person.parameter: Estimation of Person Parameters

In eRm: Extended Rasch Modeling

Estimation of Person Parameters

Description

Maximum likelihood estimation of the person parameters with spline interpolation for non-observed and 0/full responses. Extraction of information criteria such as AIC, BIC, and cAIC based on unconditional log-likelihood.

Usage

## S3 method for class 'eRm'
person.parameter(object)
## S3 method for class 'ppar'
summary(object, ...)
## S3 method for class 'ppar'
print(x, ...)
## S3 method for class 'ppar'
plot(x, xlab = "Person Raw Scores",
   ylab = "Person Parameters (Theta)", main = NULL, ...)
## S3 method for class 'ppar'
coef(object, extrapolated = TRUE, ...)
## S3 method for class 'ppar'
logLik(object, ...)
## S3 method for class 'ppar'
confint(object, parm, level = 0.95, ...)

Arguments

object

Object of class 'eRm' in person.parameter and object of class ppar in IC.

Arguments for print and plot methods:

x	Object of class ppar.
xlab	Label of the x-axis.
ylab	Label of the y-axis.
main	Title of the plot.
...	Further arguments to be passed to or from other methods. They are ignored in this function.

Arguments for the coef method:

extrapolated

either returns extrapolated values for raw scores 0 and k or sets them NA

Arguments for confint:

parm	Parameter specification (ignored).
level	Alpha-level.

Details

If the data set contains missing values, person parameters are estimated for each missing value subgroup.

Value

The function person.parameter returns an object of class ppar containing:

loglik	Log-likelihood of the collapsed data (for faster estimation persons with the same raw score are collapsed).
npar	Number of parameters.
niter	Number of iterations.
thetapar	Person parameter estimates.
se.theta	Standard errors of the person parameters.
hessian	Hessian matrix.
theta.table	Matrix with person parameters (ordered according to original data) including NA pattern group.
pers.ex	Indices with persons excluded due to 0/full raw score
X.ex	Data matrix with persons excluded
gmemb	NA group membership vector (0/full persons excluded)

The function coef returns a vector of the person parameter estimates for each person (i.e., the first column of theta.table).

The function logLik returns an object of class loglik.ppar containing:

loglik	Log-likelihood of the collapsed data (see above).
df	Degrees of freedom.

Author(s)

Patrick Mair, Reinhold Hatzinger

References

Fischer, G. H., and Molenaar, I. (1995). Rasch Models - Foundations, Recent Developements, and Applications. Springer.

Mair, P., and Hatzinger, R. (2007). Extended Rasch modeling: The eRm package for the application of IRT models in R. Journal of Statistical Software, 20(9), 1-20.

Mair, P., and Hatzinger, R. (2007). CML based estimation of extended Rasch models with the eRm package in R. Psychology Science, 49, 26-43.

See Also

itemfit.ppar,personfit.ppar

Examples

#Person parameter estimation of a rating scale model
res <- RSM(rsmdat)
pres <- person.parameter(res)
pres
summary(pres)
plot(pres)

#Person parameter estimation for a Rasch model with missing values
res <- RM(raschdat2, se = FALSE) #Rasch model without standard errors
pres <- person.parameter(res)
pres                             #person parameters
summary(pres)
logLik(pres)                     #log-likelihood of person parameter estimation

eRm documentation built on May 24, 2025, 3:01 a.m.