A history of deviance-df plots for non-nested model selection
摘要
The deviance-df plot is a visual aid to assist in model comparisons, especially for non-nested models, if applicable concurrent with commonly used fit statistics. The deviance is a measure of loss or fit between the data and the implied data as reconstructed by a fitted model. Examples are the residual sum of squares, the fitted sum of squares, or a chi-squared statistic. The df indicates the simplicity or complexity of the model. Using the deviance-df plot, deviance-df ratios between not necessarily nested models can be visually compared. A primarily historical overview of the origin of the plot will be presented, its early use, as well as various proposals in different contexts, such as Mallows Cp, L-curve, elbow plot, scree plot, Diffit criterion, CHull procedure. In addition, it will be shown that several fit statistics used in structural equation modelling can be included in the plot.