Deviance is minimized to obtain the best-fitting generalized linear model; in general, lower deviance indicates a better fit.

Deviance is minimized to obtain the best-fitting generalized linear model; in general, lower deviance indicates a better fit.

• A. True
• B. False
• C. Only for nested models
• D. It is not used for model comparison

Answer: (A)

Deviance measures how poorly the model fits the data. It’s defined as twice the difference between the log-likelihood of the saturated model (which fits the data perfectly) and the log-likelihood of the fitted model. Since the saturated model has the best possible likelihood, estimating the GLM parameters by maximum likelihood minimizes this deviance. Therefore, smaller deviance means a better fit. This is why, in general, lower deviance indicates a better-fitting model. In practice, deviance is also used to compare nested models, but deviance alone doesn’t account for model complexity, so criteria like AIC or BIC are often used for model selection.

Deviance measures how poorly the model fits the data. It’s defined as twice the difference between the log-likelihood of the saturated model (which fits the data perfectly) and the log-likelihood of the fitted model. Since the saturated model has the best possible likelihood, estimating the GLM parameters by maximum likelihood minimizes this deviance. Therefore, smaller deviance means a better fit. This is why, in general, lower deviance indicates a better-fitting model. In practice, deviance is also used to compare nested models, but deviance alone doesn’t account for model complexity, so criteria like AIC or BIC are often used for model selection.