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{\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 |
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 ( |
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.
Value
A list of:
x |
A copy of the argument |
f |
A
matrix containing the IRF values: persons (values of ( |
Author(s)
Ivailo Partchev
See Also
Examples
plot(irf(Scored2pl, item=1))