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##' @export
predict.lvmfit <- function(object,x=NULL,y=NULL,data=model.frame(object),p=coef(object),...) {
predict(Model(object),x=x,y=y,p=p,data=data,...)
}
##' @export
predict.lvm.missing <- function(object,x=NULL,y=NULL,data=model.frame(object),p=coef(object),...) {
idx <- match(coef(Model(object)),names(coef(object)))
xx <- exogenous(object)
p <- p[idx]
if (!is.null(x)) {
if (inherits(x,"formula")) {
xy <- getoutcome(x)
if (length(xy)>0) {
if (is.null(y)) y <- decomp.specials(xy)
}
x <- attributes(xy)$x
}
x <- intersect(x,endogenous(object))
if (is.null(y))
y <- setdiff(vars(object),c(x,xx))
}
obs0 <- !is.na(data[,x,drop=FALSE])
data[,xx][which(is.na(data[,xx]),arr.ind=TRUE)] <- 0
pp <- predict.lvmfit(object,x=x,y=y,data=data,p=p,...)
if (all(obs0)) return(pp)
if (!requireNamespace("mets",quietly=TRUE)) stop("Requires 'mets'")
obs <- mets::fast.pattern(obs0)
res <- matrix(nrow=nrow(data),ncol=NCOL(pp))
for (i in seq_len(nrow(obs$pattern))) {
jj <- which(obs$pattern[i,]==1)
ii <- which(obs$group==i-1)
if (length(jj)==0) {
res[ii,] <- NA
} else {
res[ii,] <- predict.lvmfit(object,...,p=p,x=x[jj],y=y,data=data[ii,,drop=FALSE])[,colnames(pp),drop=FALSE]
}
}
attributes(res) <- attributes(pp)
return(res)
}
##' Prediction in structural equation models
##'
##' Prediction in structural equation models
##' @param object Model object
##' @param x optional list of (endogenous) variables to condition on
##' @param y optional subset of variables to predict
##' @param residual If true the residuals are predicted
##' @param p Parameter vector
##' @param data Data to use in prediction
##' @param path Path prediction
##' @param quick If TRUE the conditional mean and variance given covariates are returned (and all other calculations skipped)
##' @param \dots Additional arguments to lower level function
##' @seealso predictlvm
##' @examples
##' m <- lvm(list(c(y1,y2,y3)~u,u~x)); latent(m) <- ~u
##' d <- sim(m,100)
##' e <- estimate(m,d)
##'
##' ## Conditional mean (and variance as attribute) given covariates
##' r <- predict(e)
##' ## Best linear unbiased predictor (BLUP)
##' r <- predict(e,vars(e))
##' ## Conditional mean of y3 giving covariates and y1,y2
##' r <- predict(e,y3~y1+y2)
##' ## Conditional mean gives covariates and y1
##' r <- predict(e,~y1)
##' ## Predicted residuals (conditional on all observed variables)
##' r <- predict(e,vars(e),residual=TRUE)
##'
##' @method predict lvm
##' @aliases predict.lvmfit
##' @export
predict.lvm <- function(object,x=NULL,y=NULL,residual=FALSE,p,data,path=FALSE,quick=is.null(x)&!(residual|path),...) {
## data = data.frame of exogenous variables
if (!quick && !all(exogenous(object)%in%colnames(data))) stop("data.frame should contain exogenous variables")
m <- moments(object,p,data=data,...)
if (quick) { ## Only conditional moments given covariates
ii <- index(object)
P.x <- m$P; P.x[ii$exo.idx, ii$exo.idx] <- 0
Cy.x <- (m$IAi%*% tcrossprod(P.x,m$IAi))[ii$endo.idx,ii$endo.idx,drop=FALSE]
X <- ii$exogenous
mu.0 <- m$v; mu.0[ii$exo.idx] <- 0
if (length(X)>0) {
mu.x <- matrix(0,ncol=nrow(data),nrow=length(mu.0))
mu.x[ii$exo.idx,] <- t(data[,X,drop=FALSE])
xi.x <- t(m$IAi[ii$endo.idx,,drop=FALSE]%*%(mu.0 + mu.x))
} else {
xi.x <- m$xi%x%rep(1,nrow(data))
colnames(xi.x) <- ii$endogenous
##xi.x <- matrix(as.vector(m$IAi[ii$endo.obsidx,]%*%mu.0),ncol=nrow(data),nrow=length(mu.0))
##rownames(xi.x) <- names(mu.0)
}
return(structure(xi.x,cond.var=Cy.x,
p=m$p,
e=m$e))
}
X <- exogenous(object)
Y <- setdiff(manifest(object), X)
if (path) {
X <- colnames(data)
Y <- setdiff(Y,X)
idx <- which(vars(object)%in%X)
if (length(Y)==0) stop("New data set should only contain exogenous variables and a true subset of the endogenous variables for 'path' prediction.")
