Lab exercise 8

Please upload the .pdf file on moodle by 23:59.

The following data set TEST10 contains the item parameters of 10 items following the 3PL model.

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. Draw the three histograms of the parameters (\(a, b, c\)) in a single window (2-by-2 array), by row.

  2. What is the probability of answering item 2 correctly for an examinee whose true ability is 0 (i.e., \(\theta = 0\))

  3. Draw an ICC plot of item 2.

  4. In a single window with 3-by-4 array, draw ICC plots of all 10 items.

  5. Generate \(500\) subjects’ responses to the \(10\) items in Test10. Assume that the true ability scores of the examinees follow the standard normal distribution.

  • When generating the ability scores of 500 examinees, \(\theta\)s, set the random seed by set.seed(123).
  1. Using the response data set obtained from 5, plot the total score against the true ability score \(\theta\) (theta_sim).