Linear model

Log-linear model

Statistics

Economics

Set (abstract data type)

Data mining

Computer science

Graphical model

Conditional dependence

Task (project management)

Mathematics

Management

Data set

Econometrics

Artificial intelligence

Programming language

Categorical variable

Machine learning

ETS Research Report Series

ABSTRACT There has been increasing attention to the fine structure of abilities underlying task performance (Haertel and Wiley (in press)). One of the useful approaches for this is by use of graphical models to represent relationships among abilities and test items. Building a large graphical model is always an issue. Restrictions upon experiments and data collection, among others, may result in parts of the large model. Or it may be convenient for us to build parts of the large models first, and then try to combine those parts into a larger model. This paper derives, confined to categorical variables only, a theory which may be useful in combining conditional graphical models into a larger one. The main result of the paper is that we can see partial information about a true log‐linear structure (LLS) from its conditional LLSs and use the information in trying to guess the true LLS, assuming that the true LLS is graphical. An application of the result is illustrated using a simulated data set.

COMBINATION OF CONDITIONAL LOG‐LINEAR STRUCTURES