ABSTRACT
These studies require multivariate analyses, since the variation is conditioned by a variety of phonological, grammatical, and social factors. Special techniques for the analysis of linguistic variation have been developed to take into account two particular properties of linguistic structure. First, it is impossible to fill all cells of a matrix for an ANOVA-type analysis, since in principle most intersections of linguistic features will be empty. Secondly, internal linguistic constraints typically show independent behavior, and the working assumption of independence can be used to test the fit of the model to the observations. The VARBllUL programs of Sankoff and Labov {Sankoff & Labov, 1979) have been the major tools used in the analysis of linguistic variation, though in recent years principle component analyses, multidimensional scaling, aud other transformations have been introduced. The VARBRUL programs are iterative maximum likelihood algorithms that derive the overall probability of a rule application from a model combining the independent contributions of mutually exclusive groups of environmental factors. In recent years, VARBRUL programs have been expanded to include techniques for selecting significant factors through stepwise regression on the output; to handle trinary as well as binary data; to discover any divisions of the speech community t.hat will improve the likelihood of the analysis.
