Item response function
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".
irf(ip, items = NULL, x = NULL)
ip |
Item parameters: the output of |
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. |
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:
x |
A copy of the argument |
f |
A
matrix containing the IRF values: persons (values of ( |
Ivailo Partchev
plot(irf(Scored2pl, item=1))
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