irt.link | R Documentation |
The function implements parameter linking methods to transform IRT scales. Mean-mean, mean-sigma, Haebara, and Stocking and Lord methods are available (see details).
irt.link(parm, common, model, icc, D)
parm |
A 6 column matrix containing item parameter estimates from an IRT model. The
first three columns contains the parameters for the form |
common |
A vector indicating the position where common items are located |
model |
A character string indicating the underlying IRT model: "1PL", "2PL", "3PL". |
icc |
A character string indicating the type of |
D |
A number indicating the value of the constant |
The function implments various methods of IRT parameter linking (a.k.a, scale transformation
methods). It calculates the linking constants A
and B
to tranform parameter estimates.
When assuming a 1PL model, the matrix parm
should contain a column of ones and a column of zeroes
in the places where discrimination and guessing parameters are located, respectively.
The characteristic curve methods (Haebara and Stocking and Lord) rely on the item characteristic curve p_{ij}assumed for the probability of a correct answer
p_{ij}=P(Y_{ij}=1|theta_i)=cj+(1-cj){exp[Da_j(theta_i-beta_j)]}/{1+exp[Da_j(theta_i-beta_j)]}
Besides the traditional logistic model, the irt.link()
function allows the use of an asymetric
cloglog ICC. See the help for KB36.1PL
data set, where some details on how to fit a 1PL model with
cloglog link in lmer
are given.
For more details on characteristic curve methods see Kolen and Brennan (2004).
A list with the constants A
and B
calculated using the four different methods
Currently, the cloglog ICC is only implmented for the 1PL model. A 1PL model with asymetric cloglog
link can be fitted in R using the lmer()
function in package lme4
Jorge Gonzalez jorge.gonzalez@mat.uc.cl
Gonzalez, J. (2014). SNSequate: Standard and Nonstandard Statistical Models and Methods for Test Equating. Journal of Statistical Software, 59(7), 1-30.
Kolen, M., and Brennan, R. (2004). Test Equating, Scaling and Linking. New York, NY: Springer-Verlag.
Estay, G. (2012). Characteristic Curves Scale Transformation Methods Using Asymmetric ICCs for IRT Equating. Unpublished MSc. Thesis. Pontificia Universidad Catolica de Chile
mea.eq
, lin.eq
, ker.eq
#### Example. KB, Table 6.6 data(KB36) parm.x = KB36$KBformX_par parm.y = KB36$KBformY_par comitems = seq(3,36,3) parm = as.data.frame(cbind(parm.y, parm.x)) # Table 6.6 KB irt.link(parm,comitems,model="3PL",icc="logistic",D=1.7) # Same data but assuming a 1PL model. The parameter estimates are load from # the KB36.1PL data set. See the help for KB36.1PL data for details on how these # estimates were obtained using \code{lmer()} (see also Table 6.13 in KB) data(KB36.1PL) #preparing the input data matrices for irt.link() function b.log.y<-KB36.1PL$b.logistic[,2] b.log.x<-KB36.1PL$b.logistic[,1] b.clog.y<-KB36.1PL$b.cloglog[,2] b.clog.x<-KB36.1PL$b.cloglog[,1] parm2 = as.data.frame(cbind(1,b.log.y,0, 1,b.log.x, 0)) parm3 = as.data.frame(cbind(1,b.clog.y,0, 1,b.clog.x,0)) #vector indicating common items comitems = seq(3,36,3) #Calculating the B constant under the logistic-link model irt.link(parm2,comitems,model="1PL",icc="logistic",D=1.7) #Calculating the B constant under the cloglog-link model irt.link(parm3,comitems,model="1PL",icc="cloglog",D=1.7)
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