irf: Item response function

In irtoys: A Collection of Functions Related to Item Response Theory (IRT)

Item response function

Description

Returns the item response function of the 3PL (1PL, 2PL) model, the i.e. the probabilities defined by

P(U_{ij}=1|θ_i,a_j,b_j,c_j)=c_j+(1-c_j)\frac{\displaystyle\exp(a_j(θ_i-b_j))}{1+\displaystyle\exp(a_j(θ_i-b_j))}

where U_{ij} is a binary response given by person i to item j, θ_i is the value of the latent variable ("ability") for person i, a_j is the discrimination parameter for item j, b_j is the difficulty parameter for item j, c_j is the asymptote for item j. Some authors call the IRF "the item characteristic curve".

Usage

irf(ip, items = NULL, x = NULL)

Arguments

ip	Item parameters: the output of est, or a 3-column matrix corresponding to its first element, est.
items	The item(s) for which irf is computed. If NULL (the default), irf for all items will be returned
x	The values of the latent variable (θ in the equation above), at which the IRF will be evaluated. If not given, 99 values spaced evenly between -4 and +4 will be used, handy for plotting.

Details

In the 2PL model (model="2PL"), all asymptotes c_j are 0. In the 1PL model (model="1PL"), all asymptotes c_j are 0 and the discriminations a_j are equal for all items (and sometimes to 1).

A common use of this function would be to obtain a plot of the IRF.

Value

A list of:

x	A copy of the argument x
f	A matrix containing the IRF values: persons (values of (x) as rows and items as columns

Author(s)

Ivailo Partchev

See Also

plot.irf

Examples

plot(irf(Scored2pl, item=1))

irtoys documentation built on May 12, 2022, 5:06 p.m.