5.6 Marginalized maximum likelihood estimation via EM algorithm

The log likelihood of item response matrix $\mathbf{Y}$ of all $N$ students can be written by $$\begin{equation} \ell(\mathbf{Y}) = \log \prod\limits_{i = 1}^N L ({\mathbf{Y}_i}) = \sum\limits_{i = 1}^N \log L({\mathbf{Y}_i}) \end{equation}$$ Our goal is to find $(\mathbf{g},\mathbf{s})$ that maximize $\ell(\mathbf{Y})$.

The marginal loglikelihood can be maximized via the so-called Expectation-Maximization (EM) algorithm.

The EM algorithm consists of two steps: E- and M-step.

The details of the EM algorithm for estimating the DINA model are given in de la Torre (2009).

References

de la Torre, J. (2009). DINA model and parameter estimation: A didactic. Journal of Educational and Behavioral Statistics, 34(1), 115–130. https://doi.org/10.3102/1076998607309474