Overdispersion occurs when the observed variance is bigger than expected from the logistic regression model.

Overdispersion occurs when the observed variance is bigger than expected from the logistic regression model.

• A. The observed variance is bigger than expected from the model.
• B. The observed variance is smaller than expected from the model.
• C. The variance equals the model's expectation.
• D. There is no overdispersion in logistic models.

Answer: (A)

Overdispersion means the data are more variable than the model expects. In logistic regression, outcomes are binary and the model assumes a binomial distribution with variance p(1-p) for a given probability p. If the observed variability across cases is larger than this binomial variance, there’s extra variation beyond what the model accounts for—this is overdispersion. It can arise from unmodeled heterogeneity, clustering, or misspecification. A common way to spot it is by comparing the residual deviance to its degrees of freedom; a ratio well above one signals overdispersion. So the statement that the observed variance is bigger than what the model expects correctly describes overdispersion.

Overdispersion means the data are more variable than the model expects. In logistic regression, outcomes are binary and the model assumes a binomial distribution with variance p(1-p) for a given probability p. If the observed variability across cases is larger than this binomial variance, there’s extra variation beyond what the model accounts for—this is overdispersion. It can arise from unmodeled heterogeneity, clustering, or misspecification. A common way to spot it is by comparing the residual deviance to its degrees of freedom; a ratio well above one signals overdispersion. So the statement that the observed variance is bigger than what the model expects correctly describes overdispersion.