Reply to Bi and Kuesten: ANOVA outperforms logistic regression for the analysis of CATA data

Abstract In a commentary to Meyners and Hasted (2021), Bi and Kuesten (2021) suggest the use of logistic regression for the analysis of check-all-that-apply (CATA) data. At the same time, based on theoretical considerations, they criticize the use of ANOVA for such data. We show that logistic regression is flawed due to an inflated type I error rate relative to the nominal level, and that it is therefore not reliable to use this model for inference on CATA data. At the same time, the results confirm the applicability of ANOVA-based statistical inference. We also address additional comments from their commentary, arguing that ANOVA has additional practical benefits, and exploring the potential reasons for the contrast between the theoretical concept (which suggests better performance from the logistic regression) and the empirical simulation performance.