The Mixed Assessor Model and the multiplicative mixed model

Sofie Pødenphant*, Minh H. Truong, Kasper Kristensen, Per B. Brockhoff

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

A novel possibility for easy and open source based analysis of sensory profile data by a formal multiplicative mixed model (mumm) with fixed product effects and random assessor effects is presented by means of the generic statistical R-package mumm. The package is using likelihood principles and is utilizing newer developments within Automatic Differentiation by means of the Template Model Builder R-package. We compare such formal likelihood based analysis with the Mixed Assessor Model (MAM) analysis, where MAM is a linear approximation of the multiplicative mixed model. We use real sensory data as examples together with simulated data. We found that the formal mumm approach for hypothesis testing more resembles the MAM than the standard 2-way mixed model, and that both the mumm approach and the MAM give a higher power to detect product differences than the 2-way mixed model, when a ”scaling effect” is present. We also validated that the novel contrast confidence limit method suggested previously for the MAM performs well and in line with the formal likelihood based confidence intervals of the mumm. Finally, the likelihood based mumm approach suggests that the more proper test for product difference would be a test that has a ”joint product and scaling effect” interpretation.
Original languageEnglish
JournalFood Quality and Preference
Volume74
Pages (from-to)38-48
ISSN0950-3293
DOIs
Publication statusPublished - 2018

Keywords

  • Sensory profile data
  • Analysis of variance
  • Multiplicative mixed model
  • Scaling differences
  • Disagreement
  • Template Model Builder

Cite this

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title = "The Mixed Assessor Model and the multiplicative mixed model",
abstract = "A novel possibility for easy and open source based analysis of sensory profile data by a formal multiplicative mixed model (mumm) with fixed product effects and random assessor effects is presented by means of the generic statistical R-package mumm. The package is using likelihood principles and is utilizing newer developments within Automatic Differentiation by means of the Template Model Builder R-package. We compare such formal likelihood based analysis with the Mixed Assessor Model (MAM) analysis, where MAM is a linear approximation of the multiplicative mixed model. We use real sensory data as examples together with simulated data. We found that the formal mumm approach for hypothesis testing more resembles the MAM than the standard 2-way mixed model, and that both the mumm approach and the MAM give a higher power to detect product differences than the 2-way mixed model, when a ”scaling effect” is present. We also validated that the novel contrast confidence limit method suggested previously for the MAM performs well and in line with the formal likelihood based confidence intervals of the mumm. Finally, the likelihood based mumm approach suggests that the more proper test for product difference would be a test that has a ”joint product and scaling effect” interpretation.",
keywords = "Sensory profile data, Analysis of variance, Multiplicative mixed model, Scaling differences, Disagreement, Template Model Builder",
author = "Sofie P{\o}denphant and Truong, {Minh H.} and Kasper Kristensen and Brockhoff, {Per B.}",
year = "2018",
doi = "10.1016/j.foodqual.2018.11.006",
language = "English",
volume = "74",
pages = "38--48",
journal = "Food Quality and Preference",
issn = "0950-3293",
publisher = "Pergamon Press",

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The Mixed Assessor Model and the multiplicative mixed model. / Pødenphant, Sofie; Truong, Minh H.; Kristensen, Kasper; Brockhoff, Per B.

In: Food Quality and Preference, Vol. 74, 2018, p. 38-48.

Research output: Contribution to journalJournal articleResearchpeer-review

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AU - Truong, Minh H.

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AU - Brockhoff, Per B.

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N2 - A novel possibility for easy and open source based analysis of sensory profile data by a formal multiplicative mixed model (mumm) with fixed product effects and random assessor effects is presented by means of the generic statistical R-package mumm. The package is using likelihood principles and is utilizing newer developments within Automatic Differentiation by means of the Template Model Builder R-package. We compare such formal likelihood based analysis with the Mixed Assessor Model (MAM) analysis, where MAM is a linear approximation of the multiplicative mixed model. We use real sensory data as examples together with simulated data. We found that the formal mumm approach for hypothesis testing more resembles the MAM than the standard 2-way mixed model, and that both the mumm approach and the MAM give a higher power to detect product differences than the 2-way mixed model, when a ”scaling effect” is present. We also validated that the novel contrast confidence limit method suggested previously for the MAM performs well and in line with the formal likelihood based confidence intervals of the mumm. Finally, the likelihood based mumm approach suggests that the more proper test for product difference would be a test that has a ”joint product and scaling effect” interpretation.

AB - A novel possibility for easy and open source based analysis of sensory profile data by a formal multiplicative mixed model (mumm) with fixed product effects and random assessor effects is presented by means of the generic statistical R-package mumm. The package is using likelihood principles and is utilizing newer developments within Automatic Differentiation by means of the Template Model Builder R-package. We compare such formal likelihood based analysis with the Mixed Assessor Model (MAM) analysis, where MAM is a linear approximation of the multiplicative mixed model. We use real sensory data as examples together with simulated data. We found that the formal mumm approach for hypothesis testing more resembles the MAM than the standard 2-way mixed model, and that both the mumm approach and the MAM give a higher power to detect product differences than the 2-way mixed model, when a ”scaling effect” is present. We also validated that the novel contrast confidence limit method suggested previously for the MAM performs well and in line with the formal likelihood based confidence intervals of the mumm. Finally, the likelihood based mumm approach suggests that the more proper test for product difference would be a test that has a ”joint product and scaling effect” interpretation.

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