Nothing
## RC(M) with transitional layer effect
RCTrans <- function(row, col, layer, inst=NULL) {
list(predictors = list(R1=substitute(row), C1=substitute(col), substitute(layer), R2=substitute(row), C2=substitute(col)),
term = function(predLabels, varLabels) {
sprintf("(%s + %s * (%s)^2) * (%s + %s * (%s)^2)",
predLabels[1], predLabels[4], predLabels[3],
predLabels[2], predLabels[5], predLabels[3])
},
call = as.expression(match.call()),
match = c(1, 2, 3, 1, 2),
start = function(theta) {
theta[attr(theta, "assign") == 3] <- sqrt(seq(0, 1, length.out=sum(attr(theta, "assign") == 3)))
theta
})
}
class(RCTrans) <- "nonlin"
RCTransSymm <- function(row, col, layer, inst=NULL) {
list(predictors = list(R1=substitute(row), C1=substitute(col), substitute(layer), R2=substitute(row), C2=substitute(col)),
term = function(predLabels, varLabels) {
sprintf("(%s + %s * (%s)^2) * (%s + %s * (%s)^2)",
predLabels[1], predLabels[4], predLabels[3],
predLabels[2], predLabels[5], predLabels[3])
},
call = as.expression(match.call()),
match = c(1, 2, 3, 1, 2),
common = c(1, 1, 3, 2, 2),
start = function(theta) {
theta[attr(theta, "assign") == 3] <- sqrt(seq(0, 1, length.out=sum(attr(theta, "assign") == 3)))
theta
})
}
class(RCTransSymm) <- "nonlin"
rcL.trans <- function(tab, nd=1, symmetric=FALSE, diagonal=c("none", "heterogeneous", "homogeneous"),
weighting=c("marginal", "uniform", "none"), se=c("none", "jackknife", "bootstrap"),
nreplicates=100, ncpus=getOption("boot.ncpus"),
family=poisson, weights=NULL, start=NULL, etastart=NULL, tolerance=1e-8, iterMax=5000,
trace=FALSE, verbose=TRUE, ...) {
diagonal <- match.arg(diagonal)
weighting <- match.arg(weighting)
se <- match.arg(se)
tab <- as.table(tab)
if(length(dim(tab)) < 3)
stop("tab must have (at least) three dimensions")
if(is.na(nd) || nd <= 0)
stop("nd must be strictly positive")
if(symmetric && nrow(tab) != ncol(tab))
stop("tab must be a square table for symmetric model")
if(symmetric && !all(rownames(tab) == colnames(tab)))
stop("tab must have identical row and column names for symmetric model")
if(symmetric && nd/2 > min(nrow(tab), ncol(tab)) - 1)
stop("Number of dimensions of symmetric model cannot exceed 2 * (min(nrow(tab), ncol(tab)) - 1)")
if(!symmetric && nd > min(nrow(tab), ncol(tab)) - 1)
stop("Number of dimensions cannot exceed min(nrow(tab), ncol(tab)) - 1")
if(length(dim(tab)) > 3)
tab <- margin.table(tab, 1:3)
tab <- prepareTable(tab, FALSE)
vars <- names(dimnames(tab))
if(diagonal == "homogeneous")
diagstr <- sprintf("+ Diag(%s, %s) ", vars[1], vars[2])
else if(diagonal == "heterogeneous")
diagstr <- sprintf("+ %s:Diag(%s, %s) ", vars[3], vars[1], vars[2])
else
diagstr <- ""
f1 <- sprintf("Freq ~ %s + %s + %s + %s:%s + %s:%s %s",
vars[1], vars[2], vars[3],
vars[1], vars[3], vars[2], vars[3], diagstr)
eliminate <- eval(parse(text=sprintf("quote(%s:%s)", vars[1], vars[3])))
# gnm can give incorrect results with contrasts other than treatment
contr <- getOption("contrasts")
on.exit(options(contrasts=contr))
options(contrasts=c("contr.treatment", "contr.treatment"))
if(!is.null(start) && identical(start, NA)) {
cat("Running base model to find starting values...\n")
if(symmetric) {
args <- list(formula=as.formula(sprintf("%s + instances(MultHomog(%s, %s), %i)", f1, vars[1], vars[2], nd)),
data=tab, family=family, weights=weights, eliminate=eliminate,
tolerance=1e-6, iterMax=iterMax)
base <- do.call("gnm", c(args, list(...)))
