What does a small scaled deviance indicate about the quality of fit for a model?

A small scaled deviance is indicative of a good fit for a statistical model. It reflects the difference between the observed data and the predictions made by the model. In statistical modeling, scaled deviance is a criterion used to evaluate how well a model captures the underlying patterns in the data. When the scaled deviance is small, it suggests that the model successfully explains a significant portion of the variability in the data, leading to a reliable model fit.

This contrasts with other statements regarding deviance. For instance, a saturated model, which perfectly predicts the data, would indeed have a scaled deviance of zero, not one. Scaled deviance is typically used for comparing nested models rather than non-nested ones, while a larger scaled deviance usually indicates a poorer fit, as it signifies greater discrepancies between observed values and model predictions. Therefore, a small scaled deviance is a strong positive indicator of model fit quality.