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R/lav_mvnorm_cluster_missing.R
In lavaan: Latent Variable Analysis
Defines functions
lav_mvnorm_cluster_missing_information_observed
lav_mvnorm_cluster_missing_information_firstorder
lav_mvnorm_cluster_missing_scores_2l
lav_mvnorm_cluster_missing_dlogl_2l_samplestats
lav_mvnorm_cluster_missing_loglik_samplestats_2l
# loglikelihood clustered/twolevel data in the presence of missing data
# YR:
# - objective function: first version around March 2021 (see Psych paper)
# - analytic gradient: first version around May 2021
# Mu.W, Mu.B, Sigma.W, Sigma.B are the model-implied statistics
lav_mvnorm_cluster_missing_loglik_samplestats_2l <- function(Y1 = NULL,
Y2 = NULL,
Lp = NULL,
Mp = NULL,
Mu.W = NULL,
Sigma.W = NULL,
Mu.B = NULL,
Sigma.B = NULL,
Sinv.method = "eigen",
log2pi = FALSE,
loglik.x = 0,
minus.two = TRUE) {
# map implied to 2l matrices
out <- lav_mvnorm_cluster_implied22l(
Lp = Lp, Mu.W = Mu.W, Mu.B = Mu.B,
Sigma.W = Sigma.W, Sigma.B = Sigma.B
)
mu.y <- out$mu.y
mu.z <- out$mu.z
sigma.w <- out$sigma.w
sigma.b <- out$sigma.b
sigma.zz <- out$sigma.zz
sigma.yz <- out$sigma.yz
# Lp
nclusters <- Lp$nclusters[[2]]
between.idx <- Lp$between.idx[[2]]
both.idx <- Lp$both.idx[[2]]
cluster.idx <- Lp$cluster.idx[[2]]
# sanity checks
if (any(diag(sigma.w) < 0) || any(diag(sigma.b) < 0)) {
return(+Inf)
}
# check is both.idx part of sigma.b is 'too' negative; if so, return +Inf
ev <- eigen(sigma.b[both.idx, both.idx, drop = FALSE],
symmetric = TRUE,
only.values = TRUE
)$values
if (any(ev < -0.05)) {
return(+Inf)
}
# cat("sigma.w = \n"); print(sigma.w)
# cat("sigma.b = \n"); print(sigma.b)
# cat("mu.y = \n"); print(mu.y)
# global
sigma.w.inv <- solve.default(sigma.w)
sigma.w.logdet <- log(det(sigma.w))
sigma.b <- sigma.b[both.idx, both.idx] # only both part
# y
ny <- ncol(sigma.w)
if (length(between.idx) > 0L) {
Y1w <- Y1[, -between.idx, drop = FALSE]
} else {
Y1w <- Y1
}
Y1w.c <- t(t(Y1w) - mu.y)
PIJ <- matrix(0, nrow(Y1w.c), ny)
# z
nz <- length(between.idx)
if (nz > 0L) {
# check is sigma.zz is PD; if not, return +Inf
ev <- eigen(sigma.zz, symmetric = TRUE, only.values = TRUE)$values
if (any(ev < sqrt(.Machine$double.eps))) {
return(+Inf)
}
Z <- Y2[, between.idx, drop = FALSE]
Z.c <- t(t(Z) - mu.z)
sigma.yz <- sigma.yz[both.idx, , drop = FALSE] # only both part
sigma.zy <- t(sigma.yz)
sigma.zz.inv <- solve.default(sigma.zz)
sigma.zz.logdet <- log(det(sigma.zz))
sigma.zi.zy <- sigma.zz.inv %*% sigma.zy
sigma.b.z <- sigma.b - sigma.yz %*% sigma.zi.zy
GZ <- Z.c %*% sigma.zz.inv # for complete cases only
}
# containters per cluster
q.yy.b <- q.zy <- q.zz.b <- numeric(nclusters)
IBZA.j.logdet <- numeric(nclusters)
ALIST <- rep(list(matrix(
0, length(both.idx),
length(both.idx)
)), nclusters)
# Z per missing pattern
if (nz > 0L) {
Zp <- Mp$Zp
ZPAT2J <- integer(nclusters) # which sigma.b.z per cluster
SIGMA.B.Z <- vector("list", length = Zp$npatterns + 1L)
sigma.j.zz.logdet <- q.zz.a <- 0
for (p in seq_len(Zp$npatterns)) {
freq <- Zp$freq[p]
z.na.idx <- which(!Zp$pat[p, ])
j.idx <- Zp$case.idx[[p]] # cluster indices with this pattern
ZPAT2J[j.idx] <- p
if (length(z.na.idx) > 0L) {
zp <- sigma.zz[-z.na.idx, -z.na.idx, drop = FALSE]
zp.inv <- lav_matrix_symmetric_inverse_update(
S.inv = sigma.zz.inv, rm.idx = z.na.idx,
logdet = TRUE, S.logdet = sigma.zz.logdet
)
zp.logdet <- attr(zp.inv, "logdet")
sigma.j.zz.logdet <- sigma.j.zz.logdet + (zp.logdet * freq)
GZ[j.idx, -z.na.idx] <- Z.c[j.idx, -z.na.idx] %*% zp.inv
yziy <- (sigma.yz[, -z.na.idx, drop = FALSE] %*% zp.inv %*%
sigma.zy[-z.na.idx, , drop = FALSE])
SIGMA.B.Z[[p]] <- (sigma.b - yziy)
} else {
# complete case
sigma.j.zz.logdet <-
sigma.j.zz.logdet + (sigma.zz.logdet * freq)
SIGMA.B.Z[[p]] <- sigma.b.z
}
} # p
# add empty patterns (if any)
if (length(Zp$empty.idx) > 0L) {
ZPAT2J[Zp$empty.idx] <- p + 1L
SIGMA.B.Z[[p + 1L]] <- sigma.b
}
q.zz.a <- sum(GZ * Z.c, na.rm = TRUE)
GZ0 <- GZ
GZ0[is.na(GZ0)] <- 0
GJ <- GZ0 %*% sigma.zy # only both part
}
# Y per missing pattern
W.logdet <- 0
#MPi <- integer(nrow(Y1))
for (p in seq_len(Mp$npatterns)) {
freq <- Mp$freq[p]
na.idx <- which(!Mp$pat[p, ])
j.idx <- Mp$j.idx[[p]]
j1.idx <- Mp$j1.idx[[p]]
TAB <- integer(nclusters)
TAB[j1.idx] <- Mp$j.freq[[p]]
# compute sigma.w.inv for this pattern
if (length(na.idx) > 0L) {
#MPi[Mp$case.idx[[p]]] <- p
wp <- sigma.w[-na.idx, -na.idx, drop = FALSE]
wp.inv <- lav_matrix_symmetric_inverse_update(
S.inv = sigma.w.inv, rm.idx = na.idx,
logdet = TRUE, S.logdet = sigma.w.logdet
)
wp.logdet <- attr(wp.inv, "logdet")
W.logdet <- W.logdet + (wp.logdet * freq)
PIJ[Mp$case.idx[[p]], -na.idx] <-
Y1w.c[Mp$case.idx[[p]], -na.idx] %*% wp.inv
A.j <- matrix(0, ny, ny)
A.j[-na.idx, -na.idx] <- wp.inv
for (j in j1.idx) {
ALIST[[j]] <- ALIST[[j]] + (A.j[both.idx, both.idx] * TAB[j])
}
# WIP[[p]][-na.idx, -na.idx] <- wp.inv
} else {
# complete case
W.logdet <- W.logdet + (sigma.w.logdet * freq)
PIJ[Mp$case.idx[[p]], ] <-
Y1w.c[Mp$case.idx[[p]], ] %*% sigma.w.inv
for (j in j1.idx) {
ALIST[[j]] <-
ALIST[[j]] + (sigma.w.inv[both.idx, both.idx] * TAB[j])
}
}
} # p
q.yy.a <- sum(PIJ * Y1w.c, na.rm = TRUE)
PJ <- rowsum.default(PIJ[, both.idx], cluster.idx,
reorder = FALSE,
na.rm = TRUE
) # only both part is needed
# per cluster
both.diag.idx <- lav_matrix_diag_idx(length(both.idx))
for (j in seq_len(nclusters)) {
# we only need the 'both.idx' part of A.j, sigma.b.z, p.j, g.j ,...
A.j <- ALIST[[j]]
p.j <- PJ[j, ]
if (nz > 0L) {
sigma.b.z <- SIGMA.B.Z[[ZPAT2J[j]]]
} else {
sigma.b.z <- sigma.b
}
IBZA.j <- sigma.b.z %*% A.j
IBZA.j[both.diag.idx] <- IBZA.j[both.diag.idx] + 1
# logdet IBZA.j
tmp <- determinant.matrix(IBZA.j, logarithm = TRUE)
IBZA.j.logdet[j] <- tmp$modulus * tmp$sign
# IBZA.j.inv.BZ.p
IBZA.j.inv.BZ.p <- solve.default(IBZA.j, drop(sigma.b.z %*% p.j))
q.yy.b[j] <- sum(p.j * IBZA.j.inv.BZ.p)
if (nz > 0L) {
g.j <- GJ[j, ]
IBZA.j.inv.g <- solve.default(IBZA.j, g.j)
A.IBZA.j.inv.g <- A.j %*% IBZA.j.inv.g
q.zz.b[j] <- sum(g.j * A.IBZA.j.inv.g)
q.zy[j] <- -sum(p.j * IBZA.j.inv.g)
}
}
if (nz > 0L) {
P <- Mp$nel + Zp$nel
DIST <- (q.yy.a - sum(q.yy.b)) + 2 * sum(q.zy) + (q.zz.a + sum(q.zz.b))
LOGDET <- W.logdet + sum(IBZA.j.logdet) + sigma.j.zz.logdet
} else {
P <- Mp$nel
DIST <- (q.yy.a - sum(q.yy.b))
LOGDET <- W.logdet + sum(IBZA.j.logdet)
