New Light on the 16-Fold Table

Lantent-trait theory provides a flexible and comprehensive framework for constructing models of the processes reflected in data on two dichotomous variables, each obseved twice for each member of a panel of repondents (i.e., data in the form of the so-called 16-fold table). The more important parts of the analysis developed from this theory can be carried out by elementary methods and therefore require no great mathematical or statistical sophistication. In several illustrative data sets, the observed changes are adequately accounted for with a model allowing no causal relationship between the two latent variables or their observable indicators. In other examples, a model of asymmetric causation is plausible; in still others, the situation is so complex that a convincing causal interpretation, excluding rival interpretations, is not available. The basic form of the latent-trait model can be modified to include parameters pertaining to association of the observed indicators. This modification is especially appropriate when the two variables arise from parallel observations on the memebers of dyads rather than from observations on two distict items (attitudes, actions) pertaining to individual respondent. Limitations of the illustrative analyses reported here are, for the most part, intrinsic to the 16-fold table itself, whatever the analytical strategy, or are shared with other forms of survey analysis. The latent-trait approach, however, may make such limitations easier to see.