ability: Person Ability Estimation

In nando11235813/raschreg: Item Response Theory models including explanatory variables of the ability parameter

Description

Prediction of person abilities from a Rasch (regression) model.

Usage

ability(mod, type = 'wle', R = 100)

Arguments

mod	Fitted Rasch (regression) model.
type	A character string. Possible values are eap (Expected a posteriori), bme (Bayesian modal estimation), mle (Maximum likellihood estimation) and wle (Weighted likelihood estimation). Default to 'wle'.
R	A numeric value indicating the number of simulations used to approximate theta when type eap is selected. Default is 100.

Details

Abilities are estimated as follows.

• eap. θ es estimated by approximating:

  \frac{θ P(Y=y|θ)f(θ)dθ}{\int P(Y=y|θ)f(θ)dθ}

  R values are simulated from f(θ) and the quotient is approximated by:

  \frac{∑_j θ_j P(Y=y|θ_j)}{∑_j P(Y=y|θ_j)}

• bme. θ es estimated as the solution of:

  ∑_j (x_j - P_j(θ))\frac{P^{'}(θ)}{P(θ)(1-P(θ))} - θ = 0

• mle θ es estimated as the solution of:

  ∑_j (x_j - P_j(θ))\frac{P^{'}(θ)}{P(θ)(1-P(θ))} = 0

• wleθ es estimated as the solution of:

  ∑_j (x_j - P_j(θ))\frac{P^{'}(θ)}{P(θ)(1-P(θ))} + \frac{J(θ)}{2I(θ)} = 0

Value

A numeric containing a single column with the estimated abilities.

Author(s)

Fernando Massa, [e-mail]

References

\insertRef

warm1989raschreg \insertRefmagis2016raschreg

Examples

n <- 100
x <- sim_rasch(n, ability = TRUE)
J <- ncol(x) - 1
X <- x[, 1:J]
ab <- x[,J+1]
mod <- rasch(X)

# ability estimation
ab_wle <- ability(mod, type = 'wle')
ab_mle <- ability(mod, type = 'mle')
ab_bme <- ability(mod, type = 'bme')
ab_eap <- ability(mod, type = 'eap')

# comparison
cor(cbind(ab, ab_wle, ab_mle, ab_bme, ab_eap))

nando11235813/raschreg documentation built on Oct. 2, 2021, 3:11 p.m.