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##' @export
totaleffects <- function(object,...,value) UseMethod("totaleffects")
##' @export
totaleffects.lvmfit <- function(object,to,...,level=0.95) {
p <- (1-level)/2
q <- qnorm(p)
res <- c()
if (inherits(to,"formula")) {
if (substr(deparse(to[3]),1,1)==".") {
trim <- function(x) sapply(x,function(z) gsub(" ","",z,fixed=TRUE))
to <- trim(strsplit(deparse(to),"~")[[1]][1])
} else {
to <- list(to)
}
}
if (is.null(list(...)$from) & is.character(to)[1]) {
to <- lapply(paste(to,setdiff(vars(object),to),sep="~"),FUN=as.formula)
}
ef <- function(tt) {
f <- effects(object,tt,...)
rbind(with(f$totalef,c(est,sd,est/sd,2*(pnorm(abs(est/sd),lower.tail=FALSE)),est+q*sd,est-q*sd)))
}
if (is.list(to)) {
for (tt in to) {
res <- rbind(res,ef(tt))
}
}
else
res <- ef(to)
colnames(res) <- c("Estimate","Std.Err","z value","Pr(>|z|)",
paste0(c(1-p,p)*100,"%"))
rownames(res) <- to
res
}
##' @export
effects.lvmfit <- function(object,to,from,...) {
if (missing(to)) {
return(summary(object))
}
P <- path(object,to=to,from=from,...)
if (is.null(P$path)) {
if (inherits(to,"formula")) {
f <- extractvar(to)
to <- f$y; from <- f$x
}
} else {
from <- P$path[[1]][1]
to <- tail(P$path[[1]],1)
}
cc <- coef(object,type=9,labels=FALSE) ## All parameters (fixed and variable)
cc0 <- cbind(coef(object)) ## Estimated parameters
i1 <- na.omit(match(rownames(cc),rownames(cc0)))
idx.cc0 <- which(rownames(cc)%in%rownames(cc0)); ## Position of estimated parameters among all parameters
S <- matrix(0,nrow(cc),nrow(cc)); rownames(S) <- colnames(S) <- rownames(cc)
V <- object$vcov
npar.mean <- index(object)$npar.mean
S[idx.cc0,idx.cc0] <- V[i1,i1] ## "Covariance matrix" of all parameters
cclab <- rownames(coef(object,type=9,labels=TRUE)) ## Identify equivalence constraints
cctab <- table(cclab)
equiv <- which(cctab>1)
for (i in seq_len(length(equiv))) {
orgpos <- which(cclab==(names(equiv)[i]))
pos <- orgpos[-1]
for (p in pos)
S[p,-orgpos[1]] <- S[-orgpos[1],p] <- S[orgpos[1],-p]
}
idx.orig <- unique(unlist(P$idx))
coefs.all <- cc[idx.orig]
S.all <- S[idx.orig,idx.orig]
idx.all <- numberdup(unlist(P$idx))
pos <- 1; idx.list <- P$idx; for (i in seq_len(length(idx.list))) {
K <- length(idx.list[[i]])
idx.list[[i]] <- idx.all[pos:(pos+K-1)]; pos <- pos+K
}
margef <- list()
if (length(coefs.all)==1 && is.na(coefs.all)) {
totalef <- list(est=0,sd=0)
margef <- c(margef,list(est=0,sd=NA))
} else {
totalef <- prodsumdelta(coefs.all, idx.list, S.all,...)
for (i in seq_len(length(idx.list))) {
margef <- c(margef, list(prodsumdelta(coefs.all, idx.list[i], S.all,...)))
}
}
directidx <- which(lapply(P$path,length)==2)
inef.list <- idx.list
if (length(directidx)==0) {
directef <- list(est=0, sd=NA)
} else {
inef.list <- inef.list[-directidx]
directef <- margef[[directidx]]
}
if (length(inef.list)==0) {
totalinef <- list(est=0,sd=NA,grad=NA,hess=NA)
} else {
totalinef <- prodsumdelta(coefs.all, inef.list, S.all,...)
