The analysis of contextual effects on segmental duration

In natural speech, segmental duration depends on several factors, including phonemic identity, phonetic context, phrase boundaries, lexical stress, and speaking rate. These factors interact: the magnitude of the effect of a factor-whether measured in milliseconds or as percentage change-often depends on other factors. This paper introduces two data analysis methods for constructing a duration model that best describes a given body of multi-factorially dependent durations. The methods are illustrated with a single-speaker data base consisting of vowel durations measured at two speaking rates in contexts varying in phrasal location, stress, and other factors; text materials are two-word pseudo-phrases. Both methods analyse the structure of two-way rearrangements of the N-way data matrix, in which columns correspond to combinations of levels of k factors and rows to combinations of levels of the remaining N-k factors. The first method concerns models that express duration as a sum of additive and multiplicative terms (additive-multiplicative models), such as various versions of a model by Klatt (Journal of the Acoustical Society of America, 54(4), 1973). It determines which additive-multiplicative model best describes the data, by making use of the fact that a given additive-multiplicative model predicts for any two-way rearrangement whether the between-columns covariance matrix is either constant, multiplicative, or neither. The second method determines the general functional form that best describes the data, by testing for which two-way rearrangement the durations in each column are in the same numerical order (a property known as joint independence).