}
# loglik?
if (log2pi && !minus.two) {
LOG.2PI <- log(2 * pi)
loglik <- -(P * LOG.2PI + LOGDET + DIST) / 2
} else {
loglik <- DIST + LOGDET
}
# loglik.x (only if loglik is requested)
if (length(unlist(Lp$ov.x.idx)) > 0L && log2pi && !minus.two) {
loglik <- loglik - loglik.x
}
loglik
}
# Mu.W, Mu.B, Sigma.W, Sigma.B are the model-implied statistics
lav_mvnorm_cluster_missing_dlogl_2l_samplestats <- function(
Y1 = NULL,
Y2 = NULL,
Lp = NULL,
Mp = NULL,
Mu.W = NULL,
Sigma.W = NULL,
Mu.B = NULL,
Sigma.B = NULL,
Sinv.method = "eigen",
return.list = FALSE) {
# map implied to 2l matrices
out <- lav_mvnorm_cluster_implied22l(
Lp = Lp, Mu.W = Mu.W, Mu.B = Mu.B,
Sigma.W = Sigma.W, Sigma.B = Sigma.B
)
mu.y <- out$mu.y
mu.z <- out$mu.z
sigma.w <- out$sigma.w
sigma.b <- out$sigma.b
sigma.zz <- out$sigma.zz
sigma.yz <- out$sigma.yz
# containers for dx
dx.mu.y <- numeric(length(mu.y))
dx.mu.z <- numeric(length(mu.z))
dx.sigma.zz <- matrix(0, nrow(sigma.zz), ncol(sigma.zz))
dx.sigma.yz <- matrix(0, nrow(sigma.yz), ncol(sigma.yz))
dx.sigma.b <- matrix(0, nrow(sigma.b), ncol(sigma.b))
dx.sigma.w <- matrix(0, nrow(sigma.w), ncol(sigma.w))
# Lp
nclusters <- Lp$nclusters[[2]]
between.idx <- Lp$between.idx[[2]]
cluster.idx <- Lp$cluster.idx[[2]]
both.idx <- Lp$both.idx[[2]]
# sigma.w
sigma.w.inv <- solve.default(sigma.w)
sigma.b <- sigma.b[both.idx, both.idx] # only both part
# y
ny <- ncol(sigma.w)
if (length(between.idx) > 0L) {
Y1w <- Y1[, -between.idx, drop = FALSE]
} else {
Y1w <- Y1
}
Y1w.c <- t(t(Y1w) - mu.y)
PIJ <- matrix(0, nrow(Y1w.c), ny)
# z
nz <- length(between.idx)
if (nz > 0L) {
Z <- Y2[, between.idx, drop = FALSE]
Z.c <- t(t(Z) - mu.z)
sigma.yz <- sigma.yz[both.idx, , drop = FALSE] # only both part
sigma.zy <- t(sigma.yz)
sigma.zz.inv <- solve.default(sigma.zz)
sigma.zz.logdet <- log(det(sigma.zz))
sigma.zi.zy <- sigma.zz.inv %*% sigma.zy
sigma.b.z <- sigma.b - sigma.yz %*% sigma.zi.zy
GZ <- Z.c %*% sigma.zz.inv # for complete cases only
}
# containters per cluster
# ALIST <- rep(list(matrix(0, length(both.idx),
# length(both.idx))), nclusters)
ALIST <- rep(list(matrix(0, ny, ny)), nclusters)
# Z per missing pattern
if (nz > 0L) {
Zp <- Mp$Zp
ZPAT2J <- integer(nclusters) # which pattern per cluster
SIGMA.B.Z <- vector("list", length = Zp$npatterns + 1L) # +1 for empty
ZIZY <- rep(list(matrix(
0, nrow(sigma.zy),
ncol(sigma.zy)
)), Zp$npatterns + 1L)
ZIP <- rep(list(matrix(
0, nrow(sigma.zz),
ncol(sigma.zz)
)), Zp$npatterns + 1L)
for (p in seq_len(Zp$npatterns)) {
freq <- Zp$freq[p]
z.na.idx <- which(!Zp$pat[p, ])
j.idx <- Zp$case.idx[[p]] # cluster indices with this pattern
ZPAT2J[j.idx] <- p
if (length(z.na.idx) > 0L) {
zp <- sigma.zz[-z.na.idx, -z.na.idx, drop = FALSE]
zp.inv <- lav_matrix_symmetric_inverse_update(
S.inv = sigma.zz.inv, rm.idx = z.na.idx,
logdet = FALSE
)
ZIP[[p]][-z.na.idx, -z.na.idx] <- zp.inv
GZ[j.idx, -z.na.idx] <- Z.c[j.idx, -z.na.idx] %*% zp.inv
Z.G.ZY <- zp.inv %*% sigma.zy[-z.na.idx, , drop = FALSE]
ZIZY[[p]][-z.na.idx, ] <-
zp.inv %*% sigma.zy[-z.na.idx, , drop = FALSE]
yziy <- sigma.yz[, -z.na.idx, drop = FALSE] %*% Z.G.ZY
SIGMA.B.Z[[p]] <- (sigma.b - yziy)
} else {
# complete case
ZIZY[[p]] <- sigma.zi.zy
ZIP[[p]] <- sigma.zz.inv
SIGMA.B.Z[[p]] <- sigma.b.z
}
} # p
# add empty patterns (if any)
if (length(Zp$empty.idx) > 0L) {
ZPAT2J[Zp$empty.idx] <- p + 1L
SIGMA.B.Z[[p + 1L]] <- sigma.b
}
GZ[is.na(GZ)] <- 0
GJ <- GZ %*% sigma.zy
}
# Y per missing pattern
WIP <- rep(list(matrix(0, ny, ny)), Mp$npatterns)
MPi <- integer(nrow(Y1))
for (p in seq_len(Mp$npatterns)) {
freq <- Mp$freq[p]
na.idx <- which(!Mp$pat[p, ])
j.idx <- Mp$j.idx[[p]]
j1.idx <- Mp$j1.idx[[p]]
TAB <- integer(nclusters)
TAB[j1.idx] <- Mp$j.freq[[p]]
if (length(na.idx) > 0L) {
MPi[Mp$case.idx[[p]]] <- p
wp.inv <- lav_matrix_symmetric_inverse_update(
S.inv = sigma.w.inv, rm.idx = na.idx,
logdet = FALSE
)
WIP[[p]][-na.idx, -na.idx] <- wp.inv
PIJ[Mp$case.idx[[p]], -na.idx] <-
Y1w.c[Mp$case.idx[[p]], -na.idx] %*% wp.inv
for (j in j1.idx) {
ALIST[[j]] <-
# ALIST[[j]] + (WIP[[p]][both.idx, both.idx] * TAB[j])
ALIST[[j]] + (WIP[[p]] * TAB[j])
}
} else {
# complete case
PIJ[Mp$case.idx[[p]], ] <-
Y1w.c[Mp$case.idx[[p]], ] %*% sigma.w.inv
WIP[[p]] <- sigma.w.inv
for (j in j1.idx) {
ALIST[[j]] <-
# ALIST[[j]] + (sigma.w.inv[both.idx, both.idx] * TAB[j])
ALIST[[j]] + (sigma.w.inv * TAB[j])
}
}
} # p
PJ <- rowsum.default(PIJ[, , drop = FALSE],
cluster.idx,
reorder = FALSE, na.rm = TRUE
)
# per cluster
both.diag.idx <- lav_matrix_diag_idx(length(both.idx))
for (j in seq_len(nclusters)) {
A.j.full <- ALIST[[j]]
A.j <- A.j.full[both.idx, both.idx, drop = FALSE]
p.j <- as.matrix(PJ[j, ])
pb.j <- as.matrix(PJ[j, both.idx]) # only both.idx part
if (nz > 0L) {
sigma.b.z <- SIGMA.B.Z[[ZPAT2J[j]]]
} else {
sigma.b.z <- sigma.b
}
IBZA.j <- sigma.b.z %*% A.j
IBZA.j[both.diag.idx] <- IBZA.j[both.diag.idx] + 1
IBZA.j.inv.BZ <- solve.default(IBZA.j, sigma.b.z)
IBZA.j.inv.BZ.p <- IBZA.j.inv.BZ %*% pb.j
A.IBZA.j.inv.BZ <- A.j %*% IBZA.j.inv.BZ
A.IBZA.j.inv.BZ.p <- A.IBZA.j.inv.BZ %*% pb.j
IBZA.j.inv <- solve.default(IBZA.j)
A.IBZA.j.inv <- A.j %*% IBZA.j.inv
p.IBZA.j.inv <- t(crossprod(pb.j, IBZA.j.inv))
# only if we have between-only variables
if (nz > 0L) {
g.j <- as.matrix(GJ[j, ])
zij <- as.matrix(GZ[j, ])
zizy <- ZIZY[[ZPAT2J[j]]]
zip <- ZIP[[ZPAT2J[j]]]
IBZA.j.inv.zizy <- solve.default(IBZA.j, t(zizy))
IBZA.j.inv.g <- IBZA.j.inv %*% g.j
IBZA.j.inv.p <- IBZA.j.inv %*% pb.j
A.IBZA.j.inv.g <- A.j %*% IBZA.j.inv.g
A.IBZA.j.inv.zizy <- A.j %*% IBZA.j.inv.zizy
zizy.A.IBZA.j.inv.g <- zizy %*% A.IBZA.j.inv.g
p.IBZA.j.inv.zizy <- crossprod(pb.j, IBZA.j.inv.zizy)
ggbzpp <- 2 * A.IBZA.j.inv.g + A.IBZA.j.inv.BZ.p - pb.j
ZIJzizyp <- (2 * zij - zizy %*% pb.j)
###########
# dx.mu.z #
###########
tmp <- 2 * (t(p.IBZA.j.inv.zizy) - zij - zizy.A.IBZA.j.inv.g)
dx.mu.z <- dx.mu.z + drop(tmp)
###############
# dx.sigma.zz #
###############
tmp1 <- (zip + zizy %*% A.IBZA.j.inv.zizy # logdet
- tcrossprod(zij) # ZA
- tcrossprod(zizy.A.IBZA.j.inv.g)) # ZB-1
d <- (t((2 * zizy.A.IBZA.j.inv.g + zizy %*% A.IBZA.j.inv.BZ.p)
%*% p.IBZA.j.inv.zizy)
+ ZIJzizyp %*% p.IBZA.j.inv.zizy
- 2 * tcrossprod(zizy.A.IBZA.j.inv.g, zij))
tmp2 <- (d + t(d)) / 2
tmp <- tmp1 + tmp2
# symmetry correction
ZZ <- 2 * tmp
diag(ZZ) <- diag(tmp)
dx.sigma.zz <- dx.sigma.zz + ZZ
###############
# dx.sigma.yz #
###############
t0 <- -2 * A.IBZA.j.inv.zizy
t1 <- (-2 * tcrossprod(p.IBZA.j.inv, g.j)
- 1 * tcrossprod(p.IBZA.j.inv, sigma.b.z %*% pb.j)
+ 2 * tcrossprod(A.IBZA.j.inv.g, g.j)) %*% A.IBZA.j.inv.zizy
t2 <- -ggbzpp %*% p.IBZA.j.inv.zizy
t3 <- -tcrossprod(p.IBZA.j.inv, ZIJzizyp)
t4 <- 2 * tcrossprod(A.IBZA.j.inv.g, zij)
tmp <- t0 + t1 + t2 + t3 + t4
dx.sigma.yz[both.idx, ] <- dx.sigma.yz[both.idx, , drop = FALSE] + tmp
##############
# dx.sigma.b #
##############
c <- tcrossprod(ggbzpp, p.IBZA.j.inv)
tmp <- t(A.IBZA.j.inv) - tcrossprod(A.IBZA.j.inv.g) + (c + t(c)) / 2
# symmetry correction
ZZ <- 2 * tmp
diag(ZZ) <- diag(tmp)
dx.sigma.b[both.idx, both.idx] <-
dx.sigma.b[both.idx, both.idx, drop = FALSE] + ZZ
# for dx.sigma.w
PART1.b <- -1 * (IBZA.j.inv.g %*%
(2 * t(IBZA.j.inv.BZ.p) + t(g.j) -
t(g.j) %*% A.IBZA.j.inv.BZ)
+ IBZA.j.inv.BZ + tcrossprod(IBZA.j.inv.BZ.p))
PART2.b <- 2 * (IBZA.j.inv.g + IBZA.j.inv.BZ.p) # vector
} else {
##############
# dx.sigma.b #
##############
bzpp <- A.IBZA.j.inv.BZ.p - pb.j
c <- tcrossprod(bzpp, p.IBZA.j.inv)
tmp <- t(A.IBZA.j.inv) + (c + t(c)) / 2
# symmetry correction
ZZ <- 2 * tmp
diag(ZZ) <- diag(tmp)
dx.sigma.b[both.idx, both.idx] <-
dx.sigma.b[both.idx, both.idx, drop = FALSE] + ZZ
PART1.b <- -1 * (IBZA.j.inv.BZ + tcrossprod(IBZA.j.inv.BZ.p))
PART2.b <- 2 * IBZA.j.inv.BZ.p # vector
}
##############
# dx.sigma.w #
##############
PART1 <- matrix(0, ny, ny)
PART1[both.idx, both.idx] <- PART1.b
PART2 <- matrix(0, ny, 1L)
PART2[both.idx, 1L] <- PART2.b
ij.index <- which(cluster.idx == j)
pij <- PIJ[ij.index, , drop = FALSE]
which.compl <- which(MPi[ij.index] == 0L)
