According to the TAM documentation, one has to supply a matrice for the items parameters (difficulty and discrimination)

B.fixed An optional matrix with four columns for fixing matrix entries in 2PL estimation. 1st column: item index, 2nd column: category, 3rd column: dimension, 4th column: fixed value.

Does the following code use the right syntax?

# Example data
n_cand <- 10
n_items <- 3
data <- matrix(sample(0:1, n_cand * n_items, replace = TRUE), nrow = n_cand, ncol = n_items)

# Define fixed item difficulties and discriminations
xsi.fixed <- cbind(1:n_items, diff = c(-1, 0, 1.2)) # arbitrary values
b.fixed <- cbind(1:n_items, category = 0, dimension = 1, discr = c(1, 1.2, 0.9))   # Example values

# Fit the 2PL model
library(TAM)
mod <- tam.mml.2pl(resp = data, xsi.fixed = xsi.fixed, B.fixed = b.fixed)

According to the TAM documentation, one has to supply a matrice for the items parameters (difficulty and discrimination)

B.fixed An optional matrix with four columns for fixing matrix entries in 2PL estimation. 1st column: item index, 2nd column: category, 3rd column: dimension, 4th column: fixed value.

Does the following code use the right syntax?

# Example data
n_cand <- 10
n_items <- 3
data <- matrix(sample(0:1, n_cand * n_items, replace = TRUE), nrow = n_cand, ncol = n_items)

# Define fixed item difficulties and discriminations
xsi.fixed <- cbind(1:n_items, diff = c(-1, 0, 1.2)) # arbitrary values
b.fixed <- cbind(1:n_items, category = 0, dimension = 1, discr = c(1, 1.2, 0.9))   # Example values

# Fit the 2PL model
library(TAM)
mod <- tam.mml.2pl(resp = data, xsi.fixed = xsi.fixed, B.fixed = b.fixed)

• r

1 Answer 1

OP needs to fix the loading for every category of the respective items, whereas the category column is a counter starting with 1. That ist, the category column can't be 0. Note that OP also needs to free the variance of the person distribution for estimation if the discrimination parameters are fixed.

Try

n_cand <- 10
n_items <- 3
data <- matrix(sample(0:1, n_cand * n_items, replace = TRUE), nrow = n_cand, ncol = n_items)

# Define fixed item difficulties and discriminations
xsi.fixed <- cbind(1:n_items, diff = c(-1, 0, 1.2)) # arbitrary values
b.fixed <- rbind(
  cbind(1:n_items, category = 1, dimension = 1, discr = c(0, 0, 0)),
  cbind(1:n_items, category = 2, dimension = 1, discr = c(1, 1.2, 0.9)))   # Example values

# Fit the 2PL model
mod <- tam.mml.2pl(resp = data, xsi.fixed = xsi.fixed, B.fixed = b.fixed, 
  est.variance = TRUE)
mod$B
mod$variance