eRm: person.parameter – R documentation

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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.

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.

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

Extended Rasch Modeling

v1.0-2

GPL-3

Authors

Patrick Mair [cre, aut], Reinhold Hatzinger [aut], Marco J. Maier [aut], Thomas Rusch [ctb], Rudolf Debelak [ctb]

Initial release

2021-02-11