rpf (version 1.0.14)

rpf.grm: Create a graded response model

Description

For outcomes k in 0 to K, slope vector a, intercept vector c, and latent ability vector theta, the response probability function is $$\mathrm{P}(\mathrm{pick}=0|a,c,\theta )=1-\mathrm{P}(\mathrm{pick}=1|a,c_1,\theta )$$ $$\mathrm{P}(\mathrm{pick}=k|a,c,\theta )=\frac{1}{1+\exp (-(a\theta +c_k))}-\frac{1}{1+\exp (-(a\theta +c_{k+1}))}$$ $$\mathrm{P}(\mathrm{pick}=K|a,c,\theta )=\frac{1}{1+\exp (-(a\theta +c_K))}$$

Usage

rpf.grm(outcomes = 2, factors = 1, multidimensional = TRUE)

Value

an item model

Arguments

outcomes

The number of choices available

factors

the number of factors

multidimensional

whether to use a multidimensional model. Defaults to TRUE.

Details

The graded response model was designed for a item with a series of dependent parts where a higher score implies that easier parts of the item were surmounted. If there is any chance your polytomous item has independent parts then consider rpf.nrm. If your categories cannot cross then the graded response model provides a little more information than the nominal model. Stronger a priori assumptions offer provide more power at the cost of flexibility.

See Also

Other response model: rpf.drm(), rpf.gpcmp(), rpf.grmp(), rpf.lmp(), rpf.mcm(), rpf.nrm()

Examples

spec <- rpf.grm()
rpf.prob(spec, rpf.rparam(spec), 0)