rpf.nrm {rpf} | R Documentation |
Create a nominal response model
Description
This function instantiates a nominal response model.
Usage
rpf.nrm(outcomes = 3, factors = 1, T.a = "trend", T.c = "trend")
Arguments
outcomes |
The number of choices available |
factors |
the number of factors |
T.a |
the T matrix for slope parameters |
T.c |
the T matrix for intercept parameters |
Details
The transformation matrices T.a and T.c are chosen by the analyst and not estimated. The T matrices must be invertible square matrices of size outcomes-1. As a shortcut, either T matrix can be specified as "trend" for a Fourier basis or as "id" for an identity basis. The response probability function is
where and
are the result of multiplying two vectors
of free parameters
and
by fixed matrices
and
, respectively;
and
are fixed to 0 for identification;
and
is a normalizing factor to ensure that
.
Value
an item model
References
Thissen, D., Cai, L., & Bock, R. D. (2010). The Nominal Categories Item Response Model. In M. L. Nering & R. Ostini (Eds.), Handbook of Polytomous Item Response Theory Models (pp. 43–75). Routledge.
See Also
Other response model:
rpf.drm()
,
rpf.gpcmp()
,
rpf.grmp()
,
rpf.grm()
,
rpf.lmp()
,
rpf.mcm()
Examples
spec <- rpf.nrm()
rpf.prob(spec, rpf.rparam(spec), 0)
# typical parameterization for the Generalized Partial Credit Model
gpcm <- function(outcomes) rpf.nrm(outcomes, T.c=lower.tri(diag(outcomes-1),TRUE) * -1)
spec <- gpcm(4)
rpf.prob(spec, rpf.rparam(spec), 0)