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##' @export
"nonlinear<-" <- function(object,...,value) UseMethod("nonlinear<-")
##' @export
"nonlinear" <- function(object,...) UseMethod("nonlinear")
naturalcubicspline <- function(x, knots=stats::median(x,na.rm=TRUE), boundary=range(x,na.rm=TRUE)) {
## C2 functions, piecewise cubic
breaks <- c(boundary[1],knots,boundary[2])
K <- length(breaks)
g <- function(x,tau) (x-tau)^3*((x-tau)>0)
gg <- matrix(0,nrow=length(x),ncol=K)
for (i in seq(K)) {
gg[,i] <- g(x,breaks[i])
}
B <- matrix(0,nrow=length(x),ncol=K-2)
for (i in seq(K-2)) {
B[,i] <- gg[,i] -
(breaks[K]-breaks[i])/(breaks[K]-breaks[K-1])*gg[,K-1] +
(breaks[K-1]-breaks[i])/(breaks[K]-breaks[K-1])*gg[,K]
}
cbind(x,B)
}
ncspred <- function(mu, var, knots=c(-5,0,5)) {
breaks <- knots
K <- length(breaks)
v <- as.vector(var)
k <- sqrt(v/(2*pi))
g <- function(x,tau) {
x0 <- (x-tau)
x2 <- x0^2
p0 <- 1-pnorm(-x0/sqrt(v)) # P(x>tau|...)
k*(2*v + x2)*exp(-(x0/(sqrt(2*v)))^2) +
x0*(x2+3*v)*p0
}
n <- NROW(mu)
gg <- matrix(0,nrow=n,ncol=K)
for (i in seq(K)) {
gg[,i] <- g(mu,breaks[i])
}
B <- matrix(0,nrow=n,ncol=K-2)
for (i in seq(K-2)) {
B[,i] <- gg[,i] -
(breaks[K]-breaks[i])/(breaks[K]-breaks[K-1])*gg[,K-1] +
(breaks[K-1]-breaks[i])/(breaks[K]-breaks[K-1])*gg[,K]
}
cbind(mu,B)
}
##' @export
nonlinear.lvm <- function(object, to, from=NULL, type=c("quadratic"), knots=c(-5,0,5), names, ...) {
if (missing(to)) {
return(object$attributes$nonlinear)
}
if (inherits(to,"formula")) {
yy <- decomp.specials(getoutcome(to))
myvars <- all.vars(to)
from <- setdiff(myvars,yy)
to <- yy
}
if (length(to)>1) stop("Supply only one response variable")
if (length(from)>1) stop("Supply only one explanatory variable")
object <- cancel(object, c(from,to))
variance(object) <- to
f <- pred <- NULL
if (tolower(type)[1]%in%c("ncs","spline","naturalspline","cubicspline","natural cubic spline")) {
if (is.null(knots)) stop("Need cut-points ('knots')")
if (length(knots)<3) {
warning("Supply at least three knots (one interior and boundaries)")
## Fall-back to linear
type <- "linear"
}
if (missing(names)) names <- paste0(from,"_",seq(length(knots)-1))
f <- function(p,x) {
B <- cbind(1,naturalcubicspline(x,knots=knots[-c(1,length(knots))],boundary=knots[c(1,length(knots))]))
colnames(B) <- c("(Intercept)",names)
as.vector(B%*%p)
}
pred <- function(mu,var,...) {
B <- ncspred(mu,var,knots=knots)
structure(B,dimnames=list(NULL,names))
}
}
if (tolower(type)[1]=="linear") {
if (missing(names)) names <- from
f <- function(p,x) p[1] + p[2]*x
pred <- function(mu,var,...) {
structure(cbind(mu[,1]),dimnames=list(NULL,names))
}
}
if (tolower(type)[1]=="quadratic") {
if (missing(names)) names <- paste0(from,"_",1:2)
f <- function(p,x) p[1] + p[2]*x + p[3]*(x*x)
pred <- function(mu,var,...) {
structure(cbind(mu[,1],mu[,1]^2+var[1]),dimnames=list(NULL,names))
}
}
if (tolower(type)[1]%in%c("piecewise","piecewise linear","linear")) {
if (is.null(knots)) stop("Need cut-points ('knots')")
}
if (tolower(type)[1]%in%c("exp","exponential")) {
if (missing(names)) names <- paste0(from,"_",1:2)
f <- function(p,x) p[1] + p[2]*x + p[3]*exp(x)
pred <- function(mu,var,...) {
structure(cbind(mu[,1], exp(0.5*var[1] + mu[,1])),dimnames=list(NULL,names))
}
}
if (tolower(type)[1]%in%c("exp0")) {
if (missing(names)) names <- paste0(from,"_",1)
f <- function(p,x) p[1] + p[2]*exp(x)
pred <- function(mu,var,...) {
structure(cbind(exp(0.5*var[1] + mu[,1])),dimnames=list(NULL,names))
}
}
object$attributes$nonlinear[[to]] <- list(x=from, p=length(names)+1, newx=names, f=f, pred=pred, type=tolower(type[1]))
return(object)
}
##' @export
nonlinear.lvmfit <- function(object, to, ...) {
if (missing(to)) {
return(Model(object)$attributes$nonlinear)
}
Model(object) <- nonlinear(Model(object),to=to,...)
return(object)
}
##' @export
nonlinear.twostage.lvm <- function(object, ...) {
return(object$nonlinear)
}
##' @export
nonlinear.lvmfit <- function(object, ...) {
return(object$nonlinear)
}
##' @export
`nonlinear<-.lvm` <- function(object, ..., type="quadratic", value) {
nonlinear(object,to=value,type=type,...)
}
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