Extract Empirical Estimating Functions

A function for extracting the empirical estimating functions of a fitted mirt, multipleGroup, bfactor, or mdirt model. This is the derivative of the log-likelihood with respect to the parameter vector, evaluated at the observed (case-wise) data. In other words, this function returns the case-wise scores, evaluated at the fitted model parameters. Currently, models fitted via the EM or BL method are supported. For the computations, the internal Theta grid of the model is being used which was already used during the estimation of the model itself along with its matching normalized density.

Usage

estfun.AllModelClass(
  x,
  weights = extract.mirt(x, "survey.weights"),
  centering = FALSE
)

Arguments

x

a fitted model object of class SingleGroupClass, MultipleGroupClass, or DiscreteClass

weights

by default, the survey.weights which were (optionally) specified when fitting the model are included to calculate the scores. If specified by the user, this should be a numeric vector of length equal to the total sample size. Note that if not all cases were weighted equally when fitting the model, the weights must be corrected by taking their square root if the scores are being used to compute the outer product of gradients (OPG) estimate of the variance-covariance matrix (see examples below).

centering

a boolean variable that allows the centering of the case-wise scores (i.e., setting their expected values to 0). If the case-wise scores were obtained from maximum likelihood estimates, this setting does not affect the result.

Value

An n x k matrix corresponding to n observations and k parameters

See also

mirt, multipleGroup, bfactor, mdirt

Author

Lennart Schneider lennart.sch@web.de and Phil Chalmers; centering argument contributed by Rudolf Debelak (rudolf.debelak@psychologie.uzh.ch)

Examples

if (FALSE) { # \dontrun{
# fit a 2PL on the LSAT7 data and get the scores
mod1 <- mirt(expand.table(LSAT7), 1, SE = TRUE, SE.type = "crossprod")
sc1 <- estfun.AllModelClass(mod1)
# get the gradient
colSums(sc1)
# calculate the OPG estimate of the variance-covariance matrix "by hand"
vc1 <- vcov(mod1)
all.equal(crossprod(sc1), chol2inv(chol(vc1)), check.attributes = FALSE)

# Discrete group
modd <- mdirt(expand.table(LSAT7), 2, SE = TRUE, SE.type = "crossprod")
sc1 <- estfun.AllModelClass(modd)
# get the gradient
colSums(sc1)
# calculate the OPG estimate of the variance-covariance matrix "by hand"
vc1 <- vcov(modd)
all.equal(crossprod(sc1), chol2inv(chol(vc1)), check.attributes = FALSE)

# fit a multiple group 2PL and do the same as above
group <- rep(c("G1", "G2"), 500)
mod2 <- multipleGroup(expand.table(LSAT7), 1, group, SE = TRUE,
  SE.type = "crossprod")
sc2 <- estfun.AllModelClass(mod2)
colSums(sc2)
vc2 <- vcov(mod2)
all.equal(crossprod(sc2), chol2inv(chol(vc2)), check.attributes = FALSE)

# fit a bifactor model with 2 specific factors and do the same as above
mod3 <- bfactor(expand.table(LSAT7), c(2, 2, 1, 1, 2), SE = TRUE,
  SE.type = "crossprod")
sc3 <- estfun.AllModelClass(mod3)
colSums(sc3)
vc3 <- vcov(mod3)
all.equal(crossprod(sc3), chol2inv(chol(vc3)), check.attributes = FALSE)

# fit a 2PL not weighting all cases equally
survey.weights <- c(rep(2, sum(LSAT7$freq) / 2), rep(1, sum(LSAT7$freq) / 2))
survey.weights <- survey.weights / sum(survey.weights) * sum(LSAT7$freq)
mod4 <- mirt(expand.table(LSAT7), 1, SE = TRUE, SE.type = "crossprod",
  survey.weights = survey.weights)
sc4 <- estfun.AllModelClass(mod4,
  weights = extract.mirt(mod4, "survey.weights"))
# get the gradient
colSums(sc4)
# to calculate the OPG estimate of the variance-covariance matrix "by hand",
# the weights must be adjusted by taking their square root
sc4_crp <- estfun.AllModelClass(mod4,
  weights = sqrt(extract.mirt(mod4, "survey.weights")))
vc4 <- vcov(mod4)
all.equal(crossprod(sc4_crp), chol2inv(chol(vc4)), check.attributes = FALSE)

} # }