Non-linear Association Structures

The hierarchy can shrink toward simpler association structures when the data do not justify non-linearity. The method represents the association function as f(nu)=g(nu)nu with f(0)=0. The hierarchy includes a standard linear level, a quadratic level, and a spline-deviation level. The Level 3 model uses knots and an orthogonalized second-order random walk to model smooth non-linear departures. The marker must be centered at a meaningful reference point because zero defines the reference risk.