cala {lazy.irt}

R Documentation

Calibration of Independently Estimated Sets of Item Parameters by Minimizing the LS Criterion Defined in terms of Parameter Values

Description

Calibration of Independently Estimated Sets of Item Parameters by Minimizing the LS Criterion Defined in terms of Parameter Values

Usage

cala(
  indata,
  baseform = 0,
  nsubj = 1,
  maxiter = 100,
  eps = 1e-05,
  init = 1,
  print = 1,
  debug = 0
)

Arguments

indata	data frame containing at least following: giid gfid type ncat a p1 p2 .... indata can be created from a parameter data frame by renaming name as giid and adding gfid. It is assumed that indata is sorted by gfid.
baseform	form number or 0
nsubj	a vector consisting of the # of subjects in each form or 1. To be used when calculating the mean of theta of the combined group.
maxiter	max of iteration for PCA
eps	eos for PCA
init	not used
print	> 0 to print results
debug	= 1 to print intermediate result

Details

This program finds u,v and b such taht
bhata[j,g] = u[g] + b[j] v[g] + error
j=1,2,..., # of items and g=1,2,..., # of forms,
using PCA with missing data, where bhat is the collection of estimated b-parameters.

a[g] will be estimated as the average of ahat[j,g]/r[g] ,
c[g] will be estimated as the average of chat[j,g] ,
where r[g]=1/v[g]

Value

A list of:
param Data frame containing the equated item parameters
uv Transformations from common scale to each scale
qr Transformations from each scale to common scale
nfini Vector of # of forms including each item
niinf Vector of # of items included in each form
fini List of the Forms including each item.
iinf List of the Items included in each form.
iftable Matrix of item x form indicating the inclusion pattern.
toP Vector of stating locations in ParamHat
fromP Vector of ending locations in ParamHat
iterPCA # of iterations needed for convergence.
nbPCA 3 of b-parameters processed by PCA.
nisolo # of items that are included in only one form.
ParamHat Item Paramter matrix analyzed by PCA
rmse LS criterion minimized.

References

Sayaka Arai & Shin-ichi Mayekawa (2011) A comparison of equating methods and linking designs for developing an item pool under item response theory. Behaviormetrika, Vol. 38 No. 1, pp. 1-16

Shin-ich Mayekawa (1991) Chapter 4. Parameter Estimation. In Shiba Ed. Item Response Theory. pp87-129. (in Japanese)

Examples

# Binary Items
res=cala( indata=paramCal1, baseform=1, print=2  )

# Mixture of Item Types
res=cala( indata=paramCal2, baseform=1, print=2  )

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