A new correspondence analysis for check-all-that-apply data
A new correspondence analysis procedure is introduced for exploring associations between objects and variables in data obtained from a check-all-that-apply (CATA) question. CATA responses are often coded such that 0 and 1 indicate “not checked” and “checked” respectively, then organized into a three-way binary array in which the modes are assessors (blocks), products (objects), and terms (variables). Existing correspondence analysis procedures operate on a CATA frequency table, which is obtained by collapsing the CATA array over assessors. The new procedure operates on the three-dimensional array, not the CATA frequency table. The procedure decomposes the total inertia, which is proportional to a global test statistic for CATA data proposed by Meyners et al. (2013). The proposed approach is contrasted with simple correspondence analysis (see Greenacre, 2017) and multiple-response correspondence analysis (Mahieu et al., 2021). All three analyses are applied to data from a previous study in which Uruguayan consumers evaluated fruit from six strawberry cultivars with 16 CATA terms (Jaeger & Ares, 2015). Different correspondence analyses emphasize different terms, leading to different product configurations. The proposed approach is recommended for theoretical and practical reasons. Limitations of this approach will be highlighted.
Castura, J.C. (2026). A new correspondence analysis for check-all-that-apply data. AgroStat 2026 Conference. 5-7 October. Dijon, France. (Oral Presentation).