Some Common Problems in Log-Linear Analysis

Abstract

Several problems often encountered in research using log-linear models for categorical response variables are discussed. The issues covered are (a) determining the degrees of freedom for a model, (b) analyzing sparse data, (c) analyzing weighted data, (d) modeling rates, and (e) interpreting results.

Fitting Log-Linear Models to Contingency Tables From Surveys With Complex Sampling Designs: An Investigation of the Clogg-Eliason Approach

“…Clogg and Eliason (1987) proposed, amongst many other ideas, a simple method for handling survey weights in log-linear modelling. This method has continued to be cited.…”

“…In this paper we shall consider an alternative approach proposed by Clogg and Eliason (1987), hereafter referred to as CE, for use with one specific class of modelling methods:…”

The Problem of Zero Cells in the Analysis of Contingency Tables

“…Other than collapsing variable categories, several options are available for analysing a table with zero cells: 1) add a small value (0.5 is frequently suggested) to every cell in the table when fitting the saturated model (Goodman 1970), 2) add a small quantity (such as 0.2) only to zero cells (Evers & Namboodiri 1977), 3) add the value 1 r to zero cells, where r equals the number of response categories (Grizzle, Starmer & Koch 1969), 4) arbitrarily define zero divided by zero to be zero (Fienberg 1980), 5) increase the sample size sufficiently to remove all zero cells (Knoke & Burke 1980), 6) replace sampling zeros by 0.1×10 -8 , or a smaller number and then check results against those obtained without such an adjustment (Clogg & Eliason 1988).…”

Immigration and Status Exchange in Australia and the United States

“…The outcome hwag m is the expected number of marriages between husbands in education category i and nativity status a, and wives in education category w and nativity status ݃. To ensure that our estimates are representative of the U.S. populations, each model incorporates (wife's person) weights using offset iwag t , which is equal to the inverse of the total weighted frequency of the 16 cell divided by the unweighted cell (Agresti, 2002;Clogg & Eliason, 1987;Schwartz & Mare, 2005). The baseline model for Australia is similar to that for the United States except that each spouse's education consists of six categories and weights are not needed with a complete population census.…”