Function used to define the smooth term (via P-splines) within the gcrq formula.
The function actually does not evaluate a (spline) smooth, but simply it
passes relevant information to proper fitter functions.
The quantitative covariate supposed to have a nonlinear relationships with the quantiles.
In growth charts this variable is typically the age.
monotone
Numeric value to set up monotonicity restrictions on the fitted smooth function
'0' = no constrain;
'1' = non decreasing smooth function;
'-1' = non increasing smooth function.
lambda
A supplied smoothing parameter for the smooth term. If it is a vector, cross validation is performed to select the ‘best’
value.
pdiff
The difference order of the penalty. Default to 3.
ndx
The number of intervals of the covariate range used to build the B-spline basis. If NULL, default,
the empirical rule of Ruppert is used, namely min(n/4,40).
deg
The degree of the spline polynomial. Default to 3.
var.pen
A character indicating the varying penalty. See Details.
Details
When lambda=0 an unpenalized fit is obtained. The fit gets smoother as lambda increases, and for a very large value of lambda
it approaches to a polynomial of degree pdiff-1. It is also possible to put a varying penalty to set
a different amount of smoothing. For instance for a
constant smoothing (var.pen=NULL) the penalty is lambda sum_k Δ^2_k where
Delta_k is the k-th difference (of order pdiff) of the spline coefficients. When a varying penalty is set,
the penalty becomes lambda sum_k Δ^2_k w_k. The weights w_k depend on var.pen;
for instance var.pen="((1:k)^2)" results in w_k=k^2. See model m5 in examples of gcrq.
Value
The function simply returns the covariate with added attributes relevant to
smooth term.
Author(s)
Vito M. R. Muggeo
References
For a general discussion on using B-spline and penalties in regression model see
Eilers PHC, Marx BD. (1996) Flexible smoothing with B-splines and penalties.
Statistical Sciences, 11:89-121.
providing 
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