R: Item Parameter Estimation of Unidimensional IRT

uIRT {lazy.irt}

R Documentation

Item Parameter Estimation of Unidimensional IRT

Description

Marginal likelihood will be maximized by the EM algorithm using ordinal_reg function and smn function in the M-step.
Japanese help file: (uIRT_JPH)

Usage

uIRT(
  Uc,
  U = NULL,
  items = 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
)

Arguments

`Uc`	n x nitems+1 or +2 compressed item response data frame in BILOG-MG's expanded format. (idvar and groupvar)
`U`	n x sum(ncat)+1 or +2 uncompressed item response data frame
`items`	a vector consisting of the column names of U or Uc to be used as the item responses. Or NULL to use all columns except for groupvar and idvar. (Not Yet Available)
`groupvar`	name of the grouping variable contained as a column of Uc or NULL.
`idvar`	name of the id variable 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" If NULL, P will be used.
`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 Only the subset of the items can be given. param$name and the colname(Uc) will be used to match the items.
`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 to the values given in the param data frame. Item numbers or item names
`baseform`	base form number whose theta distribution is fixed at the values given in msn[baseform,] If there are fixed items, the values of the item paramters given in the param data frame must be on the baseform scale.
`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 Seems this is important.
`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

Details

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="") is used.
ncat must be given.

When Uc is given:
Item names come 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.

Value

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
aic and bic: The information criteria
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
poststd: Estimated posterior std for theta
id: Id variable

References

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.

Examples

#
#### In the following examples, maxiter is set to 20 which is
#### not large enough to obtain convergence.
####
#
#
# Binary Items: single 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: single 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 )

[Package lazy.irt version 0.1.6 ]