# [R-sig-ME] Calculating SE from GLMM results (using glmer{lme4})

Ben Bolker bolker at ufl.edu
Thu Sep 24 15:21:15 CEST 2009

```Raldo Kruger wrote:
> Dear R users,
>
> Please excuse the basic questions, but I’m new to GLMMs and R!
>
> I’m analyzing an experiment where Seedling numbers in plots where seed
> has been sown on restoration sites is the response variable. I’m most
> interested in determining whether the Nutrients (N) and water
> absorbing polymer Gel (Ge) additions to the soil substrate contribute
> positively to the survival of the seedlings, over a 3 year time period
> (for simplicity I'm just using 3 time periods, each in the same season
> for the 3
> successive years).
> Fixed factors: Nutrients (0 and 1), Gel (0 and 1)
> Random factors: Site (4 non replicate sites), Year (3 time periods)
> Response variable: Seedling numbers (counts) / 0.25m2 plot
> The results are as follows:
> 	         Estimate	Std. Error	z value	 Pr(>|z|)
> (Intercept)	4.52982	0.24486	18.5	       <2.00E-16	***
> N	       -0.07922	0.08415	-0.94	       0.346489
> Ge	         0.20766	0.08428	2.46	        0.013744	*
> Year  	-1.62937	0.04672	-34.88	<2.00E-16	***
> N:Ge 	-0.44213	0.11898	-3.72   	0.000202	***
> N:Year	0.11705	0.06322	1.85   	0.064125	.
> Ge:Year	-0.04861	0.0645	-0.75  	0.451132
> N:Ge:Year	0.11458	0.08917	1.28  	0.198821
>

*  It looks like you fitted year as a fixed effect rather than a random
effect (probably sensible, since you only have 3 levels / years), and
incorporated all fixed effect interactions (i.e. N*Ge*Year) ?  However,
it also looks like you fitted year as a continuous covariate, which
means that R is trying to fit a linear function of time -- is that
really what you want?  There's a very large negative year effect -- if
your year values are coded 1-3, then it suggests you have very few
seedlings left in year 3?

It's also
worth considering whether you are really getting reliable answers based
on only 4 sites -- I would also try this with Site as a fixed effect
and see whether the answers differ considerably.  (I know that,
philosophically, Site and Year are both random effects, and you may
run into trouble with reviewers who are used to classical ANOVA
> 1)	So as I understand (from previous correspondence with R-users) the
> number of seedlings in the control plots in year 0 is
>         exp(4.53) = 92.7. Is the standard error calculated with
> 0.24486 (i.e. 92.7*0.24), or with 92.7*exp(0.24).

The latter.
So for example the approximate confidence intervals would be
exp(0.453 +/- 2*0.245)

> 2)	And for the N:Ge treatment, the effect is exp(-0.08+0.21-0.44)
> =0.73 (I.e. a 27% reduction compared to the control), right? So
>         is the SE for the N:Ge effect calculated as the sum of the
> SE’s too, i.e. 0.08+0.08+0.12, or is it just 0.12?

The SE for combined effects is calculated as sqrt(se1^2 + se2^2 + se3^2)

> 3)	Lastly, is it possible to fit two response variables in one GLMM?
> E.g. seedling numbers and height.

This would be hard -- you're talking about a multivariate response
with different measurement scales/error distributions for different
variables ...
>
> Many thanks,
> Raldo Krüger
> Msc student
> University of Cape Town
>
>

--
Ben Bolker
Associate professor, Biology Dep't, Univ. of Florida
bolker at ufl.edu / www.zoology.ufl.edu/bolker
GPG key: www.zoology.ufl.edu/bolker/benbolker-publickey.asc

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