Chemistry Reference
In-Depth Information
add explanatory variables that most improve the model. Selection in this example
is based on the AIC (CHOOSE = AIC) and C
p
(SELECT = CP), although simply
replacing these specifications at the end of the MODEL line with SELECTION =
FORWARD(SELECT = ADJRSQ STOP = SL SLE = 0.2) would permit selection
based on an
r
2
adjusted
instead.
PROC GLMSELECT;
MODEL TOTLEC = SOFTCON ION COVAL HYD DELE ANIP/SELECTION =
FORWARD(SELECT = SL CHOOSE = AIC SLE = 0.2);
RUN;
PROC GLMSELECT;
MODEL TOTLEC = SOFTCON ION COVAL HYD DELE ANIP/SELECTION =
FORWARD(SELECT = CP);
RUN;
PROC REG;
MODEL TOTLEC = SOFTCON ION COVAL HYD DELE ANIP/SELECTION = CP;
PLOT CP.*NP./CMALLOWS = BLACK;
RUN;
The first PROC GLMSELECT in the code uses the AIC statistic to select the combi-
nations of these six variables that produce the most parsimonious model. The model
with the lowest AIC was that combining the softness, covalence, and ionic indices
as shown in the inset table of Figure 8.2. Adding any of the other variables to the
140
120
100
80
60
40
C
p
= P
20
0
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
P (intercept + ...)
Model
AIC
Cp
Intercept
plus σ
con
plus
m
2
r
plus Z
2
/r
53.1
14.9
13.1
11.3
4.4
2.9
1.9
FIGURE 8.2
Results from the SAS code that implements AIC and Mallows's C
p
statistic-
based model selection for the bacterial bioluminescence inhibition by 20 metal ions using 6
candidate explanatory variables (see text for details). The model with the lowest AIC was that
including the softness, covalence, and ionic indices (inset table). Application of Mallows's C
p
statistic also results in selection of the model containing the softness, covalence, and ionic
indices.
