loglinear analysis

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loglinear analysis A statistical technique for analysing relationships within contingency tables. Cross-classified tables of data are very common in sociology–for example cross-tabulations of political preference by sex, educational attainment by social class, and so forth. Conventionally these tables are analysed by looking at departures from statistical independence by using the χ2 test. This principle of independence can be written as:lognnij = logni + lognj − logn (hence involving the logarithms of the data combined in an additive or linear composition). This makes the analysis simpler, more akin to analysis of variance (see VARIATION, STATISTICAL), and more easily generalizable to three or more variables. It also allows interaction effects to be studied; that is, the effect which both i and j together have, over and above the effect of i and the effect of j.

Loglinear analysis begins with a (definitionally true but trivial) ‘saturated’ model, where all possible direct and interaction effects are specified. Simpler models are then examined which leave out some of these effects (on the basis of theory or hunch) to see whether good fits to the data can be obtained with fewer effects (that is, with a more parsimonious model), and in this way the researcher may infer what variables are most important and what the pattern of effect actually is in the data. It is a very flexible multivariate procedure, best adapted to analysing attributes (variables at the nominal level of measurement), and is only feasible using computer programs.

Nigel Gilbert's Modelling Society (1981) and David Knoke and Peter J. Burke's Log Linear Models (1980) are both excellent introductions to topic. For substantive examples, and an explanation of how to read and interpret the various models, see Gordon Mashall et al. , Against the Odds? (1997