man/lsat_setConstraints.R

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

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)

\dontrun{
# Plot the IRF from the adjusted data
irf(fitML)
}

# 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)

\dontrun{
# The IRFs for fitML0 have the same slope
irf(fitML0)
}