# IRT.truescore: Converts a theta Score into a True Score tau ( theta) In TAM: Test Analysis Modules

 IRT.truescore R Documentation

## Converts a θ Score into a True Score τ ( θ)

### Description

Converts a θ score into an unweighted true score τ ( θ)=∑_i ∑_h h P_i ( θ ) . In addition, a weighted true score τ ( θ)=∑_i ∑_h q_{ih} P_i ( θ ) can also be computed by specifying item-category weights q_{ih} in the matrix `Q`.

### Usage

```IRT.truescore(object, iIndex=NULL, theta=NULL, Q=NULL)
```

### Arguments

 `object` Object for which the `CDM::IRT.irfprob` S3 method is defined `iIndex` Optional vector with item indices `theta` Optional vector with θ values `Q` Optional weighting matrix

### Value

Data frame containing θ values and corresponding true scores τ( θ ) .

See also `sirt::truescore.irt` for a conversion function for generalized partial credit models.

### Examples

```#############################################################################
# EXAMPLE 1: True score conversion for a test with polytomous items
#############################################################################

data(data.Students, package="CDM")
dat <- data.Students[, paste0("mj",1:4) ]

# fit partial credit model
mod1 <- TAM::tam.mml( dat,control=list(maxiter=20) )
summary(mod1)

# true score conversion
tmod1 <- TAM::IRT.truescore( mod1 )
round( tmod1, 4 )
# true score conversion with user-defined theta grid
tmod1b <- TAM::IRT.truescore( mod1, theta=seq( -8,8, len=33 ) )
# plot results
plot( tmod1\$theta, tmod1\$truescore, type="l",
xlab=expression(theta), ylab=expression(tau( theta ) ) )
points( tmod1b\$theta, tmod1b\$truescore, pch=16, col="brown" )

## Not run:
#############################################################################
# EXAMPLE 2: True scores with different category weightings
#############################################################################

data(data.timssAusTwn.scored)
dat <- data.timssAusTwn.scored
# extract item response data
dat <- dat[, grep("M03", colnames(dat) ) ]
# select items with do have maximum score of 2 (polytomous items)
ind <- which( apply( dat,  2, max, na.rm=TRUE )==2 )
I <- ncol(dat)
# define Q-matrix with scoring variant
Q <- matrix( 1, nrow=I, ncol=1 )
Q[ ind, 1 ] <- .5    # score of 0.5 for polyomous items

# estimate model
mod1 <- TAM::tam.mml( dat, Q=Q, irtmodel="PCM2", control=list( nodes=seq(-10,10,len=61) ) )
summary(mod1)

# true score with scoring (0,1,2) which is the default of the function
tmod1 <- TAM::IRT.truescore(mod1)
# true score with user specified weighting matrix
Q <- mod1\$B[,,1]
tmod2 <- TAM::IRT.truescore(mod1, Q=Q)

## End(Not run)
```

TAM documentation built on Aug. 29, 2022, 1:05 a.m.