Quasi-Symmetric Graphical Log-Linear Models

Quasi-Symmetric Graphical Log-Linear Models

We propose an extension of graphical log-linear models to allow for symmetry constraints on some interaction parameters that represent homologous factors. The conditional independence structure of such quasi-symmetric (QS) graphical models is described by an undirected graph with coloured edges, in which a particular colour corresponds to a set of equality constraints on a set of parameters. Un...

Graphical Log-Linear Models: Fundamental Concepts and Applications

We present a comprehensive study of graphical log-linear models for contingency tables. High dimensional contingency tables arise in many areas such as computational biology, collection of survey and census data and others. Analysis of contingency tables involving several factors or categorical variables is very hard. To determine interactions among various factors, graphical and decomposable l...

Building Measurement Models from Scratch: Graphical Models, Exchangeability Models, and Log-linear Models

Decomposable Log-linear Models Decomposable Log-linear Models

The present paper considers discrete probability models with exact computational properties. In relation to contingency tables this means closed form expressions of the maksimum likelihood estimate and its distribution. The model class includes what is known as decomposable graphical models, which can be characterized by a structured set of conditional independencies between some variables give...

Log-Linear Models

• As x gets bigger, so does expx. So raising θsolid with your slider will raise the numerators of p(solid circle) (1) and p(solid triangle) (3). To be precise, each time you increase θsolid by 1, you multiply those numerators by e. (And decreasing θsolid by 1 divides them by e.) • Finally, the four probabilities (1)–(4) always sum to 1 (thanks to their common denominator Z). That’s required bec...