Which statement about deviance is true?

Deviance is a key concept in statistical modeling, particularly in the context of generalized linear models (GLMs). The correct statement identified pertains to the role of deviance in comparing models. Specifically, deviance represents a measure of how well a model fits the data relative to a baseline model, which is often the null model that only includes the intercept.

The calculation of deviance is based on the likelihood of the models; it quantifies the difference between the likelihood of the saturated model (which perfectly fits the data) and the likelihood of the nested model being assessed, allowing one to assess the distance between these two models. In this way, it serves as a diagnostic tool for understanding how much better the fitted model explains the data compared to the simplest model, which is crucial for model comparison and selection.

In contrast, the other statements fall short because deviance indeed has applications for testing significance between models and is closely associated with the concept of residual sum of squares—especially when considering logistic regressions or other contexts where deviance serves as a form of ‘generalized’ residual sum of squares.