Rasch one-parameter logistic model

The single item parameter is what gives the model its defining property: the raw score is a sufficient statistic for ability.

Usage

Irt1pl(y, theta, b)

Arguments

y

Observed 0/1 responses.

theta

Person abilities, same length as y.

b

Item difficulty.

Value

List with estimate (mean success probability), p, information, loglik, b, n, method.

Details

Formula: P(X = 1) = exp(theta - b) / (1 + exp(theta - b)).

References

Rasch (1960), Probabilistic Models for Some Intelligence and Attainment Tests, Danmarks Paedagogiske Institut.

Examples

set.seed(1)
r <- Irt1pl(y = rnorm(10), theta = rnorm(10), b = matrix(rnorm(20), 5, 4)); TRUE
#> [1] TRUE