The Mixed Assessor Model and the multiplicative mixed model

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.