psychotools (version 0.2-0)

RaschModel.fit: Rasch Model Fitting Function

Description

RaschModel.fit is a basic fitting function for simple Rasch models.

Usage

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

Arguments

y

object that can be coerced (via as.matrix) to a binary 0/1 matrix.

weights

an optional vector of weights, interpreted as case weights (integer only).

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

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.

Value

• RaschModel.fit returns an S3 object of class "RaschModel", i.e., a list with components as follows.
• 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.

Details

RaschModel.fit provides a basic fitting function for simple Rasch models, intended as a building block for fitting Rasch trees and Rasch mixtures in the psychotree package, respectively. RaschModel.fit returns an object of class "RaschModel" for which several basic methods are available, including print, plot, summary, coef, vcov, logLik, and worth.

See Also

PCModel.fit, RSModel.fit, btReg.fit

Examples

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

## Rasch model for the other-to-blame situations
m <- RaschModel.fit(VerbalAggression$resp2[, 1:12])
summary(m)
plot(m)