Multivariate statistical methods

1
Multivariate statistical methods

• Composite indicators

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Selected types of composite indicators

• Construction techniques
• Aggregation
• Principal components

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Aggregation

• Threshold level
• definition of 1 of more thresholds level
• variables higher than threshold get 1, variables
  lower than threshold -1,
• in model of 2 threshold values which are
  between thresholds get 0
• general can be chosen 2 thresholds upper and
  lower quantile (75 , 25 )
• final composite indicator is made as sum of
  partly values (1 -1 0)

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Aggregation

• based on Standardized scores
• computed by formula (xX)/s,
• where x original value
• X... average of original value
• s standard deviation
• composite indicator is computed as average of
  standardized scores

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Aggregation

• Modified scores
• computed by relation (xX)/s,
• where x original value
• X... min. or max. value of
  original value
• s range of the variable
• composite indicator is calculated as average of
  scores

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Aggregation

• Bennets method
• used for international comparison
• for each variable is found object which has max
  (min) value (if positive max, GDP if negative
  min, unemployment)
• chosen varible get 1000 points
• other objects get from 0 to 1000 points according
  their per mille of max if positive or inverse
  value of per mille of min if negative
• composite indicator is average of scores

7
Principal components

• CI is based on results of PCA
• weighted method, weights are recounted corr coefs
  of each variable and selected component
• i is number of variables in model
• j is number of objects in model
• xij is values of i variable and of j object
• w is weight of i variable counted by PCA
• m is number of objects