This chapter gives a concise exposition of loglinear models for discrete data. Since their introduction in the 1960s and 1970s, loglinear models have been applied in a wide variety of fields, and the methodology is described in many textbooks on discrete data analysis. Notable among these are Bishop, Fienberg, and Holland (1975), Fienberg (1980), Agresti (1990), and Christensen (1990). The use of graphs and graphical models in connection with loglinear models is due to Darroch, Lauritzen, and Speed (1980); an application-oriented exposition is given in Edwards and Kreiner (1983). Christensen (1990) can be recommended as a modern introductory-level textbook on contingency table analysis that includes good coverage of the graphical modelling approach. Whittaker’s (1990) book on graphical modelling covers both discrete and continuous models. This chapter gives only a very brief account of the topic, focusing on graphs and graphical models.
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