The researchers used a Poisson regression model to analyze data on infant lower respiratory illness. They looked at factors like passive smoking, crowded living conditions, socioeconomic status, race, and age group to see which ones were linked to the illness. The study found that passive smoking and crowded living conditions were significant factors, while socioeconomic status, race, and age group did not seem to have a big impact. The researchers used statistical tests and diagnostic tools to build and evaluate their model.