start <- parameters(base)[seq(1, length(parameters(base)) - nrow(tab) * nd)]
for(i in 1:nd)
start <- c(start, parameters(base)[pickCoef(base, paste("Mult.*inst =", i))],
sqrt(seq(0, 1, length.out=dim(tab)[3])), rep(NA, nrow(tab)))
}
else {
args <- list(formula=as.formula(sprintf("%s + instances(Mult(%s, %s), %i)", f1, vars[1], vars[2], nd)),
data=tab, family=family, weights=weights, eliminate=eliminate,
tolerance=1e-6, iterMax=iterMax, verbose=verbose, trace=trace)
base <- do.call("gnm", c(args, list(...)))
start <- parameters(base)[seq(1, length(parameters(base)) - (nrow(tab) + ncol(tab)) * nd)]
for(i in 1:nd)
start <- c(start, parameters(base)[pickCoef(base, paste("Mult.*inst =", i))],
sqrt(seq(0, 1, length.out=dim(tab)[3])), rep(NA, nrow(tab) + ncol(tab)))
}
if(!is.null(etastart))
etastart <- as.numeric(predict(base))
cat("Running real model...\n")
}
f <- sprintf("Freq ~ %s + %s + %s + %s:%s + %s:%s %s+ instances(%s(%s, %s, %s), %i)",
vars[1], vars[2], vars[3], vars[1], vars[3], vars[2], vars[3], diagstr,
if(symmetric) "RCTransSymm" else "RCTrans", vars[1], vars[2], vars[3], nd)
args <- list(formula=as.formula(f), data=tab, family=family, weights=weights,
# Both constraints are really needed: the computed scores are wrong without them
# (rows are ordered along an oblique axis, and columns get weird values)
constrain=sprintf("RCTrans.*\\).\\Q%s\\E(\\Q%s\\E|\\Q%s\\E)$",
vars[3], head(dimnames(tab)[[3]], 1), tail(dimnames(tab)[[3]], 1), nd),
constrainTo=rep(0:1, nd),
start=start, etastart=etastart, eliminate=eliminate,
tolerance=tolerance, iterMax=iterMax, verbose=verbose, trace=trace)
model <- do.call("gnm", c(args, list(...)))
if(is.null(model))
return(NULL)
newclasses <- if(symmetric) c("rcL.trans.symm", "rcL.trans", "rcL", "assocmod")
else c("rcL.trans", "rcL", "assocmod")
class(model) <- c(newclasses, class(model))
model$call.gnm <- model$call
model$call <- match.call()
model$assoc <- assoc(model, weighting=weighting)
if(se %in% c("jackknife", "bootstrap")) {
jb <- jackboot(se, ncpus, nreplicates, tab, model, assoc, NULL,
weighting, NULL, NULL, family, weights,
verbose, trace, start, etastart, ...)
model$assoc$covmat <- jb$covmat
model$assoc$adj.covmats <- jb$adj.covmats
model$assoc$boot.results <- jb$boot.results
model$assoc$jack.results <- jb$jack.results
}
else {
model$assoc$covmat <- numeric(0)
model$assoc$adj.covmats <- numeric(0)
model$assoc$boot.results <- numeric(0)
model$assoc$jack.results <- numeric(0)
}
model$assoc$covtype <- se
model
}
# Number of constraints applied:
# - two layer coefficients (normally already present in the model)
# - two for each dimension of the start scores
# - two for each dimension of the end scores
assoc.rcL.trans <- function(model, weighting=c("marginal", "uniform", "none"), ...) {
if(!inherits(model, "gnm"))
stop("model must be a gnm object")
tab <- prepareTable(model$data, FALSE)
vars <- names(dimnames(tab))
nr <- nrow(tab)
nc <- ncol(tab)
nl <- dim(tab)[3]
