ns                  package:splines                  R Documentation

_G_e_n_e_r_a_t_e _a _B_a_s_i_s _M_a_t_r_i_x _f_o_r _N_a_t_u_r_a_l _C_u_b_i_c _S_p_l_i_n_e_s

_D_e_s_c_r_i_p_t_i_o_n:

     Generate the B-spline basis matrix for a natural cubic spline.

_U_s_a_g_e:

     ns(x, df = NULL, knots = NULL, intercept = FALSE,
        Boundary.knots = range(x))

_A_r_g_u_m_e_n_t_s:

       x: the predictor variable.

      df: degrees of freedom. One can supply 'df' rather than knots;
          'ns()' then chooses 'df - 1 - intercept' knots at suitably
          chosen quantiles of 'x'.

   knots: breakpoints that define the spline. The default is no knots;
          together with the natural boundary conditions this results in
          a basis for linear regression on 'x'.  Typical values are the
          mean or median for one knot, quantiles for more knots. See
          also 'Boundary.knots'.

intercept: if 'TRUE', an intercept is included in the basis; default is
          'FALSE'.

Boundary.knots: boundary points at which to impose the natural boundary
          conditions and anchor the B-spline basis (default the range
          of the data).  If both 'knots' and 'Boundary.knots' are
          supplied, the basis parameters do not depend on 'x'. Data can
          extend beyond 'Boundary.knots'

_V_a_l_u_e:

     A matrix of dimension 'length(x) * df' where either 'df' was
     supplied or if 'knots' were supplied, 'df = length(knots) + 1 +
     intercept'. Attributes are returned that correspond to the
     arguments to 'ns', and explicitly give the 'knots',
     'Boundary.knots' etc for use by 'predict.ns()'.

     'ns()' is based on the function 'spline.des'.  It generates a
     basis matrix for representing the family of piecewise-cubic
     splines with the specified sequence of interior knots, and the
     natural boundary conditions.  These enforce the constraint that
     the function is linear beyond the boundary knots, which can either
     be supplied, else default to the extremes of the data.  A primary
     use is in modeling formula to directly specify a natural spline
     term in a model.

_R_e_f_e_r_e_n_c_e_s:

     Hastie, T. J. (1992) Generalized additive models. Chapter 7 of
     _Statistical Models in S_ eds J. M. Chambers and T. J. Hastie,
     Wadsworth & Brooks/Cole.

_S_e_e _A_l_s_o:

     'bs', 'poly', 'predict.ns', 'SafePrediction'

_E_x_a_m_p_l_e_s:

     data(women)
     ns(women$height, df = 5)
     summary(fm1 <- lm(weight ~ ns(height, df = 5), data = women))

     ## example of safe prediction
     plot(women, xlab = "Height (in)", ylab = "Weight (lb)")
     ht <- seq(57, 73, len = 200)
     lines(ht, predict(fm1, data.frame(height=ht)))

