Log-Linear Analysis

Applicability

Certain conditions have to be met for log-linear models to be reasonably applied to one’s data. First, all considered variables need to be measured at nominal-scale level (each variable has to come in two or more discrete observational categories). Second, all observations should be independent of one another, meaning that each participant—or sampling unit—should contribute one and only one observation to the data set. This is an important requirement, which also holds for classical chi-square tests. If your research design involves repeated measurements from the same subjects (such that each participant contributes more than one observation to the data), cross-tabulation tests and log-linear models should not be used. Finally, like with cross-tabulation tests in general, log-linear models call for sufficiently large numbers of observations per design cell. As a rule of thumb, all cells in the multidimensional table for analysis should have expected cell counts greater than one, and at least 80% of the design cells should have expected cell counts greater than five.

Example

The following illustration is based on simulated data. Imagine a car manufacturer is planning a new advertising campaign for its latest SUV. The manufacturer is not sure which color the car should be painted in for the advert photographs, and more importantly, whether the color of the car should be different for adverts appearing in magazines that are targeted toward different age groups and genders. The company decides to run a quick online survey in which visitors of their website can click on their favorite color option (out of three depicted suggestions: “silver,” “white,” or “black”) for the car in question. Each visitor can take part only once, and the response is counted after the visitor also indicated their age group (“over 40” or “under 40”) and gender (“male” or “female”). The imaginary survey is kept online for a few days, after which a total of 526 responses has been recorded, distributed as shown in Table 1. The manufacturer is primarily interested in testing whether color choice depends on specific combinations of age group and gender—in other words, whether age group and gender interact in predicting different color choices.

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