The Great Plains region of the United States usually has a number of tornadoes during the non-winter months. Groups of scientists, called storm chasers, travel throughout the region when thunderstorms are expected in the hopes of encountering a tornado and taking various measurements on it. The file Stormchaser.csv contains the number of tornadoes encountered on 69 12-hour long storm chases during 1999-2004 for one particular storm chaser. Using these data, do the following:
(a) Make a plot comparing the observed counts of tornadoes against the Poisson PMF. Comment on the fit of the Poisson model; does zero inflation appear to be a problem?
(b) What different assumptions do the hurdle and ZIP models make regarding the cause of zero counts of tornadoes?
(c) There are many different kinds of thunderstorms, but storm chasers specifically seek those that seem to have the potential for tornadic development. With this in mind, describe what the parameter π would represent in a zero-inflated model.
(d) Fit both the ZIP and hurdle models, using only an intercept for both the mean and probability portions of the models. In each model, estimate both parameters with 95% confidence intervals and interpret the results.