to be interpreted as just having very
poor explanatory variables? Why, then, would my standard errors not be at
least in the same ballpark when just looking at the raw data group SEs?

        
On Oct 14, 2013, at 8:40 PM, Jake Westfall wrote:

        

            

      
      
      
    

        
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:

            

      
      
      
    

        
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:

            

      
      
      
    

        
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:

            

      
      
      
    

        
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:

            

      
      
      
    

        
(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.

            

      
      
      
    

        
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.

            

      
      
      
    

        
problem I am not seeing/addressing? Thank you.

            

      
      
      
    

        
-0.809

            

      
      
      
    

        
0.043  0.027

            

      
      
      
    

        
0.699 -0.348  0.136

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        

      
      
    

        
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