[R-sig-ME] Very large standard errors in lmer

[Seth Bigelow]

Well, if you don't include species as a random effect, then standard error
is greatly reduced because n is greatly increased (from 4 to 36 x 4, no?)and
standard error = sqrt (variance)/sqrt(n). But, as you've observed, this is
the wrong way to go about this analysis because species is the basic unit of
replication for the FT treatment. 

--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: Wednesday, October 16, 2013 8:42 PM
To: R-mixed models mailing list
Subject: [R-sig-ME] Very large standard errors in lmer

I am starting a new thread on a topic arising from here:
https://stat.ethz.ch/pipermail/r-sig-mixed-models/2013q4/021114.html, the
relevant background is:

> 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...

> 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...

Given the question I am asking with the data from the experiment ("Do
functional types (FT) have a different relative response to CO2 level?"),
the simplest starting model that makes biological sense is:

response ~ CO2*FT + (1|Spp)

The interaction term needs to be included as part of the fixed effects (see
above question), and species needs to be included as a random effect because
there are 4 species at each of the two levels of FT. I cannot really justify
ignoring the variation inherent in the group of 8 species that I used --
plus I and others (i.e., reviewers) are interested in quantifying that
species variation while still answering the main question at the functional
type level. (It should be noted that the sample size at each level of the
predictors is n=72, and there are n=36 individuals of each species). 

It seems that a mixed model is exactly the type of model for this particular
design and question. However, it was my understanding that by including a
random effect you should be reducing the overall variation of your fixed
effects estimates. In this case it is increasing them drastically (see
example outputs below) for every response variable that I measured.
Suggestions from previous responses to center my predictors, add/remove
chamber as a random effect, and nesting species by CO2 -- i.e., (1+CO2|Spp)
-- had little effect on the SE. 

What would be causing the standard errors to increase with just the
inclusion of species as a random effect?

data fit in lm():

> Call:
> lm(formula = HtChg ~ CO2 * FT, data = striAseasonal)
> 
> Residuals:
>    Min     1Q Median     3Q    Max 
> -74.34 -44.84 -12.64  23.46 140.66 
> 
> Coefficients:
>             Estimate Std. Error t value Pr(>|t|)    
> (Intercept)   71.814      6.835  10.506  < 2e-16 ***
> CO2E           4.526      9.599   0.471    0.638    
> FTT          -46.671      9.667  -4.828 2.28e-06 ***
> CO2E:FTT      -4.133     13.648  -0.303    0.762    
> ---
> Signif. codes:  0 *** 0.001 ** 0.01 * 0.05 . 0.1   1 
> 
> Residual standard error: 57.19 on 277 degrees of freedom
>   (7 observations deleted due to missingness)
> Multiple R-squared: 0.1563,	Adjusted R-squared: 0.1471 
> F-statistic:  17.1 on 3 and 277 DF,  p-value: 3.218e-10 



data fit in lmer() with species as random effect:

> Linear mixed model fit by REML 
> Formula: HtChg ~ CO2 * FT + (1 | Spp) 
>    Data: striAseasonal 
>   AIC  BIC logLik deviance REMLdev
>  2747 2769  -1367     2762    2735
> Random effects:
>  Groups   Name        Variance Std.Dev.
>  Spp      (Intercept) 2950.78  54.321  
>  Residual              965.36  31.070  
> Number of obs: 281, groups: Spp, 8
> 
> Fixed effects:
>             Estimate Std. Error t value
> (Intercept)   69.319     27.408   2.529
> CO2E           7.022      5.218   1.346
> FTT          -44.221     38.760  -1.141
> CO2E:FTT      -6.808      7.419  -0.918
> 
> Correlation of Fixed Effects:
>          (Intr) CO2E   FTT   
> CO2E     -0.097              
> FTT      -0.707  0.068       
> CO2E:FTT  0.068 -0.703 -0.096

	[[alternative HTML version deleted]]