This talk looks at the utility of bilinear models for score
building in contingency tables and contrasts it with the
correspondence analysis approach. The groundwork for using
bilinear models for score building was laid down by
Clogg(1982), who specified a set of rules for the instrumental
variable against which the target variable is classified.
Typical bilinear models used for this purpose include the logmultiplicative
model and the correspondence analysis model.
While this approach seems at first sight to be promising,
there are issues relating to empty cells and sample size
which often mean that the model fails to form exactly as
intended. We discuss whether Clogg’s rules need
extending and determine whether similar rules are needed
for correspondence analysis. An example is used from the
problem of scaling crime harm and impact from survey data.

Clogg, C. (1982) Using Association Models in Sociological
Research: Some Examples. American Journal of Sociology
Vol. 88(1) 114-134