Nothing
## RC(M) model
rc <- function(tab, nd=1, symmetric=FALSE, diagonal=FALSE,
weighting=c("marginal", "uniform", "none"), rowsup=NULL, colsup=NULL,
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, ...) {
weighting <- match.arg(weighting)
se <- match.arg(se)
tab <- as.table(tab)
if(length(dim(tab)) < 2)
stop("tab must have (at least) two 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)) > 2)
tab <- margin.table(tab, 1:2)
tab <- prepareTable(tab, TRUE, rowsup, colsup)
vars <- names(dimnames(tab))
if(diagonal)
diagstr <- sprintf("+ Diag(%s, %s) ", vars[1], vars[2])
else
diagstr <- ""
# 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(identical(start, NA)) {
cat("Running base model to find starting values...\n")
args <- list(formula=as.formula(sprintf("Freq ~ %s + %s %s", vars[1], vars[2], diagstr)),
data=tab, family=family, weights=weights,
tolerance=tolerance, iterMax=iterMax)
base <- do.call("gnm", c(args, list(...)))
res <- if(symmetric) residEVD(base, nd)
else residSVD(base, nd)
# Using NA for all linear parameters usually gives better results than linear parameter values
start <- c(rep(NA, length(parameters(base))), res)
if(is.null(etastart))
etastart <- as.numeric(predict(base))
cat("Running real model...\n")
}
if(symmetric)
f <- sprintf("Freq ~ %s + %s %s+ instances(MultHomog(%s, %s), %i)",
vars[1], vars[2], diagstr, vars[1], vars[2], nd)
else
f <- sprintf("Freq ~ %s + %s %s+ instances(Mult(%s, %s), %i)",
vars[1], vars[2], diagstr, vars[1], vars[2], nd)
args <- list(formula=as.formula(f), data=tab,
family=family, weights=weights, start=start, etastart=etastart,
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("rc.symm", "rc", "assocmod") else c("rc", "assocmod")
class(model) <- c(newclasses, class(model))
model$call.gnm <- model$call
model$call <- match.call()
model$assoc <- assoc(model, weighting=weighting, rowsup=rowsup, colsup=colsup)
if(se %in% c("jackknife", "bootstrap")) {
jb <- jackboot(se, ncpus, nreplicates, tab, model,
assoc1=getS3method("assoc", class(model)[1]), assoc2=NULL,
weighting, rowsup=rowsup, colsup=colsup,
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
}
assoc.rc <- function(model, weighting=c("marginal", "uniform", "none"),
rowsup=NULL, colsup=NULL, ...) {
if(!inherits(model, "gnm"))
stop("model must be a gnm object")
tab <- prepareTable(model$data, TRUE, rowsup, colsup)
vars <- names(dimnames(tab))
# Weight with marginal frequencies, cf. Clogg & Shihadeh (1994), p. 83-84, and Becker & Clogg (1989), p. 144.
weighting <- match.arg(weighting)
if(weighting == "marginal") {
rp <- prop.table(apply(tab, 1, sum, na.rm=TRUE))
cp <- prop.table(apply(tab, 2, sum, na.rm=TRUE))
}
else if(weighting == "uniform") {
rp <- rep(1/nrow(tab), nrow(tab))
cp <- rep(1/ncol(tab), ncol(tab))
}
else {
rp <- rep(1, nrow(tab))
cp <- rep(1, ncol(tab))
}
# Prepare matrices before filling them
row <- matrix(NA, nrow(tab), 0)
col <- matrix(NA, ncol(tab), 0)
nd <- 0
while(TRUE) {
mu <- parameters(model)[pickCoef(model, sprintf("Mult\\(\\., \\Q%s\\E, inst = %i\\)\\.\\Q%s\\E(\\Q%s\\E)$",
vars[2], nd + 1, vars[1],
paste(rownames(tab), collapse="\\E|\\Q")))]
nu <- parameters(model)[pickCoef(model, sprintf("Mult\\(\\Q%s\\E, \\., inst = %i\\)\\.\\Q%s\\E(\\Q%s\\E)$",
vars[1], nd + 1, vars[2],
paste(colnames(tab), collapse="\\E|\\Q")))]
if(!(length(mu) == nrow(tab) && length(nu) == ncol(tab)))
break
# This is a correct dimension, add it
nd <- nd + 1
row <- cbind(row, mu)
col <- cbind(col, nu)
}
if(nd <= 0) {
mu <- parameters(model)[pickCoef(model, sprintf("Mult\\(\\., \\Q%s\\E)\\.\\Q%s\\E(\\Q%s\\E)$",
vars[2], vars[1],
paste(rownames(tab), collapse="\\E|\\Q")))]
nu <- parameters(model)[pickCoef(model, sprintf("Mult\\(\\Q%s\\E, \\.)\\.\\Q%s\\E(\\Q%s\\E)$",
vars[1], vars[2],
paste(colnames(tab), collapse="\\E|\\Q")))]
if(length(mu) == nrow(tab) && length(nu) == ncol(tab)) {
nd <- 1
row <- cbind(row, mu)
col <- cbind(col, nu)
}
else {
stop("No dimensions found. Are you sure this is a row-column association model?")