A <- t(m$A)
A[,idx] <- 0 ## i.e., A <- A%*%J
IAi <- solve(diag(nrow=nrow(A))-t(A))
mu.0 <- m$v;
mu.0[X] <- 0
mu.x <- matrix(0,ncol=nrow(data),nrow=length(mu.0))
mu.x[idx,] <- t(data[,vars(object)[idx],drop=FALSE])
pred <- t(IAi%*%(mu.0 + mu.x))
return(pred)
## Y <- endogenous(object,top=TRUE)
## X <- setdiff(manifest(object),Y)
}
IAi <- m$IAi
eta.idx <- match(latent(object),vars(object))
obs.idx <- match(manifest(object),vars(object))
X.idx.all <- match(X, vars(object))
Y.idx.all <- match(Y, vars(object))
## Calculation of conditional variance given X=x
P.x <- m$P; P.x[X.idx.all, X.idx.all] <- 0
C.x <- (IAi%*% P.x %*%t(IAi))
Cy.x <- C.x[Y.idx.all,Y.idx.all,drop=FALSE]
## Calculation of conditional mean given X=x
mu.0 <- m$v; mu.0[X.idx.all] <- 0
if (length(X)>0) {
xs <- data[,X,drop=FALSE]
mu.x <- apply(xs, 1, FUN=function(i) {res <- rep(0,length(mu.0)); res[X.idx.all] <- i; res})
xi.x <- (IAi%*%(mu.0 + mu.x))
} else {
xi.x <- matrix(as.vector(IAi%*%mu.0),ncol=nrow(data),nrow=length(mu.0))
rownames(xi.x) <- names(mu.0)
}
attr(xi.x,"cond.var") <- Cy.x
if (path) return(t(xi.x))
Ey.x <- xi.x[Y.idx.all,,drop=FALSE]
Eeta.x <- xi.x[eta.idx,,drop=FALSE]
Cy.epsilon <- P.x%*%t(IAi) ## Covariance y,residual
##Czeta.y <- Cy.epsilon[eta.idx,index(object)$endo.idx]
A <- m$A
IA <- diag(nrow=nrow(A))-t(A)
y0 <- intersect(Y,colnames(data))
ys <- data[,y0,drop=FALSE]
y0.idx <- match(y0,Y)
ry <- t(ys)-Ey.x[y0.idx,,drop=FALSE]
if (!is.null(x)) {
if (inherits(x,"formula")) {
xy <- getoutcome(x)
if (length(xy)>0) {
if (is.null(y)) y <- decomp.specials(xy)
}
x <- attributes(xy)$x
}
if (length(x)==0) {
if (!is.null(y)) {
xi.x <- xi.x[y,,drop=FALSE]
attr(xi.x,"cond.var") <- Cy.x[y,y,drop=FALSE]
}
return(t(xi.x))
}
x <- intersect(x,endogenous(object))
if (is.null(y))
y <- setdiff(vars(object),c(x,exogenous(object)))
if (length(x)>0) {
E.x <- xi.x[y,,drop=FALSE] + C.x[y,x]%*%solve(C.x[x,x])%*%ry[x,,drop=FALSE]
} else {
E.x <- xi.x[y,,drop=FALSE]
}
if (residual) {
Vhat <- matrix(0, nrow(data), length(vars(object))); colnames(Vhat) <- vars(object)
Vhat[,obs.idx] <- as.matrix(data[,manifest(object),drop=FALSE])
Vhat[,y] <- t(E.x)
return(t((IA%*%t(Vhat)-m$v)))
}
res <- t(E.x); colnames(res) <- y
if (length(x)>0) {
attr(res,"cond.var") <-
C.x[y,y,drop=FALSE]-C.x[y,x,drop=FALSE]%*%solve(C.x[x,x,drop=FALSE])%*%C.x[x,y,drop=FALSE]
} else {
attr(res,"cond.var") <- C.x[y,y,drop=FALSE]
}
return(res)
}
ys <- data[,Y,drop=FALSE]
ry <- t(ys)-Ey.x
if (length(eta.idx)>0) {
Ceta.x <- C.x[eta.idx,eta.idx]
Lambda <- A[Y.idx.all,eta.idx,drop=FALSE] ##, ncol=length(eta.idx))
Cetay.x <- Ceta.x%*%t(Lambda)
KK <- Cetay.x %*% solve(Cy.x)
Eeta.y <- Eeta.x + KK %*% ry
Ceta.y <- Ceta.x - KK%*% t(Cetay.x)
} else {
Eeta.y <- NA
Ceta.y <- NA
}
Vhat <- matrix(0, nrow(data), length(vars(object))); colnames(Vhat) <- vars(object)
Vhat[,obs.idx] <- as.matrix(data[,manifest(object)])
if (length(eta.idx)>0)
Vhat[,latent(object)] <- t(Eeta.y)
epsilonhat <- (t( IA%*%t(Vhat) - m$v ))[,c(endogenous(object),latent(object)),drop=FALSE]
if (residual) {
return(epsilonhat)
}
mydata <- matrix(0,ncol=ncol(A),nrow=nrow(data)); colnames(mydata) <- vars(object)
mydata[,manifest(object)] <- as.matrix(data[,manifest(object)])
for (i in latent(object))
mydata[,i] <- m$v[i]
res <- cbind(t(Ey.x)) ## Conditional mean
attr(res, "cond.var") <- Cy.x
attr(res, "blup") <- t(Eeta.y)
attr(res, "var.blup") <- Ceta.y
attr(res, "Ey.x") <- Ey.x
attr(res, "eta.x") <- Eeta.x
attr(res, "epsilon.y") <- epsilonhat
attr(res, "p") <- m$p
attr(res, "e") <- m$e
class(res) <- c("lvm.predict","matrix")
return(res)
}
##' @export
print.lvm.predict <- function(x,...) print(x[,])
##' Predict function for latent variable models
##'
##' Predictions of conditinoal mean and variance and calculation of
##' jacobian with respect to parameter vector.
