| coef.prms {dexter} | R Documentation |
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 |
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 |
... |
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.