}
}
if(length(pickCoef(model, "Diag\\(")) > nrow(tab))
dg <- matrix(pickCoef(model, "Diag\\(", value=TRUE), ncol=nrow(tab))
else if(length(pickCoef(model, "Diag\\(")) > 0)
dg <- matrix(pickCoef(model, "Diag\\(", value=TRUE), 1, nrow(tab))
else
dg <- numeric(0)
# Center
row <- sweep(row, 2, colSums(sweep(row, 1, rp/sum(rp), "*")), "-")
col <- sweep(col, 2, colSums(sweep(col, 1, cp/sum(cp), "*")), "-")
# Technique proposed in Goodman (1991), Appendix 4
lambda <- matrix(0, nrow(tab), ncol(tab))
for(i in 1:nd) {
lambda <- lambda + row[,i] %o% col[,i]
}
lambda0 <- lambda * sqrt(rp %o% cp) # Eq. A.4.3
sv <- svd(lambda0)
row[] <- diag(1/sqrt(rp)) %*% sv$u[,1:nd] # Eq. A.4.7
col[] <- diag(1/sqrt(cp)) %*% sv$v[,1:nd] # Eq. A.4.7
phi <- sv$d[1:nd]
# 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:nd) {
if(row[1,i] < 0) {
row[,i] <- -row[,i]
col[,i] <- -col[,i]
}
}
## Prepare objects
phi <- rbind(c(phi))
dim(row)[3] <- dim(col)[3] <- 1
colnames(row) <- colnames(col) <- colnames(phi) <- paste("Dim", 1:nd, sep="")
rownames(row) <- rownames(tab)
rownames(col) <- colnames(tab)
if(length(dg) > 0) {
# Diag() sorts coefficients alphabetically!
dg[,order(rownames(tab))] <- dg
colnames(dg) <- if(all(rownames(tab) == colnames(tab))) rownames(tab)
else paste(rownames(tab), colnames(tab), sep=":")
if(nrow(dg) > 1)
rownames(dg) <- dimnames(tab)[[3]]
else
rownames(dg) <- "All levels"
}
if(length(dim(tab)) == 3) {
row.weights <- apply(tab, c(1, 3), sum, na.rm=TRUE)
col.weights <- apply(tab, c(2, 3), sum, na.rm=TRUE)
}
else {
row.weights <- as.matrix(apply(tab, 1, sum, na.rm=TRUE))
col.weights <- as.matrix(apply(tab, 2, sum, na.rm=TRUE))
}
obj <- list(phi = phi, row = row, col = col, diagonal = dg,
weighting = weighting, row.weights = row.weights, col.weights = col.weights,
vars = vars)
## Supplementary rows/columns
if(!is.null(rowsup) || !is.null(colsup)) {
sup <- sup.scores.rc(model, tab, obj, rowsup, colsup)
obj$row <- sup$row
obj$col <- sup$col
obj$row.weights <- sup$row.weights
obj$col.weights <- sup$col.weights
}
class(obj) <- c("assoc.rc", "assoc")
obj
}
## RC(M) model with symmetric row and column scores
assoc.rc.symm <- function(model, weighting=c("marginal", "uniform", "none"),
rowsup=NULL, colsup=NULL, ...) {
if(!inherits(model, "gnm"))
stop("model must be a gnm object")
tab <- prepareTable(model$data, TRUE, rowsup, colsup)
vars <- names(dimnames(tab))
