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