Generalized Linear Models Quiz

Answers and explanations appear as you take the quiz.

1. Which three elements define the basic GLM structure described here?
   • A response distribution, linear predictor and link function
   • A response distribution, predictor and coefficient penalty; the link is optional
   • A link function and response family, with no systematic predictor component
   • A linear predictor and link function that together define the response variance
2. In a Gaussian GLM with identity link, how does the conditional mean relate to the predictor?
   • It is the exponential of the predictor
   • It equals the linear predictor
   • It is always between zero and one
   • It is the square of the predictor
3. A binomial GLM uses a logit link. What scale does its linear predictor describe?
   • The event's square root
   • Expected event count
   • Log odds
   • A rank from zero to one
4. Why can a Poisson GLM with a log link produce positive expected counts?
   • Apply the log link directly to the expected count to recover a positive mean
   • Use an identity link and truncate negative fitted means after estimation
   • Exponentiate the observed count rather than the predictor
   • Exponentiating the linear predictor yields a positive mean
5. What does the response family specify beyond the outcome's allowable values?
   • The predictor-to-mean mapping, which is specified by the link
   • A mean-variance relationship associated with the selected family
   • The number of predictor coefficients in the systematic component
   • The linear combination of input features, which forms the predictor
6. A linear predictor for a binary event is zero under the logit link. What probability does the inverse link produce?
   • 1
   • 0
   • 0.5
   • It is undefined
7. In a count-rate GLM, what is an offset commonly used to represent?
   • An estimated exposure slope that may differ freely from one
   • An offset that multiplies the outcome after prediction
   • A residual term that absorbs unobserved exposure
   • A known exposure contribution with a fixed coefficient
8. A GLM with Poisson family is fitted to counts whose conditional variance greatly exceeds the mean. What should the analyst do?
   • Investigate whether the Poisson variance assumption is inadequate
   • Change the link to identity while retaining the same family assumption
   • Use a Gaussian family because counts have a wide variance
   • Assume the Poisson variance is adequate because the target is integer-valued