| uIRT {lazy.irtx} | R Documentation |
Marginal likelihood will be maximized by the EM algorithm using ordinal_reg funcion and smn function in the M-step.
uIRT(Uc, U = NULL, groupvar = NULL, idvar = NULL, ncat = NULL, type = NULL, itemname = NULL, DinP = 1, param = NULL, msn = NULL, fixeditems = NULL, baseform = 1, theta = NULL, thd = NULL, estmu = 0, estsigma = 0, npoints = 21, thmin = -4, thmax = 4, maxiter = 200, eps = 1e-07, epsd = 1e-06, maxiter2 = 20, eps2 = 1e-04, nstrict = 9, maxiter22 = 5, minp1 = 0.1, maxabsparam = 20, SQUAREM = 3, nSQUAREM = 1, minalpha = -999, maxalpha = -1, always = 1, reset1 = 0, reset2 = 1, print = 2, plot = 0, smallP = 0, debug = 0)
Uc |
n x nitems+1 or +2 compressed item resopnse data frame in BILOG-MG's expanded format. (idvar and groupvar) |
U |
n x sum(ncat)+1 or +2 uncompressed irem response data frame |
groupvar |
name of the grouping varible contained as a column of Uc or NULL. |
idvar |
name of the id varible contained as a column of Uc or NULL |
ncat |
nitems x 1 # of categories for each item or NULL. |
type |
nitems x 1 vector of item types consisting of:
"Bn" | "G" | "PN" | "P" |
itemname |
nitems x 1 vector of item names or NULL. |
DinP |
= 0 to exclude 1.7 from logistic function. |
param |
nitems x max(ncat) initial value data frame for
item param |
msn |
nG x 3 initial value matrix of (mean, std, n) for each group |
fixeditems |
list of items whose item parameters are to be fixed |
baseform |
base form number whose theta distribution is
fixed at the values given in msn[baseform,] |
theta |
npoints x 1 discrete theta points |
thd |
NOT used. |
estmu |
= 1 to estimate multigroup theta means |
estsigma |
= 1 to estimate mul tigroup theta std |
npoints |
# of discrete theta points between (thmin, thmax) |
thmin |
Minimum value of theta points to be generated. |
thmax |
Maximum value of theta points to be generated |
maxiter |
max # of iterations |
eps |
eps for the relative improvement of lmlh |
epsd |
eps for the max. abs. diff. of msn |
maxiter2 |
max # of iterations for ordinal_reg and smn when llll <= nstrict. |
eps2 |
eps for the relative improvement of llh in ordinal_reg and smn. |
nstrict |
maxiter2 will be reduced to maxiter22 after nstrict iterations. |
maxiter22 |
max # of iterations for ordinal_reg and smn when llll > nstrict. |
minp1 |
Minimum value of p1 parameter for type != "N" items. |
maxabsparam |
Maximum absolute value of parameters. |
SQUAREM |
= 3 : See the help of iSQUAREM in lazy.accel package. |
nSQUAREM |
when to star iSQUAREM |
minalpha |
= -999 : See the help of iSQUAREM in lazy.accel package. |
maxalpha |
= -1 : See the help of iSQUAREM in lazy.accel package. |
always |
= 0 : See the help of iSQUAREM in lazy.accel package. |
reset1 |
= 1 : See the help of iSQUAREM in lazy.accel package. |
reset2 |
= 2 : See the help of iSQUAREM in lazy.accel package. |
print |
= 1 to print the result |
plot |
= 1 to plot the estimated theta distributions |
smallP |
= Minimum value of P |
debug |
= 1 to print intermediate result |
Uc is the compressed data if it is n x nitems.
U is the uncompressed data if it is n x sum(ncat).
When U, instead of Uc, is given:
Item names come from itemname or paste("Q",1:nitems,sep="").
ncat must be given.
When Uc is given:
Item name comes from colnames(Uc) or itemname.
ncat can be calculated from Uc.
Note on the iSQUAREM:
Try always=1 with maxalpha=-1 or less first.
Changing to reset1=1 and reset2=2 or increasing nSQUAREM may help.
