Log-linear analysis is a useful but under-used technique for investigators who categorize some entity (persons, dyads, various kinds of events such as bids for attention or turns of talk in conversations, etc.) on several dimensions using nominal scales and then tally the results in a multi-dimensional contingency table.
In searching for the most parsimonious yet tolerably fitting model for such data, log-linear analysis can provide straightforward answers to a wide array of research questions. Log-linear analysis specifically and contingency table analysis generally can be facilitated by an interactive computer program such as the ILOG program described here. ILOG allows the user to re-order searches for a fitting model interactively and collapse, expand, and otherwise manipulate multi-way contingency tables in ways that most standard statistical programs do not.
Interactive Log-Linear and Contingency Table Analysis
In a line that has been quoted by many writers since, the ancient Greek poet Archilochus wrote that the fox knows many things, but the hedgehog knows one big thing. Log-linear analysis is a hedgehog among statistical techniques: It does one thing very well, which is analyze the counts of multi-dimensional contingency tables.
Investigators with ordinal and interval-scale data will need to look elsewhere for more generalized analytic methods, but investigators who categorize some entity (persons or dyads, various kinds of events such as bids for attention or turns of talk in conversations, etc.) on several dimensions using nominal scales and then tally the results in a multi-dimensional contingency table can find log-linear analysis a straightforward way to address their research questions (e.g., see Bakeman & Robinson, 1994; Wickens, 1989).
There are at least three reasons why log-linear analysis is seldom used. First, as just noted, is its specialization; its use is limited to contingency table analysis. Second, although most statistical packages include one or two log-linear analysis programs, they are not inherently interactive and, as we argue here, log-linear analysis is facilitated with an interactive computer program. Third, the applied statistics taught to behavioral scientists generally tend to de-emphasize analysis of nominal data; for example, most introductory statistic tests in the behavioral and social sciences relegate chi-square analysis—which, as we will show, is log-linear analysis for two-dimensional tables—to a final chapter, one that, in the press of time, is often ignored by instructors.
Our primary point is that log-linear analysis is a potentially useful but often-overlooked technique in behavioral research (education, psychology, sociology, etc.). Here we provide an introductory tutorial for log-linear analysis and demonstrate how easily it can be effected with ILOG. In particular, ILOG allows you to define a series of hierarchic log-linear models and re-order searches for a fitting model interactively—and also collapse, expand, and otherwise manipulate multi-way contingency tables—in ways that most standard statistical programs do not. This interactive capability facilitates both analysis and interpretation.