Logistic regression in threshold detection in replicated discrimination sensory tests

Main Article Content

Camilla Marques Barroso
https://orcid.org/0000-0003-2313-6886
Elayne Penha Veiga
https://orcid.org/0000-0001-9099-9791

Abstract

Sensory discrimination tests often consider the possibility that each assessor performs a test more than once, that is, they are performed with replications. However, these experiments are generally analyzed as if there were no repetitions or as if all judgments came from different assessors, which the usual analysis assumes that the probability of success is the same for all of them. It is emphasized the importance of considering possible differences in the perception of the assessors, which is consistent with Thurstone's psychological ideas about perception and decision processes. In this article it is suggested a mixed generalized linear model that considers the random effect of the assessor. Particularly in dose-response experiments it is showed that this model allows estimating detection thresholds for several treatments simultaneously. The results allowed to conclude that the proposed model presents good results and can be used in the analysis of replicated sensory tests. We will assume that the variation in the assessor' responses can be modeled as a random effect in a mixed generalized linear model. This model should be able to produce a better analysis, with the ability to detect differences between treatments with greater power and produce narrower confidence intervals for the estimates.

Article Details

How to Cite
Barroso, C. M., & Penha Veiga, E. (2023). Logistic regression in threshold detection in replicated discrimination sensory tests. Brazilian Journal of Biometrics, 41(4), 332–344. https://doi.org/10.28951/bjb.v41i4.630
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Articles

References

Altshuler, B. Modeling of Dose Response Relationships. Environmental Health Perspectives, 42, 23-27, 1981.

American Society for Testing and Materials, ASTM. Standard practice for determining odor and taste thresholds by a forced-choice ascending concentration series method of limits, E-679. Annual Book of Standards, 15,36-42, 2008a.

ASTM. Compilation of odor and taste threshold values data. American Society for Testing and Materials, Philadelphia, 1978.

Bates, D., Mächler, M., Bolker, B.M., & Walker, S.C. Fitting Linear Mixed-Effects Models Using lme4. Journal of Statistical Software, 67, 1-48, 2015. https://doi.org/10.18637/jss.v067.i01

Bi, J. Difficulties and a way out: A bayesian approach for sensory difference and preference tests. Journal of Sensory Studies, 18, 1-18, 2003. https://doi.org/10.1111/j.1745-459X.2003.tb00369.x

Bi, J., & Ennis, D.M. A thurstonian variant of the beta-binomial model for replicated difference tests. Journal of Sensory Studies, 13, 461-466, 1998. https://doi.org/10.1111/j.1745-459X.1998.tb00100.x

Brockhoff, P.B. The statistical power of replications in difference tests. Food Quality and Preference, 14, 405-417, 2003. https://doi.org/10.1016/S0950-3293(03)00003-X.

Brockhoff, P.B., & Christensen, R.H.B. Thurstonian models for sensory discrimination tests as generalized linear models. Food Quality and Preference, 21, 330-338, 2010. https://doi.org/10.1016/j.foodqual.2009.04.003.

Brockhoff, P.B., & Schlich, P. Handling replications in discrimination tests. Food Quality and Preference, 9, 303-312, 1998. https://doi.org/10.1016/S0950-3293(98)00014-7.

Brockhoff, P.M., & Muller, H-G. Random effect threshold models for dose-response relationships with repeated measurements. Journal of the Royal Statistical Society: Series B, 59, 431-446, 1997.

Coleman, M., & Marks, H. Topics in dose-response modelling. Journal of Food Protection, 61, 1425-1582, 1998. https://doi.org/10.1111/1467-9868.00077.

Duineveld, K., & Meyners, M. Hierarchical Bayesian analysis of true discrimination rates in replicated triangle tests. Food Quality and Preference, 19, 292-305, 2008. https://doi.org/10.1016/j.foodqual.2007.10.005.

Ennis, D.M., & Bi, J. The beta-binomial model: accounting for inter-trial variation in replicated difference and preference tests. Journal of Sensory Studies, 13, 389-412, 1998. https://doi.org/10.1111/j.1745-459X.1998.tb00097.x.

