coef.prms {dexter}

extract enorm item parameters

Description

extract enorm item parameters

Usage

## S3 method for class 'prms'
coef(object, hpd = 0.95, what = c("items", "var", "posterior"), ...)

Arguments

object

an enorm parameters object, generated by the function fit_enorm

hpd

width of Bayesian highest posterior density interval around mean_beta, value must be between 0 and 1, default is 0.95

what

which coefficients to return. Defaults to items (the item parameters). Can also be var for the variance-covariance matrix (CML only) or posterior for all draws of the item parameters (Bayes only)

...

further arguments to coef are ignored

Details

The parametrisation of IRT models is far from uniform and depends on the author. Dexter uses the following parametrisation for the extended Nominal Response Model (NRM):

$P(X=a_j|\beta,\theta) = \frac{\exp\left(a_j\theta-\sum_{g=1}^{j}\beta_g(a_g-a_{g-1})\right)}{1+\sum_h \exp\left(a_h\theta-\sum_{g=1}^{h}\beta_g(a_g-a_{g-1})\right)}$

where $a_j$ is a shorthand for the integer score belonging to the j-th category of an item.

For dichotomous items with $a_1=1$ (i.e. the only possible scores are 0 and 1) this formula simplifies to the standard Rasch model: $P(x=1|\beta,\theta)=\frac{\exp(\theta-\beta)}{1+\exp(\theta-\beta)}$. For polytomous items, when all scores are equal to the categories (i.e. $a_j=j$ for all $j$) the NRM is equal to the Partial Credit Model, although with a different parametrisation than is commonly used. For dichotomous items and for all polytomous items where $a_j-a_{j-1}$ is constant, the formulation is equal to the OPLM.

Value

Depends on the calibration method and the value of 'what'. For what="items":

CML calibration

a data.frame with columns: item_id, item_score, beta, SE_beta

Bayesian calibration

a data.frame with columns: item_id, item_score, mean_beta, SD_beta, <hpd_b_left>, <hpd_b_right>

If what="var" or what="posterior" then a matrix is returned with the variance-covariance matrix or the posterior draws respectively.