tamaanify: Function for Parsing 'TAM' Input

In alexanderrobitzsch/TAM: Test Analysis Modules

Function for Parsing TAM Input

Description

This function parses a so called tammodel which is a string used for model estimation in TAM. The function is based on the lavaan syntax and operates at the extension lavaanify.IRT.

Usage

tamaanify(tammodel, resp, tam.method=NULL, doparse=TRUE )

Arguments

tammodel	String for model definition following the rules described in Details and in Examples.
resp	Item response dataset
tam.method	One of the TAM methods tam.mml, tam.mml.2pl or tam.mml.3pl.
doparse	Optional logical indicating whether lavmodel should be parsed for DO statements.

Details

The model syntax tammodel consists of several sections. Some of them are optional.

ANALYSIS:
Possible model types are unidimensional and multidimensional item response models (TYPE="TRAIT"), latent class models ("LCA"), located latent class models ("LOCLCA"; e.g. Formann, 1989; Bartolucci, 2007), ordered latent class models ("OLCA"; only works for dichotomous item responses; e.g. Hoijtink, 1997; Shojima, 2007) and mixture distribution models ("MIXTURE"; e.g. von Davier, 2007).

LAVAAN MODEL:
For specification of the syntax, see lavaanify.IRT.

MODEL CONSTRAINT:
Linear constraints can be specified by using conventional specification in R syntax. All terms must be combined with the + operator. Equality constraints are set by using the == operator as in lavaan.

ITEM TYPE:
The following item types can be defined: Rasch model (Rasch), the 2PL model (2PL), partial credit model (PCM) and the generalized partial credit model (GPCM).

The item intercepts can also be smoothed for the PCM and the GPCM by using a Fourier basis proposed by Thissen, Cai and Bock (2010). For an item with a maximum of score of K, a smoothed partial credit model is requested by PCM(kk) where kk is an integer between 1 and K. With kk=1, only a linear function is used. The subsequent integers correspond to Fourier functions with decreasing periods. See Example 2, Model 7 of the tamaan function.

PRIOR:
Possible prior distributions: Normal distribution N(mu,sd), truncated normal distribution TN(mu,sd,low,upp) and Beta distribution Beta(a,b). Parameter labels and prior specification must be separated by ~.

Value

A list with following (optional) entries which are used as input in one of the TAM functions tam.mml, tam.mml.2pl or tam.mml.3pl:

tammodel	Model input for TAM
tammodel.dfr	Processed tammodel input
ANALYSIS	Syntax specified in ANALYSIS
ANALYSIS.list	Parsed specifications in ANALYSIS
LAVAANMODEL	Syntax specified in LAVAAN MODEL
lavpartable	Parameter table processed by the syntax in LAVAAN MODEL
items	Informations about items: Number of categories, specified item response function
maxcat	Maximum number of categories
ITEMTYPE	Syntax specified in ITEM TYPE
MODELCONSTRAINT	Syntax specified in MODEL CONSTRAINT
MODELCONSTRAINT.dfr	Processed syntax in MODEL CONSTRAINT
modelconstraint.thresh	Processed data frame for model constraint of thresholds
modelconstraint.loading	Processed data frame for loadings
resp	Data set for usage
method	Used TAM function
A	Design matrix A
Q	Design matrix for loadings
Q.fixed	Fixed values in Q matrix
B.fixed	Matrix with fixed item loadings (used for tam.mml.2pl)
L	Processed design matrix for loadings when there are model constraints for loadings
variance.fixed	Matrix for specification of fixed values in covariance matrix
est.variance	Logical indicating whether variance should be estimated (tam.mml.2pl)
theta.k	Theta design matrix
E	Design matrix E
notA	Logical indicating whether A matrix is defined
gammaslope.fixed	Fixed gammaslope parameters
gammaslope.prior	Prior distributions for gammaslope parameters
xsi.fixed	Fixed \xi parameter
xsi.prior	Prior distributions for \xi parameters

