compute standard error of theta EAP estimation under the graded response model

Usage

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

Arguments

theta: theta estimation
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::eapSem(model="GRM")
pass the EAP estimate as theta to obtain the posterior standard deviation
any other value returns the posterior root mean squared deviation around it
so the curve is minimised at the EAP estimate

Examples

bank<-matrix(c(1.227,0.845,1.694,1.012,2.103,
               -2.183,-1.542,-1.021,-2.460,-0.812,
               -0.874,-0.415,-0.231,-1.105,0.094,
               0.316,0.783,0.652,0.047,0.881,
               1.592,2.064,1.438,1.271,1.736),
             nrow=5,
             dimnames=list(c(1,2,3,4,5),
                           c("alphaj","betaj1","betaj2","betaj3","betaj4")))
response<-c(4,3,2,1,0)
catR::eapSem(0,bank,response,model="GRM")
#> [1] 0.5731984
compute_eap_se_grm(theta=0,bank=bank,x=response)
#> [1] 0.5731984