Hi all,
I have a somewhat basic question that I thought I knew the answer to before
I started to look at lattice plots of my data compared to the lmer summary
output. The output is as follows:
Summary(lf.lmer)
Is this from lmerTest? Otherwise, how are you getting p-values
on the fixed effects ... ?
Linear mixed model fit by REML
Formula: LF ~ Environ+Year+NT+Environ*NT+ (Environ+0|Male) + (1|Male)
By the way, the main effects Environ and NT are redundant (but
harmless) here: Environ*NT is equivalent to Environ+NT+Environ:NT
(main effects plus interaction), so you could write the fixed effects
as Environ*NT+Year
Data: data
AIC BIC logLik REMLdev
10375 10508 -5160 10611 10319
Random effects:
Groups Name Variance Std.Dev.
Male Environ 19339.7 139.067
Male (Intercept) 136682.2 369.706
Residual 8494.6 92.166
Number of obs: 864, groups: Male, 59
Fixed effects:
Estimate Std. Error t value Pr(>|t|)
Environ 224985 224985 9.4594 37.189 0.003926
Year 74638 74638 4.3218 46.033 0.043227
NT 602363 54760 6.5773 46.192 1.86e-06
Environ:NT 272641 24786 2.9015 37.309 0.007367
Note that these are mostly questions about basic R model formulations,
not specific to mixed models. The answers are specific to the
default "treatment" contrasts.
1). Is the population LF 3882.30 and the average response to an increase
in 1 unit of Environ 181.37 or are these NT1's results? If these are the
population estimates and note NT1's results, where are NT1's results?
If you used default treatment contrasts, LF is the effect in the
baseline level (NT1).
2). Is LF in Year2012 227.81 lower than 2011 or 227.81 lower than the
population?
LF *in the baseline level* (NT1, Environ=0) is 227.81 lower in Year 2012
than in Year 2011 *in the baseline level*
3). Is NT2's intercept -695.88 lower than NT1 or the population?
NT1 (in the base level: Year 2011, Environ=0)
4). How do I interpret the interaction between Environ and NT? I am
assuming that I ignore Environ and pay attention to the significance of
each interaction, which in that case means there is not significant change
in LF in response to Environ for each NT. Is this true? If so, why does
that anova table say that this interaction is highly significant
(p=0.007367)?
Because the combined significance of all the individual Environ-by-NT
interactions is significant.
I'm sorry if this seems overly trivial and easy, but I am second guessing
myself a lot right now. Any help would be greatly appreciated. I tried to
format the output so all items are lined up neatly, I apologize if after
posting, things are not aligned.
You should probably read a more general treatment of model formulation
and contrasts in R, e.g. Faraway's book on linear regression (I believe
there's a version in the 'contributed documentation' section on CRAN).
good luck
Ben Bolker