irf {irtoys}R Documentation

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|theta_i,a_j,b_j,c_j)=c_j+(1-c_j)frac{displaystyleexp(Da_j(theta_i-b_j))}{1+displaystyleexp(Da_j(theta_i-b_j))}

where U_{ij} is a binary response given by person i to item j, theta_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, and D is a constant usually set to either 1.7 or 1. Some authors call the IRF "the item characteristic curve".

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.

Usage

irf(ip, x = NULL)

Arguments

ip Item parameters: a matrix with one row per item, and three columns: [,1] item discrimination a, [,2] item difficulty b, and [,3] asymptote c.
x The values of the latent variable (theta 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.

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

data(Scored)
p.2pl  <- est(Scored, model="2PL", engine="ltm")
plot(irf(p.2pl[1,]))

[Package irtoys version 0.1.1 Index]