}
nn <- c("total","direct","indirect")
for (i in seq_len(length(margef))) {
if (length(P$path[[i]])>2) {
nn <- c(nn,paste(rev(P$path[[i]]),collapse=lava.options()$symbol[1]))
}
}
b <- c(totalef$est,directef$est,totalinef$est,totalinef$b)
names(b) <- nn
D <- t(cbind(totalef$grad,directef$grad,totalinef$grad,totalinef$D))
V <- D%*%S.all%*%t(D)
val <- list(coef=b, vcov=V, grad=D, paths=P$path, totalef=totalef, directef=directef, totalinef=totalinef, margef=margef, from=from, to=to)
class(val) <- "effects"
val
}
##' @export
print.effects <- function(x,digits=4,...) {
s <- summary(x,...)
print(s$coef,digits=digits,...)
cat("\n")
print(s$medprop$coefmat[,c(1,3,4),drop=FALSE],digits=digits,...)
return(invisible(x))
}
##' @export
coef.effects <- function(object,...) {
object$coef
}
##' @export
vcov.effects <- function(object,...) {
object$vcov
}
##' @export
summary.effects <- function(object,...) {
totalef <- with(object$totalef, cbind(est,sd[1]))
directef <- with(object$directef, cbind(est,sd[1]))
totindirectef <- with(object$totalinef, cbind(est,sd[1]))
rownames(totalef) <- "Total"
rownames(directef) <- "Direct"
rownames(totindirectef) <- "Indirect"
nn <- indirectef <- c()
K <- seq_len(length(object$margef))
for (i in K) {
if (length(object$paths[[i]])>2) {
nn <- c(nn,paste(rev(object$paths[[i]]),collapse=lava.options()$symbol[1]))
indirectef <- rbind(indirectef, with(object$margef[[i]], c(est,sd)))
}
}; rownames(indirectef) <- nn
mycoef <- rbind(totalef,directef,totindirectef,indirectef)
mycoef <- cbind(mycoef,mycoef[,1]/mycoef[,2])
mycoef <- cbind(mycoef,2*(pnorm(abs(mycoef[,3]),lower.tail=FALSE)))
colnames(mycoef) <- c("Estimate","Std.Err","z value","Pr(>|z|)")
medprop <- NULL
if (totindirectef[1]!=0) {
if (abs(coef(object)[2])<1e-12) {
medprop <- estimate(NULL,coef=c("Mediation proportion"=1),vcov=matrix(NA))
} else {
medprop <- estimate(object, function(x) list("Mediation proportion"=1-x[2]/x[1]))
##medprop <- estimate(object, function(x) list("Mediation proportion"=logit(x[3]/x[1])),back.transform=expit)
}
}
list(coef=mycoef,medprop=medprop)
}
##' @export
confint.effects <- function(object,parm,level=0.95,...) {
mycoef <- summary(object)$coef
p <- 1-(1-level)/2
res <- mycoef[,1] + + qnorm(p)*cbind(-1,1)%x%mycoef[,2]
colnames(res) <- paste0(c(1-p,p)*100,"%")
rownames(res) <- rownames(mycoef)
res
}
prodtrans <- function(betas) {
k <- length(betas)
res <- prod(betas)
nabla <- numeric(k)
for (i in seq_len(k))
nabla[i] <- prod(betas[-i])
H <- matrix(0,k,k)
if (k>1)
for (i in seq_len(k-1))
for (j in (i+1):k)
H[j,i] <- H[i,j] <- prod(c(1,betas[-c(i,j)]))
attr(res,"gradient") <- nabla
attr(res,"hessian") <- H
return(res)
}
prodsumdelta <- function(betas,prodidx,S,order=1) { ## Delta-method
k <- length(prodidx)
p <- length(betas)
if (p==1) {
return(list(est=betas, sd=sqrt(S), grad=0, beta=betas, D=0, hess=0))
}
val <- 0; grad <- numeric(p)
D <- matrix(0,nrow=p,ncol=k)
beta <- numeric(k)
H <- matrix(0,p,p)
for (i in seq_len(k)) {
ii <- prodidx[[i]]
myterm <- prodtrans(betas[ii]);
if (order>1) {
H0 <- attributes(myterm)$hessian
Sigma <- S[ii,ii]
print(sum(diag(Sigma%*%H0))/2)
val <- val + (myterm + sum(diag(Sigma%*%H0))/2)
} else {
val <- val + myterm
beta[i] <- myterm
}
D[ii,i] <- attributes(myterm)$gradient
grad[ii] <- grad[ii] + attributes(myterm)$gradient
}; grad <- matrix(grad,ncol=1)
return(list(est=val, sd=sqrt(t(grad)%*%S%*%grad), grad=grad, b=beta, D=D, hess=H))
}
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