library(ggplot2)
# loading data
data(GMAT, package = "difNLR")
data <- GMAT[, 1:20]
score <- rowSums(data) # total score
# logistic model for item 1
fit <- glm(data[, 1] ~ score, family = binomial)
# coefficients
coef(fit) # estimates
sqrt(diag(vcov(fit))) # SE
summary(fit)$coefficients[, 1:2] # estimates and SE
# function for plot
fun <- function(x, b0, b1) {
exp(b0 + b1 * x) / (1 + exp(b0 + b1 * x))
}
# empirical probabilities calculation
df <- data.frame(
x = sort(unique(score)),
y = tapply(data[, 1], score, mean),
size = as.numeric(table(score))
)
# 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(
b0 = coef(fit)[1],
b1 = coef(fit)[2]
),
size = 1,
color = "darkblue"
) +
xlab("Total score") +
ylab("Probability of correct answer") +
ylim(0, 1) +
ggtitle("Item 1") +
theme_app()
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