##' @export
##' @param object Model object
##' @param formula Formula specifying which variables to predict and which to condition on
##' @param p Parameter vector
##' @param data Data.frame
##' @param ... Additional arguments to lower level functions
##' @seealso predict.lvm
##' @examples
##' m <- lvm(c(x1,x2,x3)~u1,u1~z,
##' c(y1,y2,y3)~u2,u2~u1+z)
##' latent(m) <- ~u1+u2
##' d <- simulate(m,10,"u2,u2"=2,"u1,u1"=0.5,seed=123)
##' e <- estimate(m,d)
##'
##' ## Conditional mean given covariates
##' predictlvm(e,c(x1,x2)~1)$mean
##' ## Conditional variance of u1,y1 given x1,x2
##' predictlvm(e,c(u1,y1)~x1+x2)$var
predictlvm <- function(object,formula,p=coef(object),data=model.frame(object),...) {
model <- Model(object)
if (!missing(formula)) {
yx <- getoutcome(formula)
y <- decomp.specials(yx)
x <- attr(yx,"x")
x <- setdiff(x,index(model)$exogenous)
} else {
y <- index(model)$latent
x <- index(model)$endogenous
}
endo <- with(index(model),setdiff(vars,exogenous))
idxY <- match(y,endo)
idxX <- match(x,endo)
ny <- length(y)
if (ny==0) return(NULL)
m <- modelVar(model,p,conditional=TRUE,data=data,latent=TRUE)
D <- deriv.lvm(model,p,conditional=TRUE,data=data,latent=TRUE)
N <- nrow(data)
ii0 <- seq(N)
iiY <- sort(unlist(lapply(idxY,function(x) ii0+N*(x-1))))
k <- ncol(m$xi)
J <- matrix(seq(k^2),k)
if (length(idxX)==0) { ## Return conditional mean and variance given covariates
M <- m$xi[,idxY,drop=FALSE]
dM <- D$dxi[iiY,,drop=FALSE]
V <- m$C[idxY,idxY,drop=FALSE]
dV <- D$dS[as.vector(J[idxY,idxY]),,drop=FALSE]
} else {
iiX <- sort(unlist(lapply(idxX,function(x) ii0+N*(x-1))))
X <- as.matrix(data[,x,drop=FALSE])
rX <- X-m$xi[,idxX,drop=FALSE]
dX <- D$dxi[iiX,,drop=FALSE]
ic <- solve(m$C[idxX,idxX,drop=FALSE])
c2 <- m$C[idxY,idxX,drop=FALSE]
B <- c2%*%ic
## Conditional variance
V <- m$C[idxY,idxY,drop=FALSE]-B%*%t(c2)
dV <- D$dS[as.vector(J[idxY,idxY]),,drop=FALSE] -
(
(B%x%diag(nrow=ny))%*%D$dS[as.vector(J[idxY,idxX]),,drop=FALSE] +
-(B%x%B)%*%D$dS[as.vector(J[idxX,idxX]),,drop=FALSE] +
(diag(nrow=ny)%x%B)%*%D$dS[as.vector(J[idxX,idxY]),,drop=FALSE]
)
## Conditional mean
M <- m$xi[,idxY,drop=FALSE]+rX%*%t(B)
dB <- (ic%x%diag(nrow=ny))%*%D$dS[as.vector(J[idxY,idxX]),,drop=FALSE]+
-(ic%x%B)%*%D$dS[as.vector(J[idxX,idxX]),,drop=FALSE]
## Find derivative of transposed matrix
n0 <- as.vector(matrix(seq(prod(dim(B))),ncol=nrow(B),byrow=TRUE))
dB. <- dB[n0,,drop=FALSE]
dM <- D$dxi[iiY,,drop=FALSE] +
((diag(nrow=ny)%x%rX)%*%dB.) - kronprod(B,dX)
}
colnames(M) <- y
dimnames(V) <- list(y,y)
return(list(mean=M,mean.jacobian=dM,var=V,var.jacobian=dV))
}
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