fisher.info.TSLS <- function(par, rdata, edata, omega, par.pos){
id1 <- omega$id1
id10 <- omega$id10
id11 <- omega$id11
id2 <- omega$id2
id20 <- omega$id20
id21 <- omega$id21
id3 <- omega$id3
id30 <- omega$id30
id31 <- omega$id31
m1 <- length(id1)
m10 <- length(id10)
m11 <- length(id11)
m2 <- length(id2)
m20 <- length(id20)
m21 <- length(id21)
m3 <- length(id3)
m30 <- length(id30)
m31 <- length(id31)
ne <- nrow(edata$data)
nr <- nrow(rdata$data)
a <- par['a']
if('b' %in% names(par)){
b <- par['b']
est.b <- TRUE
}else{
b <- 0
est.b <- FALSE
}
c <- par['c']
alp.0 <- par['alp.0']
if('alp.x' %in% par.pos$par.name){
alp.x <- par[par.pos['alp.x', 'start']:par.pos['alp.x', 'end']]
nx <- length(alp.x)
}else{
alp.x <- NA
nx <- 0
}
if('alp.h' %in% par.pos$par.name){
alp.h <- par[par.pos['alp.h', 'start']:par.pos['alp.h', 'end']]
nh <- length(alp.h)
}else{
alp.h <- NA
nh <- 0
}
alp.g <- par[par.pos['alp.g', 'start']:par.pos['alp.g', 'end']]
ng <- length(alp.g)
if('bet.y' %in% par.pos$par.name){
bet.y <- par[par.pos['bet.y', 'start']:par.pos['bet.y', 'end']]
ny <- length(bet.y)
}else{
bet.y <- NA
ny <- 0
}
if('bet.x' %in% par.pos$par.name){
bet.x <- par[par.pos['bet.x', 'start']:par.pos['bet.x', 'end']]
}else{
bet.x <- NA
}
bet.z <- par[par.pos['bet.z', 'start']:par.pos['bet.z', 'end']]
##################
rg <- as.matrix(rdata$data[, rdata$vg, drop = FALSE])
eg <- as.matrix(edata$data[, edata$vg, drop = FALSE])
if(m10 > 0){
rg10 <- rg[id10, , drop = FALSE]
}
if(m11 > 0){
rg11 <- rg[id11, , drop = FALSE]
}
if(m20 > 0){
eg20 <- eg[id20, , drop = FALSE]
}
if(m21 > 0){
eg21 <- eg[id21, , drop = FALSE]
}
if(m30 > 0){
rg30 <- rg[id30, , drop = FALSE]
eg30 <- eg[id30, , drop = FALSE]
}
if(m31 > 0){
rg31 <- rg[id31, , drop = FALSE]
eg31 <- eg[id31, , drop = FALSE]
}
if(m2 > 0){
eg2 <- eg[id2, , drop = FALSE]
}
if(m3 > 0){
eg3 <- eg[id3, , drop = FALSE]
}
eta <- as.vector(rg %*% alp.g)
names(eta) <- rownames(rdata$data)
if(nx > 0){
rx <- as.matrix(rdata$data[, rdata$vx, drop = FALSE])
ex <- as.matrix(edata$data[, edata$vx, drop = FALSE])
if(m10 > 0){
rx10 <- rx[id10, , drop = FALSE]
}
if(m11 > 0){
rx11 <- rx[id11, , drop = FALSE]
}
if(m20 > 0){
ex20 <- ex[id20, , drop = FALSE]
}
if(m21 > 0){
ex21 <- ex[id21, , drop = FALSE]
}
if(m30 > 0){
rx30 <- rx[id30, , drop = FALSE]
ex30 <- ex[id30, , drop = FALSE]
}
if(m31 > 0){
rx31 <- rx[id31, , drop = FALSE]
ex31 <- ex[id31, , drop = FALSE]
}
if(m2 > 0){
ex2 <- ex[id2, , drop = FALSE]
}
if(m3 > 0){
ex3 <- ex[id3, , drop = FALSE]
}
}
if(nh > 0){
eh <- as.matrix(edata$data[, edata$vh, drop = FALSE])
if(m2 > 0){
eh2 <- eh[id2, , drop = FALSE]
}
if(m3 > 0){
eh3 <- eh[id3, , drop = FALSE]
}
if(m21 > 0){
eh21 <- eh[id21, , drop = FALSE]
}
if(m31 > 0){
eh31 <- eh[id31, , drop = FALSE]
}
}
if(ny > 0){
ry <- as.matrix(rdata$data[, rdata$vy, drop = FALSE])
}
rd <- as.vector(rdata$data[, rdata$vd])
names(rd) <- rownames(rdata$data)
n1 <- sum(rd)
n0 <- nr - n1
ed <- as.vector(edata$data[, edata$vd])
