tamaan: Wrapper Function for TAM Language

Description

This function is a convenience wrapper function for several item response models in TAM. Using the tamaanify framework, multidimensional item response models, latent class models, located and ordered latent class models and mixture item response models can be estimated.

Usage

tamaan(tammodel, resp, tam.method=NULL, control=list(), doparse=TRUE, ...)
# S3 method for tamaan
summary(object,file=NULL,…)
# S3 method for tamaan
print(x,…)

Arguments

tammodel

String for specification in TAM, see also tamaanify.

resp

Dataset with item responses

tam.method

One of the TAM methods tam.mml, tam.mml.2pl or tam.mml.3pl.

control

List with control arguments. See tam.mml.

doparse

Optional logical indicating whether lavmodel should be parsed for DO statements, see doparse.

…

Further arguments to be passed to tam.mml, tam.mml.2pl or tam.mml.3pl.

object

Object of class tamaan

file

A file name in which the summary output will be written

Object of class tamaan

Value

Values generated by tam.mml, tam.mml.2pl or tam.mml.3pl. In addition, the list also contains the (optional) entries

tamaanify

Output produced by tamaanify

lcaprobs

Matrix with probabilities for latent class models

locs

Matrix with cluster locations (for TYPE="LOCLCA")

probs_MIXTURE

Class probabilities (for TYPE="MIXTURE")

moments_MIXTURE

Distribution parameters (for TYPE="MIXTURE")

itempartable_MIXTURE

Item parameters (for TYPE="MIXTURE")

ind_classprobs

Individual posterior probabilities for latent classes (for TYPE="MIXTURE")

Examples

Run this code

# NOT RUN {
#############################################################################
# EXAMPLE 1: Examples dichotomous data data.read
#############################################################################

library(sirt)
data(data.read,package="sirt")
dat <- data.read

#*********************************************************************
#*** Model 1: Rasch model

tammodel <- "
LAVAAN MODEL:
  F1=~ A1__C4
  F1 ~~ F1
ITEM TYPE:
  ALL(Rasch);
    "
# estimate model
mod1 <- TAM::tamaan( tammodel, resp=dat)
summary(mod1)

# }
# NOT RUN {
#*********************************************************************
#*** Model 2: 2PL model with some selected items

tammodel <- "
LAVAAN MODEL:
  F1=~ A1__B1 + B3 + C1__C3
  F1 ~~ F1
    "
mod2 <- TAM::tamaan( tammodel, resp=dat)
summary(mod2)

#*********************************************************************
#*** Model 3: Multidimensional IRT model

tammodel <- "
LAVAAN MODEL:
  G=~ A1__C4
  F1=~ A1__B4
  F2=~ C1__C4
  F1 ~~ F2
  # specify fixed entries in covariance matrix
  F1 ~~ 1*F1
  F2 ~~ 1*F2
  G  ~~ 0*F1
  G  ~~ 0.3*F2
  G  ~~ 0.7*G
    "
mod3 <- TAM::tamaan( tammodel, resp=dat, control=list(maxiter=30))
summary(mod3)

#*********************************************************************
#*** Model 4: Some linear constraints for item slopes and intercepts

tammodel <- "
LAVAAN MODEL:
  F=~ lam1__lam10*A1__C2
  F=~ 0.78*C3
  F ~~ F
  A1 | a1*t1
  A2 | a2*t1
  A3 | a3*t1
  A4 | a4*t1
  B1 | b1*t1
  B2 | b2*t1
  B3 | b3*t1
  C1 | t1
MODEL CONSTRAINT:
  # defined parameters
  # only linear combinations are permitted
  b2==1.3*b1 + (-0.6)*b3
  a1==q1
  a2==q2 + t
  a3==q1 + 2*t
  a4==q2 + 3*t
  # linear constraints for loadings
  lam2==1.1*lam1
  lam3==0.9*lam1 + (-.1)*lam0
  lam8==lam0
  lam9==lam0
    "
mod4 <- TAM::tamaan( tammodel, resp=dat, control=list(maxiter=5) )
summary(mod4)

#*********************************************************************
#*** Model 5: Latent class analysis with three classes

tammodel <- "
ANALYSIS:
  TYPE=LCA;
  NCLASSES(3);   # 3 classes
  NSTARTS(5,20); # 5 random starts with 20 iterations
LAVAAN MODEL:
  F=~ A1__C4
    "
mod5 <- TAM::tamaan( tammodel, resp=dat, control=list(maxiter=100)  )
summary(mod5)

