Multiway data analysis: Difference between revisions

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== Composition of multiway data analysis ==

===Multiway data array===

Multiway data analysts use the term ''way'' to refer to a "dimension" of the data while reserving the word ''mode'' for the methods or models used to analyze the data.<ref name=Kroonenberg2008/>{{rp|xviii}}.

In this sense, we can define the various ''ways'' of data to analyze:

* ''One-way data array'' iswith a''N'' entried (dimensions) stores an ''N''-dimensional [[Vector (mathematics and physics)|vector]], with a single data value for each discrete or continuous value of the single dimension.

* ''Two-way data array'' isstores a grid of data, a "data [[matrix (mathematics)|matrix]], with a single data value for each discrete or continuous value of two separate dimensions"; a [[spreadsheet]] can be used to visualize such data in the case of discrete dimensions.

* ''Three-way data array'' can be viewed asstores a stackcube of matrices (or similarly, as a workbook of multiple [[spreadsheet]]s), adding a third dimensiondata. Such data might represent the temperature at different locations (two-way data) sampled over different times (the third dimension, leading to three-way data)

* ''Four-way data array'', using the same spreadsheet analogy, can be represented as a file folder full of separate workbooks.

* ''Five-way data array'' and ''six-way data'' can be represented by similarly higher levels of data aggregation.

In general, thea several dimensions represented in themultway data setarray may be measured at different times, or in different places, using different methodologies, and may contain inconsistencies such as missing data or discrepancies in data representation.

===Multiway model===