irtoys (version 0.2.2)

irf: Item response function

Description

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

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.

See Also

plot.irf

Examples

# NOT RUN {
plot(irf(Scored2pl, item=1))

# }