3.17 Assignment I

  1. Monotonicity is an important concept in not only CDM but also IRT models. In CDM context, monotonicity means students who master additional required attributes should not have lower success probability on an item. For example, if item \(j\) measures two attributes, then\[ P(Y_{j}=1|\alpha_{lj}^*=10)\geq P(Y_{j}=1|\alpha_{lj}^*=00) \]Please discuss what constraints the parameters need to meet to satisify monotonicity for the DINA, DINO, A-CDM, LLM and R-RUM. (For example: For DINA model, the monotonicity is met when \(1-s_j-g_j\geq 0\) )

  2. When a test measures \(K=10\) attributes, how many parameters do you have in the (1) saturated joint attribute distribution, (2) independent model, (3) 2PL higher-order model and (4) a linear structure model (\(A1\rightarrow A2\rightarrow \ldots \rightarrow A10\)).

  3. Please read Henson et al. (2009) and Davier (2008) and discuss how the loglinear CDM and general diagnostic model are related to the G-DINA model.

  4. Please discuss how DINA, DINO, LLM, and R-RUM models are special cases of GDINA model.

References

Davier, M. (2008). A general diagnostic model applied to language testing data. British Journal of Mathematical and Statistical Psychology, 61(2), 287–307. https://doi.org/10.1348/000711007X193957
Henson, R. A., Templin, J. L., & Willse, J. T. (2009). Defining a Family of Cognitive Diagnosis Models Using Log-Linear Models with Latent Variables. Psychometrika, 74(2), 191–210. https://doi.org/10.1007/s11336-008-9089-5