The columns of a model matrix M is projected on the
orthogonal complement to the matrix (1,t),
resp. (1,t,t^2).
Orthogonality is w.r.t. an inner product defined by the positive
definite matrix matrix diag(weight). Non-diagonal matrices
defining the inner product is not supported.
detrend( M, t, weight = rep(1, nrow(M)) )
decurve( M, t, weight = rep(1, nrow(M)) )A model matrix.
The trend defining a subspace. A numerical vector of length
nrow(M).
Weights defining the inner product of vectors x
and y as sum(x*w*y).
A numerical vector of length nrow(M), defaults to a vector of
1s. Must be all non-negative.
detrend returns full-rank matrix with columns orthogonal to
(1,t);
decurve returns full-rank matrix with columns orthogonal to
(1,t,t^2).
The functions are intended to be used in construction of particular parametrizations of age-period-cohort models.