Cross validation residuals for generalised least squares and other correlated data models
This work provides a methodological extension for statistical modeling with correlated data, but it is incremental as it builds on existing cross validation techniques.
The authors extended leave-M-out cross validation to generalized least squares models, showing that cross validation residuals relate to Cook's distance and can be computed without refitting models on reduced datasets, similar to ordinary least squares.
Cross validation residuals are well known for the ordinary least squares model. Here leave-M-out cross validation is extended to generalised least squares. The relationship between cross validation residuals and Cook's distance is demonstrated, in terms of an approximation to the difference in the generalised residual sum of squares for a model fit to all the data (training and test) and a model fit to a reduced dataset (training data only). For generalised least squares, as for ordinary least squares, there is no need to refit the model to reduced size datasets as all the values for K fold cross validation are available after fitting the model to all the data.