3.8 The LLM

Stands for the linear logistic model (Maris, 1999)

Is also referred to as Compensatory Reparameterized Unified Model (CRUM)

In this model, mastering an attribute has a certain impact on the logit of the probability of success

Its IRF can be written as

$$\log \frac{P(Y_j=1|\alpha_{lj}^*)}{ P(Y_j=0|\alpha_{lj}^*) }=\delta_{j0} + \sum_{k=1}^{K_j^*}\delta_{jk}\alpha_{lk}$$

Please calculate probabilities based on the parameters in the graph below:

$$P[Y_j=1|\alpha_{lj}^*=(0,0)]=?\\ P[Y_j=1|\alpha_{lj}^*=(1,0)]=?\\ P[Y_j=1|\alpha_{lj}^*=(0,1)]=?\\ P[Y_j=1|\alpha_{lj}^*=(1,1)]=?\\ $$

References

Maris, E. (1999). Estimating multiple classification latent class models. Psychometrika, 64(2), 187–212. https://doi.org/10.1007/bf02294535