•Simulated Type I errors rates of ANOVA based on GLM and LM models for CATA data.•Simulated testing powers of ANOVA based on the GLM and LM models for CATA data.•Predicted precisions using GLM and LM models for CATA data.•The claim that logistic regressions violate Type I error rates is not generally true.•Liberty or conservativeness is not a criterion of validity or invalidity of a test. Some discussions about statistical models used for analysis of CATA data appear in recent issues of this journal. This paper is a further discussion on the topic, following Bi and Kuesten (2022) (Food Quality and Preference, 95), related to Meyners and Hasted (2021, 2022) (Food Quality and Preference, 92, 95). This paper presents some statistical analyses for a real consumer CATA dataset using a generalized linear model (GLM) and a linear model (LM), respectively. The main objectives are to simulate Type I error levels of ANOVA; to simulate the empirical testing powers of ANOVA; and to compare testing results and predicted precisions based on different models. Meyners and Hasted (2022) claim that logistic regressions violate Type I error rates. The simulation results show that the claim is not generally true and suggest that violating Type I error rates is due to two-way ANOVA with a special type of Sums of Squares (Type2SS), not due to the GLM. Meyners and Hasted (2022) conclude that the GLM or logistic regression is invalid and flawed for analysis of CATA data. We disagree with the conclusion because we cannot find any convincing reasoning supporting the conclusion. It is true that the test of two-way ANOVA with Type2SS based on the GLM is more liberal than that with Type1SS and that based on the LM. Liberty and conservativeness are a characteristic of a test, not a criterion to judge validity or invalidity of a test. Meyners and Hasted (2022) advocate that GLM should be precluded for the use of CATA data. Our position is that the GLM deserves to be a standard and first selected practice, at least one of the useful and valid methods for analysis of CATA data. The advocacy of precluding the GLM for analysis of CATA data is unacceptable.