library(msm)
library(ShinyItemAnalysis)
library(VGAM)
# loading data
data(Science, package = "mirt")
# standardized total score calculation
zscore <- scale(rowSums(Science))
Science[, 1] <- factor(
Science[, 1],
levels = sort(unique(Science[, 1])), ordered = TRUE
)
# cumulative logit model for item 1
fit <- vglm(Science[, 1] ~ zscore,
family = cumulative(reverse = TRUE, parallel = TRUE)
)
# coefficients under intercept/slope parametrization
coef(fit) # estimates
sqrt(diag(vcov(fit))) # SE
# IRT parametrization
# delta method
num_par <- length(coef(fit))
formula <- append(
paste0("~ x", num_par),
as.list(paste0("~ -x", 1:(num_par - 1), "/", "x", num_par))
)
formula <- lapply(formula, as.formula)
se <- deltamethod(
formula,
mean = coef(fit),
cov = vcov(fit),
ses = TRUE
)
# estimates and SE in IRT parametrization
cbind(c(coef(fit)[num_par], -coef(fit)[-num_par] / coef(fit)[num_par]), se)
# plot of estimated cumulative probabilities
plotCumulative(fit, type = "cumulative", matching.name = "Standardized total score")
# plot of estimated category probabilities
plotCumulative(fit, type = "category", matching.name = "Standardized total score")
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