Stat 470/670: Exploratory Data Analysis Homework 8
The dataset roaches, which can be obtained either by installing the package rstanarm and then running library(rstanarm); data(roaches) or by downloading the file from http:// jfukuyama.github.io/teaching/stat670/assignments/roaches.rda and running load(’roaches.rda’).
The dataset has information about a roach treatment program. The columns are
– y: The number of roaches that were trapped.
– roach1: The number of roaches before treatment.
– treatment: Whether the residence was treated or not (0/1).
– senior: Whether the building was for seniors only (0/1).
– exposure2: How long the traps were set out for.
Notice that the number of roaches trapped should be some multiple of exposure2, and so when you fit a model you should use log(exposure2) as an offset.
– Fit a Poisson regression where the number of roaches trapped is a function of roach1, treatment, and senior. Make sure to include an offset for the exposure2 variable.
– Using expand.grid to make a grid of predictor variables at which to get fited values and augment to get the fitted values at the grid of predictors, make a plot that shows the model you just fit. What does your plot show you about the effect of treatment? Of the effect of a seniors-only building?
– Make a residuals-vs.-fitted values plot (it might be easier to visualize if you plot the logfitted values instead of the raw fitted values). Does the residual plot suggest that overdispersion is a problem? What would you do to solve this issue (no need to run a new model)?