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.