library(ggplot2)
library(msm)
# loading data
data(GMAT, package = "difNLR")
data <- GMAT[, 1:20]
zscore <- scale(rowSums(data)) # standardized total score
# logistic model for item 1
fit <- glm(data[, 1] ~ zscore, family = binomial)
# coefficients
(coef <- c(a = coef(fit)[2], b = -coef(fit)[1] / coef(fit)[2])) # estimates
# SE using delta method
(se <- deltamethod(
list(~x2, ~ -x1 / x2),
mean = coef(fit),
cov = vcov(fit),
ses = TRUE
))
cbind(coef, se) # estimates and SE
# function for plot
fun <- function(x, a, b) {
exp(a * (x - b)) / (1 + exp(a * (x - b)))
}
# empirical probabilities calculation
df <- data.frame(
x = sort(unique(zscore)),
y = tapply(data[, 1], zscore, mean),
size = as.numeric(table(zscore))
)
# plot of estimated curve
ggplot(df, aes(x = x, y = y)) +
geom_point(aes(size = size),
color = "darkblue",
fill = "darkblue",
shape = 21, alpha = 0.5
) +
stat_function(
fun = fun, geom = "line",
args = list(
a = coef[1],
b = coef[2]
),
size = 1,
color = "darkblue"
) +
xlab("Standardized total score") +
ylab("Probability of correct answer") +
ylim(0, 1) +
ggtitle("Item 1") +
theme_app()
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