An EM Algorithm for Estimating Log Linear Models with Additional Marginal Constraints

摘要: In this paper we consider a class of parametric models for two-way multinomial tables, where the cell probabilities, pij, are function K dimensional parameter vector θ, pij =pij(θ), and ML estimator, has property that $$\hat{p}_i.=n_i./n$$ and $$\hat{p}._j=n._j/n$$ (1.1) ni., n.j, pi pj denote usual row column sums data probabilities \(\hat{p}._ij=p_{ij}(\hat{\theta} )\). That is, MLE marginals is precisely observed marginal frequencies. This includes tables with positive local odds ratios, Smith (1989) Dykstra Lemke (1988), wide log linear models, Bishop, Fienberg Holland (1975), as well unconstrained \(\hat{p}_{ij}=n_{ij}/n\)