Discriminant Analysis

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Discriminant Analysis

1. Introduction
2. Types of DA
3. Assumptions
4. Model representation, data type/sample size
5. Measurements
6. Steps to solve DA problems
7. An numerical example
8. SPSS commands

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Discriminant Analysis

• is a powerful statistical tool used to study the
  differences between groups of objects
• Here, objects could be
• an individual person or firms, and
• classifying them can be based on prior or
  posterior factors or characteristics

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Types of DA

• Two groups
• refer to as two-group discriminant analysis
• Its dependent variable is termed as dichotomous

• Three or more group
• Refer to as multiple discriminant analysis (MDA)
• Its corresponding dependent variables are termed
  as multichotomous

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Assumptions

• 1) multivariate normality,
• uses the normal probability plot approach
• uses the most common statistical tests are the
  calculation of skewness value
• 2) equal covariance matrices
• Use covariance to check their corelations

• 3) multicollinearity, among independent variables
  
• That is to check independent variables are not
  correlated to each other
• 4) Outliers
• "the observations with a unique combination of
  characteristics identifiable as distinctly
  different from the other observations".

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Model representation
Data type Dependent variables non-metric
format Indep variables metric format Sample
size between 5-20 obs for each independent
variables
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Measurements

• Group categorizations
• Hit ratio
• Discriminating power

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Group categorizations
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Hit ratio

• Used to measure the model fitness
• Is a maximum chance criteria

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Note We need to compute this value for our
original sample size and then compare to
the value that produced by the SPSS and computer
value should not be less than the formal
value in order to claim the significant of
fitness of model
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Discriminating power
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References refer to hit ratio for details
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Steps to solve DA problems

• Step 1 Assess the assumptions
• Step 2 Estimate the discriminant function(s)
• and its (their) significance
• Step 3 Assess the overall fit

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Example
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You can obtain this paper by clicking
Discriminant paper from my web site
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• Objective
• To discriminate the difference practices between
  the high and low performance of firms practicing
  TQM is ISF
• Use score of overall satisfaction as a mean for
  discriminating factor
• Steps
• Step 1, refer to p 762
• Step 2, refer to p763
• Step 3, refer to p763
• Discussion, you can refer to the discussion
  section

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Step 1, refer to p 762
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Step 2, refer to p763
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Step 3, refer to p763
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SPSS commands
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SPSS Windows
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SPSS windows

• Steps to compute Discriminant Analysis
• Step 0
• Prior the study of analysis, we need to firstly
  define a new variable as follows
• - Define group and assign a value of either
  0, 1, 2 to them, as 0 as neural
• Step 1
• Select Analyze
• Select Classify
• Select Discriminant
• click group variable
• and select group variable as above
• click define range
• state its max and min ranges
• (this range same as min1, and max2 for above
  case)
• click Independent
• select variables
• that a group of factors that wish to be
  clustering
• Click option use stepwise method
• select Statistics

Learn from iconic base Pls refer to my website