eRm (version 0.15-3)

person.parameter: 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.

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.

extrapolated

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

parm

Parameter specification (ignored).

level

Alpha-level.

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.

Details

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

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