| Library: | gam |
| See also: | intest intest2d |
| Quantlet: | interact | |
| Description: | interact estimates a model with interaction terms. It is using the marginal integration estimator with a local polynomial smoother. For details see Sperlich, Tjostheim, Yang (1997) |
| Usage: | {fh,c} = interact(t,y,h,g,loc,incl{,tg}) | |
| Input: | ||
| t | n x p matrix , the observed explanatory variable | |
| y | n x 1 vector , the observed response variables | |
| h | p x 1 or 1 x 1 matrix , chosen bandwidth for the directions of interest in the estimation step | |
| g | p x 1 or 1 x 1 matrix , chosen bandwidth for the directions not of interest in the estimation step | |
| loc | scalar in {0,1,2}, the degree of the local polynomial smoother | |
| incl | pp x 2 matrix, in the rows have to be all pairs of indices for interactions which shall be included in the model. | |
| tg | ng x p matrix , if grid is wished, tg is the grid on which we will estimate. Attention ! If you estimate on a grid, the estimates of the interaction functions are estimated up to a constant shift. Further, if you try to extrapolate, the estimate will be zero minus a centering constant. | |
| Output: | ||
| mod.fh | n x (p+pp) matrix, estimates for the functions | |
| mod.c | scalar, the overall constant | |
library("gam")
randomize(12345)
t = grid(#(-0.9,-0.9),#(0.2,0.2),#(10,10))
n = rows(t)
t = t~(uniform(n)*2-1)
g1 = 2*t[,1]
g2 = t[,2]^2 - mean(t[,2]^2)
g3 = sin(3*t[,3])
g12 = t[,1].*t[,2]
y = g1+g2+g3+g12+normal(n)*sqrt(0.5)
h = #(0.9, 0.9, 0.9)
g = #(1.0, 1.0, 1.0)
incl = 1~2
f = interact(t,y,h,g,1,incl)
library("graphic")
pic = createdisplay(2,2)
dat11 = sort(t[,2]~g2)
datf1 = sort(t[,2]~f.fh[,2])
dat12 = sort(t[,3]~g3)
datf2 = sort(t[,3]~f.fh[,3])
setmaskp(dat11,1,3,8)
setmaskp(dat12,1,3,8)
setmaskp(datf1,4,3,8)
setmaskp(datf2,4,3,8)
setmaskl(datf1,(1:rows(datf1))',4,1,1)
setmaskl(datf2,(1:rows(datf2))',4,1,1)
show(pic,1,1,dat11,datf1)
show(pic,1,2,dat12,datf2)
dat21 = grsurface(t[,1:2]~g12)
dat22 = grsurface(t[,1:2]~f.fh[,4])
gc = grcube( dat21|dat22 )
show(pic,2,1,dat21,gc.box,gc.x,gc.y,gc.z,gc.c)
show(pic,2,2,dat22,gc.box,gc.x,gc.y,gc.z,gc.c)
function estimates