Loglinear analysis of cross-classified ordinal data: applications in developmental research

This article provides an introduction to loglinear analysis of cross-classification tables, including tables with nominal and ordinal variables. Loglinear models offer several advantages over the more commonly used chi-square test of independence, including the ability to analyze 3-, 4-, and higher-way interactions, the ability to determine whether the association between variables is linear or nonlinear, and the ability to interpret scale scores assigned to categories of an ordinal variable. After a review of the advantages of loglinear modeling, the chi-square test of independence is compared with the loglinear model of independence. This comparison serves to introduce the notation and terminology of loglinear modeling. The overall strategy of loglinear modeling is introduced next; then special loglinear models for ordinal data are reviewed. Each model discussed in the article is applied to data from the developmental literature.