Geoscience Reference
In-Depth Information
TABLE 11.4
Predicted Intercepts and Slope Deviations from the
Linear Mixed-Model Random Coefficient Model of the
Mercury Concentration Data
Station
Intercept
Slope
81
0.2133
0.0061
82
0.2056
0.0128
83
0.1977
0.0077
84
0.1856
0.0081
85
0.1953
0.0113
86
0.1744
0.0201
87
0.1707
0.0154
88
0.1745
0.0168
89
0.1982
0.0085
90
0.1488
0.0244
and
merc
_
conc
=
0.2133 0.0061
+
year
.
81
Hence, the yearly expected change in mercury concentration ranged from
0.0061 to 0.0244 ppm across the study area.
11.5 Checking for Model Adequacy
As with any model-fitting analysis, it is important to check that the proposed
model is a reasonable approximation to the underlying true population pro-
cess, and that no assumptions used in the analysis are violated.
One of the ways to review the model for adequacy is to look at the model
residuals. For a linear regression model, as used in this example, the model
residuals should appear to be normally distributed. However, because of the
use of a linear mixed model, there are two other components of the model that
need to be checked for normality. These are the random slopes and the random
intercepts. Normal Q-Q plots of the predicted coefficients for the slope and the
intercept are shown in Figure 11.8. In both graphs, the line appears to be straight
so that the normality assumptions for the intercept and slope are satisfied.
Given the structure of the data, checking for normality in the model resid-
uals involves looking at each set of residuals from each station as shown in
Figure 11.9, where the residuals are displayed in a box plot for each station.
There does not appear to be any reason to be concerned with the assumption
of normality for the residuals.
