Geoscience Reference
In-Depth Information
0
2
4
6810
89
90
0.5
0.4
0.3
0.2
0.1
85
86
87
88
0.5
0.4
0.3
0.2
0.1
81
82
83
84
0.5
0.4
0.3
0.2
0.1
0
2
4
6810
0
Ye ar
2
4
6
810
FIGURE 11.5
Observation-specific and population-averaged fits, dashed and solid lines, respectively, of
mercury concentration by study year.
merc
_
conc
=β +δ
+β
year
+δ
year
+ε
ij
0
0,
i
1
j
1,
i
j
ij
(11.5)
=β+δ
(
)
+β+δ
(
)
year
+ε
0
0,
i
1
1,
i
j
ij
where in Equation (11.5) β
0
represents the population-averaged intercept and
δ
0,
i
denotes the random fluctuation from β
0
associated with the
i
ith station.
B a s i c a l ly, β
0
denotes the average mercury concentration for the entire study
area in the initial year of monitoring and δ
0,
i
denotes the deviation from this
population-averaged value for the
i
ith station. Similarly, β
1
in the equation
denotes the expected yearly change in mercury concentration for the entire
study area, whereas δ
1,
i
denotes how the yearly change associated with sta-
tion
i
differs from the population average change. It is generally assumed for
linear mixed models that the δ
0,
i
follow independent and identically distrib-
uted normal distributions with mean 0 and variance σ
δ
2
0
. The same is also
