5.9 Joint attribute distribution parameters

In addition to item parameters, one also needs to estimate the joint attribute distribution parameters. Here we consider the saturated or unstructed joint attribute distribution with population proportions as the parameters.

The population proportion \(p(\alpha_c)\) can also be updated as in \[ \hat{p}(\alpha_c)=\frac{1}{N}\sum_i P(\mathbf{\alpha}_c| {\mathbf{Y}_i}) \]

For the previous example, the updated \(p(\alpha_c)\)

Code

updated.p.alphac <- colMeans(P.alphac.given.yi)
updated.p.alphac

##    00    10    01    11 
## 0.072 0.202 0.250 0.477

The E- and M-steps will repeat until some convergence criteria meet.