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

In: Computing Science and Statistics

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  • Woollcott Smith

    (School of Business and Management Temple University, Statistics Department)

Abstract

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

Suggested Citation

  • Woollcott Smith, 1992. "An EM Algorithm for Estimating Log Linear Models with Additional Marginal Constraints," Springer Books, in: Connie Page & Raoul LePage (ed.), Computing Science and Statistics, pages 529-533, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2856-1_93
    DOI: 10.1007/978-1-4612-2856-1_93
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