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R / mgcv:なぜte()とti()テンソル積が異なる表面を生成するのですか?
のmgcvパッケージにRは、テンソル積の相互作用をフィッティングするための2つの関数がte()ありti()ます。私は2つの作業の基本的な分業を理解しています(非線形の相互作用を当てはめるか、この相互作用を主効果と相互作用に分解するか)。私が理解していないのは、なぜte(x1, x2)、そしてti(x1) + ti(x2) + ti(x1, x2)(わずかに)異なる結果を生成するのかということです。 MWE(から適応?ti): require(mgcv) test1 <- function(x,z,sx=0.3,sz=0.4) { x <- x*20 (pi**sx*sz)*(1.2*exp(-(x-0.2)^2/sx^2-(z-0.3)^2/sz^2)+ 0.8*exp(-(x-0.7)^2/sx^2-(z-0.8)^2/sz^2)) } n <- 500 x <- runif(n)/20;z <- runif(n); xs <- seq(0,1,length=30)/20;zs <- seq(0,1,length=30) pr <- data.frame(x=rep(xs,30),z=rep(zs,rep(30,30))) truth <- matrix(test1(pr$x,pr$z),30,30) f <- test1(x,z) y <- f + rnorm(n)*0.2 par(mfrow = c(2,2)) # …
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