which.incompl <- which(MPi[ij.index] != 0L)
AP2 <- rep(list(sigma.w.inv %*% PART2), length(ij.index))
AP1A.a <- AP1A.b <- matrix(0, ny, ny)
# A.j.full <- matrix(0, ny, ny)
if (length(which.compl) > 0L) {
tmp <- (sigma.w.inv %*% PART1 %*% sigma.w.inv)
AP1A.a <- tmp * length(which.compl)
# A.j.full <- A.j.full + sigma.w.inv * length(which.compl)
}
if (length(which.incompl) > 0L) {
p.idx <- MPi[ij.index][which.incompl]
tmp <- lapply(WIP[p.idx], function(x) {
x %*% PART1 %*% x
})
AP1A.b <- Reduce("+", tmp)
AP2[which.incompl] <-
lapply(WIP[p.idx], function(x) {
x %*% PART2
})
# A.j.full <- A.j.full + Reduce("+", WIP[ p.idx ])
}
t1 <- AP1A.a + AP1A.b
t2 <- (do.call("cbind", AP2) - t(pij)) %*% pij
AA.wj <- t1 + t2
tmp <- A.j.full + (AA.wj + t(AA.wj)) / 2
# symmetry correction
ZZ <- 2 * tmp
diag(ZZ) <- diag(tmp)
dx.sigma.w <- dx.sigma.w + ZZ
###########
# dx.mu.y #
###########
tmp <- numeric(ny)
if (nz > 0L) {
tmp[both.idx] <- IBZA.j.inv.g + IBZA.j.inv.BZ.p
} else {
tmp[both.idx] <- IBZA.j.inv.BZ.p
}
gbzpp <- A.j.full %*% tmp - p.j
dx.mu.y <- dx.mu.y + drop(2 * gbzpp)
} # j
# rearrange
dout <- lav_mvnorm_cluster_2l2implied(
Lp = Lp,
sigma.w = dx.sigma.w, sigma.b = dx.sigma.b,
sigma.yz = dx.sigma.yz, sigma.zz = dx.sigma.zz,
mu.y = dx.mu.y, mu.z = dx.mu.z
)
if (return.list) {
out <- dout
} else {
out <- c(
dout$Mu.W, lav_matrix_vech(dout$Sigma.W),
dout$Mu.B, lav_matrix_vech(dout$Sigma.B)
)
}
out
}
# cluster-wise scores -2*logl wrt Mu.W, Mu.B, Sigma.W, Sigma.B
lav_mvnorm_cluster_missing_scores_2l <- function(
Y1 = NULL,
Y2 = NULL,
Lp = NULL,
Mp = NULL,
Mu.W = NULL,
Sigma.W = NULL,
Mu.B = NULL,
Sigma.B = NULL,
Sinv.method = "eigen") {
# map implied to 2l matrices
out <- lav_mvnorm_cluster_implied22l(
Lp = Lp, Mu.W = Mu.W, Mu.B = Mu.B,
Sigma.W = Sigma.W, Sigma.B = Sigma.B
)
mu.y <- out$mu.y
mu.z <- out$mu.z
sigma.w <- out$sigma.w
sigma.b <- out$sigma.b
sigma.zz <- out$sigma.zz
sigma.yz <- out$sigma.yz
# Lp
nclusters <- Lp$nclusters[[2]]
between.idx <- Lp$between.idx[[2]]
cluster.idx <- Lp$cluster.idx[[2]]
both.idx <- Lp$both.idx[[2]]
# sigma.w
sigma.w.inv <- solve.default(sigma.w)
sigma.b <- sigma.b[both.idx, both.idx] # only both part
# y
ny <- ncol(sigma.w)
if (length(between.idx) > 0L) {
Y1w <- Y1[, -between.idx, drop = FALSE]
} else {
Y1w <- Y1
}
Y1w.c <- t(t(Y1w) - mu.y)
PIJ <- matrix(0, nrow(Y1w.c), ny)
# z
nz <- length(between.idx)
if (nz > 0L) {
Z <- Y2[, between.idx, drop = FALSE]
Z.c <- t(t(Z) - mu.z)
sigma.yz <- sigma.yz[both.idx, , drop = FALSE] # only both part
sigma.zy <- t(sigma.yz)
sigma.zz.inv <- solve.default(sigma.zz)
sigma.zz.logdet <- log(det(sigma.zz))
sigma.zi.zy <- sigma.zz.inv %*% sigma.zy
sigma.b.z <- sigma.b - sigma.yz %*% sigma.zi.zy
GZ <- Z.c %*% sigma.zz.inv # for complete cases only
}
# containters per cluster
# ALIST <- rep(list(matrix(0, length(both.idx),
# length(both.idx))), nclusters)
ALIST <- rep(list(matrix(0, ny, ny)), nclusters)
# both level-1 and level-2
G.muy <- matrix(0, nclusters, length(mu.y))
G.Sigma.w <- matrix(0, nclusters, length(lav_matrix_vech(sigma.w)))
G.Sigma.b <- matrix(0, nclusters, length(lav_matrix_vech(out$sigma.b)))
G.muz <- matrix(0, nclusters, length(mu.z))
G.Sigma.zz <- matrix(0, nclusters, length(lav_matrix_vech(sigma.zz)))
G.Sigma.yz <- matrix(0, nclusters, length(lav_matrix_vec(out$sigma.yz)))
# Z per missing pattern
if (nz > 0L) {
Zp <- Mp$Zp
ZPAT2J <- integer(nclusters) # which pattern per cluster
SIGMA.B.Z <- vector("list", length = Zp$npatterns + 1L) # +1 for empty
ZIZY <- rep(list(matrix(
0, nrow(sigma.zy),
ncol(sigma.zy)
)), Zp$npatterns + 1L)
ZIP <- rep(list(matrix(
0, nrow(sigma.zz),
ncol(sigma.zz)
)), Zp$npatterns + 1L)
for (p in seq_len(Zp$npatterns)) {
freq <- Zp$freq[p]
z.na.idx <- which(!Zp$pat[p, ])
j.idx <- Zp$case.idx[[p]] # cluster indices with this pattern
ZPAT2J[j.idx] <- p
if (length(z.na.idx) > 0L) {
zp <- sigma.zz[-z.na.idx, -z.na.idx, drop = FALSE]
zp.inv <- lav_matrix_symmetric_inverse_update(
S.inv = sigma.zz.inv, rm.idx = z.na.idx,
logdet = FALSE
)
ZIP[[p]][-z.na.idx, -z.na.idx] <- zp.inv
GZ[j.idx, -z.na.idx] <- Z.c[j.idx, -z.na.idx] %*% zp.inv
Z.G.ZY <- zp.inv %*% sigma.zy[-z.na.idx, , drop = FALSE]
ZIZY[[p]][-z.na.idx, ] <-
zp.inv %*% sigma.zy[-z.na.idx, , drop = FALSE]
yziy <- sigma.yz[, -z.na.idx, drop = FALSE] %*% Z.G.ZY
SIGMA.B.Z[[p]] <- (sigma.b - yziy)
} else {
# complete case
ZIZY[[p]] <- sigma.zi.zy
ZIP[[p]] <- sigma.zz.inv
SIGMA.B.Z[[p]] <- sigma.b.z
}
} # p
# add empty patterns (if any)
if (length(Zp$empty.idx) > 0L) {
ZPAT2J[Zp$empty.idx] <- p + 1L
SIGMA.B.Z[[p + 1L]] <- sigma.b
}
GZ[is.na(GZ)] <- 0
GJ <- GZ %*% sigma.zy
}
# Y per missing pattern
WIP <- rep(list(matrix(0, ny, ny)), Mp$npatterns)
MPi <- integer(nrow(Y1))
for (p in seq_len(Mp$npatterns)) {
freq <- Mp$freq[p]
na.idx <- which(!Mp$pat[p, ])
j.idx <- Mp$j.idx[[p]]
j1.idx <- Mp$j1.idx[[p]]
TAB <- integer(nclusters)
TAB[j1.idx] <- Mp$j.freq[[p]]
if (length(na.idx) > 0L) {
MPi[Mp$case.idx[[p]]] <- p
wp.inv <- lav_matrix_symmetric_inverse_update(
S.inv = sigma.w.inv, rm.idx = na.idx,
logdet = FALSE
)
WIP[[p]][-na.idx, -na.idx] <- wp.inv
PIJ[Mp$case.idx[[p]], -na.idx] <-
Y1w.c[Mp$case.idx[[p]], -na.idx] %*% wp.inv
for (j in j1.idx) {
ALIST[[j]] <-
# ALIST[[j]] + (WIP[[p]][both.idx, both.idx] * TAB[j])
ALIST[[j]] + (WIP[[p]] * TAB[j])
}
} else {
# complete case
PIJ[Mp$case.idx[[p]], ] <-
Y1w.c[Mp$case.idx[[p]], ] %*% sigma.w.inv
WIP[[p]] <- sigma.w.inv
for (j in j1.idx) {
ALIST[[j]] <-
# ALIST[[j]] + (sigma.w.inv[both.idx, both.idx] * TAB[j])
ALIST[[j]] + (sigma.w.inv * TAB[j])
}
}
} # p
PJ <- rowsum.default(PIJ[, , drop = FALSE],
cluster.idx,
reorder = FALSE, na.rm = TRUE
)
# per cluster
both.diag.idx <- lav_matrix_diag_idx(length(both.idx))
for (j in seq_len(nclusters)) {
A.j.full <- ALIST[[j]]
A.j <- A.j.full[both.idx, both.idx, drop = FALSE]
p.j <- as.matrix(PJ[j, ])
pb.j <- as.matrix(PJ[j, both.idx]) # only both.idx part
if (nz > 0L) {
sigma.b.z <- SIGMA.B.Z[[ZPAT2J[j]]]
} else {
sigma.b.z <- sigma.b
}
IBZA.j <- sigma.b.z %*% A.j
IBZA.j[both.diag.idx] <- IBZA.j[both.diag.idx] + 1
IBZA.j.inv.BZ <- solve.default(IBZA.j, sigma.b.z)
IBZA.j.inv.BZ.p <- IBZA.j.inv.BZ %*% pb.j
A.IBZA.j.inv.BZ <- A.j %*% IBZA.j.inv.BZ
A.IBZA.j.inv.BZ.p <- A.IBZA.j.inv.BZ %*% pb.j
IBZA.j.inv <- solve.default(IBZA.j)
A.IBZA.j.inv <- A.j %*% IBZA.j.inv
p.IBZA.j.inv <- t(crossprod(pb.j, IBZA.j.inv))
# only if we have between-only variables
if (nz > 0L) {
g.j <- as.matrix(GJ[j, ])
zij <- as.matrix(GZ[j, ])
zizy <- ZIZY[[ZPAT2J[j]]]
zip <- ZIP[[ZPAT2J[j]]]
IBZA.j.inv.zizy <- solve.default(IBZA.j, t(zizy))
IBZA.j.inv.g <- IBZA.j.inv %*% g.j
IBZA.j.inv.p <- IBZA.j.inv %*% pb.j
A.IBZA.j.inv.g <- A.j %*% IBZA.j.inv.g
A.IBZA.j.inv.zizy <- A.j %*% IBZA.j.inv.zizy
zizy.A.IBZA.j.inv.g <- zizy %*% A.IBZA.j.inv.g
p.IBZA.j.inv.zizy <- crossprod(pb.j, IBZA.j.inv.zizy)
ggbzpp <- 2 * A.IBZA.j.inv.g + A.IBZA.j.inv.BZ.p - pb.j
ZIJzizyp <- (2 * zij - zizy %*% pb.j)
###########
# dx.mu.z #
###########
tmp <- 2 * (t(p.IBZA.j.inv.zizy) - zij - zizy.A.IBZA.j.inv.g)
G.muz[j, ] <- drop(tmp)
###############
# dx.sigma.zz #
###############
tmp1 <- (zip + zizy %*% A.IBZA.j.inv.zizy # logdet
- tcrossprod(zij) # ZA
- tcrossprod(zizy.A.IBZA.j.inv.g)) # ZB-1
d <- (t((2 * zizy.A.IBZA.j.inv.g + zizy %*% A.IBZA.j.inv.BZ.p)
%*% p.IBZA.j.inv.zizy)
+ ZIJzizyp %*% p.IBZA.j.inv.zizy
- 2 * tcrossprod(zizy.A.IBZA.j.inv.g, zij))
tmp2 <- (d + t(d)) / 2
tmp <- tmp1 + tmp2
# symmetry correction
ZZ <- 2 * tmp
diag(ZZ) <- diag(tmp)
G.Sigma.zz[j, ] <- lav_matrix_vech(ZZ)
###############
# dx.sigma.yz #
###############
t0 <- -2 * A.IBZA.j.inv.zizy
t1 <- (-2 * tcrossprod(p.IBZA.j.inv, g.j)
- 1 * tcrossprod(p.IBZA.j.inv, sigma.b.z %*% pb.j)
+ 2 * tcrossprod(A.IBZA.j.inv.g, g.j)) %*% A.IBZA.j.inv.zizy
t2 <- -ggbzpp %*% p.IBZA.j.inv.zizy
t3 <- -tcrossprod(p.IBZA.j.inv, ZIJzizyp)
t4 <- 2 * tcrossprod(A.IBZA.j.inv.g, zij)
tmp <- t0 + t1 + t2 + t3 + t4
tmp2 <- matrix(0, nrow(out$sigma.yz), ncol(out$sigma.yz))
tmp2[both.idx, ] <- tmp
