Description
1. In a study of nesting horseshoe crabs, each female horseshoe crab had a male crab
attached to her in her nest. The study investigated factors that affect whether the
female crab had any other males, called satellites, residing near her. Explanatory
variables that are thought to affect this included the female crab’s color (C), spine
condition (S), carapace width (W) and weight (Wt). The response outcome for each
female crab is her number of satellites (Sa). There are 173 females in this study.
Data are provided in the crab.txt.
(a) Fit a Poisson model (M1) with log link with W as the single predictor. Check
the goodness of fit and interpret your model.
(b) Fit a model (M2) with W and Wt as predictors. Compare it with the model
in (a). Interpret your results.
(c) Check over dispersion in M2. Interpret the model after adjusting for over
dispersion.
2. Researchers examined a large number of fish to determine the prevalence of parasites. The dataset (parasite.txt) includes the variables Intensity (i.e., the number
of parasites), Area (a categorical variable), Year (to be treated as categorical), and
Length of the fish.
(a) Fit a Poisson model with log link to the data with area, year, and length as
predictors. Interpret each model parameter.
(b) Test for goodness of fit of the model in (a) and state conclusions.
(c) Researchers suspect that there may be two strains of fish, one that is susceptible
to parasites and one that is not. Without knowing which fish are susceptible,
this could be regarded as a zero-inflated model. Building on the model in (a)
(using the same predictors), fit an appropriate model to the data that can
account for extra zeros. Provide an interpretation for each model parameter
in terms of the problem.
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