irf function

Item response function

Returns the item response function of the 3PL (1PL, 2PL) model, the i.e. the probabilities defined by [REMOVE_ME]$P(U_{ij}=1|\theta_i,a_j,b_j,c_j)=c_j+(1-c_j)\frac{\displaystyle\exp(a_j(\theta_i-b_j))}{1+\displaystyle\exp(a_j(\theta_i-b_j))} [REMOVE_ME_2]$

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 $j$. Some authors call the IRF "the item characteristic curve".

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 ($\theta$ 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.

Returns

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

Description

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

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 $j$. Some authors call the IRF "the item characteristic curve".

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.

Examples

plot(irf(Scored2pl, item=1))

See Also

plot.irf

Author(s)

Ivailo Partchev