G.Sigma.yz[j, ] <- lav_matrix_vec(tmp2)
##############
# dx.sigma.b #
##############
c <- tcrossprod(ggbzpp, p.IBZA.j.inv)
tmp <- t(A.IBZA.j.inv) - tcrossprod(A.IBZA.j.inv.g) + (c + t(c)) / 2
# symmetry correction
ZZ <- 2 * tmp
diag(ZZ) <- diag(tmp)
ZZ2 <- matrix(0, nrow(out$sigma.b), ncol(out$sigma.b))
ZZ2[both.idx, both.idx] <- ZZ
G.Sigma.b[j, ] <- lav_matrix_vech(ZZ2)
# dx.sigma.b[both.idx, both.idx] <-
# dx.sigma.b[both.idx, both.idx, drop = FALSE] + ZZ
# for dx.sigma.w
PART1.b <- -1 * (IBZA.j.inv.g %*%
(2 * t(IBZA.j.inv.BZ.p) + t(g.j) -
t(g.j) %*% A.IBZA.j.inv.BZ)
+ IBZA.j.inv.BZ + tcrossprod(IBZA.j.inv.BZ.p))
PART2.b <- 2 * (IBZA.j.inv.g + IBZA.j.inv.BZ.p) # vector
} else {
##############
# dx.sigma.b #
##############
bzpp <- A.IBZA.j.inv.BZ.p - pb.j
c <- tcrossprod(bzpp, p.IBZA.j.inv)
tmp <- t(A.IBZA.j.inv) + (c + t(c)) / 2
# symmetry correction
ZZ <- 2 * tmp
diag(ZZ) <- diag(tmp)
ZZ2 <- matrix(0, nrow(out$sigma.b), ncol(out$sigma.b))
ZZ2[both.idx, both.idx] <- ZZ
G.Sigma.b[j, ] <- lav_matrix_vech(ZZ2)
# dx.sigma.b[both.idx, both.idx] <-
# dx.sigma.b[both.idx, both.idx, drop = FALSE] + ZZ
PART1.b <- -1 * (IBZA.j.inv.BZ + tcrossprod(IBZA.j.inv.BZ.p))
PART2.b <- 2 * IBZA.j.inv.BZ.p # vector
}
##############
# dx.sigma.w #
##############
PART1 <- matrix(0, ny, ny)
PART1[both.idx, both.idx] <- PART1.b
PART2 <- matrix(0, ny, 1L)
PART2[both.idx, 1L] <- PART2.b
ij.index <- which(cluster.idx == j)
pij <- PIJ[ij.index, , drop = FALSE]
which.compl <- which(MPi[ij.index] == 0L)
which.incompl <- which(MPi[ij.index] != 0L)
AP2 <- rep(list(sigma.w.inv %*% PART2), length(ij.index))
AP1A.a <- AP1A.b <- matrix(0, ny, ny)
# A.j.full <- matrix(0, ny, ny)
if (length(which.compl) > 0L) {
tmp <- (sigma.w.inv %*% PART1 %*% sigma.w.inv)
AP1A.a <- tmp * length(which.compl)
# A.j.full <- A.j.full + sigma.w.inv * length(which.compl)
}
if (length(which.incompl) > 0L) {
p.idx <- MPi[ij.index][which.incompl]
tmp <- lapply(WIP[p.idx], function(x) {
x %*% PART1 %*% x
})
AP1A.b <- Reduce("+", tmp)
AP2[which.incompl] <-
lapply(WIP[p.idx], function(x) {
x %*% PART2
})
# A.j.full <- A.j.full + Reduce("+", WIP[ p.idx ])
}
t1 <- AP1A.a + AP1A.b
t2 <- (do.call("cbind", AP2) - t(pij)) %*% pij
AA.wj <- t1 + t2
tmp <- A.j.full + (AA.wj + t(AA.wj)) / 2
# symmetry correction
ZZ <- 2 * tmp
diag(ZZ) <- diag(tmp)
G.Sigma.w[j, ] <- lav_matrix_vech(ZZ)
# dx.sigma.w <- dx.sigma.w + ZZ
###########
# dx.mu.y #
###########
tmp <- numeric(ny)
if (nz > 0L) {
tmp[both.idx] <- IBZA.j.inv.g + IBZA.j.inv.BZ.p
} else {
tmp[both.idx] <- IBZA.j.inv.BZ.p
}
gbzpp <- A.j.full %*% tmp - p.j
# dx.mu.y <- dx.mu.y + drop(2 * gbzpp)
G.muy[j, ] <- drop(2 * gbzpp)
} # j
# browser()
# rearrange columns to Mu.W, Mu.B, Sigma.W, Sigma.B
ov.idx <- Lp$ov.idx
p.tilde <- length(unique(c(ov.idx[[1]], ov.idx[[2]])))
# Mu.W (for within-only)
Mu.W.tilde <- matrix(0, nclusters, p.tilde)
Mu.W.tilde[, ov.idx[[1]]] <- G.muy
Mu.W.tilde[, Lp$both.idx[[2]]] <- 0 # ZERO!!!
Mu.W <- Mu.W.tilde[, ov.idx[[1]], drop = FALSE]
# Mu.B
Mu.B.tilde <- matrix(0, nclusters, p.tilde)
Mu.B.tilde[, ov.idx[[1]]] <- G.muy
if (length(between.idx) > 0L) {
Mu.B.tilde[, between.idx] <- G.muz
}
Mu.B <- Mu.B.tilde[, ov.idx[[2]], drop = FALSE]
# Sigma.W
Sigma.W <- G.Sigma.w
# Sigma.B
if (length(between.idx) > 0L) {
p.tilde.star <- p.tilde * (p.tilde + 1) / 2
B.tilde <- lav_matrix_vech_reverse(seq_len(p.tilde.star))
Sigma.B.tilde <- matrix(0, nclusters, p.tilde.star)
col.idx <- lav_matrix_vech(B.tilde[ov.idx[[1]], ov.idx[[1]],
drop = FALSE
])
Sigma.B.tilde[, col.idx] <- G.Sigma.b
col.idx <- lav_matrix_vec(B.tilde[ov.idx[[1]], between.idx,
drop = FALSE
])
Sigma.B.tilde[, col.idx] <- G.Sigma.yz
col.idx <- lav_matrix_vech(B.tilde[between.idx, between.idx,
drop = FALSE
])
Sigma.B.tilde[, col.idx] <- G.Sigma.zz
col.idx <- lav_matrix_vech(B.tilde[ov.idx[[2]], ov.idx[[2]],
drop = FALSE
])
Sigma.B <- Sigma.B.tilde[, col.idx, drop = FALSE]
} else {
p.tilde.star <- p.tilde * (p.tilde + 1) / 2
B.tilde <- lav_matrix_vech_reverse(seq_len(p.tilde.star))
Sigma.B.tilde <- matrix(0, nclusters, p.tilde.star)
col.idx <- lav_matrix_vech(B.tilde[ov.idx[[1]], ov.idx[[1]],
drop = FALSE
])
Sigma.B.tilde[, col.idx] <- G.Sigma.b
col.idx <- lav_matrix_vech(B.tilde[ov.idx[[2]], ov.idx[[2]],
drop = FALSE
])
Sigma.B <- Sigma.B.tilde[, col.idx, drop = FALSE]
# Sigma.B <- G.Sigma.b
}
SCORES <- cbind(Mu.W, Sigma.W, Mu.B, Sigma.B)
SCORES
}
# first-order information: outer crossprod of scores per cluster
lav_mvnorm_cluster_missing_information_firstorder <- function(
Y1 = NULL,
Y2 = NULL,
Lp = NULL,
Mp = NULL,
Mu.W = NULL,
Sigma.W = NULL,
Mu.B = NULL,
Sigma.B = NULL,
x.idx = NULL,
divide.by.two = FALSE,
Sinv.method = "eigen") {
N <- NROW(Y1)
SCORES <- lav_mvnorm_cluster_missing_scores_2l(
Y1 = Y1,
Y2 = Y2,
Lp = Lp,
Mp = Mp,
Mu.W = Mu.W,
Sigma.W = Sigma.W,
Mu.B = Mu.B,
Sigma.B = Sigma.B,
Sinv.method = Sinv.method
)
# divide by 2 (if we want scores wrt objective function)
if (divide.by.two) {
SCORES <- SCORES / 2
}
# unit information
information <- crossprod(SCORES) / Lp$nclusters[[2]]
# if x.idx, set rows/cols to zero
if (length(x.idx) > 0L) {
nw <- length(as.vector(Mu.W))
nw.star <- nw * (nw + 1) / 2
nb <- length(as.vector(Mu.B))
ov.idx <- Lp$ov.idx
x.idx.w <- which(ov.idx[[1]] %in% x.idx)
if (length(x.idx.w) > 0L) {
xw.idx <- c(
x.idx.w,
nw + lav_matrix_vech_which_idx(n = nw, idx = x.idx.w)
)
} else {
xw.idx <- integer(0L)
}
x.idx.b <- which(ov.idx[[2]] %in% x.idx)
if (length(x.idx.b) > 0L) {
xb.idx <- c(
x.idx.b,
nb + lav_matrix_vech_which_idx(n = nb, idx = x.idx.b)
)
} else {
xb.idx <- integer(0L)
}
all.idx <- c(xw.idx, nw + nw.star + xb.idx)
information[all.idx, ] <- 0
information[, all.idx] <- 0
}
information
}
# observed information
# order: mu.w within, vech(sigma.w) within, mu.b between, vech(sigma.b) between
# mu.w rows/cols that are splitted within/between are forced to zero
#
# numerical approximation (for now)
lav_mvnorm_cluster_missing_information_observed <- function(
Y1 = NULL,
Y2 = NULL,
Lp = NULL,
Mp = NULL,
YLp = NULL,
Mu.W = NULL,
Sigma.W = NULL,
Mu.B = NULL,
Sigma.B = NULL,
x.idx = integer(0L),
Sinv.method = "eigen") {
nobs <- Lp$nclusters[[1]]
nw <- length(as.vector(Mu.W))
nw.star <- nw * (nw + 1) / 2
nb <- length(as.vector(Mu.B))
nb.star <- nb * (nb + 1) / 2
ov.idx <- Lp$ov.idx
p.tilde <- length(unique(c(ov.idx[[1]], ov.idx[[2]])))
# Mu.W (for within-only)
Mu.W.tilde <- numeric(p.tilde)
Mu.W.tilde[ov.idx[[1]]] <- Mu.W
# local function -- gradient
GRAD <- function(x) {
# Mu.W (for within-only)
Mu.W.tilde2 <- numeric(p.tilde)
Mu.W.tilde2[ov.idx[[1]]] <- x[1:nw]
Mu.W.tilde2[Lp$both.idx[[2]]] <- Mu.W.tilde[Lp$both.idx[[2]]]
Mu.W2 <- Mu.W.tilde2[ov.idx[[1]]]
Sigma.W2 <- lav_matrix_vech_reverse(x[nw + 1:nw.star])
Mu.B2 <- x[nw + nw.star + 1:nb]
Sigma.B2 <- lav_matrix_vech_reverse(x[nw + nw.star + nb + 1:nb.star])
dx <- lav_mvnorm_cluster_missing_dlogl_2l_samplestats(
Y1 = Y1, Y2 = Y2, Lp = Lp, Mp = Mp,
Mu.W = Mu.W2, Sigma.W = Sigma.W2,
Mu.B = Mu.B2, Sigma.B = Sigma.B2,
return.list = FALSE,
Sinv.method = Sinv.method
)
# dx is for -2*logl
-1 / 2 * dx
}
# start.x
start.x <- c(
as.vector(Mu.W), lav_matrix_vech(Sigma.W),
as.vector(Mu.B), lav_matrix_vech(Sigma.B)
)
# total information
information <- -1 * numDeriv::jacobian(func = GRAD, x = start.x)
# unit information
information <- information / Lp$nclusters[[2]]
# if x.idx, set rows/cols to zero
if (length(x.idx) > 0L) {
x.idx.w <- which(ov.idx[[1]] %in% x.idx)
if (length(x.idx.w) > 0L) {
xw.idx <- c(
x.idx.w,
nw + lav_matrix_vech_which_idx(n = nw, idx = x.idx.w)
)
} else {
xw.idx <- integer(0L)
}
x.idx.b <- which(ov.idx[[2]] %in% x.idx)
if (length(x.idx.b) > 0L) {
xb.idx <- c(
x.idx.b,
nb + lav_matrix_vech_which_idx(n = nb, idx = x.idx.b)
)
} else {
xb.idx <- integer(0L)
}
all.idx <- c(xw.idx, nw + nw.star + xb.idx)
information[all.idx, ] <- 0
information[, all.idx] <- 0
}
information
}
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lavaan documentation built on Sept. 27, 2024, 9:07 a.m.
