| sm {BNSP} | R Documentation |
Smooth terms in mvrm formulae
Description
Function used to define smooth effects in the mean and variance formulae of function mvrm.
The function is used internally to construct the design matrices.
Usage
sm(..., k = 10, knots = NULL, bs = "rd")Arguments
... |
one or two covariates that the smooth term is a function of. If two covariates are used,
they may be both continuous or one continuous and one discrete. Discrete variables should be defined as |
k |
the number of knots to be utilized in the basis function expansion. |
knots |
the knots to be utilized in the basis function expansion. |
bs |
a two letter character indicating the basis functions to be used. Currently, the options are
|
Details
Use this function within calls to function mvrm to specify smooth terms in the mean and/or variance function
of the regression model.
Univariate radial basis functions with q basis functions or q-1 knots are defined by
\mathcal{B}_1 = \left\{\phi_{1}(u)=u , \phi_{2}(u)=||u-\xi_{1}||^2 \log\left(||u-\xi_{1}||^2\right), \dots,
\phi_{q}(u)=||u-\xi_{q-1}||^2 \log\left(||u-\xi_{q-1}||^2\right)\right\},
where ||u|| denotes the Euclidean norm of u and \xi_1,\dots,\xi_{q-1} are the knots that
are chosen as the quantiles of the observed values of explanatory variable u,
with \xi_1=\min(u_i), \xi_{q-1}=\max(u_i) and the remaining knots chosen as equally spaced quantiles between
\xi_1 and \xi_{q-1}.
Thin plate splines are defined by
\mathcal{B}_2 = \left\{\phi_{1}(u)=u , \phi_{2}(u)=(u-\xi_{1})_{+}, \dots, \phi_{q}(u)=(u-\xi_{q})_{+}\right\},
where (a)_+ = \max(a,0).
Radial basis functions for bivariate smooths are defined by
\mathcal{B}_3 = \left\{u_1,u_2,\phi_{3}(u)=||u-\xi_{1}||^2 \log\left(||u-\xi_{1}||^2\right), \dots,
\phi_{q}(u)=||u-\xi_{q-1}||^2 \log\left(||u-\xi_{q-1}||^2\right)\right\}.
Value
Specifies the design matrices of an mvrm call
Author(s)
Georgios Papageorgiou gpapageo@gmail.com
See Also
Examples
#see \code{mvrm} example