# Lab exercise 8

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).