Discriminant analysis





Discriminant analysis is a statistical technique used in marketing and the
social sciences. It is applicable when there is only one dependent variable
but multiple independent variables (similar to ANOVA and regression). But
unlike ANOVA and regression analysis, the dependent variable must be
categorical. It is similar to factor analysis in that both look for
underlying dimensions in responses given to questions about product
attributes. But it differs from factor analysis in that it builds these
underlying dimensions based on differences rather than similarities.
Discriminant analysis is also different from factor analysis in that it is
not an interdependence technique : a distinction between independent
variables and dependent variables ( also called criterion variables) must be made.

Discriminant Analysis Involves:

  1. Formulate the problem and gather data - Identify the salient attributes
     consumers use to evaluate products in this category - Use quantitative
     marketing research techniques (such as surveys) to collect data from a
     sample of potential customers concerning their ratings of all the
     product attributes. The data collection stage is usually done by
     marketing research professionals. Survey questions ask the respondent
     to rate a product from one to five (or 1 to 7, or 1 to 10) on a range
     of attributes chosen by the researcher. Anywhere from five to twenty
     attributes are chosen. They could include things like: ease of use,
     weight, accuracy, durability, colourfulness, price, or size. The
     attributes chosen will vary depending on the product being studied. The
     same question is asked about all the products in the study. The data
     for multiple products is codified and input into a statistical program
     such as SPSS or SAS. (This step is the same as in Factor analysis).
  2. Estimate the Discriminant Function Coefficients and determine the
     statistical significance and validity - Choose the appropriate
     discimininant analysis method. The direct method involves estimating
     the discriminant function so that all the predictors are assessed
     simultaneously. The stepwise method enters the predictors sequentially.
     The two-group method should be used when the dependant variable has two
     categories or states. The multiple discriminant method is used when the
     dependent variable has three or more categorical states. Use WilksÕs
     Lambda to test for significance in SPSS or F stat in SAS. The most
     common method used to test validity is to split the sample into an
     estimation or analysis sample, and a validation or holdout sample. The
     estimation sample is used in constructing the discriminant function.
     The validation sample is used to construct a classification matrix
     which contains the number of correctly classified and incorrectly
     classified cases. The percentage of correctly classified cases is
     called the hit ratio.
  3. Plot the results on a two dimensional map, define the dimensions, and
     interpret the results. The statistical program (or a related module)
     will map the results. The map will plot each product (usually in two
     dimensional space). The distance of products to each other indicate
     either how different they are. The dimensions must be labelled by the
     researcher. This requires subjective judgement and is often very
     challenging.