Variable Rules: Performance as a Statistical Reflection of Competence

Speech performances are here considered as statistical samples drawn from a probabilistic language competence. This competence is modeled in conventional generative terms, except that optional rules are assigned application probabilities as functions of the structure of the input strings, possibly depending on the extralinguistic environment as well. We develop the mathematical background for these variable rules, which were introduced by Labov, and we apply the theory and methodology to examples from Spanish, French, and English. The data consist of relative frequencies of rule application for different types of input string, and they provide a check on the frequencies predicted by variable rules. This study supports the hypothesis that the various features in rule structural descriptions tend to act independently, in the statistical sense, on rule probabilities. The analytic framework for variable rules is easily and naturally extendable to take into account the effect of sociolinguistic and stylistic features on application frequencies.