#*********************************************************************
#*** Model 6: Ordered latent class analysis with three classes

tammodel <- "
ANALYSIS:
  TYPE=OLCA;
  NCLASSES(3);    # 3 classes
  NSTARTS(20,40); # 20 random starts with 40 iterations
LAVAAN MODEL:
  F=~ A1__C4
    "
mod6 <- TAM::tamaan( tammodel, dat )
summary(mod6)

#*********************************************************************
#*** Model 7: Unidimensional located latent class model with three classes

tammodel <- "
ANALYSIS:
  TYPE=LOCLCA;
  NCLASSES(3)
  NSTARTS(10,40)
LAVAAN MODEL:
  F=~ A1__C4
  B2 | 0*t1
    "
mod7 <- TAM::tamaan( tammodel, resp=dat)
summary(mod7)

#*********************************************************************
#*** Model 8: Two-dimensional located latent class analysis with some
#             priors and equality constraints among thresholds

tammodel <- "
ANALYSIS:
  TYPE=LOCLCA;
  NCLASSES(4);
  NSTARTS(10,20);
LAVAAN MODEL:
  AB=~ A1__B4
  C=~ C1__C4
  A1 | a1diff*t1
  B2 | 0*t1
  C2 | 0*t1
  B1 | a1diff*t1
MODEL PRIOR:
  # prior distributions for cluster locations
  DO2(1,4,1,1,2,1)
    Cl%1_Dim%2 ~ N(0,2);
  DOEND
    "
# estimate model
mod8 <- TAM::tamaan( tammodel, resp=dat )
summary(mod8)

#*********************************************************************
#*** Model 9: Two-dimensional model with constraints on parameters

tammodel <- "
LAVAAN MODEL:
  FA=~ A1+b*A2+A3+d*A4
  FB=~ B1+b*B2+B3+d*B4
  FA ~~ 1*FA
  FA ~~ FB
  FB ~~ 1*FB
  A1 | c*t1
  B1 | c*t1
  A2 | .7*t1
    "
# estimate model
mod9 <- TAM::tamaan( tammodel, resp=dat, control=list(maxiter=30) )
summary(mod9)

#############################################################################
# EXAMPLE 2: Examples polytomous data | data.Students
#############################################################################

library(CDM)
data( data.Students, package="CDM")
dat <- data.Students[,3:13]
  ##   > colnames(dat)
  ##    [1] "act1" "act2" "act3" "act4" "act5" "sc1"  "sc2"  "sc3"  "sc4"  "mj1"  "mj2"

#*********************************************************************
#*** Model 1: Two-dimensional generalized partial credit model

tammodel <- "
LAVAAN MODEL:
  FA=~ act1__act5
  FS=~ sc1__sc4
  FA ~~ 1*FA
  FS ~~ 1*FS
  FA ~~ FS
    "
# estimate model
mod1 <- TAM::tamaan( tammodel, dat, control=list(maxiter=10)  )
summary(mod1)

#*********************************************************************
#*** Model 2: Two-dimensional model, some constraints

tammodel <- "
LAVAAN MODEL:
  FA=~ a1__a4*act1__act4 + 0.89*act5
  FS=~ 1*sc1 + sc2__sc4
  FA ~~ FA
  FS ~~ FS
  FA ~~ FS
  # some equality constraints
  act1 + act3 | a13_t1 * t1
  act1 + act3 | a13_t2 * t2
    "
# only create design matrices with tamaanify
mod2 <- TAM::tamaanify( tammodel, dat  )
mod2$lavpartable
# estimate model (only few iterations as a test)
mod2 <- TAM::tamaan( tammodel, dat, control=list(maxiter=10)  )
summary(mod2)

#*********************************************************************
#*** Model 3: Two-dimensional model, some more linear constraints

tammodel <- "
LAVAAN MODEL:
  FA=~ a1__a5*act1__act5
  FS=~ b1__b4*sc1__sc4
  FA ~~ 1*FA
  FA ~~ FS
  FS ~~ 1*FS
  act1 + act3 | a13_t1 * t1
  act1 + act3 | a13_t2 * t2
MODEL CONSTRAINT:
  a1==q0
  a2==q0
  a3==q0    + q1
  a4==q2
  a5==q2 + q1
    "
# estimate
mod3 <- TAM::tamaan( tammodel, dat, control=list(maxiter=300 )  )
summary(mod3)

#*********************************************************************
#*** Model 4: Latent class analysis with three latent classes

tammodel <- "
ANALYSIS:
  TYPE=LCA;
  NCLASSES(3);    # 3 classes
  NSTARTS(10,30); # 10 random starts with 30 iterations
LAVAAN MODEL:
  F=~ act1__act5
    "
# estimate model
mod4 <- TAM::tamaan( tammodel, resp=dat)
summary(mod4)

#*********************************************************************
#*** Model 5: Partial credit model with "PCM2" parametrization

