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OTE/SPH
OTE/SPH
August 31, 2006
JWBK119-12
Introduction to the Analysis of Categorical Data
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Table 12.14 Comparison of possible logistic regression models with only main effects.
95% CI of
odds ratio
SE p- Odds
Predictors Coefficient Coeff. Z value ratio Lower Upper
Constant −19.761 6.515 −3.03 0.002

Dummy variable
combinations
Spine
condition c 21 c 22

2 1 0 −0.962 1.397 −0.69 0.491 0.38 0.02 5.91
3 0 1 −2.097 1.055 −1.99 0.047 0.12 0.02 0.97
Width 0.837 0.256 3.27 0.001 2.31 1.40 3.82

variable is added. Here, a model with spine and carapace width is adopted. The logis-
tic regression table for the refined logistic regression model with spine and carapace
width is shown in Table 12.14.
From Table 12.14, it can be observed from the p-value for the coefficient estimates
that the dummy variable representing spine condition 2 (p-value 0.491) appears to
be unnecessary. Spine conditions 1 and 2 can potentially be grouped together. It is
expected that this will not affect the predictive power of the simplified model. Hence,
a simplified model is fitted with only one dummy variable to differentiate crabs with
spine condition 3 from the others. The parameter MLEs together with their corre-
sponding p-value and odds ratio are shown in Table 12.15. From equation (12.16), this
model gives a likelihood ratio statistic of 21.964 with 2 degrees of freedom. Compared
with the earlier model with an additional dummy variable distinguishing spine con-
dition 2, the difference in the likelihood ratio statistic, G D , is 0.479. The p-value based
2
on an approximate null χ distribution with 1 degree of freedom, is 0.5 implying that
this simplified model is no different from the earlier model with 2 dummy variables
differentiating spine conditions 1, 2 and 3.

Table 12.15 Comparison of possible logistic regression models with only main effects.
95% CI of
odds ratio
SE p- Odds
Predictors Coefficient Coeff. Z value ratio Lower Upper
Constant −20.871 6.339 −3.29 0.001
Spine Condition 3 −1.732 0.857 −2.02 0.043 0.18 0.03 0.95
Width 0.866 0.251 3.44 0.001 2.38 1.45 3.90