irf: Item response function
In lebebr01/irtoys-2: Simple interface to the estimation and plotting of IRT models

Description Usage Arguments Details Value Author(s) See Also Examples

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".

1	irf(ip, x = NULL)

`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 (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.

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.

A list of: