10.6. Marginal Tables

To understand the literature on loglinear models, it’s helpful to have some appreciation of marginal tables and their relationship to the parameters in the loglinear model and to the maximum likelihood estimates. A marginal table is just a contingency table that is obtained by summing the frequencies in some larger contingency table over one or more of the variables. For example, if we have a three-way table for variables X, Y, and Z, there are several possible marginal tables:

  • the X × Y table, obtained by summing over Z

  • the X × Z table, obtained by summing over Y

  • the Y × Z table, obtained by summing over X

  • the X table, obtained by summing over both Y and Z

  • the Y table, obtained by summing over both X and Z

  • the Z table, obtained ...

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