calr {lazy.irt}

R Documentation

Calibration of Independently Estimated Sets of Item Parameters

Description

This function calibrates (equates) independently estimated sets of item parameters (with common linking items) by minimizing the LS criterion defined in terms of item response functions (irf)
Japanese help file: (calr_JPH)

Usage

calr(
  indata,
  baseform = 0,
  nsubj = 0,
  npoints = 21,
  thmin = -3,
  thmax = 3,
  maxiter = 100,
  eps = 1e-05,
  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.
npoints	# of discrete theta points to be used.
thmin	Minimum value of theta points.
thmax	Maximum value of theta points.
maxiter	max of iterations
eps	Criterion of convergence for the relative improvement of rss value.
print	> 0 to print results
debug	= 1 to print intermediate result

Details

This program finds q, r and item param such taht
P(theta_g | est_param_g) = P( q[g] + r[g] theta | param ) + error
j=1,2,..., # of items and g=1,2,..., # of forms,
where param is the item parameters on the common scale.

First, those items which are included in at least two forms will be picked up and analyzed.
Then, the item parameters for the solo items will be converted using estimated q and r.

Subscript j is for item, g for form, q is for theta point.

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.
iter # of iteration required for convergence
rss # LS criterion minimized
rssimpr Final relative improvement of rss.
eps Convergence criterion for rssimpr
rmse rmse calculated from rss
nisolo # of items that are included in only one form.
gradI Final gradients of common item parameters.
gradF Final gredients or transformation constants.

References

Sayaka Arai, Tomohiro Ohtani, & Shin-ichi Mayekawa (2013) Simultaneous Equating of Separately Calibrated Polytomous IRT Test Items. IMPS 2013, CITO, Arnhem, The Netherland. 23-26 July 2013

Shin-ichi Mayekawa (2012) Simultaneous equating of separately calibrated item parameters under the common item design. COMPSTAT 2012, Amathus Beach Hotel, Limassol, Cyprus. 27-31 August 2012

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=calr( indata=paramCal1, baseform=1, print=2  )

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

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