Path analysis with partial association measures

This paper discusses the use of partial association measures for carrying out path analyses on categorical data. The measures considered are essentially PRE (proportion of reduction in error of prediction) measures for nominal variables and concordance-discordance indices for ordinal ones. These measures provide a natural way to evaluate the strength of the path linking a non-measurable response variable to one of several categorical explanatory factors. Concerning the decomposition of raw association into direct and indirect effects, it is shown, however, that they do not share the properties of conventional path coefficients for measurable variables. Especially purely nominal association measures need to be interpreted with care. The scope of the partial measures for path analysis is illustrated through a study of the relationships between the educational styles experienced by swiss adolescents and their selfesteem.