References

Bartolucci, F. (2007). A class of multidimensional IRT models for testing unidimensionality and clustering items. Psychometrika, 72, 141-157. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11336-005-1376-9")}

Formann, A. K. (1989). Constrained latent class models: Some further applications. British Journal of Mathematical and Statistical Psychology, 42, 37-54. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/j.2044-8317.1989.tb01113.x")}

Hojtink, H., & Molenaar, I. W. (1997). A multidimensional item response model: Constrained latent class analysis using the Gibbs sampler and posterior predictive checks. Psychometrika, 62(2), 171-189. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/BF02295273")}

Thissen, D., Cai, L., & Bock, R. D. (2010). The nominal categories item response model. In M. L. Nering & Ostini, R. (Eds.). Handbook of Polytomous Item Response Models (pp. 43-75). New York: Routledge.

Shojima, K. (2007). Latent rank theory: Estimation of item reference profile by marginal maximum likelihood method with EM algorithm. DNC Research Note 07-12.

von Davier, M. (2007). Mixture distribution diagnostic models. ETS Research Report ETS RR-07-32. Princeton, ETS. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/j.2333-8504.2007.tb02074.x")}

See Also

See tamaan for more examples. Other examples are included in tam.mml and tam.mml.3pl.

lavaanify.IRT

Examples

## Not run: 

#############################################################################
# EXAMPLE 1: Examples dichotomous data data.read
#############################################################################

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

#*********************************************************************
#*** Model 1: 2PL estimation with some fixed parameters and
#             equality constraints
tammodel <- "
LAVAAN MODEL:
  F2=~ C1__C2 + 1.3*C3 + C4
  F1=~ A1__B1
  # fixed loading of 1.4 for item B2
  F1=~ 1.4*B2
  F1=~ B3
  F1 ~~ F1
  F2 ~~ F2
  F1 ~~ F2
  B1 | 1.23*t1 ; A3 | 0.679*t1
  A2 | a*t1 ; C2 | a*t1 ; C4 | a*t1
  C3 | x1*t1 ; C1 | x1*t1
ITEM TYPE:
  A1__A3 (Rasch) ;
  A4 (2PL) ;
  B1__C4 (Rasch) ;
    "
# process model
out <- TAM::tamaanify( tammodel, resp=dat)
# inspect some output
out$method          # used TAM function
out$lavpartable     # lavaan parameter table

#*********************************************************************
#*** Model 2: 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
    "
# process syntax
out <- TAM::tamaanify( tammodel, resp=dat)
str(out$E)     # E design matrix for estimation with tam.mml.3pl function

#*********************************************************************
#*** Model 3: Linear constraints for item intercepts and item loadings
tammodel <- "
LAVAAN MODEL:
  F=~ lam1__lam10*A1__C2
  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
    "
# parse syntax
mod1 <- TAM::tamaanify( tammodel, resp=dat)
mod1$A          # design matrix A for intercepts
mod1$L[,1,]     # design matrix L for loadings

## End(Not run)

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

library(CDM)
data( data.Students, package="CDM")
dat <- data.Students[,3:13]

#*********************************************************************
#*** 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
  act1__act3 | t1
  sc2 | t2
    "
out <- TAM::tamaanify( tammodel, resp=dat)
out$A    # design matrix for item intercepts
out$Q    # loading matrix for items

#*********************************************************************
#*** Model 2: Linear constraints

# In the following syntax, linear equations for multiple constraints
# are arranged over multiple lines.
tammodel <- "
  LAVAAN MODEL:
    F=~ a1__a5*act1__act5
    F ~~ F
  MODEL CONSTRAINT:
      a1==delta +
                tau1
      a2==delta
      a3==delta + z1
      a4==1.1*delta +
              2*tau1
                + (-0.2)*z1
  "
# tamaanify model
res <- TAM::tamaanify( tammodel, dat )
res$MODELCONSTRAINT.dfr
res$modelconstraint.loading

alexanderrobitzsch/TAM documentation built on Feb. 21, 2024, 5:59 p.m.