Geoscience Reference
In-Depth Information
0.5
0.4
0.3
0.2
1996
1998
2000
2002
2004
2006
Ye ar
FIGURE 11.6
Regression fit for station 90 with a normal distribution overlaid for the year 2002 demonstrat-
ing the interpretation of the within-unit variation.
in Table  11.2, but before interpreting the output in Table  11.2, consider the
analysis for the Equation (11.5) model in Table  11.3, which accommodates
both random intercepts and random slopes.
In Tables 11.2 and 11.3, the first section of output is a section that provides
an indication of the model fit. Akaike's information criterion (AIC) is widely
accepted as a model comparison statistic, and lower values of AIC are associ-
ated with better-fitting models. Comparing the AICs of the random intercept
and random coefficient models (Tables 11.2 and 11.3, respectively), there is a
slightly better fit with the random coefficient model. A difference in AIC of
less than 2 units is generally taken to indicate models of similar fit. The next
section of output provides summaries of the variance components analysis,
and the header for this section is “Random Effects.” When fitting the random
coefficient model, the estimated standard deviation among the intercepts is
σ δ
ˆ
0 = 0.0294, the estimated standard deviation among the random slopes is
ˆ 1 = 0.0074, and the estimated residual standard deviation is σ ˆ = 0.0703.
One additional estimate in the “Random Effects” section of Table  11.3
is the correlation between the random intercepts and the random slopes,
given by ρ
σ δ
ˆ
, 01 . This negative correlation suggests that those sta-
tions that began with lower mercury levels tended to have more substantial
yearly changes during the study period. This can be seen by plotting the
estimated random intercepts against the estimated random slopes as shown
in Figure 11.7.
0.8110
δδ
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