# Weight with marginal frequencies, cf. Clogg & Shihadeh (1994), p. 83-84, and Becker & Clogg (1989), p. 144.
weighting <- match.arg(weighting)
if(weighting == "marginal")
p <- prop.table(apply(tab, 1, sum, na.rm=TRUE) + apply(tab, 2, sum, na.rm=TRUE))
else if(weighting == "uniform")
p <- rep(1/nrow(tab), nrow(tab))
else
p <- rep(1, nrow(tab))
sc <- matrix(NA, nrow(tab), 0)
nd <- 0
while(TRUE) {
mu <- parameters(model)[pickCoef(model, sprintf("MultHomog\\(\\Q%s\\E\\, \\Q%s\\E\\, inst = %i\\)(\\Q%s\\E)$",
vars[1], vars[2], nd + 1,
paste(c(rownames(tab), colnames(tab)), collapse="\\E|\\Q")))]
if(!(length(mu) == nrow(tab)))
break
# This is a correct dimension, add it
nd <- nd + 1
sc <- cbind(sc, mu)
}
if(nd <= 0) {
mu <- parameters(model)[pickCoef(model, sprintf("MultHomog\\(\\Q%s\\E\\, \\Q%s\\E\\)(\\Q%s\\E)$",
vars[1], vars[2],
paste(c(rownames(tab), colnames(tab)), collapse="\\E|\\Q")))]
if(length(mu) == nrow(tab)) {
nd <- 1
sc <- cbind(sc, mu)
}
else {
stop("No dimensions found. Are you sure this is a row-column association model with symmetric row and column scores?")
}
}
if(length(pickCoef(model, "Diag\\(")) > nrow(tab))
dg <- matrix(pickCoef(model, "Diag\\(", value=TRUE), ncol=nrow(tab))
else if(length(pickCoef(model, "Diag\\(")) > 0)
dg <- matrix(pickCoef(model, "Diag\\(", value=TRUE), 1, nrow(tab))
else
dg <- numeric(0)
# Center
sc <- sweep(sc, 2, colSums(sweep(sc, 1, p/sum(p), "*")), "-")
# Technique proposed in Goodman (1991), Appendix 4, but with eigenvalues decomposition
lambda <- matrix(0, nrow(tab), ncol(tab))
for(i in 1:nd)
lambda <- lambda + sc[,i] %o% sc[,i]
lambda0 <- lambda * sqrt(p %o% p) # Eq. A.4.3
eigen <- eigen(lambda0, symmetric=TRUE)
sc[,1:nd] <- diag(1/sqrt(p)) %*% eigen$vectors[,1:nd] # Eq. A.4.7
phi <- eigen$values[1:nd]
# Since the sign of scores is arbitrary, conventionally choose positive scores
# for the first category: this ensures the results are stable when jackknifing.
for(i in 1:nd) {
if(sc[1,i] < 0)
sc[,i] <- -sc[,i]
}
## Prepare objects
phi <- rbind(c(phi))
dim(sc)[3] <- 1
colnames(sc) <- colnames(phi) <- paste("Dim", 1:nd, sep="")
rownames(sc) <- rownames(tab)
if(length(dg) > 0) {
# Diag() sorts coefficients alphabetically!
dg[,order(rownames(tab))] <- dg
colnames(dg) <- if(all(rownames(tab) == colnames(tab))) rownames(tab)
else paste(rownames(tab), colnames(tab), sep=":")
if(nrow(dg) > 1)
rownames(dg) <- dimnames(tab)[[3]]
else
rownames(dg) <- "All levels"
}
if(length(dim(tab)) == 3) {
row.weights <- apply(tab, c(1, 3), sum, na.rm=TRUE)
col.weights <- apply(tab, c(2, 3), sum, na.rm=TRUE)
}
else {
row.weights <- as.matrix(apply(tab, 1, sum, na.rm=TRUE))
col.weights <- as.matrix(apply(tab, 2, sum, na.rm=TRUE))
}
obj <- list(phi = phi, row = sc, col= sc, diagonal = dg,
weighting = weighting, row.weights = row.weights, col.weights = col.weights,
vars = vars)
## Supplementary rows/columns
if(!is.null(rowsup) || !is.null(colsup)) {
sup <- sup.scores.rc(model, tab, obj, rowsup, colsup, symmetry="symmetric")
obj$row <- sup$row
obj$col <- sup$col
obj$row.weights <- sup$row.weights
obj$col.weights <- sup$col.weights
}
class(obj) <- c("assoc.rc", "assoc.symm", "assoc")
obj
}
assoc <- function(model, weighting, rowsup, colsup, ...) UseMethod("assoc", model)
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