sirt (version 0.36-30)

rm.facets: Rater Facets Models with Item/Rater Intercepts and Slopes

Description

This function estimates the unidimensional rater facets model (Lincare, 1994) and an extension to slopes (see Details). The estimation is conducted by an EM algorithm employing Marginal Maximum Likelihood.

Usage

rm.facets(dat, pid=NULL, rater=NULL, Qmatrix=NULL, theta.k=seq(-9, 9, len=30), 
    est.b.rater=TRUE, est.a.item=FALSE, est.a.rater=FALSE, max.b.increment=1, 
    numdiff.parm=0.001, maxdevchange=0.1, globconv=0.001, maxiter=1000, 
    msteps=4, mstepconv=0.001)

## S3 method for class 'rm.facets':
summary(object,...)

Arguments

dat

Original data frame. Ratings on variables must be in rows, i.e. every row corresponds to a person-rater combination.

pid

Person identifier.

rater

Rater identifier

Qmatrix

An optional Q-matrix. If this matrix is not provided, then by default the ordinary scoring of categories (from 0 to the maximum score of $K$) is used.

theta.k

A grid of theta values for the ability distribution.

est.b.rater

Should the rater severities $b_r$ be estimated?

est.a.item

Should the item slopes $a_i$ be estimated?

est.a.rater

Should the rater slopes $a_r$ be estimated?

max.b.increment

Maximum increment of item parameters during estimation

numdiff.parm

Numerical differentiation step width

maxdevchange

Maximum relative deviance change as a convergence criterion

globconv

Maximum parameter change

maxiter

Maximum number of iterations

msteps

Maximum number of iterations during an M step

mstepconv

Convergence criterion in an M step

object

Object of class rm.facets

...

Further arguments to be passed

Value

• A list with following entries:
• deviance
  Deviance
• ic
  Information criteria and number of parameters
• item
  Data frame with item parameters
• rater
  Data frame with rater parameters
• person
  Data frame with person parameters: EAP and corresponding standard errors
• EAP.rel
  EAP reliability
• sigma
  Standard deviation of the trait
• tau.item
  Item parameters $\tau_{ik}$
• se.tau.item
  Standard error of item parameters $\tau_{ik}$
• a.item
  Item slopes $a_i$
• se.a.item
  Standard error of item slopes $a_i$
• b.rater
  Rater severity parameter $b_r$
• se.b.rater
  Standard error of rater severity parameter $b_r$
• a.rater
  Rater slope parameter $a_r$
• se.a.rater
  Standard error of rater slope parameter $a_r$
• f.yi.qk
  Individual likelihood
• f.qk.yi
  Individual posterior distribution
• probs
  Item probabilities at grid theta.k
• n.ik
  Expected counts
• maxK
  Maximum number of categories
• procdata
  Processed data
• iter
  Number of iterations
• ...
  Further values

Details

This function models ratings $X_{pri}$ for person $p$, rater $r$ and item $i$ and category $k$ $$P( X_{pri} = k | \theta_p ) \propto exp( a_i a_r q_{ik} \theta_p - q_{ik} b_r - \tau_{ik} ) \quad , \quad \theta_p \sim N( 0 , \sigma^2 )$$ By default, the scores in the $Q$ matrix are $q_{ik}=k$. Item slopes $a_i$ and rater slopes $a_r$ are standardized such that their product equals one, i.e. $\prod_i a_i = \prod_r a_r = 1$.

References

Linacre, J. M. (1994). Many-Facet Rasch Measurement. Chicago: MESA Press.

See Also

See also the TAM package for the estimation of more complicated facet models. See rm.hrm for estimating a hierarchical rater model.

Examples

#############################################################################
# EXAMPLE 1: Partial Credit Model and
#  Generalized partial credit model for one rater
#############################################################################
data(data.ratings1)
dat <- data.ratings1

# select rater db01
dat <- dat[ paste(dat$rater) == "db01" , ]

# Model 1: Partial Credit Model
mod1 <- rm.facets( dat[ , paste0( "k",1:5) ] , maxiter=15)

# Model 2: Generalized Partial Credit Model
mod2 <- rm.facets( dat[ , paste0( "k",1:5) ] , est.a.item=TRUE , maxiter=15)

summary(mod1)
summary(mod2)

#############################################################################
# EXAMPLE 2: Facets Model: 5 items, 7 raters
#############################################################################

data(data.ratings1)
dat <- data.ratings1

# Model 1: Partial Credit Model: no rater effects
mod1 <- rm.facets( dat[ , paste0( "k",1:5) ] , rater=dat$rater , 
            est.b.rater=FALSE  , maxiter=15)

# Model 2: Partial Credit Model: intercept rater effects
mod2 <- rm.facets( dat[ , paste0( "k",1:5) ] , rater=dat$rater  , maxiter=15)

# Model 2a: compare results with TAM package
#   Results should be similar to Model 2
library(TAM)
mod2a <- tam.mml.mfr( resp= dat[ , paste0( "k",1:5) ] , 
        facets= dat[ , "rater" , drop=FALSE] ,
	pid= dat$pid , formulaA = ~ item*step + rater )

# Model 3: estimated rater slopes
mod3 <- rm.facets( dat[ , paste0( "k",1:5) ] , rater=dat$rater , 
            est.a.rater=TRUE  , maxiter=15)

# Model 4: estimated item slopes
mod4 <- rm.facets( dat[ , paste0( "k",1:5) ] , rater=dat$rater , 
             est.a.item=TRUE , maxiter=15)

# Model 5: estimated rater and item slopes
mod5 <- rm.facets( dat[ , paste0( "k",1:5) ] , rater=dat$rater , 
            est.a.rater=TRUE , est.a.item=TRUE , maxiter=15)

summary(mod1)
summary(mod2)
summary(mod2a)
summary(mod3)
summary(mod4)
summary(mod5)