Geoscience Reference
In-Depth Information
11.6 Summary
This chapter discussed some ways to assess trend using the mercury con-
centration in a lake as an example, with measurements from fish tissue of
mercury concentration (in ppm) taken each year from 1995 to 2006 from
10 stations. The feature of this data set is that the data were collected from
sample units (stations) repeatedly over time, so that they are referred to as
repeated measures data.
First, a test for a difference between any two time periods was considered.
Then, a unit analysis of trend was carried out with separate analyses for each
of the 10 sampling stations using linear regressions. By taking the average for
all stations, the mean mercury concentration was estimated with a confidence
interval. To be able to make inferences for the entire study area from the sam-
ple, a pooled analysis approach was considered. Linear mixed models were
used with variation in trend lines for the slope and intercept among the 10 sta-
tions explicitly included in the model, with the stations considered as random
effects and the year as a fixed factor. It was found that there was some varia-
tion among stations in the mercury concentration to begin with as well as with
the rate at which levels were increasing, with some stations staying nearly the
same. Stations with higher levels of mercury at the beginning tended not to
increase at as high a rate as those stations with lower initial levels.
This example data set illustrates the usefulness of the linear mixed model
for assessing trend. The example had balanced data with an equal number of
repeated observations for each station, but linear mixed models can be used
for unbalanced data and with more complex nested experimental designs.
An example of a more complex nested design would be if there were sur-
veys over the four seasons within each year, surveys in repeat months within
each season, and multiple days of surveying within each month. The model
can also be further extended to accommodate data that are not normally
distributed; this extension would use a more flexible class of models called
generalized linear mixed models (Myers et al
.
, 2010).