names(ed) <- rownames(edata$data)
ez <- as.vector(edata$data[, edata$vz])
names(ez) <- rownames(edata$data)
lin <- a + rg %*% alp.g * bet.z
if(nx > 0){
lin <- lin + rx %*% bet.x
}
if(ny > 0){
lin <- lin + ry %*% bet.y
}
lin <- as.vector(lin)
names(lin) <- rownames(rdata$data)
delta <- exp(lin)
p0 <- 1/ n0 / (1 + n1/n0 * delta) # 1 / (n0 + n1 * delta)
p1 <- p0 * delta
Delta <- -1 + 1 / (1 + n1/n0 * delta) # -n1 p delta
xi <- Delta * (1 + Delta)
r <- ez - alp.0 - eg %*% alp.g - b * ed
if(nx > 0){
r <- r - ex %*% alp.x
}
if(nh > 0){
r <- r - eh %*% alp.h
}
r <- as.vector(r)
names(r) <- rownames(edata$data)
one.e <- rep(1, ne)
one1 <- rep(1, m1)
one2 <- rep(1, m2)
one3 <- rep(1, m3)
one21 <- rep(1, m21)
one31 <- rep(1, m31)
one.r <- rep(1, nr)
name.alp.g <- paste0('alp.', edata$vg)
name.alp.x <- paste0('alp.', edata$vx)
name.alp.h <- paste0('alp.', edata$vh)
name.bet.x <- paste0('bet.', rdata$vx)
name.bet.y <- paste0('bet.', rdata$vy)
name.bet.z <- paste0('bet.', edata$vz)
###########################
## calculate information ##
###########################
sc <- matrix(0, nrow = m1 + m2 + m3, ncol = length(par))
rownames(sc) <- c(id1, id2, id3)
colnames(sc) <- names(par)
id.r <- c(id1, id3)
id.e <- c(id2, id3)
## c
sc[id.e, 'c'] <- -1/c/2 + 1/c^2/2 * r[id.e]^2
## alp.0
sc[id.e, 'alp.0'] <- 1/c * r[id.e]
## alp.x
if(nx > 0){
sc[id.e, name.alp.x] <- 1/c * (r[id.e] * ex[id.e, , drop = FALSE])
}
## alp.h
if(nh > 0){
sc[id.e, name.alp.h] <- 1/c * (r[id.e] * eh[id.e, , drop = FALSE])
}
## alp.g
sc[id.e, name.alp.g] <- 1/c * (r[id.e] * eg[id.e, , drop = FALSE])
##
if(est.b){
sc[id.e, 'b'] <- 1/c * ed[id.e] * r[id.e]
}
## a
sc[id.r, 'a'] <- rd[id.r] + Delta[id.r]
## bet.x
if(nx > 0){
sc[id.r, name.bet.x] <- (rd[id.r] + Delta[id.r]) * rx[id.r, , drop = FALSE]
}
## bet.y
if(ny > 0){
sc[id.r, name.bet.y] <- (rd[id.r] + Delta[id.r]) * ry[id.r, , drop = FALSE]
}
## bet.z
sc[id.r, name.bet.z] <- (rd[id.r] + Delta[id.r]) * eta[id.r]
n <- m1 + m2 + m3
if(m10 > 0){
cov10 <- (m10 - 1) * cov(sc[id10, ])
}else{
cov10 <- NULL
}
if(m11 > 0){
cov11 <- (m11 - 1) * cov(sc[id11, ])
}else{
cov11 <- NULL
}
if(m20 > 0){
cov20 <- (m20 - 1) * cov(sc[id20, ])
}else{
cov20 <- NULL
}
if(m21 > 0){
cov21 <- (m21 - 1) * cov(sc[id21, ])
}else{
cov21 <- NULL
}
if(m30 > 0){
cov30 <- (m30 - 1) * cov(sc[id30, ])
}else{
cov30 <- NULL
}
if(m31 > 0){
cov31 <- (m31 - 1) * cov(sc[id31, ])
}else{
cov31 <- NULL
}
info <- NULL
if(!is.null(cov10)){
if(is.null(info)){
info <- cov10
}else{
info <- info + cov10
}
}
if(!is.null(cov11)){
if(is.null(info)){
info <- cov11
}else{
info <- info + cov11
}
}
if(!is.null(cov20)){
if(is.null(info)){
info <- cov20
}else{
info <- info + cov20
}
}
if(!is.null(cov21)){
if(is.null(info)){
info <- cov21
}else{
info <- info + cov21
}
}
if(!is.null(cov30)){
if(is.null(info)){
info <- cov30
}else{
info <- info + cov30
}
}
if(!is.null(cov31)){
if(is.null(info)){
info <- cov31
}else{
info <- info + cov31
}
}
info
}
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