Hello,

I am looking for guidance on using linear mixed models for a repeated
measures, blocked analysis of count data.  The details are given below,
but the shorter version of where I am stuck at this point: the data do
not match up well the examples I can find for repeated measures in mixed
models (e.g the sleep study in the mixed models guide to lmer by Bates).
For my data set, there is no linear relationship between time/census and
the response (plant abundance).  Instead, abundances and potentially
treatment effects vary up and down substantially over the repeated
censuses, in relation to annual rainfall and the timing of counts within
the growing season.  It seems to me that for this reason the individual
censuses that are repeated within subjects (plots) over time should be
treated more as a categorical/factor variable in the analysis, but I am
not sure whether this interpretation is correct or exactly how to write
the model in lmer/glmmadmb syntax.

The counts are overdispersed and also likely zero inflated (about 20-30%
of the observations), so I ultimately want to run the analyses in
glmmadmb, where I can compare the fit of negative binomial and zero
inflated nb models.

Many thanks in advance for any thoughts/suggestions,

Diane

 

Details:

The data are counts of native plant abundances from a factorial, blocked
experiment (factors: removal of invasive competitors and seeding, two
levels each).  This experiment was replicated in two years (8 blocks per
year).  The counts were made in 6 censuses taken over three years
subsequent to completion of the initial experiment to test for longer
term effects of the seeding in particular; in each year one census took
place early in the growing season and one late.  There are a total of
362 observations taken for 80 plots divided among the 16 blocks; some
data are missing, so not every plot was counted at all 6 of the
censuses.

Summary of factors:

Fixed: Invasive removal (yes/no), Seeding (yes/no), Timing of census
(early/late)

                Also: growing season rainfall (continuous), year of
treatment (1 or 2)

Plots and initial analyses also show evidence for effects of growing
season rainfall on abundances in a given year (both early and late
counts are higher in years with more rain).  Since the year of initial
treatment also might change longer term responses (half the blocks were
treated in year 1 of the experiment, and half in year 2), I would like
to start off with a model that allows me to test for year of treatment
by experimental factor interactions.

Random: Block

                Repeated within subjects (plots): Census (6 total,
across 3 years)

The main challenge I am running into is figuring out how to correctly
model the repeated measures and get the syntax right for the random
effects.  Most of the examples I have found for repeated measures in
mixed models involve longitudinal data sets where the researchers are
measuring continuous change in a response over time- so, for example, if
the seeding effects were at the maximum in census 1 and dropped off in a
linear way over the subsequent censuses, or vice versa.  In that case,
if I understand right, the repeated measures would be modeled by
creating a random effect that lets the regression (intercept, slopes or
both) of the time vs. abundance vary among plots, e.g. census would be a
numeric/continuous variable and the model might read something like:

Abundance~ fixed effects + 1|Block + Census|plot

However, in this case, there is no clear linear relationship between the
census number and the response- instead, the abundances go up and down
from year to year (a lot of this variation appears to be explained by
rainfall).  Also, within any given year the early census abundances are
higher than the late ones.   I am also not clear on how to handle the
early vs. late factor- this is a fixed effect, but since some censuses
are by definition early and others late, should this be nested in the
random effect for the repeated measure in some way?  Or perhaps rather
than using "census" to define the repeated measure, I need to write the
effect in terms of year (the three years over which data were collected)
and timing (early vs. late)?

 


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