Multi-block analysis techniques

Multi-block analysis can address the limitation of the loss of individual data when single- block methods are used. Currently, in sensory science, multi-block analyses are mainly used to investigate the differences and similarities between the data obtained from (1) individual judges and (2) different sensory methodologies. In addition, it can be used to compare different panels (Bécue-Bertaut & Lê, 2011).

2.4.2.1 Multiple factor analysis (MFA) and multiple correspondence analysis

(MCA)

MFA consists of multiple PCA or CA analyses depending on the data types of the different data blocks also called data tables (Pagès, 2005; Nestrud & Lawless, 2008; Le Dien & Pagès, 2003; Ares, et al., 2010a, 2010b).

MFA can be used to analyse PM data. When PM data are analysed the coordinates of the products can be subjected to MFA (Escofier & Pagès, 1990) keeping the data for each judge separate as a different data table in the MFA analysis. The Euclidean distance configuration of the products for each judge is calculated simultaneously and a biplot containing the data from all the sensory judges is obtained with this procedure. PCA is thus performed on the coordinate data from each judge. The descriptor data are added as a

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separate data table that is frequently added as supplementary data and projected onto the MFA compromise map. In this case both the product positioning and the attributes used, to describe the positioning, are represented on a single graph or sensory map (Perrin et al., 2008).

Another less frequently used application for MFA is the analysis of PSP data as proposed by Telliet et al. (2010). MFA can provide a measure for similarity between different data sets that can be visualised by inspection of the partial projections map. This map can be used to visualise differences between sensory judges. In addition, data from different sensory methods can be analysed as different data tables to be compared. Dehlholm et al. (2012a) used MFA to compare different sensory methods to each other.

MCA is a restricted version of MFA where multiple CA analyses are conducted. To be historically correct it should be noted that MCA is an older technique than MFA and from that perspective MFA is an enriched MCA that uses both CA and PCA to analyse the separate data blocks. MCA was used in sensory research for the analysis of CATA (Varela & Ares, 2012), sorting (Cadoret et al., 2009) and PSP data (Ares et al., 2013).

2.4.2.2 Generalised procrustes analysis (GPA)

Until recently GPA (Gower, 1975) was a popular statistical analysis method used for the analysis of PM data (Risvik et al., 1994). When GPA is conducted the data is transformed by: (1) translation, where all the individual PM configurations, obtained from the different sensory judges, are moved to the middle of the PM sheet; (2) rotation and reflection to align the individual PM data sets and (3) isotopic scaling, where the individual data is stretched or shrank to obtain the best fit and reduce the individual differences.

MDS was compared to GPA for the analysis of PM data by King et al. (1998), even though it was concluded that higher dimensions could be investigated using MDS than GPA, MDS is not commonly used for analysing PM data

Tomic et al. (2015) found that MFA and GPA produced similar results for simulated data, but different results for “real data”, in a study where these two methods were compared when analysing PM. MFA can provide data with a higher dimensionality than GPA which is an advantage. Thus, MFA is the most popular technique for analysing PM data currently.

Kennedy et al. (2009) proposed procrustes multiple factor analysis (PMFA) a method where procrustes rotation is incorporated into the MFA analysis. This method is, however not commonly used. GPA can also be used to analyse FP data by performing PCA for each individual judges’ data which is then subjected to translation, rotation and isotopic scaling while integrating the different data sets to obtain a single multivariate map (Gower, 1975 ; Moussaoui & Varela, 2010).

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2.4.2.3 INDSCAL

INDSCAL is a multi-block generalisation of MDS applied to the individual sensory judges’

distance matrices. The weighted Euclidean model is used to transform the product coordinates into distances (Bárcenas et al., 2004; Nestrud & Lawless, 2011).

In a recent study Næs et al. (2017) compared INDSCAL and MFA when analysing PM data. It was found that, even though MFA is based on coordinate data and INDSCAL on distance data similar results were obtained. MFA, however, performed slightly better as a consensus indicator, explaining how well judges agreed in terms of sensory perception of the products.

2.4.2.4 DISTATIS

DISTATIS (Abdi et al., 2007) was proposed as a generalised MDS-based method to address the fact that individual differences between judges are not taken into account when MDS is performed. When DISTATIS is performed the individual distance matrix of each judge is transformed into a cross-product matrix which is normalised. The individual matrices are combined prior to eigenvalue decomposition producing a DISTATIS compromise cross- product matrix. The DISTATIS compromise map is used to visualise the similarities between the products. The attributes used to describe the groups made by the sensory judges are projected onto the DISTATIS compromise map as supplementary variable not playing a role in the product configuration. DISTATIS is currently the most popular statistical analysis technique used for analysing sorting data (Abdi et al., 2007).

2.4.2.5 Less frequently used methods

The FAST method was proposed by Cadoret et al. (2009) to optimally represent all sensory judges, using MFA, and samples, using MCA, when the multivariate sensory map is constructed (Cadoret et al. 2009). SORT CC was proposed by Qannari et al. 2009 as another multi-block technique for the analysis of sorting data where individual data are taken into account. Hierarchical multiple factor analysis (HMFA) was used by Bécue-Bertaut and Lê (2011) to analyse and compare sorting data generated by more than one panel. FAST, SORT CC and HMFA is not currently frequently used although the ideas behind the development of these techniques are scientifically justified. These methods might be used more frequently in future.

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