Society of Actuaries (SOA) PA Practice Exam

What characterizes overdispersion in a count variable model?

1. The variance is larger than the mean

2. The mean is larger than the variance

3. The variance equals the mean

4. The model has too many predictors

The correct answer is: The variance is larger than the mean

Overdispersion in a count variable model is characterized by a situation where the variance of the count data exceeds the mean. This phenomenon is important in statistical modeling because many common approaches, such as the Poisson regression, assume that the mean and variance of the count data are equal. When this assumption does not hold—specifically when the variance is greater than the mean—this indicates the presence of overdispersion. In real-world scenarios, overdispersion often occurs due to unaccounted heterogeneity in the data or the influence of external factors leading to greater variability in counts than what is indicated by a simple Poisson distribution. Thus, recognizing overdispersion is critical for selecting the appropriate statistical model or making necessary adjustments (like using a negative binomial regression) to better fit the data. The other options do not capture the essence of overdispersion. The second option describes a situation that is contrary to overdispersion, while the third option represents the typical condition of a Poisson distribution, and the fourth option pertains to model complexity rather than the distribution of the count data itself. Understanding these distinctions is vital for effectively modeling count variables and interpreting their behaviors.