Klimova, AnnaIST Austria; Rudas, Tamás
Relational models for contingency tables are generalizations of log-linear models, allowing effects associated with arbitrary subsets of cells in the table, and not necessarily containing the overall effect, that is, a common parameter in every cell. Similarly to log-linear models, relational models can be extended to non-negative distributions, but the extension requires more complex methods. An extended relational model is defined as an algebraic variety, and it turns out to be the closure of the original model with respect to the Bregman divergence. In the extended relational model, the MLE of the cell parameters always exists and is unique, but some of its properties may be different from those of the MLE under log-linear models. The MLE can be computed using a generalized iterative scaling procedure based on Bregman projections.
Journal of Multivariate Analysis
440 - 452
Klimova A, Rudas T. On the closure of relational models. Journal of Multivariate Analysis. 2016;143:440-452. doi:10.1016/j.jmva.2015.10.005
Klimova, A., & Rudas, T. (2016). On the closure of relational models. Journal of Multivariate Analysis, 143, 440–452. https://doi.org/10.1016/j.jmva.2015.10.005
Klimova, Anna, and Tamás Rudas. “On the Closure of Relational Models.” Journal of Multivariate Analysis 143 (2016): 440–52. https://doi.org/10.1016/j.jmva.2015.10.005.
A. Klimova and T. Rudas, “On the closure of relational models,” Journal of Multivariate Analysis, vol. 143, pp. 440–452, 2016.
Klimova A, Rudas T. 2016. On the closure of relational models. Journal of Multivariate Analysis. 143, 440–452.
Klimova, Anna, and Tamás Rudas. “On the Closure of Relational Models.” Journal of Multivariate Analysis, vol. 143, Elsevier, 2016, pp. 440–52, doi:10.1016/j.jmva.2015.10.005.