What characterizes a saturated model?

What characterizes a saturated model?

• A. A model that perfectly fits the data and contains all possible main effects and interactions.
• B. A model with no interactions between variables.
• C. A model with zero parameters.
• D. A model that excludes higher-order terms.

Answer: (A)

A saturated model is one that has enough parameters to fit every observation exactly, leaving no residual error. In practice, this means the model includes an intercept plus all main effects and all possible interactions among predictors, so the number of estimated parameters matches the number of data points. Because of this, the model reproduces the data perfectly. The option describing a model that perfectly fits the data and contains all possible main effects and interactions captures both the exact fit and the complete specification of effects, which is what a saturated model is. The other ideas don’t fit: a model with no interactions lacks the full set of terms that makes a model saturated; a model with zero parameters could not fit the data; excluding higher-order terms reduces the number of parameters and prevents saturation.

A saturated model is one that has enough parameters to fit every observation exactly, leaving no residual error. In practice, this means the model includes an intercept plus all main effects and all possible interactions among predictors, so the number of estimated parameters matches the number of data points. Because of this, the model reproduces the data perfectly.

The option describing a model that perfectly fits the data and contains all possible main effects and interactions captures both the exact fit and the complete specification of effects, which is what a saturated model is. The other ideas don’t fit: a model with no interactions lacks the full set of terms that makes a model saturated; a model with zero parameters could not fit the data; excluding higher-order terms reduces the number of parameters and prevents saturation.