Refer to the discussion of residuals for Poisson models on page 288. Demonstrate how well the standard normal approximation holds for large residuals from a Poisson model with different means. Specifically, for counts y
(a) Compute Pearson residuals pear
(b) Compute both the Poisson and the standard normal cumulative probabilities for a larger value than the Pearson residual, pp
(c) Use cbind(y,pear,pp,pn) to print the results. Compare these probabilities for any Pearson residual above 2, 3, and 4. Are the probabilities similar? Are there any other Pearson residuals below 2 that have probability < 0.05? Are there any other Pearson residuals above 2 that have probability > 0.05?
(d) From parts (a) - (c), what can you conclude about interpreting Pearson residuals from models where yˆ = 2? (e) Repeat these steps for yˆ = 1, 0.5, 0.25, 0.1. Comment on whether you are comfortable using the above 2, 3, and 4 guidelines to identify large Pearson residuals in these cases.