For the horseshoe crab data with width, color, and spine as predictors, suppose you start a backward elimination process with the most complex model possible. Denoted by C ∗ S ∗ W, it uses main effects for each term as well as the three two-factor interactions and the three-factor interaction. Table 5.9 shows the fit for this model and various simpler models d.Finally, compare the working model at this stage to the main-effects model C + S + W. Is it permissible to simplify to this model? e. Of the models shown in the table, which is preferred according to the AIC?

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For the horseshoe crab data with width, color, and spine as predictors, suppose you start a backward elimination process with the most complex model possible. Denoted by C ∗ S ∗ W, it uses main effects for each term as well as the three two-factor interactions and the three-factor interaction. Table 5.9 shows the fit for this model and various simpler models

d.Finally, compare the working model at this stage to the main-effects model C + S + W. Is it permissible to simplify to this model? e. Of the models shown in the table, which is preferred according to the AIC?

Table 5.9. Logistic Regression Models for Horseshoe
Crab Data
Model
Predictors
Deviance
df
AIC
1
C * S * W
170.44
152
212.4
С *S+C* W + S* W
С* S+S*W
2
173.68
155
209.7
За
177.34
158
207.3
3b
C * W + S * W
181.56
161
205.6
3c
C * S +C * W
173.69
157
205.7
S+ C * W
W + C * S
4а
181.64
163
201.6
4b
177.61
160
203.6
5
C+ S+ W
186.61
166
200.6
Transcribed Image Text:Table 5.9. Logistic Regression Models for Horseshoe Crab Data Model Predictors Deviance df AIC 1 C * S * W 170.44 152 212.4 С *S+C* W + S* W С* S+S*W 2 173.68 155 209.7 За 177.34 158 207.3 3b C * W + S * W 181.56 161 205.6 3c C * S +C * W 173.69 157 205.7 S+ C * W W + C * S 4а 181.64 163 201.6 4b 177.61 160 203.6 5 C+ S+ W 186.61 166 200.6
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