Hi all,

Thanks for your patience. I see now that I was confused regarding the
output of the .mer model, thinking that the standard deviation listed was
the sd around the estimate of the variance component rather than a simple
reformulation of the variance of the random effects parameters. I then read
in Douglas Bates' draft of the lme4 book an explicit admonishment against
this conclusion! My apologies. Based on log-likelihood tests comparing
random effects structures, then, I think my model output makes sense at
this point:

>anova(fm1,fm2,fm3,fm4)

Data: subset
Data: m1200
Data: species == "PIGL"
Models:
fm1: log(photo) ~ vegtrt * gappos2 + (1 | block)
fm2: log(photo) ~ vegtrt * gappos2 + (1 | block/transect)
fm3: log(photo) ~ vegtrt * gappos2 + (1 | block/transect/gappos2)
fm4: log(photo) ~ vegtrt * gappos2 + (1 | block/transect/gappos2/ind)
            Df     AIC         BIC          logLik       Chisq     Chi Df
  Pr(>Chisq)
fm1      10    138.16    164.60    -59.078
fm2      11    125.12    154.21    -51.559    15.037      1
0.0001054
fm3      12    129.12    160.85    -52.560     0.000       1
1.0000000
fm4      13    131.12    165.50    -52.560     0.000       1
1.0000000

>summary(fm2)

Linear mixed model fit by REML
Formula: log(photo) ~ vegtrt * gappos2 + (1 | block/transect)
   Data: subset(m1200, species == "PIGL")
   AIC        BIC        logLik     deviance      REMLdev
 139.4      168.5     -58.71    103.1           117.4
Random effects:
 Groups                Name             Variance         Std.Dev.
 transect:block      (Intercept)      1.3527e-01    3.6779e-01
 block                    (Intercept)      9.3044e-19    9.6459e-10
 Residual                                     1.5127e-01    3.8893e-01
Number of obs: 104, groups: transect:block, 4; block, 2

Fixed effects:
                            Estimate       Std. Error       t value
(Intercept)            1.077206      0.279364      3.856
vegtrts                  0.170651      0.390206      0.437
gappos2SE           0.177259      0.151711      1.168
gappos2C             0.862518      0.151711      5.685
gappos2NE           0.513357      0.151711      3.384
vegtrts:gappos2SE -0.005348   0.205438     -0.026
vegtrts:gappos2C  -0.356389   0.240038      -1.485
vegtrts:gappos2NE -0.324070   0.205438     -1.577

Correlation of Fixed Effects:
                     (Intr)       vgtrts    gpp2SE    gpps2C    gpp2NE
 vg:2SE    vgt:2C
vegtrts           -0.716
gappos2SE   -0.246    0.176
gappos2C     -0.246    0.176    0.452
gappos2NE   -0.246    0.176    0.452        0.452
vgtrts:g2SE    0.181   -0.212   -0.738      -0.334      -0.334
vgtrts:gp2C    0.155   -0.180   -0.286      -0.632      -0.286       0.342

vgtrts:g2NE    0.181   -0.212   -0.334      -0.334      -0.738       0.403
      0.342

I still am left with the question as to whether to alter the random-effects
structure for each gas-exchange response variable of interest (Anet, WUE,
etc.), or whether to develop a random-effects structure that is sensible
based on experimental design and stick to it? In other words, because of
experimental design, is there potentially an argument for maintaining the
more complex random effects structure of fm4 above through all my models,
even though it does not necessarily provide the best fits in a given model?
Does it even matter if I am mostly concerned with hypothesis testing of
fixed-effects?

-Nathan

-- 
*Nathan E. Rutenbeck*
PhD Student
Silviculture and Forest Ecology

231 Nutting Hall
School of Forest Resources
University of Maine

207.664.9581 (cell)

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