[R-sig-ME] Trend in total number of animals

[ONKELINX, Thierry]

Dear all,

Thanky you for your comments.

Adding (1|Year) seems to effect both the estimate and the standard error
of Year. The standard error increases a factor 1.68. That seems logical
to me since (1|Year) and Year compete for information on the data. The
estimate of the trend (fixed effect) changes 37%. And that worries me
more. Therefore I will drop the (1|Year) term and look for some relevant
weather data. We know that there is some correlation with the
temperature at the moment of observation.

The actual dataset is much longer than ten years, but we use only the
years were we have unambiguous information on the room in which an
individual was recorded. Our dataset contains a row with the number of
individuals, the room and year for all observed rooms, thus including
rooms without bats but excluding rooms that were not visited in a given
year. Hence the dataset contains no NA values for the number of
individuals. MAR seems a reasonal assumumption on the missingness.

Since the bats are known to change their location within the fortress,
several bats moving from one room to another is not that relevant. Hence
a trend in the total numbers is more important than a trend in the
number in an average room. Therefore I used the model on the data per
room to get an estimating of the number in the entire fortress (= all
rooms with at least one observation).

To upscale the predictions , I calculated the fitted values using both
the fixed and the random effects manually. So it would be something
equivalent as predict.lme(model, newdata = entire.fortress, level = 1).
This yields for each room and each year a prediction on the log-scale.
The number of bats is simulated by rpois with lambda = exp(prediction).
Summing the simulated counts per year over all rooms gives a possible
realisation of total number of bats in a given year. Next I fit a simple
glm(total ~ year) and saved the trend. Repeating that for 1000
simulations gives a interval for the trend on the total number. 

The model using only the the observed totals (discarding information on
the visited rooms), indicate an increase of 30% every five years. The
mixed model, using the information on the rooms, gave an increase of 61%
every five years. Using the mixed model to interpolate the counts to the
non visited rooms and running a large number of simulation yields an
increase of 4% per five years. That last number corresponds with my gut
feeling since some rooms with high numbers were not visited in the early
years. In the recent years most of the rooms are visited and the total
number seems to be more or less stable.

Best regards,

Thierry

------------------------------------------------------------------------
----
ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek
team Biometrie & Kwaliteitszorg
Gaverstraat 4
9500 Geraardsbergen
Belgium

Research Institute for Nature and Forest
team Biometrics & Quality Assurance
Gaverstraat 4
9500 Geraardsbergen
Belgium

tel. + 32 54/436 185
Thierry.Onkelinx at inbo.be
www.inbo.be

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to
say what the experiment died of.
~ Sir Ronald Aylmer Fisher

The plural of anecdote is not data.
~ Roger Brinner

The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of
data.
~ John Tukey

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