calr {lazy.irt}  R Documentation 
Calibration of Independently Estimated Sets of Item Parameters by Minimizing the LS Criterion Defined in terms of Probability Values
calr( indata, baseform = 0, nsubj = 0, npoints = 21, thmin = 3, thmax = 3, maxiter = 100, eps = 1e05, print = 1, debug = 0 )
indata 
data frame containing at least following: 
baseform 
form number or 0 
nsubj 
a vector consisting of the # of subjects in each form or 1.

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 
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.
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.
rmse LS criterion minimized.
Sayaka Arai, Tomohiro Ohtani, \& Shinichi Mayekawa (2013)
Simultaneous Equating of Separately Calibrated Polytomous IRT Test Items.
IMPS 2013, CITO, Arnhem, The Netherland. 2326 July 2013
Shinichi Mayekawa (2012)
Simultaneous equating of separately calibrated item parameters
under the common item design.
COMPSTAT 2012, Amathus Beach Hotel, Limassol, Cyprus. 2731 August 2012
Sayaka Arai & Shinichi 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. 116
Shinich Mayekawa (1991) Chapter 4. Parameter Estimation. In Shiba Ed. Item Response Theory. pp87129. (in Japanese)
# Binary Items res=calr( indata=paramCal1, baseform=1, print=2 ) # Mixture of Item Types res=calr( indata=paramCal2, baseform=1, print=2 )