| mono.con {mgcv} | R Documentation |
Finds linear constraints sufficient for monotonicity (and
optionally upper and/or lower boundedness) of a cubic regression
spline. The basis representation assumed is that given by the
gam, "cr" basis: that is the spline has a set of knots,
which have fixed x values, but the y values of which constitute the
parameters of the spline.
mono.con(x,up=TRUE,lower=NA,upper=NA)
x |
The array of knot locations. |
up |
If TRUE then the constraints imply increase, if
FALSE then decrease. |
lower |
This specifies the lower bound on the spline unless it is
NA in which case no lower bound is imposed. |
upper |
This specifies the upper bound on the spline unless it is
NA in which case no upper bound is imposed. |
Consider the natural cubic spline passing through the points:
(x_i,p_i), i=1..n. Then it is possible
to find a relatively small set of linear constraints on p
sufficient to ensure monotonicity (and bounds if required):
Ap>=b. Details are given in Wood (1994).
This function returns a list containing A and b.
The function returns a list containing constraint matrix
A and constraint vector b.
Simon N. Wood simon.wood@r-project.org
Gill, P.E., Murray, W. and Wright, M.H. (1981) Practical Optimization. Academic Press, London.
Wood, S.N. (1994) Monotonic smoothing splines fitted by cross validation SIAM Journal on Scientific Computing 15(5):1126-1133
http://www.stats.gla.ac.uk/~simon/
## see ?pcls