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Defines functions lav_mvnorm_cluster_missing_information_observed lav_mvnorm_cluster_missing_information_firstorder lav_mvnorm_cluster_missing_scores_2l lav_mvnorm_cluster_missing_dlogl_2l_samplestats lav_mvnorm_cluster_missing_loglik_samplestats_2l
# loglikelihood clustered/twolevel data in the presence of missing data
# YR:
# - objective function: first version around March 2021 (see Psych paper)
# - analytic gradient: first version around May 2021
# Mu.W, Mu.B, Sigma.W, Sigma.B are the model-implied statistics
lav_mvnorm_cluster_missing_loglik_samplestats_2l <- function(Y1 = NULL,
Y2 = NULL,
Lp = NULL,
Mp = NULL,
Mu.W = NULL,
Sigma.W = NULL,
Mu.B = NULL,
Sigma.B = NULL,
Sinv.method = "eigen",
log2pi = FALSE,
loglik.x = 0,
minus.two = TRUE) {
# map implied to 2l matrices
out <- lav_mvnorm_cluster_implied22l(
Lp = Lp, Mu.W = Mu.W, Mu.B = Mu.B,
Sigma.W = Sigma.W, Sigma.B = Sigma.B
)
mu.y <- out$mu.y
mu.z <- out$mu.z
sigma.w <- out$sigma.w
sigma.b <- out$sigma.b
sigma.zz <- out$sigma.zz
sigma.yz <- out$sigma.yz
# Lp
nclusters <- Lp$nclusters[[2]]
between.idx <- Lp$between.idx[[2]]
both.idx <- Lp$both.idx[[2]]
cluster.idx <- Lp$cluster.idx[[2]]
# sanity checks
if (any(diag(sigma.w) < 0) || any(diag(sigma.b) < 0)) {
return(+Inf)
}
# check is both.idx part of sigma.b is 'too' negative; if so, return +Inf
ev <- eigen(sigma.b[both.idx, both.idx, drop = FALSE],
symmetric = TRUE,
only.values = TRUE
)$values
if (any(ev < -0.05)) {
return(+Inf)
}
# cat("sigma.w = \n"); print(sigma.w)
# cat("sigma.b = \n"); print(sigma.b)
# cat("mu.y = \n"); print(mu.y)
# global
sigma.w.inv <- solve.default(sigma.w)
sigma.w.logdet <- log(det(sigma.w))
sigma.b <- sigma.b[both.idx, both.idx] # only both part
# y
ny <- ncol(sigma.w)
if (length(between.idx) > 0L) {
Y1w <- Y1[, -between.idx, drop = FALSE]
} else {
Y1w <- Y1
}
Y1w.c <- t(t(Y1w) - mu.y)
PIJ <- matrix(0, nrow(Y1w.c), ny)
# z
nz <- length(between.idx)
if (nz > 0L) {
# check is sigma.zz is PD; if not, return +Inf
ev <- eigen(sigma.zz, symmetric = TRUE, only.values = TRUE)$values
if (any(ev < sqrt(.Machine$double.eps))) {
return(+Inf)
}
Z <- Y2[, between.idx, drop = FALSE]
Z.c <- t(t(Z) - mu.z)
sigma.yz <- sigma.yz[both.idx, , drop = FALSE] # only both part
sigma.zy <- t(sigma.yz)
sigma.zz.inv <- solve.default(sigma.zz)
sigma.zz.logdet <- log(det(sigma.zz))
sigma.zi.zy <- sigma.zz.inv %*% sigma.zy
sigma.b.z <- sigma.b - sigma.yz %*% sigma.zi.zy
GZ <- Z.c %*% sigma.zz.inv # for complete cases only
}
# containters per cluster
q.yy.b <- q.zy <- q.zz.b <- numeric(nclusters)
IBZA.j.logdet <- numeric(nclusters)
ALIST <- rep(list(matrix(
0, length(both.idx),
length(both.idx)
)), nclusters)
# Z per missing pattern
if (nz > 0L) {
Zp <- Mp$Zp
ZPAT2J <- integer(nclusters) # which sigma.b.z per cluster
SIGMA.B.Z <- vector("list", length = Zp$npatterns + 1L)
sigma.j.zz.logdet <- q.zz.a <- 0
for (p in seq_len(Zp$npatterns)) {
freq <- Zp$freq[p]
z.na.idx <- which(!Zp$pat[p, ])
j.idx <- Zp$case.idx[[p]] # cluster indices with this pattern
ZPAT2J[j.idx] <- p
if (length(z.na.idx) > 0L) {
zp <- sigma.zz[-z.na.idx, -z.na.idx, drop = FALSE]
zp.inv <- lav_matrix_symmetric_inverse_update(
S.inv = sigma.zz.inv, rm.idx = z.na.idx,
logdet = TRUE, S.logdet = sigma.zz.logdet
)
zp.logdet <- attr(zp.inv, "logdet")
sigma.j.zz.logdet <- sigma.j.zz.logdet + (zp.logdet * freq)
GZ[j.idx, -z.na.idx] <- Z.c[j.idx, -z.na.idx] %*% zp.inv
yziy <- (sigma.yz[, -z.na.idx, drop = FALSE] %*% zp.inv %*%
sigma.zy[-z.na.idx, , drop = FALSE])
SIGMA.B.Z[[p]] <- (sigma.b - yziy)
} else {
# complete case
sigma.j.zz.logdet <-
sigma.j.zz.logdet + (sigma.zz.logdet * freq)
SIGMA.B.Z[[p]] <- sigma.b.z
}
} # p
# add empty patterns (if any)
if (length(Zp$empty.idx) > 0L) {
ZPAT2J[Zp$empty.idx] <- p + 1L
SIGMA.B.Z[[p + 1L]] <- sigma.b
}
q.zz.a <- sum(GZ * Z.c, na.rm = TRUE)
GZ0 <- GZ
GZ0[is.na(GZ0)] <- 0
GJ <- GZ0 %*% sigma.zy # only both part
}
# Y per missing pattern
W.logdet <- 0
#MPi <- integer(nrow(Y1))
for (p in seq_len(Mp$npatterns)) {
freq <- Mp$freq[p]
na.idx <- which(!Mp$pat[p, ])
j.idx <- Mp$j.idx[[p]]
j1.idx <- Mp$j1.idx[[p]]
TAB <- integer(nclusters)
TAB[j1.idx] <- Mp$j.freq[[p]]
# compute sigma.w.inv for this pattern
if (length(na.idx) > 0L) {
#MPi[Mp$case.idx[[p]]] <- p
wp <- sigma.w[-na.idx, -na.idx, drop = FALSE]
wp.inv <- lav_matrix_symmetric_inverse_update(
S.inv = sigma.w.inv, rm.idx = na.idx,
logdet = TRUE, S.logdet = sigma.w.logdet
)
wp.logdet <- attr(wp.inv, "logdet")
W.logdet <- W.logdet + (wp.logdet * freq)
PIJ[Mp$case.idx[[p]], -na.idx] <-
Y1w.c[Mp$case.idx[[p]], -na.idx] %*% wp.inv
A.j <- matrix(0, ny, ny)
A.j[-na.idx, -na.idx] <- wp.inv
for (j in j1.idx) {
ALIST[[j]] <- ALIST[[j]] + (A.j[both.idx, both.idx] * TAB[j])
}
# WIP[[p]][-na.idx, -na.idx] <- wp.inv
} else {
# complete case
W.logdet <- W.logdet + (sigma.w.logdet * freq)
PIJ[Mp$case.idx[[p]], ] <-
Y1w.c[Mp$case.idx[[p]], ] %*% sigma.w.inv
for (j in j1.idx) {
ALIST[[j]] <-
ALIST[[j]] + (sigma.w.inv[both.idx, both.idx] * TAB[j])
}
}
} # p
q.yy.a <- sum(PIJ * Y1w.c, na.rm = TRUE)
PJ <- rowsum.default(PIJ[, both.idx], cluster.idx,
reorder = FALSE,
na.rm = TRUE
) # only both part is needed
# per cluster
both.diag.idx <- lav_matrix_diag_idx(length(both.idx))
for (j in seq_len(nclusters)) {
# we only need the 'both.idx' part of A.j, sigma.b.z, p.j, g.j ,...
A.j <- ALIST[[j]]
p.j <- PJ[j, ]
if (nz > 0L) {
sigma.b.z <- SIGMA.B.Z[[ZPAT2J[j]]]
} else {
sigma.b.z <- sigma.b
}
IBZA.j <- sigma.b.z %*% A.j
IBZA.j[both.diag.idx] <- IBZA.j[both.diag.idx] + 1
# logdet IBZA.j
tmp <- determinant.matrix(IBZA.j, logarithm = TRUE)
IBZA.j.logdet[j] <- tmp$modulus * tmp$sign
# IBZA.j.inv.BZ.p
IBZA.j.inv.BZ.p <- solve.default(IBZA.j, drop(sigma.b.z %*% p.j))
q.yy.b[j] <- sum(p.j * IBZA.j.inv.BZ.p)
if (nz > 0L) {
g.j <- GJ[j, ]
IBZA.j.inv.g <- solve.default(IBZA.j, g.j)
A.IBZA.j.inv.g <- A.j %*% IBZA.j.inv.g
q.zz.b[j] <- sum(g.j * A.IBZA.j.inv.g)
q.zy[j] <- -sum(p.j * IBZA.j.inv.g)
}
}
if (nz > 0L) {
P <- Mp$nel + Zp$nel
DIST <- (q.yy.a - sum(q.yy.b)) + 2 * sum(q.zy) + (q.zz.a + sum(q.zz.b))
LOGDET <- W.logdet + sum(IBZA.j.logdet) + sigma.j.zz.logdet
} else {
P <- Mp$nel
DIST <- (q.yy.a - sum(q.yy.b))
LOGDET <- W.logdet + sum(IBZA.j.logdet)
