Refer to the hospital visit data described in Exercise 16 of Chapter 4. Use BMA with a BIC criterion on a zero-inflated Poisson model to identify which of the explanatory variables are related to the number of physician office visits for a person (ofp) and the probability of zero visits. Note that health_excellent and health_poor are really just two levels of a three-level factor. Combine them into a single new variable with three levels, e.g., by taking health = as.factor(health_excellent - health_poor).
For each variable, report:
(a) the estimated probability that it belongs in the model,
(b) its parameter estimate and confidence interval in both parts of the model.
Draw conclusions from your investigation. Because this problem requires programming a model-fitting function to use in glmulti() (a ZIP model is not normally fit using glm()), we have provided some of the necessary code in the program glmultiFORzeroinfl.R. This code needs to be run before glmulti() is called on the zeroinflclass model fit. Please see the comments in the program file for help on how to use glmulti() for this model.12
Exercise 16
Deb and Trivedi (1997) and Zeileis et al. (2008) examine the relationship between the number of physician office visits for a person (ofp) and a set of explanatory variables for individuals on Medicare. Their data are contained in the file dt.csv. The explanatory variables are number of hospital stays (hosp), number of chronic conditions (numchron), gender (gender; male =
1, female = 0), number of years of education (school), and private insurance (privins; yes = 1, no = 0). Two additional explanatory variables given by the authors are denoted as health_excellent and health_poor in the data file. These are self-perceived health status indicators that take on a value of yes = 1 or no = 0, and they cannot both be 1 (both equal to 0 indicates "average" health). Using these data, complete the following:
(a) Estimate the Poisson regression model to predict the number of physician office visits. Use all of the explanatory variables in a linear form without any transformations.
(b) Interpret the effect that each explanatory variable has on the number of physician office visits.
(c) Compare the number of zero-visit counts in the data to the number predicted by the model and comment. Can you think of a possible explanation for why there are so many zeroes in the data?
(d) Estimate the zero-inflated Poisson regression model to predict the number of physician office visits. Use all of the explanatory variables in a linear form without any transformations for the log(µi) part of the model and no explanatory variables in the πi part of the model. Interpret the model fit results.
(e) Complete part (d) again, but now use all of the explanatory variables in a linear form to estimate πi. Interpret the model fit results and compare this model to the previous ZIP model using a LRT.
(f) Examine how well each model estimates the number of 0 counts.