Description Usage Arguments Details Value Decomposition References See Also
Constructs a set of basis vectors C_0 and K_1 used to
constrain distributed lag coefficients, β,
using splines. The basis vectors depend on the radii that define
ring-shaped areas around participant locations.
Typical usage relies on calling basis application functions, like
cr
(e.g. in dlm
model
formulas); users should not often have to interact with basis
directly.
1 |
x |
radii that define ring-shaped areas around participant locations |
center |
if |
scale |
if |
.fun |
a function to define the type of basis. The default is to compute a cubic radial basis based on pairwise cubed absolute differences among the radii. See Details |
... |
other parameters passed to |
Alternative distance functions, .fun
, may be specified, and
error checking on the user's choice of .fun
is deliberately
missing. Proper candidates for .fun
should return an
(L \times L) matrix, where L is the same as length(x)
;
elements of this matrix are typically non-negative.
In addition, new distance function definitions should follow the idiom:
function(x, y, ...)
if (missing(y)) y <- x
...
The default value of .fun
computes cubic radial distance,
which amounts to abs(outer(x, y, "-"))^3
; the computed vectors are
then transformed following Rupert, Wand, and Carroll (2003), such that
the spline can be fitted (and penalized) as a mixed-model.
An object of class LagBasis
Once a basis function (δ()) and radii (r) are chosen, define the matrix, C_1[i, j] = δ(r_i, r_j), and let,
C_0 = [1, r]
C_1 = Q * R
M_1 = Q[-(1:2)]
K_1 = C_1 * M_1 * (M_1' * C_1 * M_1)^-0.5
where A[-j] denotes a matrix A with column(s) j removed. Then the (scaled) distributed lag effects are β = C_0 * α + K_1 * b, where b_l ~ N(0, σ^2_b), for l = 1, ..., L - 2.
Rupert D, Wand MP, & Carroll RJ (2003) Semiparametric Regression. New York: Cambridge University Press.
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