[R-sig-ME] Help with Interpretation of LMER Output--Correctly Formatted Post (I Hope)

[Ben Bolker]

AvianResearchDivision <segerfan83 at ...> writes:

> 
> 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|)
 (Intercept)    3882.30      146.14       26.565    < 2e-16 ***
> Environ      181.37       81.29        2.231    0.030498 *
> Year2012     -227.81      109.46       -2.081   0.043033 *
> NT2         -695.88      204.01       -3.411    0.001332 **
> NT3         -512.99      169.77       -3.022    0.003990 **
> NT4         -923.74      257.62       -3.58     0.000793 ***
> NT5         -497.34      301.71       -1.648    0.106198
> NT6         -492.54      205.25       -2.400    0.020442 *
> NT7         -140.23      256.88       -0.546    0.587749
> NT8         89.31        191.34       0.467     0.642776
> NT9         288.10       295.87       0.974     0.335439 
> NT10        956.39       297.30       3.217     0.002381 **
> NT11        -462.32      258.87       -1.786    0.080401 .
> NT12        788.41       398.64       1.978     0.054255 .
> Environ:NT2   202.60       107.99       1.876   0.069236 .
> Environ:NT3   -178.25      97.34        -1.831  0.074108 .
> Environ:NT4   -167.50      141.26       -1.186  0.243358
> Environ:NT5   149.19      157.95       -0.945   0.350711
> Environ:NT6   161.91       113.32       1.429   0.161585
> Environ:NT7   -227.35      138.57       -1.641  0.111677
> Environ:NT8   -86.25       107.79       -0.800  0.428252
> Environ:NT9   -106.92      156.84       -0.682  0.499778
> Environ:NT10  -43.84       153.00       -0.287  0.776171
> Environ:NT11  -106.55      143.89       -0.740  0.463213
> Environ:NT12  -275.49      197.23       -1.397  0.172351
> 
> Anova(lf.lmer,ddf=Kenward-Rogers)
> 
> Analysis of Variance Table with Kenward-Roger approximation for degrees
> of freedom
> 
             Sum Sq     Mean Sq    F value    Denom  Pr(>F)
> 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