4.11 Exercises

Please use data2 and Q2 for the following exercises.

Fit the G-DINA model to the data, then answer the following questions

1. For Item 15, the G-DINA model parameter estimates are P(100) = 0.4 $\rule{0.25cm}{0.15mm}$ 57, P(101) = 0.6 $\rule{0.25cm}{0.15mm}$ 96.

2. The corresponding SEs for P(100) and P(101) are 0.0 $\rule{0.25cm}{0.15mm}$ 37 and 0.0 $\rule{0.25cm}{0.15mm}$ 30, respectively.

3. The proportion of individuals having an attribute pattern of 111 in the population is estimated to be 0.3 $\rule{0.25cm}{0.15mm}$ 12

4. The proportion of individuals who master $\mathbf{\alpha}_1$ in the population is estimated to be 0.80 $\rule{0.25cm}{0.15mm}$ 7.

5. Plot item success probabilities for Items 5, 8 and 15. Which item(s) appear to follow the DINO models?

6. Find the EAP estimate of attribute pattern for the third individual.

Fit reduced models for the following questions:

1. Fit LLM to the data: the number of parameters for LLM is 5 $\rule{0.25cm}{0.15mm}$.

2. Fit DINA to the data: guessing and slip parameter estimates of Item 10 are 0.3 $\rule{0.25cm}{0.15mm}$ 16 and 0.2 $\rule{0.25cm}{0.15mm}$ 32, respectively. The corresponding SEs are 0.0 $\rule{0.25cm}{0.15mm}$ 79 and 0.0 $\rule{0.25cm}{0.15mm}$ 12.