Individual differences in replicated multi-product experiments with Thurstonian mixed models for binary paired comparison data

Abstract

Often sensory discrimination tests are performed with replications for the assessors. In this paper, we suggest a new way of analyzing data from a discrimination study. The model suggested in this paper is a Thurstonian mixed model, in which the variation from the assessors is modelled as a random effect in a generalized linear mixed model. The setting is a multi-product discrimination study with a binary paired comparison. This model makes it possible to embed the analyses of products into one analysis rather than having to do an analysis for each product separately. In addition, it is possible to embed the model into the Thurstonian framework obtaining d-prime interpretations of the estimates. Furthermore, it is possible to extract information about the assessors, even across the products. More specifically, assessor specific d-prime estimates are obtained providing a way to get information about the panel. These estimates are interesting because they make it possible to investigate if the assessors are assessing in a specific way.

Principal component analysis of d-prime values from sensory discrimination tests using binary paired comparisons

“…The psychometric function in (1) is used by many authors (e.g. Linander et al (2019) and Brockhoff & Christensen (2010)) but derived in earlier work by Ennis (1993) and dating all the way back to Thurstone's pioneering work (Thurstone, 1927). The d-prime values found by (1) are the so-called raw d-prime values that are used in the PCA.…”

“…In this section, we describe an existing discrimination study that we use as an example in the remainder of this paper. This study is the same discrimination study as is used in Linander et al (2019). We briefly explain the structure of the discrimination study and refer the reader to Linander et al (2019) for further details.…”

“…In this section, we describe the Thurstonian mixed model (Linander et al, 2019) that we use to find the d-prime values for the PCA. The Thurstonian mixed model analyzes data for one sensory attribute at a time.…”

“…One approach is to do an analysis for one attribute at a time (e.g. Linander et al (2019)). For other types of sensory data, e.g.…”

“…We will consider two approaches; one analyzing the raw d-prime values, transforming data by the inverse of the psychometric function, and one where the d-prime values are obtained from analyzing data by a model. More specifically, Linander et al (2019) introduced a Thurstonian mixed model for binary paired comparison data. This model can be used to analyze multiple sensory attributes one at a time.…”