The following code block uses mirt to define population parameters for 250 graded response IRT models.
This will be used to set up a CAT interface that can be used for on-line use or
off-line use (for testing or Monte Carlo simulation research).
library('mirtCAT')
set.seed(1)
bank <- 250 #bank size
N <- 500 #calibration sample size
a <- matrix(rlnorm(bank*2, .2,.3), bank)
a[1:75, 1] <- a[250:175, 2] <- 0
d <- matrix(seq(1.25, -1.25, length.out=4), bank, 4, byrow=TRUE) + rnorm(bank)
pars <- data.frame(a, d)
colnames(pars) <- c('a1', 'a2', paste0('d', 1:4))
mod <- generate.mirt_object(pars, itemtype = 'graded')
head(coef(mod, simplify=TRUE)$items)
## a1 a2 d1 d2 d3 d4
## Item.1 0 1.272351 1.32730312 0.4939698 -0.3393635 -1.1726969
## Item.2 0 1.380092 0.95313136 0.1197980 -0.7135353 -1.5468686
## Item.3 0 1.196145 0.06675776 -0.7665756 -1.5999089 -2.4332422
## Item.4 0 1.133943 1.26129269 0.4279594 -0.4053740 -1.2387073
## Item.5 0 1.504808 2.24160104 1.4082677 0.5749344 -0.2583990
## Item.6 0 1.722658 2.84396745 2.0106341 1.1773008 0.3439675
This next section generates a plausible response vector given \(\theta_1 = -1\) and
\(\theta_2 = 0.5\), and passes the response vector to mirtCAT() for off-line use.
## generate random response pattern
set.seed(1)
pattern <- generate_pattern(mod, Theta = c(-1, 0.5))
head(pattern[1L,])
## [1] 2 2 2 4 2 4
# use adaptive method using Kullback-Leibler item selection with root-N adjustment
# with MAP estimation of latent traits
result <- mirtCAT(mo=mod, local_pattern=pattern, criteria='KLn',
design = list(min_SEM=.2), method = 'MAP')
print(result)
## n.items.answered Theta_1 Theta_2 SE.Theta_1 SE.Theta_2 True.Theta_1
## 119 -1.008349 0.3731586 0.1994405 0.1831658 -1
## True.Theta_2
## 0.5
plot(result, scales = list(x = list(at = NULL)), SE = 1.96) #95% confidence interval