Purpose

Data Format

Background

The idea of preference mapping is to derive a common perceptual map of the products (see first chart below) and then to see how individual consumers fit on to that map (see second chart below). There are therefore two main aims of the mapping.  Firstly, the map can be used to show, in terms of their proximity on the map, how similar or dissimilar products are to each other.  Secondly, the locations where consumers fit onto to the map can be used to study the various patterns of liking that people have.  Often, groups of consumers will cluster together in different regions of the plot, and so reveal clusters each with their own pattern of liking.  This type of information can help product developers target different products to different groups of people.  In practice, the mapping is achieved by creating a PCA biplot on the product-by-consumer table of liking scores.  In the maps below calculated on the example data set, the majority of consumers have vectors that point to the right-hand side of the plot indicating there is a general liking for the bread products on the right-hand side of the plot, and a particular dislike of ‘Sliced Right’ and ‘Red Door’ on the left-hand side of the plot.  Some of the consumer vectors are pointing below the X-axis suggesting that they might also be satisfied by the three products ‘Real Break Co.’, ‘Seeds and Grains’ and ‘Golden Grain’.

Options

1. Type of PCA  – The PCA may be performed on either the correlation or covariance matrix.  Only choose the covariance matrix if all your supplementary variables have been measured on the same scale, and you wish to give more importance to variables that use the full range of the scale.
2. Use Sensory Attributes – if you have supplementary variables that you would like to be projected on to the preference map then select ‘Yes’, otherwise select ‘No’. 
   
3. Sensory Attributes – A list of variable names of all supplementary variables from the data file. Only active if you have chosen to use sensory attributes (see option above). 
   
4. Number of decimals for values – The number of decimals to show in all numeric output.

Results and Interpretation

1. Eigenvalues tab shows a table with eigenvalues and the percentage of variance associated with each preference dimension.  This can be used to interpret the relative importance of the preference dimensions, since a dimension that explains 30% of the variation in consumer liking is three times as important as a dimension that explains only 10% of the variation. 
   
2. Products tab show results relating to the observations or products in the PCA.
   
1. Coord shows the principal component scores on each dimension. 
   
2. Cos2 shows a table of squared cosines, the sum of the squared cosines in each row is 1, so they can be interpreted as the amount that each product is attributable to each dimension. 
   
3. Contrib shows a table of contributions, these sum to 100 for each dimension and therefore summarise the relative importance of products on each dimension. 
   
4. Graph shows a plot of the principal component scores on the first two dimensions.
   
3. Variables tab show results relating to the consumers or variables in the PCA. 
   
1. Coord shows the principal component loadings on each dimension.
   
2. Cor shows a table of correlation coefficients between each variable and each PC dimension. 
   
3. Cos2 shows a table of squared cosines, the sum of the squared cosines in each row is 1, so they can be interpreted as the amount that each consumer is attributable to each dimension. 
   
4. Contrib shows a table of contributions, these sum to 100 for each dimension and therefore summarise the relative importance of the consumers on each dimension. 
   
5. Graph shows a plot of the principal component loading on the first two dimensions. 
   
4. Attributes tab shows results relating to the supplementary variables in the PCA. 
   
1. Coord shows the projected principal component loadings on each dimension. 
   
2. Cor shows a table of correlation coefficients between each supplementary variable and each PC dimension. 
   
3. Cos2 shows a table of squared cosines, the sum of the squared cosines in each row is 1, so they can be interpreted as the amount that each supplementary variable is attributable to each dimension. 
   
4. Graph shows a plot of the projected principal component loadings of the supplementary variables on the first two dimensions. 
   
5. Biplot tab shows the main result of the analysis, which is the simultaneous plot of the rescaled product scores, consumer loadings, and supplementary variable loadings, on the first two dimensions.

Technical Information

1. The R package Factominer is used.

References

1. Lawless, H.T. and Heymann, H. (2010).  Sensory Evaluation of Food – Principles and Practices.  Springer. 
   
2. McEwan, J.A. (1996).  Preference Mapping for Product Optimization.  In Naes, T. and Risvik, E. (Eds).  Multivariate Analysis of Data in Sensory Science.