Description Usage Arguments Details Value Author(s) References See Also Examples
Function used to define the smooth term (via Psplines) within the gcrq formula. The function actually does not evaluate a (spline) smooth, but simply it passes relevant information to proper fitter functions.
1 2 3 
... 
The quantitative covariate supposed to have a nonlinear relationships with the quantiles. In growth charts this variable is typically the age. 
lambda 
A supplied smoothing parameter for the smooth term. If it is negative scalar, the smoothing parameter is estimated iteratively as discussed in Muggeo et al. (2020). If a positive scalar, it represents the actual smoothing parameter. If it is a vector, cross validation is performed to select the ‘best’ value. See Details in 
d 
The difference order of the penalty. Default to 3. 
by 
if different from 
ndx 
The number of intervals of the covariate range used to build the Bspline basis. Noninteger values are rounded by 
deg 
The degree of the spline polynomial. Default to 3. The Bspline basis is composed by 
knots 
The knots locations. If 
monotone 
Numeric value to set up monotonicity restrictions on the first derivative of fitted smooth function

concave 
Numeric value to set up monotonicity restrictions on the second derivative of fitted smooth function

var.pen 
A character indicating the varying penalty. See Details. 
pen.matrix 
if provided, a penalty matrix A, say, such that A'A is the penalty matrix actually used in the estimation process. It overwrites 
dropc 
logical. Should the first column of the Bspline basis be dropped for the basis identifiability? Default to 
center 
logical. If 
K 
A factor tuning selection of wiggliness of the smoothed curve. The larger 
ridge 
logical. If 
decompose 
logical. If 
When lambda
=0 an unpenalized fit is obtained. At 'middle' lambda values, the fitted curve is a piecewise polynomial of order d1
.
The fit gets smoother as lambda increases, and for a very large value of lambda, it approaches to a polynomial of degree d1
.
It is also possible to put a varying penalty to set a different amount of smoothing. Namely for a
constant smoothing (var.pen=NULL
) the penalty is lambda sum_k Δ^d_k where
Delta^d_k is the kth difference (of order d
) of the spline coefficients. For instance if d=1,
Δ^1_k=b_kb_{k1} where the b_k are the spline coefficients.
When a varying penalty is set, the penalty becomes lambda sum_k Δ^d_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
.
The function simply returns the covariate with added attributes relevant to smooth term.
Vito M. R. Muggeo
Muggeo VMR, Torretta F, Eilers PHC, Sciandra M, Attanasio M (2020). Multiple smoothing parameters selection in additive regression quantiles, Statistical Modelling, to appear.
For a general discussion on using Bspline and penalties in regression model see
Eilers PHC, Marx BD. (1996) Flexible smoothing with Bsplines and penalties. Statistical Sciences, 11:89121.
1 2 3 4 5  ##see ?gcrq
##gcrq(y ~ ps(x),..) #it works (default: center = TRUE, dropc = TRUE)
##gcrq(y ~ 0 + ps(x, center = TRUE, dropc = FALSE)) #it does NOT work
##gcrq(y ~ 0 + ps(x, center = FALSE, dropc = FALSE)) #it works

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