Introduction to Categorical Data Analysis

6.1 LOGIT MODELS FOR NOMINAL RESPONSES 175
Table 6.1. Alligator Size (Meters) and Primary Food Choice, a for 59 Florida Alligators
1.24 I 1.30 I 1.30 I 1.32 F 1.32 F 1.40 F 1.42 I 1.42 F
1.45 I 1.45 O 1.47 I 1.47 F 1.50 I 1.52 I 1.55 I 1.60 I
1.63 I 1.65 O 1.65 I 1.65 F 1.65 F 1.68 F 1.70 I 1.73 O
1.78 I 1.78 I 1.78 O 1.80 I 1.80 F 1.85 F 1.88 I 1.93 I
1.98 I 2.03 F 2.03 F 2.16 F 2.26 F 2.31 F 2.31 F 2.36 F
2.36 F 2.39 F 2.41 F 2.44 F 2.46 F 2.56 O 2.67 F 2.72 I
2.79 F 2.84 F 3.25 O 3.28 O 3.33 F 3.56 F 3.58 F 3.66 F
3.68 O 3.71 F 3.89 F
aF = Fish, I = Invertebrates, O = Other.
Source: Thanks to M. F. Delany and Clint T. Moore for these data.
Let Y = primary food choice and x = alligator length. For model (6.1) with J = 3,
Table 6.2 shows some output (from PROC LOGISTIC in SAS), with “other” as the
baseline category. The ML prediction equations are
and
log( ˆπ1/ ˆπ3) = 1.618 − 0.110x
log( ˆπ2/ ˆπ3) = 5.697 − 2.465x
Table 6.2. Computer Output for Baseline-Category Logit Model with Alligator Data
Testing Global Null Hypothesis: BETA = 0
Test Chi-Square DF Pf > ChiSq
Likelihood Ratio 16.8006 2 0.0002
Score 12.5702 2 0.0019
Wald 8.9360 2 0.0115
Analysis of Maximum Likelihood Estimates
Standard Wald
Parameter choice DF Estimate Error Chi-Square Pr > ChiSq
Intercept F 1 1.6177 1.3073 1.5314 0.2159
Intercept I 1 5.6974 1.7938 10.0881 0.0015
length F 1 -0.1101 0.5171 0.0453 0.8314
length I 1 -2.4654 0.8997 7.5101 0.0061
Odds Ratio Estimates
Point 95% Wald
Effect choice Estimate Confidence Limits
length F 0.896 0.325 2.468
length I 0.085 0.015 0.496