The measure of association lambda for nominal variables (Goodman and Kruskal 1954) has V(Y) = 1 — max{π +J ) and VY|i = 1 — max{π J|i }. Interpret lambda as a proportional reduction in prediction...

The measure of association lambda for nominal variables (Goodman and Kruskal 1954) has V(Y) = 1 — max{π_+J) and VY|i = 1 — max{π_J|i}. Interpret lambda as a proportional reduction in prediction error for predictions which select the response category that is most likely. Show that independence implies γ = 0 but that the converse is not true.