# Weight with marginal frequencies, cf. Clogg & Shihadeh (1994), p. 83-84, and Becker & Clogg (1989), p. 144.
weighting <- match.arg(weighting)
if(weighting == "marginal") {
rp <- prop.table(apply(tab, 1, sum, na.rm=TRUE))
cp <- prop.table(apply(tab, 2, sum, na.rm=TRUE))
}
else if(weighting == "uniform") {
rp <- rep(1/nr, nr)
cp <- rep(1/nc, nc)
}
else {
rp <- rep(1, nr)
cp <- rep(1, nc)
}
# Find out the number of dimensions
nd <- 0
while(length(pickCoef(model, sprintf("RCTrans.*inst = %s\\)\\.[RC][12]%s", nd+1, vars[1]))) > 0)
nd <- nd + 1
# One dimension, or none
if(nd <= 0) {
mu <- parameters(model)[pickCoef(model, sprintf("RCTrans.*\\)\\.R1\\Q%s\\E(\\Q%s\\E)$", vars[1],
paste(rownames(tab), collapse="\\E|\\Q")))]
nu <- parameters(model)[pickCoef(model, sprintf("RCTrans.*\\)\\.C1\\Q%s\\E(\\Q%s\\E)$", vars[2],
paste(colnames(tab), collapse="\\E|\\Q")))]
mu1 <- parameters(model)[pickCoef(model, sprintf("RCTrans.*\\)\\.R2\\Q%s\\E(\\Q%s\\E)",vars[1],
paste(rownames(tab), collapse="\\E|\\Q")))]
nu1 <- parameters(model)[pickCoef(model, sprintf("RCTrans.*\\)\\.C2\\Q%s\\E(\\Q%s\\E)", vars[2],
paste(colnames(tab), collapse="\\E|\\Q")))]
phi <- parameters(model)[pickCoef(model, sprintf("RCTrans.*\\)\\.\\Q%s\\E(\\Q%s\\E)", vars[3],
paste(dimnames(tab)[[3]], collapse="\\E|\\Q")))]
if(length(mu) == nr && length(nu) == nc
&& length(mu1) == nr && length(nu1) == nc
&& length(phi) == nl) {
nd <- 1
row <- matrix(mu, nr, 1)
col <- matrix(nu, nc, 1)
row1 <- matrix(mu1, nr, 1)
col1 <- matrix(nu1, nc, 1)
layer <- matrix(phi, nl, 1)
}
else {
stop("No dimensions found. Are you sure this is a row-column association model with transitional layer effect?")
}
}
else {
# Several dimensions: prepare matrices before filling them
row <- matrix(NA, nr, nd)
col <- matrix(NA, nc, nd)
row1 <- matrix(NA, nr, nd)
col1 <- matrix(NA, nc, nd)
layer <- matrix(NA, nl, nd)
for(i in 1:nd) {
mu <- parameters(model)[pickCoef(model, sprintf("RCTrans.*inst = %s\\)\\.R1\\Q%s\\E(\\Q%s\\E)$",
i, vars[1],
paste(rownames(tab), collapse="\\E|\\Q")))]
nu <- parameters(model)[pickCoef(model, sprintf("RCTrans.*inst = %s\\)\\.C1\\Q%s\\E(\\Q%s\\E)$",
i, vars[2],
paste(colnames(tab), collapse="\\E|\\Q")))]
mu1 <- parameters(model)[pickCoef(model, sprintf("RCTrans.*inst = %s\\)\\.R2\\Q%s\\E(\\Q%s\\E)$",
i, vars[1],
paste(rownames(tab), collapse="\\E|\\Q")))]
nu1 <- parameters(model)[pickCoef(model, sprintf("RCTrans.*inst = %s\\)\\.C2\\Q%s\\E(\\Q%s\\E)$",
i, vars[2],
paste(colnames(tab), collapse="\\E|\\Q")))]
phi <- parameters(model)[pickCoef(model, sprintf("RCTrans.*inst = %s\\)\\.\\Q%s\\E(\\Q%s\\E)$",
i, vars[3],
paste(dimnames(tab)[[3]], collapse="\\E|\\Q")))]
if(length(mu) == nr && length(nu) == nc
&& length(mu1) == nr && length(nu1) == nc
&& length(phi) == nl) {
row[,i] <- mu
col[,i] <- nu
row1[,i] <- mu1
col1[,i] <- nu1
layer[,i] <- phi
}
else {
stop("Invalid dimensions found. Are you sure this is a row-column association model with transitional layer effect?")
}
}
}
if(length(pickCoef(model, "Diag\\(") > 0)) {
dg <- matrix(NA, nl, nr)
dg[] <- pickCoef(model, "Diag\\(", value=TRUE)
}
else {
dg <- numeric(0)
}
# Layer coefficients are squared internally by RCTrans
layer <- layer^2
# Center
row <- sweep(row, 2, colSums(sweep(row, 1, rp/sum(rp), "*")), "-")
col <- sweep(col, 2, colSums(sweep(col, 1, cp/sum(cp), "*")), "-")
row1 <- sweep(row1, 2, colSums(sweep(row1, 1, rp/sum(rp), "*")), "-")
col1 <- sweep(col1, 2, colSums(sweep(col1, 1, cp/sum(cp), "*")), "-")
# Compute layer scores and scale
row <- array(row, dim=c(nrow(row), nd, nl)) +
sweep(array(row1, dim=c(nrow(row1), nd, nl)), 3:2, layer, "*")
col <- array(col, dim=c(nrow(col), nd, nl)) +
sweep(array(col1, dim=c(nrow(col1), nd, nl)), 3:2, layer, "*")
phir <- sqrt(margin.table(sweep(row^2, 1, rp, "*"), 2:3))
phic <- sqrt(margin.table(sweep(col^2, 1, cp, "*"), 2:3))
row <- sweep(row, 2:3, phir, "/")
col <- sweep(col, 2:3, phic, "/")
layer <- t(phir * phic)
# Order dimensions according to phi on first layer category
ord <- order(abs(layer[1,]), decreasing=TRUE)
layer <- layer[,ord, drop=FALSE]
row <- row[,ord,, drop=FALSE]
col <- col[,ord,, drop=FALSE]
