Constrained and Unconstrained Multivariate Normal Finite Mixture Modeling of Piagetian Data.

We present the results of multivariate normal mixture modeling of Piagetian data. The sample consists of 101 children, who carried out a (pseudo-)conservation computer task on four occasions. We fitted both cross-sectional mixture models, and longitudinal models based on a Markovian transition model. Piagetian theory of cognitive development provides a strong basis for the number and interpretation of the components in the mixtures. Most studies of Piagetian development have been based on mixture modeling of discrete responses. The present results show that normal mixture modeling is a useful approach, when responses are continuous and approximately normal within the components. Multivariate normal mixture modeling has the advantage that the covariance structure within the components may be modeled. Generally the results are consistent with the presence of distinct modes of responding. This provides support for the hypothesis of stage-wise development.