Perceptual maps can be a useful way to concisely visualize associations among multiple variables. Protobi can create a perceptual map based on principal components analysis for many types of crosstabs.

Algorithm

The algorithm uses principal components analysis to project the columns as axes onto a two dimensional chart, and plot the row values with a minimum of disortion.

Principal components attempts to preserve the absolute not just the relative values. For instance an attribute where brands are all rated equally highly will be considered quite different from an attribute where brands are all rated equally poorly.

Protobi automatically rotates the axes of the axes to your preferred orientation, shows the exact details in a tooltip when you hover, and draws the projection lines.

Applicability

Perceptual Maps can be calculated for crosstabs where the rows are defined by an individual categorical variable, or by a compact group of variables summarized by their mean or top-box percentages.

Here the perceptual map is created for this crosstab

To specify a Perceptual Map for a crosstab, select “More properties…” from the context menu and under “Chart Type” choose “PMap”.

Chart options

Some customization may be useful, for instance:

  • setting filters to exclude columns with small N sizes
  • exclude certain rows with outlier values, like “Other (specify)”

Under the JSON, you can select additional options:

  • rotateAxis: (default 0) Specify which axis to rotate the graph. 0 is the first column, 1 is the second, etc.
  • rotateAngle: (default 0) Specify angle the axis should be rotated, in degrees. 0 is horizontal to the right, 90 is one quarter turn counterclockwise.
  • flip: (default false) Whether to flip chart into mirror image.

  • showLabels: (default `true’) Whether to show labels next to points

  • showLegend: (default `true’) Whether to to show the legend
  • legendWidth: (default `200’) Width of legend

Reference

See J. Gowert, P. Groenen, M. Van de Velden (2010) “Perceptual maps: the good, the bad and the ugly”, Erasmus School of Economics, Erasmus University, Rotteradam. John Gower (http://statistics.open.ac.uk/802576CB00593013/(httpInfoFiles)/F8DD66935DE1C1218025778900364290/$file/perceptual5.pdf)

Beta availability

Perceptual maps are currently available to clients on request.