8.4 For 63 alligators caught in Lake George, Florida, Table 8.17 classifies primary food choice as (fish, invertebrate, other) and shows length in meters. Alligators are called subadults if length 1.83 meters. a. Measuring length as (adult, subadult), find a model that adequately describes effects of gender and length on food choice. Interpret the effects. For adult females, find the estimated probabilities of the food choice categories. b. Using only observations for which primary food choice was fish or invertebrate, find a model that adequately describes effects of gender and binary length. Com- pare parameter estimates and standard errors for this separate-fitting approach to those obtained with simultaneous fitting, including the other category. c. Treating length as binary loses information. Adapt the model in part (a) to use the continuous length measurements. Interpret, explaining how the estimated outcome probabilities vary with length. Find the estimated length at which the invertebrate and other categories are equally likely. EXERCISES 331 Table 8.17 Data for Exercise 8.4" on Alligator Food Choice Males Females Length Length Length Length (m) Choice (m) Choice (m) Choice (m) Choice 1.30 1.70 3.33 1.78 1.32 1.73 3.56 1.80 1.32 1.78 3.58 F 1.88 1.40 1.78 3.66 2.16 1.42 1.80 3.68 2.26 1.42 1.85 3.71 2.31 1.47 1.93 3.89 F 2.36 1.47 1.93 1.24 2.39 1.50 1.98 1.30 2.41 1.52 2.03 1.45 2.44 1.63 2.03 1.45 2.56 1.65 2.31 1.55 2.67 1.65 2.36 1.60 2.72 1.65 2.46 1.60 2.79 79-0 1.65 3.25 1.65 2.84 1.68 3.28 1.78 " F. fish: /, invertebrates; O. other