Geoscience Reference
In-Depth Information
81
0.21
82
0.20
83 89
85
0.19
84
0.18
88
86
87
0.17
0.16
90
0.15
0.010
0.015
0.020
0.025
Predicted Slopes
FIGURE 11.7
A scatter plot of the predicted intercepts ˆ
0, versus the predicted slopes ˆ
1, for the study data.
i
i
The negative trend is consistent with ρ
ˆ
0.8220
in Table 11.3.
δδ
, 01
The total estimated variation in the response, merc_conc ij , from Equation
(11.5) is given by
ˆ
2
ˆ
2
2
ˆ
2
.
(11.7)
Var(
merc
_
conc
)
2
year
year
ij
δ
δ
,
δ
j
δ
j
ε
0
0
1
1
See the work of Myers et al . (2010) for more details on this calculation.
Regarding notation, σ
ˆ
ˆ
ˆ
ˆ
01 01 0 1 , and using this expression, the esti-
mated variance for any station during the initial study year is given by
ρ⋅ σ σ
δδ
, ,
δδ
δ
δ
ˆ
2
2 ˆ
ˆ
2
ˆ
2
Var(
merc
_
conc year
==σ+σ⋅
0)
0
⋅+σ
0
ij
,
δ
δ
δ
δ
ε
0
0
1
1
(11.8)
2
2
=
0.0294
+
0.0703
=
0.0058
ˆ , 01 −0.8110 · 0.0294 · 0.0074. One of the uses for
the estimated variance in the mercury concentrations for stations is to discern
how much of the response variation is attributable to variation across the study
site (i.e., variation among stations, δ
ˆ
where σ δδ
, 01 is calculated as σ=
δδ
0 1 ) and how much of the variation is
caused by the within-site variation (i.e., variation within stations σ ε
and
δ
i
i
2
).
The proportion of response variation attributable to differences among sta-
tions (sites) for a given year is
ˆ
2
2 ˆ
ˆ
2
2
σ+σ
year
+ σ
year
δ
δ
,
δ
j
δ
j
Proportion due to stations
=
0
0
1
1
.
(11.9)
ˆ
2
2 ˆ
ˆ
2
2
ˆ
2
σ+σ
year
+ σ
year
+ σ
δ
δ
,
δ
j
δ
j
ε
0
0
1
1
Search WWH ::




Custom Search