raschmodel: Rasch Model Fitting Function

Description

raschmodel is a basic fitting function for simple Rasch models.

Usage

raschmodel(y, weights = NULL, start = NULL, reltol = 1e-10,
  deriv = c("sum", "diff", "numeric"), hessian = TRUE,
  maxit = 100L, full = TRUE, gradtol = reltol, iterlim = maxit, ...)

Value

raschmodel returns an S3 object of class "raschmodel", i.e., a list with the following components:

coefficients: estimated item difficulty parameters (without first item parameter which is always constrained to be 0),
vcov: covariance matrix of the parameters in the model,
loglik: log-likelihood of the fitted model,
df: number of estimated parameters,
data: the original data supplied (excluding columns without variance),
weights: the weights used (if any),
n: number of observations (with non-zero weights),
items: status indicator (0, 0/1, 1) of all original items,
na: logical indicating whether the data contains NAs,
elementary_symmetric_functions: List of elementary symmetric functions for estimated parameters (up to order 2; or 1 in case of numeric derivatives),
code: convergence code from optim,
iterations: number of iterations used by optim,
reltol: tolerance passed to optim,
deriv: type of derivatives used for computing gradient and Hessian matrix,
call: original function call.

Arguments

y: item response object that can be coerced (via as.matrix) to a binary 0/1 matrix (e.g., from class itemresp.
weights: an optional vector of weights (interpreted as case weights).
start: an optional vector of starting values.
deriv: character. Which type of derivatives should be used for computing gradient and Hessian matrix? Analytical with sum algorithm ("sum"), analytical with difference algorithm ("diff", faster but numerically unstable), or numerical.
hessian: logical. Should the Hessian of the final model be computed? If set to FALSE, the vcov method can only return NAs and consequently no standard errors or tests are available in the summary.
reltol, maxit, ...: further arguments passed to optim.
full: logical. Should a full model object be returned? If set to FALSE, no variance-covariance matrix and no matrix of estimating functions are computed.
gradtol, iterlim: numeric. For backward compatibility with previous versions these arguments are mapped to reltol and maxit, respectively.

Details

raschmodel provides a basic fitting function for simple Rasch models, intended as a building block for fitting Rasch trees and Rasch mixtures in the psychotree and psychomix packages, respectively.

raschmodel returns an object of class "raschmodel" for which several basic methods are available, including print, plot, summary, coef, vcov, logLik, estfun, discrpar, itempar, threshpar, and personpar.

Examples

Run this code

o <- options(digits = 4)

## Verbal aggression data
data("VerbalAggression", package = "psychotools")

## Rasch model for the other-to-blame situations
m <- raschmodel(VerbalAggression$resp2[, 1:12])
## IGNORE_RDIFF_BEGIN
summary(m)
## IGNORE_RDIFF_END

## visualizations
plot(m, type = "profile")
plot(m, type = "regions")
plot(m, type = "curves")
plot(m, type = "information")
plot(m, type = "piplot")

options(digits = o$digits)