setConstraintsRasch: Set and check constraints for the parameters of IRT models

In ikosmidis/brRasch: Maximum likelihood and bias reduction for fixed-effets Rasch models

Set and check constraints for the parameters of IRT models

Description

'setConstraintsRasch' is used to set constraints on the parameters for fixed-effects IRT models.

Usage

setConstraintsRasch(data, dim, which, values, restricted)

Arguments

data	a matrix of counts or an object of class compressed. If a matrix of counts is inputted then the rows must correspond to subjects and the columns to items.
dim	non-negative integer. It specifies the dimension of the Rasch model. See Details in brRasch for more information
which	a vector of integers indicating which parameters are to be constrained
values	a vector with elements the values at which the parameters in which should be constrained

Value

setConstraintsRasch returns an object of class setConstraints, which is a list with the following components:

constrained	a logical vector of the same length as the number of parameters in the model
constrainedTo	a numeric vector with the values of the constrained parameters, in the same order they appear in constrained
dim	the dim used

Examples

data(LSAT)

# Use the weighted Bernoulli representation to get the
# coefficients quickly
LSATCompressed <- compress(LSAT)

# Fit a 2PL model to an adjusted version of LSAT data using ML the
# adjustment is p/(2n) which is bias-reducing in logistic regression
# and ensures finiteness of the estimates (see Cordeiro & McCullagh,
# 1991 for details)
adj <- (nrow(LSAT) + 2*ncol(LSAT))/(2*nrow(LSAT)*ncol(LSAT))
lsatCompressed <- within.list(LSATCompressed, data <- adj + data*(1 - 2*adj))


# Set the contrasts so that the first easiness and first
# discrimination parameters are 0 and 1, respectively
constrc <- setConstraintsRasch(data = lsatCompressed$data,
                               dim = 1,
                               which = c(1, 6),
                               values = c(0, 1))

# Fit the 2PL model under those constraints
fitML <- brRasch(lsatCompressed, constraints = constrc, br = FALSE)

## Not run: 
# Plot the IRF from the adjusted data
irf(fitML)

## End(Not run)

# In order to fit a Rasch model to the same data set the constraints so
# that all discrimination parameters are 1
# The warning ia reminder that a model with dim = 1 requires only 2 identifiability constraints
constrc0 <- setConstraintsRasch(data = lsatCompressed$data,
                                dim = 1,
                                which = c(1, 6, 7, 8, 9, 10),
                                values = c(0, 1, 1, 1, 1, 1))

# Fit the 2PL model under those constraints.
fitML0 <- brRasch(lsatCompressed, constraints = constrc0, br = FALSE)

## Not run: 
# The IRFs for fitML0 have the same slope
irf(fitML0)

## End(Not run)

ikosmidis/brRasch documentation built on May 16, 2022, 10:12 a.m.