# select data
dat1 <- dat[, paste0("act",1:5) ]
# specify tamaan model
tammodel <- "
  LAVAAN MODEL:
    F=~ act1__act5
    F ~~ F
    # use DO statement as shortages
    DO(1,5,1)
      act% | b%_1 * t1
      act% | b%_2 * t2
    DOEND
  MODEL CONSTRAINT:
    DO(1,5,1)
      b%_1==delta% + tau%_1
      b%_2==2*delta%
    DOEND
  ITEM TYPE:
    ALL(PCM)
  "
# estimate model
mod5 <- TAM::tamaan( tammodel, dat1 )
summary(mod5)
# compare with PCM2 parametrization in tam.mml
mod5b <- TAM::tam.mml( dat1, irtmodel="PCM2" )
summary(mod5b)

#*********************************************************************
#*** Model 6: Rating scale model

# select data
dat1 <- dat[, paste0("sc",1:4) ]
psych::describe(dat1)

# specify tamaan model
tammodel <- "
  LAVAAN MODEL:
    F=~ sc1__sc4
    F ~~ F
    # use DO statement as shortages
    DO(1,4,1)
      sc% | b%_1 * t1
      sc% | b%_2 * t2
      sc% | b%_3 * t3
    DOEND
  MODEL CONSTRAINT:
    DO(1,4,1)
      b%_1==delta% + step1
      b%_2==2*delta% + step1 + step2
      b%_3==3*delta%
    DOEND
  ITEM TYPE:
    ALL(PCM)
  "
# estimate model
mod6 <- TAM::tamaan( tammodel, dat1 )
summary(mod6)
# compare with RSM in tam.mml
mod6b <- TAM::tam.mml( dat1, irtmodel="RSM" )
summary(mod6b)

#*********************************************************************
#*** Model 7: Partial credit model with Fourier basis for
#             item intercepts (Thissen, Cai & Bock, 2010)
# see ?tamaanify manual

# define tamaan model
tammodel <- "
LAVAAN MODEL:
   mj=~ mj1__mj4
   mj ~~ 1*mj
ITEM TYPE:
  mj1(PCM,2)
  mj2(PCM,3)
  mj3(PCM)
  mj4(PCM,1)
   "
# estimate model
mod7 <- TAM::tamaan( tammodel, dat )
summary(mod7)
# -> This function can also be applied for the generalized partial credit
#    model (GPCM).

#############################################################################
# EXAMPLE 3: Rasch model and mixture Rasch model (Geiser & Eid, 2010)
#############################################################################

data(data.geiser, package="TAM")
dat <- data.geiser

#*********************************************************************
#*** Model 1: Rasch model
tammodel <- "
LAVAAN MODEL:
  F=~ mrt1__mrt6
  F ~~ F
ITEM TYPE:
  ALL(Rasch);
    "
mod1 <- TAM::tamaan( tammodel, resp=dat  )
summary(mod1)

#*********************************************************************
#*** Model 2: Mixed Rasch model with two classes
tammodel <- "
ANALYSIS:
  TYPE=MIXTURE ;
  NCLASSES(2);
  NSTARTS(20,25);
LAVAAN MODEL:
  F=~ mrt1__mrt6
  F ~~ F
ITEM TYPE:
  ALL(Rasch);
    "
mod2 <- TAM::tamaan( tammodel, resp=dat  )
summary(mod2)

# plot item parameters
ipars <- mod2$itempartable_MIXTURE[ 1:6, ]
plot( 1:6, ipars[,3], type="o", ylim=c(-3,2), pch=16,
        xlab="Item", ylab="Item difficulty")
lines( 1:6, ipars[,4], type="l", col=2, lty=2)
points( 1:6, ipars[,4],  col=2, pch=2)

# extract individual posterior distribution
post2 <- IRT.posterior(mod2)
str(post2)
# num [1:519, 1:30] 0.000105 0.000105 0.000105 0.000105 0.000105 ...
# - attr(*, "theta")=num [1:30, 1:30] 1 0 0 0 0 0 0 0 0 0 ...
# - attr(*, "prob.theta")=num [1:30, 1] 1.21e-05 2.20e-04 2.29e-03 1.37e-02 4.68e-02 ...
# - attr(*, "G")=num 1

# There are 2 classes and 15 theta grid points for each class
# The loadings of the theta grid on items are as follows
mod2$E[1,2,,"mrt1_F_load_Cl1"]
mod2$E[1,2,,"mrt1_F_load_Cl2"]

# compute individual posterior probability for class 1 (first 15 columns)
round( rowSums( post2[, 1:15] ), 3 )
# columns 16 to 30 refer to class 2

# }

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Description

Usage

Arguments

Value

See Also

Examples