Symmetry and quasi-symmetry: an example in modelling pairs of sounds from children's early speech.

The models of symmetry and quasi-symmetry may have use in the analysis of categorical data in square tables where the row and column classifications are the same. Under the model of symmetry, the probability that an observation falls in, say, the (i,j) cell of a square table is the same as the probability that it falls in the (j,i) cell. The model of symmetry requires that the expected marginal total for any one row of the table be the same as the expected marginal total for the corresponding column. The model of quasi-symmetry, which is a generalization of the model of symmetry, does not require this equality of expected row and column totals. In this paper, we illustrate the use of the models of symmetry and quasi-symmetry in the analysis of categorical data that summarize pairs of sounds in infants' and toddlers' early utterances. In the past, the complexity of infants' early vocalizations has been difficult to measure because of a lack of methods to quantify prelinguistic phonetic variables. We use the models of symmetry and quasi-symmetry as a first attempt to quantify the complexity of infants' early speech. We hope that the discovery of models appropriate for quantification of language development in normal children will have later use in identification of children at risk for communicative disorders.