Statistical Word of the Week

Jul 23, 2013

Week #30 - Discriminant analysis

Discriminant analysis is a method of distinguishing between classes of objects.  The objects are typically represented as rows in a matrix.

The  values of various attributes (variables) of an object are measured (the matrix columns) and a linear classification function is developed that maximizes the ratio of between-class variability to within-class variability.  The function measures statistical distance between an observation and each class, and is used to assign a classification to each object..

For example, a rule is desired to distinguish between responders and non-responders to a particular medication for multiple sclerosis. The medication has potentially harmful side effects, so it is desirable to discontinue its use in non-responders (while not removing responders from the medication). We could measure:

  • # of brain lesions in the past month
  • Average brain lesions per month since medication started
  • Average brain lesions per month before medication started
  • Average number of seizures per month since medication started
  • Average number of seizures per month before medication started

Discriminant analysis seeks to establish a rule that accurately divides patients into responders and non-responders based on the above variables. Typically, the rule will be established using a portion of the data (the training data) and tested on another portion of the data.

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