item.params.convert: Convert item parameters from one parametrization to another

In jeppebundsgaard/RDigram: Analysis of Items from Tests and Surveys

Convert item parameters from one parametrization to another

Description

Convert item parameters from one parametrization to another

Usage

item.params.convert(
  from.model = NULL,
  item.params = c(),
  from = c("pcm", "pcm.cent", "andersen", "psd", "conquest"),
  to = c("pcm", "pcm.cent", "andersen", "psd", "conquest"),
  return.vector = F
)

Arguments

from.model	A model of class TAM or eRm.
item.params	A matrix of item parameters (items in rows, thresholds in columns) (not needed if from.model is given)
from, to	Type of item parameters. One of pcm, pcm.cent, andersen, psd, conquest (from not needed if from.model is given).
return.vector	Get result as a vector of category values instead of the default data.frame

Details

The Rasch model can be parameterized in multiple ways. This function translates parameters from one to the other. The following models are supported:

• Power series distribution parametrization (psd)
  \xi^x\gamma_x \over G(\xi,\gamma_1 ... \gamma_k), where \xi is the person parameter (ability), and \gamma_x are the item parameters. Related through \xi=exp(\theta) and \gamma_x=exp(\delta_x) to the Andersen parametrization

• Andersen parametrization (andersen)
  exp(x\theta+\delta_x) \over G(\theta,\delta_1 ... \delta_k), where \theta is the person parameter (ability), and \delta_x are the item (easiness) parameters

• Partial Credit Model (PCM)/Masters' parametrization (pcm)
  exp(x\theta-\sum\limits_{i=1}^x\tau_i) \over G(\theta,\tau_1 ... \tau_k), where \theta is the person parameter (ability), and \tau_x are the item step parameters

• Partial Credit Model (PCM)/Masters' parametrization with centralized item step parameters (pcm.cent)
  exp(x(\theta-\beta)-\sum\limits_{i=1}^x\beta_i) \over G(\theta,\beta_1 ... \beta_k), where \theta is the person parameter (ability), \beta={1 \over k}\sum\limits_{i=1}^k \tau_i is the average of the \tau parameters from the PCM parametrization, and \beta_x=\tau_x-{1 \over k}\sum\limits_{i=1}^k \tau_i are the centralized item step parameters

• Conquest parametrization (conquest)
  exp(x(\theta-\psi-\sum\limits_{i=1}^x \psi_x) \over G(\theta,\psi_1 ... \psi_k), where \sum\limits_{i=1}^x \psi_i \equiv 0. And where \theta is the person parameter (ability), \psi={1 \over k}\sum\limits_{i=1}^k \tau_i is the average of the \tau parameters from the PCM parametrization, and \psi_x=\tau_x-{1 \over k}\sum\limits_{i=1}^k \tau_i are the centralized item step parameters

TAM uses Conquest parametrization. eRm uses Andersen parametrization. RUMM 2030 uses Partial Credit parametrization with centralized item step parameters. DIGRAM uses Power Series Distribution parametrization.

Value

Returns item parameters in the parametrization specified in to.

Author(s)

Jeppe Bundsgaard & Svend Kreiner

References

Andersen, B. E. (1970). Asymptotic properties of conditional likelihood estimators. Journal of the Royal Statistical Society, Series B, 32,283-301.

Brown, N. J. S. (2004). Interpreting Ordered Partition Model Parameters from ConQuest. https://bearcenter.berkeley.edu/sites/default/files/report%20-%20opm_parameters.pdf

Hatzinger, R., & Rusch, T. (2009). IRT models with relaxed assumptions in eRm: A manual-like instruction. Psychology Science Quarterly, 51(1), 87–120.

Kreiner, S. (n.d.). Om beregning af item-parametre I TAM.

Kreiner, s. (n.d.). Parameterization of graphical loglinear Rasch models.

Bundsgaard, J. & Kreiner, S. (2019). Undersøgelse af De Nationale Tests måleegenskaber. 2nd Ed. Copenhagen: DPU, Aarhus University.

Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149–174.

Examples

item.params<-matrix(c(0,1,2,3,1,2,3,4),nrow=4)
item.params.convert(item.params=item.params,from="conquest",to="psd")

jeppebundsgaard/RDigram documentation built on Oct. 29, 2023, 7:15 p.m.