}
# loglik?
if (log2pi && !minus.two) {
LOG.2PI <- log(2 * pi)
loglik <- -(P * LOG.2PI + LOGDET + DIST) / 2
} else {
loglik <- DIST + LOGDET
}
# loglik.x (only if loglik is requested)
if (length(unlist(Lp$ov.x.idx)) > 0L && log2pi && !minus.two) {
loglik <- loglik - loglik.x
}
loglik
}
# Mu.W, Mu.B, Sigma.W, Sigma.B are the model-implied statistics
lav_mvnorm_cluster_missing_dlogl_2l_samplestats <- function(
Y1 = NULL,
Y2 = NULL,
Lp = NULL,
Mp = NULL,
Mu.W = NULL,
Sigma.W = NULL,
Mu.B = NULL,
Sigma.B = NULL,
Sinv.method = "eigen",
return.list = FALSE) {
# map implied to 2l matrices
out <- lav_mvnorm_cluster_implied22l(
Lp = Lp, Mu.W = Mu.W, Mu.B = Mu.B,
Sigma.W = Sigma.W, Sigma.B = Sigma.B
)
mu.y <- out$mu.y
mu.z <- out$mu.z
sigma.w <- out$sigma.w
sigma.b <- out$sigma.b
sigma.zz <- out$sigma.zz
sigma.yz <- out$sigma.yz
# containers for dx
dx.mu.y <- numeric(length(mu.y))
dx.mu.z <- numeric(length(mu.z))
dx.sigma.zz <- matrix(0, nrow(sigma.zz), ncol(sigma.zz))
dx.sigma.yz <- matrix(0, nrow(sigma.yz), ncol(sigma.yz))
dx.sigma.b <- matrix(0, nrow(sigma.b), ncol(sigma.b))
dx.sigma.w <- matrix(0, nrow(sigma.w), ncol(sigma.w))
# Lp
nclusters <- Lp$nclusters[[2]]
between.idx <- Lp$between.idx[[2]]
cluster.idx <- Lp$cluster.idx[[2]]
both.idx <- Lp$both.idx[[2]]
# sigma.w
sigma.w.inv <- solve.default(sigma.w)
sigma.b <- sigma.b[both.idx, both.idx] # only both part
# y
ny <- ncol(sigma.w)
if (length(between.idx) > 0L) {
Y1w <- Y1[, -between.idx, drop = FALSE]
} else {
Y1w <- Y1
}
Y1w.c <- t(t(Y1w) - mu.y)
PIJ <- matrix(0, nrow(Y1w.c), ny)
# z
nz <- length(between.idx)
if (nz > 0L) {
Z <- Y2[, between.idx, drop = FALSE]
Z.c <- t(t(Z) - mu.z)
sigma.yz <- sigma.yz[both.idx, , drop = FALSE] # only both part
sigma.zy <- t(sigma.yz)
sigma.zz.inv <- solve.default(sigma.zz)
sigma.zz.logdet <- log(det(sigma.zz))
sigma.zi.zy <- sigma.zz.inv %*% sigma.zy
sigma.b.z <- sigma.b - sigma.yz %*% sigma.zi.zy
GZ <- Z.c %*% sigma.zz.inv # for complete cases only
}
# containters per cluster
# ALIST <- rep(list(matrix(0, length(both.idx),
# length(both.idx))), nclusters)
ALIST <- rep(list(matrix(0, ny, ny)), nclusters)
# Z per missing pattern
if (nz > 0L) {
Zp <- Mp$Zp
ZPAT2J <- integer(nclusters) # which pattern per cluster
SIGMA.B.Z <- vector("list", length = Zp$npatterns + 1L) # +1 for empty
ZIZY <- rep(list(matrix(
0, nrow(sigma.zy),
ncol(sigma.zy)
)), Zp$npatterns + 1L)
ZIP <- rep(list(matrix(
0, nrow(sigma.zz),
ncol(sigma.zz)
)), Zp$npatterns + 1L)
for (p in seq_len(Zp$npatterns)) {
freq <- Zp$freq[p]
z.na.idx <- which(!Zp$pat[p, ])
j.idx <- Zp$case.idx[[p]] # cluster indices with this pattern
ZPAT2J[j.idx] <- p
if (length(z.na.idx) > 0L) {
zp <- sigma.zz[-z.na.idx, -z.na.idx, drop = FALSE]
zp.inv <- lav_matrix_symmetric_inverse_update(
S.inv = sigma.zz.inv, rm.idx = z.na.idx,
logdet = FALSE
)
ZIP[[p]][-z.na.idx, -z.na.idx] <- zp.inv
GZ[j.idx, -z.na.idx] <- Z.c[j.idx, -z.na.idx] %*% zp.inv
Z.G.ZY <- zp.inv %*% sigma.zy[-z.na.idx, , drop = FALSE]
ZIZY[[p]][-z.na.idx, ] <-
zp.inv %*% sigma.zy[-z.na.idx, , drop = FALSE]
yziy <- sigma.yz[, -z.na.idx, drop = FALSE] %*% Z.G.ZY
SIGMA.B.Z[[p]] <- (sigma.b - yziy)
} else {
# complete case
ZIZY[[p]] <- sigma.zi.zy
ZIP[[p]] <- sigma.zz.inv
SIGMA.B.Z[[p]] <- sigma.b.z
}
} # p
# add empty patterns (if any)
if (length(Zp$empty.idx) > 0L) {
ZPAT2J[Zp$empty.idx] <- p + 1L
SIGMA.B.Z[[p + 1L]] <- sigma.b
}
GZ[is.na(GZ)] <- 0
GJ <- GZ %*% sigma.zy
}
# Y per missing pattern
WIP <- rep(list(matrix(0, ny, ny)), Mp$npatterns)
MPi <- integer(nrow(Y1))
for (p in seq_len(Mp$npatterns)) {
freq <- Mp$freq[p]
na.idx <- which(!Mp$pat[p, ])
j.idx <- Mp$j.idx[[p]]
j1.idx <- Mp$j1.idx[[p]]
TAB <- integer(nclusters)
TAB[j1.idx] <- Mp$j.freq[[p]]
if (length(na.idx) > 0L) {
MPi[Mp$case.idx[[p]]] <- p
wp.inv <- lav_matrix_symmetric_inverse_update(
S.inv = sigma.w.inv, rm.idx = na.idx,
logdet = FALSE
)
WIP[[p]][-na.idx, -na.idx] <- wp.inv
PIJ[Mp$case.idx[[p]], -na.idx] <-
Y1w.c[Mp$case.idx[[p]], -na.idx] %*% wp.inv
for (j in j1.idx) {
ALIST[[j]] <-
# ALIST[[j]] + (WIP[[p]][both.idx, both.idx] * TAB[j])
ALIST[[j]] + (WIP[[p]] * TAB[j])
}
} else {
# complete case
PIJ[Mp$case.idx[[p]], ] <-
Y1w.c[Mp$case.idx[[p]], ] %*% sigma.w.inv
WIP[[p]] <- sigma.w.inv
for (j in j1.idx) {
ALIST[[j]] <-
# ALIST[[j]] + (sigma.w.inv[both.idx, both.idx] * TAB[j])
ALIST[[j]] + (sigma.w.inv * TAB[j])
}
}
} # p
PJ <- rowsum.default(PIJ[, , drop = FALSE],
cluster.idx,
reorder = FALSE, na.rm = TRUE
)
# per cluster
both.diag.idx <- lav_matrix_diag_idx(length(both.idx))
for (j in seq_len(nclusters)) {
A.j.full <- ALIST[[j]]
A.j <- A.j.full[both.idx, both.idx, drop = FALSE]
p.j <- as.matrix(PJ[j, ])
pb.j <- as.matrix(PJ[j, both.idx]) # only both.idx part
if (nz > 0L) {
sigma.b.z <- SIGMA.B.Z[[ZPAT2J[j]]]
} else {
sigma.b.z <- sigma.b
}
IBZA.j <- sigma.b.z %*% A.j
IBZA.j[both.diag.idx] <- IBZA.j[both.diag.idx] + 1
IBZA.j.inv.BZ <- solve.default(IBZA.j, sigma.b.z)
IBZA.j.inv.BZ.p <- IBZA.j.inv.BZ %*% pb.j
A.IBZA.j.inv.BZ <- A.j %*% IBZA.j.inv.BZ
A.IBZA.j.inv.BZ.p <- A.IBZA.j.inv.BZ %*% pb.j
IBZA.j.inv <- solve.default(IBZA.j)
A.IBZA.j.inv <- A.j %*% IBZA.j.inv
p.IBZA.j.inv <- t(crossprod(pb.j, IBZA.j.inv))
# only if we have between-only variables
if (nz > 0L) {
g.j <- as.matrix(GJ[j, ])
zij <- as.matrix(GZ[j, ])
zizy <- ZIZY[[ZPAT2J[j]]]
zip <- ZIP[[ZPAT2J[j]]]
IBZA.j.inv.zizy <- solve.default(IBZA.j, t(zizy))
IBZA.j.inv.g <- IBZA.j.inv %*% g.j
IBZA.j.inv.p <- IBZA.j.inv %*% pb.j
A.IBZA.j.inv.g <- A.j %*% IBZA.j.inv.g
A.IBZA.j.inv.zizy <- A.j %*% IBZA.j.inv.zizy
zizy.A.IBZA.j.inv.g <- zizy %*% A.IBZA.j.inv.g
p.IBZA.j.inv.zizy <- crossprod(pb.j, IBZA.j.inv.zizy)
ggbzpp <- 2 * A.IBZA.j.inv.g + A.IBZA.j.inv.BZ.p - pb.j
ZIJzizyp <- (2 * zij - zizy %*% pb.j)
###########
# dx.mu.z #
###########
tmp <- 2 * (t(p.IBZA.j.inv.zizy) - zij - zizy.A.IBZA.j.inv.g)
dx.mu.z <- dx.mu.z + drop(tmp)
###############
# dx.sigma.zz #
###############
tmp1 <- (zip + zizy %*% A.IBZA.j.inv.zizy # logdet
- tcrossprod(zij) # ZA
- tcrossprod(zizy.A.IBZA.j.inv.g)) # ZB-1
d <- (t((2 * zizy.A.IBZA.j.inv.g + zizy %*% A.IBZA.j.inv.BZ.p)
%*% p.IBZA.j.inv.zizy)
+ ZIJzizyp %*% p.IBZA.j.inv.zizy
- 2 * tcrossprod(zizy.A.IBZA.j.inv.g, zij))
tmp2 <- (d + t(d)) / 2
tmp <- tmp1 + tmp2
# symmetry correction
ZZ <- 2 * tmp
diag(ZZ) <- diag(tmp)
dx.sigma.zz <- dx.sigma.zz + ZZ
###############
# dx.sigma.yz #
###############
t0 <- -2 * A.IBZA.j.inv.zizy
t1 <- (-2 * tcrossprod(p.IBZA.j.inv, g.j)
- 1 * tcrossprod(p.IBZA.j.inv, sigma.b.z %*% pb.j)
+ 2 * tcrossprod(A.IBZA.j.inv.g, g.j)) %*% A.IBZA.j.inv.zizy
t2 <- -ggbzpp %*% p.IBZA.j.inv.zizy
t3 <- -tcrossprod(p.IBZA.j.inv, ZIJzizyp)
t4 <- 2 * tcrossprod(A.IBZA.j.inv.g, zij)
tmp <- t0 + t1 + t2 + t3 + t4
dx.sigma.yz[both.idx, ] <- dx.sigma.yz[both.idx, , drop = FALSE] + tmp
##############
# dx.sigma.b #
##############
c <- tcrossprod(ggbzpp, p.IBZA.j.inv)
tmp <- t(A.IBZA.j.inv) - tcrossprod(A.IBZA.j.inv.g) + (c + t(c)) / 2
# symmetry correction
ZZ <- 2 * tmp
diag(ZZ) <- diag(tmp)
dx.sigma.b[both.idx, both.idx] <-
dx.sigma.b[both.idx, both.idx, drop = FALSE] + ZZ
# for dx.sigma.w
PART1.b <- -1 * (IBZA.j.inv.g %*%
(2 * t(IBZA.j.inv.BZ.p) + t(g.j) -
t(g.j) %*% A.IBZA.j.inv.BZ)
+ IBZA.j.inv.BZ + tcrossprod(IBZA.j.inv.BZ.p))
PART2.b <- 2 * (IBZA.j.inv.g + IBZA.j.inv.BZ.p) # vector
} else {
##############
# dx.sigma.b #
##############
bzpp <- A.IBZA.j.inv.BZ.p - pb.j
c <- tcrossprod(bzpp, p.IBZA.j.inv)
tmp <- t(A.IBZA.j.inv) + (c + t(c)) / 2
# symmetry correction
ZZ <- 2 * tmp
diag(ZZ) <- diag(tmp)
dx.sigma.b[both.idx, both.idx] <-
dx.sigma.b[both.idx, both.idx, drop = FALSE] + ZZ
PART1.b <- -1 * (IBZA.j.inv.BZ + tcrossprod(IBZA.j.inv.BZ.p))
PART2.b <- 2 * IBZA.j.inv.BZ.p # vector
}
##############
# dx.sigma.w #
##############
PART1 <- matrix(0, ny, ny)
PART1[both.idx, both.idx] <- PART1.b
PART2 <- matrix(0, ny, 1L)
PART2[both.idx, 1L] <- PART2.b
ij.index <- which(cluster.idx == j)
pij <- PIJ[ij.index, , drop = FALSE]
