Poisson Regression for Count Data Quiz

Answers and explanations appear as you take the quiz.

1. A Poisson model predicts a mean of 2.4 incidents for a site-week. How should that prediction be read?
   • As an expected count across comparable site-weeks
   • As a claim that 2.4 incidents must occur
   • As a probability of exactly 2.4 incidents
   • As an integer label that must be rounded before evaluation
2. With a log link, how is the Poisson expected count obtained from the linear predictor?
   • Take the logarithm of the predictor to recover the expected count
   • Exponentiate the predictor
   • Use the linear predictor itself as the expected count
   • Round the linear predictor before applying the inverse link
3. A site operates four times as many hours as another. What can a log-exposure offset represent?
   • Estimate a separate free coefficient for log exposure
   • Treat exposure hours as the response instead of an offset
   • The greater opportunity to observe events
   • Divide every observed count by exposure and omit exposure from the model
4. After conditioning on predictors, count variance is much larger than the fitted mean. Which concern does this raise?
   • A mean-link mismatch rather than excess conditional variability
   • A structural-zero process established by any observed zero
   • Proof that the expected count must be biased downward
   • Overdispersion relative to the basic Poisson assumption
5. Why can ignoring overdispersion make standard Poisson inference misleading?
   • The coefficient estimates must be biased even if the mean is correct
   • Standard errors may be too small
   • Fitted means become negative under a log link
   • The count outcomes cease to be integers
6. A log-link coefficient is log(1.2) for a predictor's one-unit increase. What multiplicative comparison does it imply?
   • Probability rises by 20 percentage points
   • Expected count rises by exactly 1.2 incidents in every case
   • Expected count is multiplied by 1.2, holding other terms fixed
   • Variance is multiplied by zero
7. When may a negative-binomial model be worth comparing with Poisson regression?
   • Use a negative-binomial model for every count outcome
   • Use a zero-inflated model whenever any zero is present
   • Prefer the model with more parameters regardless of validation
   • When overdispersion is supported by diagnostics and context
8. What should guide the choice between Poisson and a more complex count model?
   • The count-generating process, diagnostics and intended evaluation use
   • Choose whichever model has the smallest training deviance alone
   • Select the model with coefficients that are easiest to explain, regardless of fit
   • Choose the model with the largest number of available predictors