Hello,

We are analyzing data on the number of insects of certain species on
individual plants.  There are 3 species of plants (fixed effect) nested
within 8 different sites (random effect).  We have structured the model as
follows, after tentatively dropping the intercept of site:

>lmer(insects ~ plantsp + (0+ plantsp|site) , family = poisson, REML = TRUE
)

We then went on to do contrasts between levels of the fixed effect:

>glht(bestmod, linfct = mcp(plantsp = "Tukey"))

This seems to work ok for some contrasts, but not others.  In particular,
sometimes we have the situation where an insect was not found at all on one
particular plant species (hence all observations are 0 for that level of the
fixed effect).   This returns the unsatisfactory result that the level with
the highest mean is different from the level with the intermediate mean, but
not at all different from the level with the low (i.e. 0) mean.  Furthermore,
adding a single insect to a random plant within the all 0s group makes all
the contrasts highly significant.  The data are overdispersed and
zero-inflated but that doesn’t seem to be responsible for this particular
problem.  We may end up using MCMCglmm but we still would like to understand
why this is happening in LMER.

Thanks for your assistance,

Sarah

Here are the results from a test where this happens:

Generalized linear mixed model fit by the Laplace approximation

Formula: insects ~ plantsp + (0 + plantsp | site)

  AIC  BIC logLik deviance

 1002 1042 -491.9    983.9

Random effects:

 Groups Name      Variance Std.Dev. Corr

 site   plantspTA 0.13088  0.36177

        plantspTG 1.81646  1.34776  0.000

        plantspTL 1.62193  1.27355  0.000 0.325

Number of obs: 626, groups: site, 8

Fixed effects:

            Estimate Std. Error z value Pr(>|z|)

(Intercept)   -18.71     907.10  -0.021    0.984

plantspTG      16.97     907.10   0.019    0.985

plantspTL      19.10     907.10   0.021    0.983

Correlation of Fixed Effects:

          (Intr) plntTG

plantspTG -1.000

plantspTL -1.000  1.000



Simultaneous Tests for General Linear Hypotheses

Multiple Comparisons of Means: Tukey Contrasts

Fit: glmer(formula = insects ~ plantsp + (0 + plantsp | site), family =
poisson,

    REML = TRUE)

Linear Hypotheses:

             Estimate Std. Error z value Pr(>|z|)

TG - TA == 0  16.9673   907.1004   0.019 0.999777

TL - TA == 0  19.1032   907.1003   0.021 0.999718

TL - TG == 0   2.1358     0.6068   3.520 0.000864 ***

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Adjusted p values reported -- single-step method)

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