which.compl <- which(MPi[ij.index] == 0L)
which.incompl <- which(MPi[ij.index] != 0L)
AP2 <- rep(list(sigma.w.inv %*% PART2), length(ij.index))
AP1A.a <- AP1A.b <- matrix(0, ny, ny)
# A.j.full <- matrix(0, ny, ny)
if (length(which.compl) > 0L) {
tmp <- (sigma.w.inv %*% PART1 %*% sigma.w.inv)
AP1A.a <- tmp * length(which.compl)
# A.j.full <- A.j.full + sigma.w.inv * length(which.compl)
}
if (length(which.incompl) > 0L) {
p.idx <- MPi[ij.index][which.incompl]
tmp <- lapply(WIP[p.idx], function(x) {
x %*% PART1 %*% x
})
AP1A.b <- Reduce("+", tmp)
AP2[which.incompl] <-
lapply(WIP[p.idx], function(x) {
x %*% PART2
})
# A.j.full <- A.j.full + Reduce("+", WIP[ p.idx ])
}
t1 <- AP1A.a + AP1A.b
t2 <- (do.call("cbind", AP2) - t(pij)) %*% pij
AA.wj <- t1 + t2
tmp <- A.j.full + (AA.wj + t(AA.wj)) / 2
# symmetry correction
ZZ <- 2 * tmp
diag(ZZ) <- diag(tmp)
dx.sigma.w <- dx.sigma.w + ZZ
###########
# dx.mu.y #
###########
tmp <- numeric(ny)
if (nz > 0L) {
tmp[both.idx] <- IBZA.j.inv.g + IBZA.j.inv.BZ.p
} else {
tmp[both.idx] <- IBZA.j.inv.BZ.p
}
gbzpp <- A.j.full %*% tmp - p.j
dx.mu.y <- dx.mu.y + drop(2 * gbzpp)
} # j
# rearrange
dout <- lav_mvnorm_cluster_2l2implied(
Lp = Lp,
sigma.w = dx.sigma.w, sigma.b = dx.sigma.b,
sigma.yz = dx.sigma.yz, sigma.zz = dx.sigma.zz,
mu.y = dx.mu.y, mu.z = dx.mu.z
)
if (return.list) {
out <- dout
} else {
out <- c(
dout$Mu.W, lav_matrix_vech(dout$Sigma.W),
dout$Mu.B, lav_matrix_vech(dout$Sigma.B)
)
}
out
}
# cluster-wise scores -2*logl wrt Mu.W, Mu.B, Sigma.W, Sigma.B
lav_mvnorm_cluster_missing_scores_2l <- function(
Y1 = NULL,
Y2 = NULL,
Lp = NULL,
Mp = NULL,
Mu.W = NULL,
Sigma.W = NULL,
Mu.B = NULL,
Sigma.B = NULL,
Sinv.method = "eigen") {
# map implied to 2l matrices
out <- lav_mvnorm_cluster_implied22l(
Lp = Lp, Mu.W = Mu.W, Mu.B = Mu.B,
Sigma.W = Sigma.W, Sigma.B = Sigma.B
)
mu.y <- out$mu.y
mu.z <- out$mu.z
sigma.w <- out$sigma.w
sigma.b <- out$sigma.b
sigma.zz <- out$sigma.zz
sigma.yz <- out$sigma.yz
# Lp
nclusters <- Lp$nclusters[[2]]
between.idx <- Lp$between.idx[[2]]
cluster.idx <- Lp$cluster.idx[[2]]
both.idx <- Lp$both.idx[[2]]
# sigma.w
sigma.w.inv <- solve.default(sigma.w)
sigma.b <- sigma.b[both.idx, both.idx] # only both part
# y
ny <- ncol(sigma.w)
if (length(between.idx) > 0L) {
Y1w <- Y1[, -between.idx, drop = FALSE]
} else {
Y1w <- Y1
}
Y1w.c <- t(t(Y1w) - mu.y)
PIJ <- matrix(0, nrow(Y1w.c), ny)
# z
nz <- length(between.idx)
if (nz > 0L) {
Z <- Y2[, between.idx, drop = FALSE]
Z.c <- t(t(Z) - mu.z)
sigma.yz <- sigma.yz[both.idx, , drop = FALSE] # only both part
sigma.zy <- t(sigma.yz)
sigma.zz.inv <- solve.default(sigma.zz)
sigma.zz.logdet <- log(det(sigma.zz))
sigma.zi.zy <- sigma.zz.inv %*% sigma.zy
sigma.b.z <- sigma.b - sigma.yz %*% sigma.zi.zy
GZ <- Z.c %*% sigma.zz.inv # for complete cases only
}
# containters per cluster
# ALIST <- rep(list(matrix(0, length(both.idx),
# length(both.idx))), nclusters)
ALIST <- rep(list(matrix(0, ny, ny)), nclusters)
# both level-1 and level-2
G.muy <- matrix(0, nclusters, length(mu.y))
G.Sigma.w <- matrix(0, nclusters, length(lav_matrix_vech(sigma.w)))
G.Sigma.b <- matrix(0, nclusters, length(lav_matrix_vech(out$sigma.b)))
G.muz <- matrix(0, nclusters, length(mu.z))
G.Sigma.zz <- matrix(0, nclusters, length(lav_matrix_vech(sigma.zz)))
G.Sigma.yz <- matrix(0, nclusters, length(lav_matrix_vec(out$sigma.yz)))
# Z per missing pattern
if (nz > 0L) {
Zp <- Mp$Zp
ZPAT2J <- integer(nclusters) # which pattern per cluster
SIGMA.B.Z <- vector("list", length = Zp$npatterns + 1L) # +1 for empty
ZIZY <- rep(list(matrix(
0, nrow(sigma.zy),
ncol(sigma.zy)
)), Zp$npatterns + 1L)
ZIP <- rep(list(matrix(
0, nrow(sigma.zz),
ncol(sigma.zz)
)), Zp$npatterns + 1L)
for (p in seq_len(Zp$npatterns)) {
freq <- Zp$freq[p]
z.na.idx <- which(!Zp$pat[p, ])
j.idx <- Zp$case.idx[[p]] # cluster indices with this pattern
ZPAT2J[j.idx] <- p
if (length(z.na.idx) > 0L) {
zp <- sigma.zz[-z.na.idx, -z.na.idx, drop = FALSE]
zp.inv <- lav_matrix_symmetric_inverse_update(
S.inv = sigma.zz.inv, rm.idx = z.na.idx,
logdet = FALSE
)
ZIP[[p]][-z.na.idx, -z.na.idx] <- zp.inv
GZ[j.idx, -z.na.idx] <- Z.c[j.idx, -z.na.idx] %*% zp.inv
Z.G.ZY <- zp.inv %*% sigma.zy[-z.na.idx, , drop = FALSE]
ZIZY[[p]][-z.na.idx, ] <-
zp.inv %*% sigma.zy[-z.na.idx, , drop = FALSE]
yziy <- sigma.yz[, -z.na.idx, drop = FALSE] %*% Z.G.ZY
SIGMA.B.Z[[p]] <- (sigma.b - yziy)
} else {
# complete case
ZIZY[[p]] <- sigma.zi.zy
ZIP[[p]] <- sigma.zz.inv
SIGMA.B.Z[[p]] <- sigma.b.z
}
} # p
# add empty patterns (if any)
if (length(Zp$empty.idx) > 0L) {
ZPAT2J[Zp$empty.idx] <- p + 1L
SIGMA.B.Z[[p + 1L]] <- sigma.b
}
GZ[is.na(GZ)] <- 0
GJ <- GZ %*% sigma.zy
}
# Y per missing pattern
WIP <- rep(list(matrix(0, ny, ny)), Mp$npatterns)
MPi <- integer(nrow(Y1))
for (p in seq_len(Mp$npatterns)) {
freq <- Mp$freq[p]
na.idx <- which(!Mp$pat[p, ])
j.idx <- Mp$j.idx[[p]]
j1.idx <- Mp$j1.idx[[p]]
TAB <- integer(nclusters)
TAB[j1.idx] <- Mp$j.freq[[p]]
if (length(na.idx) > 0L) {
MPi[Mp$case.idx[[p]]] <- p
wp.inv <- lav_matrix_symmetric_inverse_update(
S.inv = sigma.w.inv, rm.idx = na.idx,
logdet = FALSE
)
WIP[[p]][-na.idx, -na.idx] <- wp.inv
PIJ[Mp$case.idx[[p]], -na.idx] <-
Y1w.c[Mp$case.idx[[p]], -na.idx] %*% wp.inv
for (j in j1.idx) {
ALIST[[j]] <-
# ALIST[[j]] + (WIP[[p]][both.idx, both.idx] * TAB[j])
ALIST[[j]] + (WIP[[p]] * TAB[j])
}
} else {
# complete case
PIJ[Mp$case.idx[[p]], ] <-
Y1w.c[Mp$case.idx[[p]], ] %*% sigma.w.inv
WIP[[p]] <- sigma.w.inv
for (j in j1.idx) {
ALIST[[j]] <-
# ALIST[[j]] + (sigma.w.inv[both.idx, both.idx] * TAB[j])
ALIST[[j]] + (sigma.w.inv * TAB[j])
}
}
} # p
PJ <- rowsum.default(PIJ[, , drop = FALSE],
cluster.idx,
reorder = FALSE, na.rm = TRUE
)
# per cluster
both.diag.idx <- lav_matrix_diag_idx(length(both.idx))
for (j in seq_len(nclusters)) {
A.j.full <- ALIST[[j]]
A.j <- A.j.full[both.idx, both.idx, drop = FALSE]
p.j <- as.matrix(PJ[j, ])
pb.j <- as.matrix(PJ[j, both.idx]) # only both.idx part
if (nz > 0L) {
sigma.b.z <- SIGMA.B.Z[[ZPAT2J[j]]]
} else {
sigma.b.z <- sigma.b
}
IBZA.j <- sigma.b.z %*% A.j
IBZA.j[both.diag.idx] <- IBZA.j[both.diag.idx] + 1
IBZA.j.inv.BZ <- solve.default(IBZA.j, sigma.b.z)
IBZA.j.inv.BZ.p <- IBZA.j.inv.BZ %*% pb.j
A.IBZA.j.inv.BZ <- A.j %*% IBZA.j.inv.BZ
A.IBZA.j.inv.BZ.p <- A.IBZA.j.inv.BZ %*% pb.j
IBZA.j.inv <- solve.default(IBZA.j)
A.IBZA.j.inv <- A.j %*% IBZA.j.inv
p.IBZA.j.inv <- t(crossprod(pb.j, IBZA.j.inv))
# only if we have between-only variables
if (nz > 0L) {
g.j <- as.matrix(GJ[j, ])
zij <- as.matrix(GZ[j, ])
zizy <- ZIZY[[ZPAT2J[j]]]
zip <- ZIP[[ZPAT2J[j]]]
IBZA.j.inv.zizy <- solve.default(IBZA.j, t(zizy))
IBZA.j.inv.g <- IBZA.j.inv %*% g.j
IBZA.j.inv.p <- IBZA.j.inv %*% pb.j
A.IBZA.j.inv.g <- A.j %*% IBZA.j.inv.g
A.IBZA.j.inv.zizy <- A.j %*% IBZA.j.inv.zizy
zizy.A.IBZA.j.inv.g <- zizy %*% A.IBZA.j.inv.g
p.IBZA.j.inv.zizy <- crossprod(pb.j, IBZA.j.inv.zizy)
ggbzpp <- 2 * A.IBZA.j.inv.g + A.IBZA.j.inv.BZ.p - pb.j
ZIJzizyp <- (2 * zij - zizy %*% pb.j)
###########
# dx.mu.z #
###########
tmp <- 2 * (t(p.IBZA.j.inv.zizy) - zij - zizy.A.IBZA.j.inv.g)
G.muz[j, ] <- drop(tmp)
###############
# dx.sigma.zz #
###############
tmp1 <- (zip + zizy %*% A.IBZA.j.inv.zizy # logdet
- tcrossprod(zij) # ZA
- tcrossprod(zizy.A.IBZA.j.inv.g)) # ZB-1
d <- (t((2 * zizy.A.IBZA.j.inv.g + zizy %*% A.IBZA.j.inv.BZ.p)
%*% p.IBZA.j.inv.zizy)
+ ZIJzizyp %*% p.IBZA.j.inv.zizy
- 2 * tcrossprod(zizy.A.IBZA.j.inv.g, zij))
tmp2 <- (d + t(d)) / 2
tmp <- tmp1 + tmp2
# symmetry correction
ZZ <- 2 * tmp
diag(ZZ) <- diag(tmp)
G.Sigma.zz[j, ] <- lav_matrix_vech(ZZ)
###############
# dx.sigma.yz #
###############
t0 <- -2 * A.IBZA.j.inv.zizy
t1 <- (-2 * tcrossprod(p.IBZA.j.inv, g.j)
- 1 * tcrossprod(p.IBZA.j.inv, sigma.b.z %*% pb.j)
+ 2 * tcrossprod(A.IBZA.j.inv.g, g.j)) %*% A.IBZA.j.inv.zizy
t2 <- -ggbzpp %*% p.IBZA.j.inv.zizy
t3 <- -tcrossprod(p.IBZA.j.inv, ZIJzizyp)
t4 <- 2 * tcrossprod(A.IBZA.j.inv.g, zij)
tmp <- t0 + t1 + t2 + t3 + t4
tmp2 <- matrix(0, nrow(out$sigma.yz), ncol(out$sigma.yz))
