How do you identify overdispersion in a model?

How do you identify overdispersion in a model?

• A. Check deviance and its degrees of freedom; deviance > df signals overdispersion.
• B. Check the AIC
• C. Compare the p-values
• D. It cannot be detected

Answer: (A)

Overdispersion shows up when the variability in the data is larger than what the model’s variance assumption allows. In a generalized linear model, the residual deviance should follow a chi-square distribution with degrees of freedom equal to the residual degrees of freedom, assuming the model is correct. If the observed deviance is much larger than the residual degrees of freedom, that mismatch signals extra dispersion not captured by the model. A quick practical check is the deviance divided by the residual degrees of freedom (or similarly the Pearson chi-square divided by the df); values notably greater than one point to overdispersion. If you detect it, you’d consider alternatives like a quasi-likelihood approach or a different distribution (for example, a negative binomial) or adjust standard errors. AIC, p-values, or the claim that dispersion cannot be detected do not diagnose overdispersion.

Overdispersion shows up when the variability in the data is larger than what the model’s variance assumption allows. In a generalized linear model, the residual deviance should follow a chi-square distribution with degrees of freedom equal to the residual degrees of freedom, assuming the model is correct. If the observed deviance is much larger than the residual degrees of freedom, that mismatch signals extra dispersion not captured by the model. A quick practical check is the deviance divided by the residual degrees of freedom (or similarly the Pearson chi-square divided by the df); values notably greater than one point to overdispersion. If you detect it, you’d consider alternatives like a quasi-likelihood approach or a different distribution (for example, a negative binomial) or adjust standard errors. AIC, p-values, or the claim that dispersion cannot be detected do not diagnose overdispersion.