Loglinear Symmetry and Quasi‐Symmetry Models for the Analysis of Change

Abstract

AbstractLoglinear symmetry and quasi‐symmetry models are proposed as tools for investigating various hypotheses about change. First, a survey of model representations is provided, including model specification in terms of hierarchical loglinear models and in design matrix notation. Secondly, the range of symmetry and quasi‐symmetry models is extended to the joint analysis of several groups. Parameter constraints are discussed which allow one to test specific hypotheses about group differences in symmetric frequency distributions. Finally, symmetry and quasi‐symmetry models are considered for multiway contigency tables. In this context, loglinear total score models are proposed for the analysis of symmetry in several marginal distributions. The proposed models reflect cross‐sectional as well as longitudinal facets of development.