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#' fit_nodk
#'
#' @title Goodness of fit statistics for data without don't know
#'
#' @description For data without Don't Know, chi-square goodness of fit between true and model based multivariate distribution
#'
#' @param pre_test data.frame carrying pre_test items
#' @param pst_test data.frame carrying pst_test items
#' @param g estimates of \eqn{\gamma} produced from \code{\link{guesstimate}}
#' @param est.param estimated parameters produced from \code{\link{guesstimate}}
#' @return matrix with two rows: top row carrying chi-square value, and bottom row probability of observing that value
#' @export
#' @examples
#' \dontrun{fit_nodk(pre_test, pst_test, g, est.param)}
fit_nodk <- function(pre_test, pst_test, g, est.param) {
data <- multi_transmat(pre_test, pst_test)
data <- data[(1:nrow(data)-1),] # remove the agg.
expec <- matrix(ncol=nrow(data), nrow=4)
fit <- matrix(ncol=nrow(data), nrow=2)
colnames(fit) <- rownames(data)
rownames(fit) <- c("chi-square", "p-value")
for (i in 1:nrow(data)) {
gi <- g[[i]]
expec[1, i] <- (1 - gi)*(1 - gi)*est.param[1,i]*sum(data[i,])
expec[2, i] <- ((1 - gi)*gi*est.param[1, i] + (1 - gi)*est.param[2, i])*sum(data[i, ])
expec[3, i] <- ((1 - gi)*est.param[3, i]*est.param[1, i])*sum(data[i, ])
expec[4, i] <- (gi*gi*est.param[1, i] + gi*est.param[2, i] + est.param[3, i])*sum(data[i, ])
test <- suppressWarnings(chisq.test(expec[, i], p=data[i,]/sum(data[i, ])))
fit[1:2, i] <- unlist(test[c(1, 3)])
}
fit
}
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