Kirkpatrick's normalization, phi_n(x) = sqrt((2n+1)/2) P_n(x), with x scaled to
[-1, 1] by the OBSERVED minimum and maximum (or by the given limits). Returns a matrix
with order+1 columns, phi0..phiN, ready to enter as the basis of a reaction-norm
term:
Usage
legendre(x, order = 1L, limits = NULL)
Arguments
- x
the observed gradient
- order
polynomial order, 0 to 6
- limits
minimum and maximum for scaling; if omitted, the observed ones are used
Value
a numeric matrix with one row per element of x and order + 1 columns, named
phi0 to phiN, ready to be bound to the data.
Details
d <- cbind(d, legendre(d$thi, order = 1))
model(y ~ cg + rn(id, base = c("phi0", "phi1")), d, ped)
Scaling by the observed range is part of the MODEL: two data sets with different ranges
give different bases. To compare fits, fix limits.
References
Kirkpatrick, M., Lofsvold, D. & Bulmer, M. (1990). Analysis of the
inheritance, selection and evolution of growth trajectories. Genetics
124:979-993.
