sm {BNSP}  R Documentation 
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.
sm(..., k = 10, knots = NULL, bs = "rd")
... 
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

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 q1 knots are defined by
\mathcal{B}_1 = ≤ft\{φ_{1}(u)=u , φ_{2}(u)=uξ_{1}^2 \log≤ft(uξ_{1}^2\right), …, φ_{q}(u)=uξ_{q1}^2 \log≤ft(uξ_{q1}^2\right)\right\},
where u denotes the Euclidean norm of u and ξ_1,…,ξ_{q1} are the knots that are chosen as the quantiles of the observed values of explanatory variable u, with ξ_1=\min(u_i), ξ_{q1}=\max(u_i) and the remaining knots chosen as equally spaced quantiles between ξ_1 and ξ_{q1}.
Thin plate splines are defined by
\mathcal{B}_2 = ≤ft\{φ_{1}(u)=u , φ_{2}(u)=(uξ_{1})_{+}, …, φ_{q}(u)=(uξ_{q})_{+}\right\},
where (a)_+ = \max(a,0).
Radial basis functions for bivariate smooths are defined by
\mathcal{B}_3 = ≤ft\{u_1,u_2,φ_{3}(u)=uξ_{1}^2 \log≤ft(uξ_{1}^2\right), …, φ_{q}(u)=uξ_{q1}^2 \log≤ft(uξ_{q1}^2\right)\right\}.
Specifies the design matrices of an mvrm
call
Georgios Papageorgiou gpapageo@gmail.com
#see \code{mvrm} example