6.9 Assignment 2

  1. Why is model identifiability important and what are the possible consequences of interpreting results from a non-identified model?

  2. What are model parameters for a CDM when marginalized maximum likelihood estimation (MMLE) is used? Why are person attribute profiles not considered as model parameters? (Hint: see Xu, 2019)

  3. Please use data3 and Q3 for the following exercises.

Fit the ACDM model to the data, then answer the following questions

  1. For Item 14, the ACDM model parameter estimates are
  • P(100) = ?
  • P(101) = ?

  1. Find the corresponding SEs for P(100) and P(101).

  2. The proportion of individuals having an attribute pattern of 111 in the population is estimated to be: ______________?

  3. The proportion of individuals who master \(\mathbf{\alpha}_1\) in the population is estimated to be _________________?

  4. Plot item success probabilities for Items 5, 8 and 10. Which item(s) appear to follow the DINO models?

  5. Find the EAP estimate of attribute pattern for the second individual.

Fit reduced models for the following questions:

  1. Fit LLM to the data: the number of parameters for LLM is ___________.

  2. Fit DINA to the data: guessing and slip parameter estimates of Item 10 are ____________ and _____________, respectively. The corresponding SEs are ______________ and ____________________.

  3. Fit the GDINA model to the data, and estimate the delta parameters for item 11.

  1. Fit a higher-order LLM to data3 with Q3 (for the higher-order component, please use 2PL-type model) and answer the following questions:

  1. What is the number of estimated parameters?

  2. What is the number of parameters for the joint attribute distribution?

  3. The proportion of individuals having an attribute pattern of 111 in the population is estimated to be ____________.

  4. The proportion of individuals who master \(\alpha_1\) in the population is estimated to be ______________.

  5. What are the estimated higher-order parameters? Please interpret them.

References

Xu, G. (2019). Identifiability and Cognitive Diagnosis Models (M. von Davier & Y.-S. Lee, Eds.; pp. 333–357). Springer International Publishing. http://link.springer.com/10.1007/978-3-030-05584-4_16