rasch <-
function (data, constraint = NULL, IRT.param = TRUE, start.val = NULL, na.action = NULL,
control = list(), Hessian = TRUE) {
cl <- match.call()
if ((!is.data.frame(data) & !is.matrix(data)) || ncol(data) == 1)
stop("'data' must be either a numeric matrix or a data.frame, with at least two columns.\n")
X <- data.matrix(data)
if (any(its <- apply(X, 2, function (x) { x <- x[!is.na(x)]; length(unique(x)) } ) > 2))
stop("'data' contain more that 2 distinct values for item(s): ", paste(which(its), collapse = ", "))
X <- apply(X, 2, function (x) if (all(unique(x) %in% c(1, 0, NA))) x else x - 1)
if (!is.null(na.action))
X <- na.action(X)
colnamsX <- colnames(X)
dimnames(X) <- NULL
n <- nrow(X)
p <- ncol(X)
con <- list(iter.qN = 150, GHk = 21, method = "BFGS", verbose = getOption("verbose"))
con[names(control)] <- control
betas <- start.val.rasch(start.val, X)
if (!is.null(constraint)) {
if (!is.matrix(constraint) || (nrow(constraint) > p + 1 | ncol(constraint) != 2))
stop("'constraint' should be a 2-column matrix with at most ", p + 1, " rows (read help file).\n")
if (any(constraint[, 1] < 1 | constraint[, 1] > p + 1))
stop("the 1st column of 'constraint' should between 1 and ", p + 1, " (read help file).\n")
constraint <- constraint[order(constraint[, 1]), , drop = FALSE]
constraint[, 1] <- round(constraint[, 1])
betas[constraint[, 1]] <- NA
}
pats <- apply(X, 1, paste, collapse = "/")
freqs <- table(pats)
nfreqs <- length(freqs)
obs <- as.vector(freqs)
X <- unlist(strsplit(cbind(names(freqs)), "/"))
X[X == "NA"] <- as.character(NA)
X <- matrix(as.numeric(X), nfreqs, p, TRUE)
mX <- 1 - X
if (any(na.ind <- is.na(X)))
X[na.ind] <- mX[na.ind] <- 0
GH <- GHpoints(data ~ z1, con$GHk)
Z <- GH$x
GHw <- GH$w
logLik.rasch <- function (betas, constraint) {
betas <- betas.rasch(betas, constraint, p)
pr <- probs(Z %*% t(betas))
p.xz <- exp(X %*% t(log(pr)) + mX %*% t(log(1 - pr)))
p.x <- rep(c(p.xz %*% GHw), obs)
-sum(log(p.x))
}
score.rasch <- function (betas, constraint) {
betas <- betas.rasch(betas, constraint, p)
pr <- probs(Z %*% t(betas))
p.xz <- exp(X %*% t(log(pr)) + mX %*% t(log(1 - pr)))
p.x <- c(p.xz %*% GHw)
p.zx <- (p.xz / p.x) * obs
scores <- matrix(0, p, 2)
for (i in 1:p) {
ind <- na.ind[, i]
Y <- outer(X[, i], pr[, i], "-")
Y[ind, ] <- 0
scores[i, ] <- -colSums((p.zx * Y) %*% (Z * GHw))
}
if (!is.null(constraint))
c(scores[, 1], sum(scores[, 2]))[-constraint[, 1]]
else
c(scores[, 1], sum(scores[, 2]))
}
res.qN <- optim(betas[!is.na(betas)], fn = logLik.rasch, gr = score.rasch, method = con$method, hessian = Hessian,
control = list(maxit = con$iter.qN, trace = as.numeric(con$verbose)), constraint = constraint)
if (Hessian && all(!is.na(res.qN$hessian) & is.finite(res.qN$hessian))) {
ev <- eigen(res.qN$hessian, TRUE, TRUE)$values
if (!all(ev >= -1e-06 * abs(ev[1])))
warning("Hessian matrix at convergence is not positive definite; unstable solution.\n")
}
if (Hessian && any(!is.finite(res.qN$hessian))) {
warning("Hessian matrix at convergence contains infinite or missing values; unstable solution.\n")
}
betas <- betas.rasch(res.qN$par, constraint, p)
rownames(betas) <- if (!is.null(colnamsX)) colnamsX else paste("Item", 1:p)
colnames(betas) <- c("beta.i", "beta")
max.sc <- max(abs(score.rasch(res.qN$par, constraint)))
X[na.ind] <- NA
fit <- list(coefficients = betas, log.Lik = -res.qN$value, convergence = res.qN$conv, hessian = res.qN$hessian,
counts = res.qN$counts, patterns = list(X = X, obs = obs), GH = list(Z = Z, GHw = GHw), max.sc = max.sc,
constraint = constraint, IRT.param = IRT.param, X = data, control = con, na.action = na.action, call = cl)
class(fit) <- "rasch"
fit
}
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