Definition:Loglinear Model

Definition

A loglinear model is used in the context of a contingency table.

Let $\CC$ be a contingency table with $r$ rows and $c$ columns.

Let rows and columns of $\CC$ be independent.

The expected frequency of cell $\tuple {i, j}$ is:

$m_{i j} = \dfrac {n_{i+} n_{+j} } N$

where:

$N$ is the total for $\CC$

$n_{i+}$ and $n_{+j}$ denote the totals for the $i$th row and $j$th column.

Then taking logarithms:

$\ln m_{i j} = \ln n_{i+} + n_{+j} - \ln N$

That is, the logarithm of the expected number in each cell is a linear function of the logarithms of the row, column and grand totals.

Also see

• Results about loglinear models can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): loglinear model
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): loglinear model