[R-sig-ME] Zero variance and Std. Dev. using lmer?

[Jude Phillips]

Hi, I have a similar problem to Luciano.  I am running a mixed effects
model with a continuous dependent variable, a categorical fixed effect
and a categorical random effect.  The dependent variable has a
distribution that is skewed to the left, which can be normalized by a
log transformation.  There is a huge difference in the results I get,
depending on whether I use the transformation, and I am not sure why.
When I run

spime1<-lmer(X13c ~ crop + (1|field.single), spi)

I get

Linear mixed model fit by REML
Formula: X13c ~ crop + (1 | field.single)
   Data: spi
   AIC   BIC    logLik    deviance    REMLdev
 422.5  440.1  -204.2    414.3        408.5
Random effects:
 Groups          Name        Variance Std.Dev.
 field.single    (Intercept)    0.0000   0.0000
 Residual                          5.8811   2.4251
Number of obs: 91, groups: field.single, 27

Fixed effects:
                  Estimate Std. Error   t value
(Intercept)   -21.3635     0.5882    -36.32
cropHay      -2.6131     0.9997      -2.61
cropHedge   -2.0445     0.6715     -3.04
cropSoy      3.7215     1.2338        3.02
cropWheat   0.6910     1.3477        0.51

Correlation of Fixed Effects:
                  (Intr)     cropHy crpHdg  cropSy
cropHay     -0.588
cropHedge  -0.876  0.515
cropSoy     -0.477   0.280    0.418
cropWheat  -0.436  0.257    0.382    0.208

then

> spime1 at deviance
          ML         REML               ldL2                ldRX2
          sigmaML            sigmaREML        pwrss               disc
                  usqr                  wrss
4.143326e+02   4.084787e+02   3.301496e-08   1.205152e+01
2.357530e+00    2.425094e+00      5.057730e+02    5.057730e+02
1.514514e-07    5.057730e+02
         dev         llik      NULLdev
          NA           NA           NA

However,

spimelog<-lmer(log(X13c +28) ~ crop + (1|field.single), spi)

gives

Linear mixed model fit by REML
Formula: log(X13c + 28) ~ crop + (1 | field.single)
   Data: spi
   AIC     BIC       logLik      deviance   REMLdev
  143.9   161.5     -64.95    120.7        129.9
Random effects:
 Groups       Name        Variance   Std.Dev.
 field.single (Intercept)   0.024557   0.15671
 Residual                     0.212558   0.46104
Number of obs: 91, groups: field.single, 27

Fixed effects:
                  Estimate    Std. Error    t value
(Intercept)    1.8692      0.1341       13.937
cropHay      -0.7846      0.2242      -3.500
cropHedge    -0.4403     0.1545      -2.850
cropSoy       0.4236     0.2705        1.566
cropWheat     0.1113     0.2888      0.385

Correlation of Fixed Effects:
          (Intr) cropHy crpHdg cropSy
cropHay   -0.598
cropHedge -0.868  0.519
cropSoy   -0.496  0.297  0.431
cropWheat -0.464  0.278  0.403  0.230

> spimelog at deviance
         ML        REML              ldL2           ldRX2
sigmaML     sigmaREML       pwrss           disc              usqr
       wrss                dev
120.7413657   129.9082247   8.5530877  10.4710000   0.4481952
0.4610400         18.2799815   17.0420840   1.2381553  17.0418262
    NA
       llik        NULLdev
         NA          NA


>From the previous posts, I think I understand that the first model has
0 std.dev and var for the random effects because the log-likelihood is
not being evaluated correctly, but why is the result so different when
the dependent variable is transformed.  (note that the dependent
variable happens to take negative values, the lowest of which is
-27.5, which is why I add 28 before the log transformation).

Thanks for your attention

Jude Phillips

PhD Candidate
GLEL, Biology Dept.  Carleton University.