Harries, J.M., & Smith, G.L. The two-factor triangle test. Food Science Technology, 17, 153-162, 1982. https://doi.org/10.1111/j.1365-2621.1982.tb00172.x.

Hunter, E.A., Piggot, J.R., & Lee, K.Y.M. Analysis of discrimination tests. In: Société Française de Statistique (Ed.), Actes des 6èmes Journées Européennes Agro-Industrie et Méthodes Statistiques, Pau, January, 19-21, 2000.

Kemp, S.E., Hollowood, T., & Hort J. Sensory Evaluation: a pratical handbook (1st ed.). John Wiley & Sons, 2009.

Kunert, J. On repeated difference testing. Food Quality and Preference, 12, 385-391, 2001. https://doi.org/10.1016/S0950-3293(01)00029-5.

Kunert, J., & Meyners, M. One the triangle test with replications. Food Quality and Preference, 10, 477-482, 1999. https://doi.org/10.1016/S0950-3293(99)00047-6.

Lawless, H.T., & Heymann, H. Sensory evaluation of food: principles and practices (2nd ed.). Springer, 2010.

Lima Filho, T., Minim, V. P. R., da Silva, R. C. S. N., Lucia, S. M. D., & Minim, L. A. Methodology for determination of two new sensory thresholds: Compromised acceptance threshold and rejection threshold. Food Research International, 76, 561-566, 2015. https://doi.org/10.1016/j.foodres.2015.07.037.

Linander, C.B., Christensen, R.H.B., Cleaver, G., & Brockhoff, P.B. Individual differences in replicated multi product experiments with Thurstonian mixed models for binary paired comparison data. Food Quality and Preference, 75, 220-229, 2019.

Meilgaard, M.C. Testing for Sensory Threshold of Added Substances. American Society of Brewing Chemist, 1991.

Meilgaard, M.C., Carr, B.T., & Civille, G.V. Sensory Evaluation Techniques (4th ed.). CRC Press, 2006.

Meyners, M., & Brockhoff, P.B. The design of replicated difference tests. Journal of sensory studies, 18,291-324, 2003. http://doi.org/10.1111/j.1745-459x.2003.tb00391.x.

Murray, N.M., Jacquier, J.C., O'Sullivan, M., Hallihan, A., Murphy, E., Feeney, E.L., & O'Riordan, D. Using rejection thresholds to determine acceptability of novel bioactive compounds added to milk-based beverages. Food Quality and Preference, 73, 276-283, 2019. https://doi.org/10.1016/j.foodqual.2018.10.014.

Peltier, C., Brockhoff, P.B., Visalli, M., & Schlich, P. The MAM-CAP table: A new tool for monitoring panel performances. Food Quality and Preference, 32, 24-27, 2014.

Prescott, J., Norris, L., Kunst, M., & Kim, S. Estimating a consumer rejection threshold for cork taint in white wine. Food Quality and Preference, 16, 345-349, 2005.

R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, 2020. URL: https://www.R-project.org/.

Roessler, E.B., Pangborn, R.M., Sidel, J.L., & Stone, H. Expanded statistical tables for estimating significance in paired-preference, paired-difference, duo-trio and tringle tests. Journal of Food Science, 43, 940-943, 1978.

Skellam, J.G. A Probability Distribution Derived from the Binomial Distribution by Regarding the Probability of Success as Variable Between the Sets of Trials. Journal of the Royal Statistical Society. Series B (Methodological), 10, 257-261, 1948.

Thurstone, L.L. A law of comparative judgment. Psychology Review, 34, 273-286, 1927. https://doi.org/10.1037/h0070288.

Ziegler, M., Gok, R., Bechtloff, P., Winterhalter, P., Schmarr, H-G., & Fischer, U. Impact of matrix variables and expertise of panelists on sensory thresholds of 1,1,6-trimethyl-1,2-dihydronaphthalene known as petrol off flavor compound in Riesling wines. Food Quality and Preference, 78, 103735, 2019. https://doi.org/10.1016/j.foodqual.2019.103735.