If it seems not working, use always=0 with maxalpha=1 or less.
Changing to reset1=1 and reset2=2 may help.
If all of the above fail, be patient and use SQUAREM=0.
A list of:
param Estimated Item Parameters in a data frame
msn Estimated means, standard deviations, and n for each group.
theta Discrete theta points used.
thd Theta distribution
converged = 1 if converged, = 0 otherwise.
lmlh Log Marginal LIkelihood maximized
iter_hist A list of iteration history
H Posterior distribution of theta given U.
NN Estimated # of persons at each of theta points
EAP Estimated ability
pstdtd Estimated posterior std for theta
id Id variable
Varadhan, R. and Roland, C.(2007) Simple and Globally Convergent Methods for Accelerating the Convergence of Any EM Algorithm. Scandinavian Journal of Statistics, Vol. 35: 335-353.
#
#### In the following examples, maxiter is set to 20 which is
#### not large enough to obtain convergence.
####
#
#
# Binary Items: simgle group analysis from compressed data: Uc
# generate 3PLM data
set.seed(1701)
Uc <- gendataIRT( 1, paramB2, npoints=500, thdist="rnorm", compress=1 )$U
Uc <- as.data.frame(Uc)
# 2PLM analysis
itemtype <- rep("B2",nrow(paramB2))
res1 <- uIRT( Uc, type=itemtype, maxiter=200 )
# 3PLM analysis
itemtype <- rep("B3",nrow(paramB2))
res1 <- uIRT( Uc, type=itemtype, maxiter=200 )
# Mixed Type Items: simgle group analysis from compressed data: Uc
# generate data
set.seed(1701)
Uc <- gendataIRT( 1, paramS1, npoints=500, thdist="rnorm"
, compress=1 )$U
Uc <- as.data.frame(Uc)
itemtype <- paramS1$type
res1 <- uIRT( Uc, type=itemtype, maxiter=20 )
# convert compressed data to uncompressed data: U
temp=dummy_expand( Uc )
U=data.frame( temp$U )
ncat=temp$ncat
rm(temp)
res2 <- uIRT( U=U, ncat=ncat, type=itemtype, maxiter=20 )
# should be identical
Print(res1$param, res2$param)
# fixed parameter values
paramF <- paramS1[2:3,]; fixeditems=c("Q2","Q3")
res1 <- uIRT( Uc, type=itemtype, maxiter=20, param=paramF
, fixeditems=fixeditems )
# multi-group analysis with different theta distributions
set.seed(1701)
indata1 <- gendataIRT( 1, paramS1, npoints=500, thdist="rnorm"
, compress=1 )$U
indata1 <- as.data.frame(indata1,row.names=NULL)
indata1 <- data.frame(group="G1",indata1, stringsAsFactors=0
,row.names=NULL)
indata2 <- gendataIRT( 1, paramS1, npoints=500, thdist="rnorm", compress=1
, thmean=1, thstd=1 )$U
indata2 <- as.data.frame(indata2,row.names=NULL)
indata2 <- data.frame(group="G2",indata2, stringsAsFactors=0
,row.names=NULL)
indata12 <- rbind(indata1,indata2)
itemtype <- paramS1$type
# This will not converge: increase maxiter.
res1 <- uIRT( indata12, groupvar="group", type=itemtype, maxiter=10
, baseform=1, estmu=1, estsigma=1, minalpha=-2, SQUAREM=3, plot=1 )
# example of U matrix input with unequal # of trials per item.
set.seed(1701)
npoints=2000
param=paramS2
nitems=nrow(param)
ncat=param$ncat
Nmat=matrix(sample(1:9,npoints*nitems,replace=1),npoints,nitems)
pmiss=0.2
for( j in 1:nitems ){
Nmat[sample(1:npoints,npoints*pmiss),j]=0
}
temp <- gendataIRT( 1, param, Nmat=Nmat, npoints=npoints
, thdist="rnorm", compress=0 )
ncat=temp$ncat
UN <- as.data.frame(temp$U)
res3 <- uIRT( U=UN, ncat=ncat, maxiter=20 )