# Since the sign of scores is arbitrary, conventionally choose positive scores
# for the first row category: this ensures the results are stable when jackknifing.
for(i in 1:dim(row)[3]) {
for(j in 1:nd) {
if(row[1,j,i] < 0) {
row[,j,i] <- -row[,j,i]
col[,j,i] <- -col[,j,i]
}
}
}
# Scores can switch sides from one layer to another
# Reverse axes for each layer state so that the scores are positively correlated to the first layer scores for rows
for(i in seq_len(dim(row)[3] - 1)) {
chg <- ifelse(diag(as.matrix(cor(row[,,i+1], row[,,1]))) >= 0, 1, -1)
row[,,i+1] <- sweep(row[,,i+1, drop=FALSE], 2, chg, "*")
col[,,i+1] <- sweep(col[,,i+1, drop=FALSE], 2, chg, "*")
}
## Prepare objects
colnames(layer) <- colnames(row) <- colnames(col) <- paste("Dim", 1:nd, sep="")
rownames(row) <- rownames(tab)
rownames(col) <- colnames(tab)
rownames(layer) <- dimnames(row)[[3]] <- dimnames(col)[[3]] <- dimnames(tab)[[3]]
if(length(dg) > 0) {
colnames(dg) <- if(all(rownames(tab) == colnames(tab))) rownames(tab)
else paste(rownames(tab), colnames(tab), sep=":")
rownames(dg) <- dimnames(tab)[[3]]
}
row.weights <- apply(tab, c(1, 3), sum, na.rm=TRUE)
col.weights <- apply(tab, c(2, 3), sum, na.rm=TRUE)
obj <- list(phi = layer, row = row, col = col, diagonal = dg,
weighting = weighting, row.weights = row.weights, col.weights = col.weights,
vars = vars)
class(obj) <- c("assoc.rcL.trans", "assoc.rcL", "assoc")
obj
}
assoc.rcL.trans.symm <- function(model, weighting=c("marginal", "uniform", "none"), ...) {
if(!inherits(model, "gnm"))
stop("model must be a gnm object")
tab <- prepareTable(model$data, FALSE)
vars <- names(dimnames(tab))
nr <- nrow(tab)
nc <- ncol(tab)
nl <- dim(tab)[3]
stopifnot(nr == nc)
# Weight with marginal frequencies, cf. Clogg & Shihadeh (1994), p. 83-84, and Becker & Clogg (1989), p. 144.
weighting <- match.arg(weighting)
if(weighting == "marginal")
p <- prop.table(apply(tab, 1, sum, na.rm=TRUE) + apply(tab, 2, sum, na.rm=TRUE))
else if(weighting == "uniform")
rp <- rep(1/nr, nr)
else
rp <- rep(1, nr)
# Find out the number of dimensions
nd <- 0
while(length(pickCoef(model, sprintf("RCTransSymm.*inst = %s\\)[RC][12]\\.\\Q%s\\E\\|\\Q%s\\E",
nd+1, vars[1], vars[2]))) > 0)
nd <- nd + 1
# One dimension, or none
if(nd <= 0) {
mu <- parameters(model)[pickCoef(model, sprintf("RCTransSymm.*\\)[RC]1\\.\\Q%s\\E\\|\\Q%s\\E(\\Q%s\\E)$",
vars[1], vars[2],
paste(rownames(tab), collapse="\\E|\\Q")))]
mu1 <- parameters(model)[pickCoef(model, sprintf("RCTransSymm.*\\)[RC]2\\.\\Q%s\\E\\|\\Q%s\\E(\\Q%s\\E)$",
vars[1], vars[2],
paste(rownames(tab), collapse="\\E|\\Q")))]
phi <- parameters(model)[pickCoef(model, sprintf("RCTransSymm.*\\)\\.\\Q%s\\E(\\Q%s\\E)$", vars[3],
paste(dimnames(tab)[[3]], collapse="\\E|\\Q")))]
if(length(mu) == nr && length(mu1) == nr && length(phi) == nl) {
nd <- 1
sc <- matrix(mu, nr, 1)
sc1 <- matrix(mu1, nr, 1)
layer <- matrix(phi, nl, 1)
}
else {
stop("No dimensions found. Are you sure this is a row-column association model with transitional layer effect?")
