compute theta EAP estimation under the partial credit model

Usage

compute_eap_pcm(
  bank,
  x,
  D = 1,
  priorPar = c(0, 1),
  lower = -4,
  upper = 4,
  nqp = 33
)

Arguments

bank: matrix of item parameters
x: vector of item responses scored 0 to m
D: metric constant can be 1 or 1.702
priorPar: mean and sd for normal distribution default is mean 0 and sd 1
lower: lower bound for numerical integration
upper: upper bound for numerical integration
nqp: number of quadrature points

Note

this function should return the same result as catR::eapEst(model="PCM")
the total score sum(x) is a sufficient statistic so two response patterns
with the same total score on the same items give the same EAP estimate
mirt estimates the variance of theta for a Rasch model so a bank taken from
mirt is used with priorPar=c(0,sqrt(pars$cov)) where
pars<-mirt::coef(model,IRTpars=TRUE,simplify=TRUE)

Examples

bank<-matrix(c(-1.853,-2.214,-0.936,-1.508,-0.412,
               -0.627,-0.504,-1.215,-0.183,0.338,
               0.418,0.692,0.284,0.735,1.102,
               1.636,1.927,1.405,2.118,2.285),
             nrow=5,
             dimnames=list(c(1,2,3,4,5),
                           c("deltaj1","deltaj2","deltaj3","deltaj4")))
response<-c(4,3,2,1,0)
catR::eapEst(bank,response,model="PCM")
#> [1] 0.1350411
compute_eap_pcm(bank,response)
#> [1] 0.1350411