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

Usage

compute_eap_se_nrm(
  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 coded 0 to m
D: metric constant kept for the same interface as the other files and not used
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="NRM")
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(0.614,0.782,0.297,1.036,0.521,
               1.187,0.906,1.523,0.418,0.694,
               1.395,1.487,1.103,0.688,1.214,
               1.812,1.093,2.176,1.407,1.032,
               2.106,2.391,1.724,2.012,1.873,
               1.264,0.517,1.936,0.793,0.186,
               2.918,3.087,2.215,2.604,3.382,
               0.097,-0.814,1.012,-0.296,-1.618),
             nrow=5,
             dimnames=list(c(1,2,3,4,5),
                           c("alpha1","c1","alpha2","c2","alpha3","c3","alpha4","c4")))
response<-c(4,3,2,1,0)
catR::eapSem(0,bank,response,model="NRM") # this will work with catR package installed
#> [1] 0.6111826
compute_eap_se_nrm(theta=0,bank=bank,x=response)
#> [1] 0.6111826