}
}
else {
# Several dimensions: prepare matrices before filling them
sc <- matrix(NA, nr, nd)
sc1 <- matrix(NA, nr, nd)
layer <- matrix(NA, nl, nd)
for(i in 1:nd) {
mu <- parameters(model)[pickCoef(model, sprintf("RCTransSymm.*inst = %i\\)[RC]1\\.\\Q%s\\E\\|\\Q%s\\E(\\Q%s\\E)$",
i, vars[1], vars[2],
paste(rownames(tab), collapse="\\E|\\Q")))]
mu1 <- parameters(model)[pickCoef(model, sprintf("RCTransSymm.*inst = %i\\)[RC]2\\.\\Q%s\\E\\|\\Q%s\\E(\\Q%s\\E)$",
i, vars[1], vars[2],
paste(rownames(tab), collapse="\\E|\\Q")))]
phi <- parameters(model)[pickCoef(model, sprintf("RCTransSymm.*inst = %i\\)\\.\\Q%s\\E(\\Q%s\\E)$",
i, vars[3],
paste(dimnames(tab)[[3]], collapse="\\E|\\Q")))]
if(length(mu) == nr && length(mu1) == nr && length(phi) == nl) {
sc[,i] <- mu
sc1[,i] <- mu1
layer[,i] <- phi
}
else {
stop("Invalid dimensions found. Are you sure this is a row-column association model with transitional layer effect?")
}
}
}
if(length(pickCoef(model, "Diag\\(") > 0)) {
dg <- matrix(NA, nl, nr)
dg[] <- pickCoef(model, "Diag\\(", value=TRUE)
}
else {
dg <- numeric(0)
}
# Layer coefficients are squared internally by RCTrans
layer <- layer^2
# Center
sc <- sweep(sc, 2, colSums(sweep(sc, 1, p/sum(p), "*")), "-")
sc1 <- sweep(sc1, 2, colSums(sweep(sc1, 1, p/sum(p), "*")), "-")
# Compute layer scores and scale
sc <- array(sc, dim=c(nrow(sc), nd, nl)) +
sweep(array(sc1, dim=c(nrow(sc1), nd, nl)), 3:2, layer, "*")
phi <- sqrt(margin.table(sweep(sc^2, 1, p, "*"), 2:3))
sc <- sweep(sc, 2:3, phi, "/")
layer <- t(phi)
# Order dimensions according to phi on first layer category
ord <- order(abs(layer[1,]), decreasing=TRUE)
layer <- layer[,ord, drop=FALSE]
sc <- sc[,ord,, drop=FALSE]
# Since the sign of scores is arbitrary, conventionally choose positive scores
# for the first category: this ensures the results are stable when jackknifing.
for(i in 1:dim(sc)[3]) {
for(j in 1:nd) {
if(sc[1,j,i] < 0)
sc[,j,i] <- -sc[,j,i]
}
}
# Scores can switch sides from one layer to another
# Reverse axes for each layer state so that the scores are positively correlated to the first layer scores for rows
for(i in seq_len(dim(sc)[3] - 1)) {
chg <- ifelse(diag(as.matrix(cor(sc[,,i+1], sc[,,1]))) >= 0, 1, -1)
sc[,,i+1] <- sweep(sc[,,i+1, drop=FALSE], 2, chg, "*")
}
## Prepare objects
colnames(layer) <- colnames(sc) <- paste("Dim", 1:nd, sep="")
rownames(sc) <- rownames(tab)
rownames(layer) <- dimnames(sc)[[3]] <- dimnames(tab)[[3]]
if(length(dg) > 0) {
colnames(dg) <- if(all(rownames(tab) == colnames(tab))) rownames(tab)
else paste(rownames(tab), colnames(tab), sep=":")
rownames(dg) <- dimnames(tab)[[3]]
}
row.weights <- apply(tab, c(1, 3), sum, na.rm=TRUE)
col.weights <- apply(tab, c(2, 3), sum, na.rm=TRUE)
obj <- list(phi = layer, row = sc, col = sc, diagonal = dg,
weighting = weighting, row.weights = row.weights, col.weights = col.weights)
class(obj) <- c("assoc.rcL.trans", "assoc.rcL", "assoc.symm", "assoc")
obj
}
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