tmp2[both.idx, ] <- tmp
G.Sigma.yz[j, ] <- lav_matrix_vec(tmp2)
##############
# dx.sigma.b #
##############
c <- tcrossprod(ggbzpp, p.IBZA.j.inv)
tmp <- t(A.IBZA.j.inv) - tcrossprod(A.IBZA.j.inv.g) + (c + t(c)) / 2
# symmetry correction
ZZ <- 2 * tmp
diag(ZZ) <- diag(tmp)
ZZ2 <- matrix(0, nrow(out$sigma.b), ncol(out$sigma.b))
ZZ2[both.idx, both.idx] <- ZZ
G.Sigma.b[j, ] <- lav_matrix_vech(ZZ2)
# dx.sigma.b[both.idx, both.idx] <-
# dx.sigma.b[both.idx, both.idx, drop = FALSE] + ZZ
# for dx.sigma.w
PART1.b <- -1 * (IBZA.j.inv.g %*%
(2 * t(IBZA.j.inv.BZ.p) + t(g.j) -
t(g.j) %*% A.IBZA.j.inv.BZ)
+ IBZA.j.inv.BZ + tcrossprod(IBZA.j.inv.BZ.p))
PART2.b <- 2 * (IBZA.j.inv.g + IBZA.j.inv.BZ.p) # vector
} else {
##############
# dx.sigma.b #
##############
bzpp <- A.IBZA.j.inv.BZ.p - pb.j
c <- tcrossprod(bzpp, p.IBZA.j.inv)
tmp <- t(A.IBZA.j.inv) + (c + t(c)) / 2
# symmetry correction
ZZ <- 2 * tmp
diag(ZZ) <- diag(tmp)
ZZ2 <- matrix(0, nrow(out$sigma.b), ncol(out$sigma.b))
ZZ2[both.idx, both.idx] <- ZZ
G.Sigma.b[j, ] <- lav_matrix_vech(ZZ2)
# dx.sigma.b[both.idx, both.idx] <-
# dx.sigma.b[both.idx, both.idx, drop = FALSE] + ZZ
PART1.b <- -1 * (IBZA.j.inv.BZ + tcrossprod(IBZA.j.inv.BZ.p))
PART2.b <- 2 * IBZA.j.inv.BZ.p # vector
}
##############
# dx.sigma.w #
##############
PART1 <- matrix(0, ny, ny)
PART1[both.idx, both.idx] <- PART1.b
PART2 <- matrix(0, ny, 1L)
PART2[both.idx, 1L] <- PART2.b
ij.index <- which(cluster.idx == j)
pij <- PIJ[ij.index, , drop = FALSE]
which.compl <- which(MPi[ij.index] == 0L)
which.incompl <- which(MPi[ij.index] != 0L)
AP2 <- rep(list(sigma.w.inv %*% PART2), length(ij.index))
AP1A.a <- AP1A.b <- matrix(0, ny, ny)
# A.j.full <- matrix(0, ny, ny)
if (length(which.compl) > 0L) {
tmp <- (sigma.w.inv %*% PART1 %*% sigma.w.inv)
AP1A.a <- tmp * length(which.compl)
# A.j.full <- A.j.full + sigma.w.inv * length(which.compl)
}
if (length(which.incompl) > 0L) {
p.idx <- MPi[ij.index][which.incompl]
tmp <- lapply(WIP[p.idx], function(x) {
x %*% PART1 %*% x
})
AP1A.b <- Reduce("+", tmp)
AP2[which.incompl] <-
lapply(WIP[p.idx], function(x) {
x %*% PART2
})
# A.j.full <- A.j.full + Reduce("+", WIP[ p.idx ])
}
t1 <- AP1A.a + AP1A.b
t2 <- (do.call("cbind", AP2) - t(pij)) %*% pij
AA.wj <- t1 + t2
tmp <- A.j.full + (AA.wj + t(AA.wj)) / 2
# symmetry correction
ZZ <- 2 * tmp
diag(ZZ) <- diag(tmp)
G.Sigma.w[j, ] <- lav_matrix_vech(ZZ)
# dx.sigma.w <- dx.sigma.w + ZZ
###########
# dx.mu.y #
###########
tmp <- numeric(ny)
if (nz > 0L) {
tmp[both.idx] <- IBZA.j.inv.g + IBZA.j.inv.BZ.p
} else {
tmp[both.idx] <- IBZA.j.inv.BZ.p
}
gbzpp <- A.j.full %*% tmp - p.j
# dx.mu.y <- dx.mu.y + drop(2 * gbzpp)
G.muy[j, ] <- drop(2 * gbzpp)
} # j
# browser()
# rearrange columns to Mu.W, Mu.B, Sigma.W, Sigma.B
ov.idx <- Lp$ov.idx
p.tilde <- length(unique(c(ov.idx[[1]], ov.idx[[2]])))
# Mu.W (for within-only)
Mu.W.tilde <- matrix(0, nclusters, p.tilde)
Mu.W.tilde[, ov.idx[[1]]] <- G.muy
Mu.W.tilde[, Lp$both.idx[[2]]] <- 0 # ZERO!!!
Mu.W <- Mu.W.tilde[, ov.idx[[1]], drop = FALSE]
# Mu.B
Mu.B.tilde <- matrix(0, nclusters, p.tilde)
Mu.B.tilde[, ov.idx[[1]]] <- G.muy
if (length(between.idx) > 0L) {
Mu.B.tilde[, between.idx] <- G.muz
}
Mu.B <- Mu.B.tilde[, ov.idx[[2]], drop = FALSE]
# Sigma.W
Sigma.W <- G.Sigma.w
# Sigma.B
if (length(between.idx) > 0L) {
p.tilde.star <- p.tilde * (p.tilde + 1) / 2
B.tilde <- lav_matrix_vech_reverse(seq_len(p.tilde.star))
Sigma.B.tilde <- matrix(0, nclusters, p.tilde.star)
col.idx <- lav_matrix_vech(B.tilde[ov.idx[[1]], ov.idx[[1]],
drop = FALSE
])
Sigma.B.tilde[, col.idx] <- G.Sigma.b
col.idx <- lav_matrix_vec(B.tilde[ov.idx[[1]], between.idx,
drop = FALSE
])
Sigma.B.tilde[, col.idx] <- G.Sigma.yz
col.idx <- lav_matrix_vech(B.tilde[between.idx, between.idx,
drop = FALSE
])
Sigma.B.tilde[, col.idx] <- G.Sigma.zz
col.idx <- lav_matrix_vech(B.tilde[ov.idx[[2]], ov.idx[[2]],
drop = FALSE
])
Sigma.B <- Sigma.B.tilde[, col.idx, drop = FALSE]
} else {
p.tilde.star <- p.tilde * (p.tilde + 1) / 2
B.tilde <- lav_matrix_vech_reverse(seq_len(p.tilde.star))
Sigma.B.tilde <- matrix(0, nclusters, p.tilde.star)
col.idx <- lav_matrix_vech(B.tilde[ov.idx[[1]], ov.idx[[1]],
drop = FALSE
])
Sigma.B.tilde[, col.idx] <- G.Sigma.b
col.idx <- lav_matrix_vech(B.tilde[ov.idx[[2]], ov.idx[[2]],
drop = FALSE
])
Sigma.B <- Sigma.B.tilde[, col.idx, drop = FALSE]
# Sigma.B <- G.Sigma.b
}
SCORES <- cbind(Mu.W, Sigma.W, Mu.B, Sigma.B)
SCORES
}
# first-order information: outer crossprod of scores per cluster
lav_mvnorm_cluster_missing_information_firstorder <- function(
Y1 = NULL,
Y2 = NULL,
Lp = NULL,
Mp = NULL,
Mu.W = NULL,
Sigma.W = NULL,
Mu.B = NULL,
Sigma.B = NULL,
x.idx = NULL,
divide.by.two = FALSE,
Sinv.method = "eigen") {
N <- NROW(Y1)
SCORES <- lav_mvnorm_cluster_missing_scores_2l(
Y1 = Y1,
Y2 = Y2,
Lp = Lp,
Mp = Mp,
Mu.W = Mu.W,
Sigma.W = Sigma.W,
Mu.B = Mu.B,
Sigma.B = Sigma.B,
Sinv.method = Sinv.method
)
# divide by 2 (if we want scores wrt objective function)
if (divide.by.two) {
SCORES <- SCORES / 2
}
# unit information
information <- crossprod(SCORES) / Lp$nclusters[[2]]
# if x.idx, set rows/cols to zero
if (length(x.idx) > 0L) {
nw <- length(as.vector(Mu.W))
nw.star <- nw * (nw + 1) / 2
nb <- length(as.vector(Mu.B))
ov.idx <- Lp$ov.idx
x.idx.w <- which(ov.idx[[1]] %in% x.idx)
if (length(x.idx.w) > 0L) {
xw.idx <- c(
x.idx.w,
nw + lav_matrix_vech_which_idx(n = nw, idx = x.idx.w)
)
} else {
xw.idx <- integer(0L)
}
x.idx.b <- which(ov.idx[[2]] %in% x.idx)
if (length(x.idx.b) > 0L) {
xb.idx <- c(
x.idx.b,
nb + lav_matrix_vech_which_idx(n = nb, idx = x.idx.b)
)
} else {
xb.idx <- integer(0L)
}
all.idx <- c(xw.idx, nw + nw.star + xb.idx)
information[all.idx, ] <- 0
information[, all.idx] <- 0
}
information
}
# observed information
# order: mu.w within, vech(sigma.w) within, mu.b between, vech(sigma.b) between
# mu.w rows/cols that are splitted within/between are forced to zero
#
# numerical approximation (for now)
lav_mvnorm_cluster_missing_information_observed <- function(
Y1 = NULL,
Y2 = NULL,
Lp = NULL,
Mp = NULL,
YLp = NULL,
Mu.W = NULL,
Sigma.W = NULL,
Mu.B = NULL,
Sigma.B = NULL,
x.idx = integer(0L),
Sinv.method = "eigen") {
nobs <- Lp$nclusters[[1]]
nw <- length(as.vector(Mu.W))
nw.star <- nw * (nw + 1) / 2
nb <- length(as.vector(Mu.B))
nb.star <- nb * (nb + 1) / 2
ov.idx <- Lp$ov.idx
p.tilde <- length(unique(c(ov.idx[[1]], ov.idx[[2]])))
# Mu.W (for within-only)
Mu.W.tilde <- numeric(p.tilde)
Mu.W.tilde[ov.idx[[1]]] <- Mu.W
# local function -- gradient
GRAD <- function(x) {
# Mu.W (for within-only)
Mu.W.tilde2 <- numeric(p.tilde)
Mu.W.tilde2[ov.idx[[1]]] <- x[1:nw]
Mu.W.tilde2[Lp$both.idx[[2]]] <- Mu.W.tilde[Lp$both.idx[[2]]]
Mu.W2 <- Mu.W.tilde2[ov.idx[[1]]]
Sigma.W2 <- lav_matrix_vech_reverse(x[nw + 1:nw.star])
Mu.B2 <- x[nw + nw.star + 1:nb]
Sigma.B2 <- lav_matrix_vech_reverse(x[nw + nw.star + nb + 1:nb.star])
dx <- lav_mvnorm_cluster_missing_dlogl_2l_samplestats(
Y1 = Y1, Y2 = Y2, Lp = Lp, Mp = Mp,
Mu.W = Mu.W2, Sigma.W = Sigma.W2,
Mu.B = Mu.B2, Sigma.B = Sigma.B2,
return.list = FALSE,
Sinv.method = Sinv.method
)
# dx is for -2*logl
-1 / 2 * dx
}
# start.x
start.x <- c(
as.vector(Mu.W), lav_matrix_vech(Sigma.W),
as.vector(Mu.B), lav_matrix_vech(Sigma.B)
)
# total information
information <- -1 * numDeriv::jacobian(func = GRAD, x = start.x)
# unit information
information <- information / Lp$nclusters[[2]]
# if x.idx, set rows/cols to zero
if (length(x.idx) > 0L) {
x.idx.w <- which(ov.idx[[1]] %in% x.idx)
if (length(x.idx.w) > 0L) {
xw.idx <- c(
x.idx.w,
nw + lav_matrix_vech_which_idx(n = nw, idx = x.idx.w)
)
} else {
xw.idx <- integer(0L)
}
x.idx.b <- which(ov.idx[[2]] %in% x.idx)
if (length(x.idx.b) > 0L) {
xb.idx <- c(
x.idx.b,
nb + lav_matrix_vech_which_idx(n = nb, idx = x.idx.b)
)
} else {
xb.idx <- integer(0L)
}
all.idx <- c(xw.idx, nw + nw.star + xb.idx)
information[all.idx, ] <- 0
information[, all.idx] <- 0
}
information
}
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