Lab exercise 9

Please upload the knitted .pdf file on Moodle by 23:59.

Use the following data set TEST10 containing the item parameters of 10 items to answer the questions.

Test10 <- read.table("https://raw.githubusercontent.com/sunbeomk/PSYC490/main/Test10.txt")
head(Test10)
##      a     b    c
## 1 0.62 -0.82 0.12
## 2 0.75  0.49 0.15
## 3 0.99  0.74 0.12
## 4 1.39  0.58 0.05
## 5 0.54 -0.31 0.21
## 6 1.38  1.51 0.17
  1. Complete the code chunk below to write a function called irt.sim that takes four vectors as inputs (theta_sim,a,b,c) and generates a random response data set from a 3PL IRT model.
irt_sim <- function(theta,a,b,c){ #ability and item parameters as vectors
  n_items <- length()
    
  n_subjects <- length()
    
  resp <- matrix(NA,nrow = n_subjects, ncol = n_items)
  for(i in 1:n_subjects){
    for(j in 1:n_items){
      
      pij <- irt_p( , , , )
      
      resp[i, j] <- 
    }
  }
  
  resp
}

  1. Randomly generate true abilities \(\theta\)s for 500 examinees from a standard normal distribution.

  2. Using the irt_sim function, randomly generate a response data set resp for the 500 examinees on the 10 items in Test10. The generated response data set resp should be a \(500 \times 10\) matrix.

  3. Using the mirt function from the mirt package, estimate the item parameters from a 3PL model. Create 3 vectors, a_est, b_est, c_est, representing the \(a, b, c\) estimates for the Test10 items.

  4. Estimate the ability \(\theta\)s for the 500 examinees. Print the ability estimates for the first five examinees.

  5. In a single window (3-by-4 array), draw item information curves of the 10 items. The result should look like the plot below.

  • hints: par(mfrow=c(3,4))