mono.con                package:mgcv                R Documentation

Monotonicity constraints for a cubic regression spline

Description:

     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.

Usage:

     mono.con(x,up=TRUE,lower=NA,upper=NA)

Arguments:

       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.

Details:

     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'.

Value:

     The function returns a list containing constraint matrix 'A' and
     constraint vector 'b'.

Author(s):

     Simon N. Wood simon.wood@r-project.org

References:

     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

     <URL: http://www.maths.bath.ac.uk/~sw283/>

See Also:

     'mgcv ' 'pcls'

Examples:

     ## see ?pcls

