Module: Statsample::Factor

Defined in:
lib/statsample/factor.rb,
lib/statsample/factor/map.rb,
lib/statsample/factor/pca.rb,
lib/statsample/factor/rotation.rb,
lib/statsample/factor/principalaxis.rb,
lib/statsample/factor/parallelanalysis.rb

Overview

Factor Analysis toolbox.

  • Classes for Extraction of factors:

    • Statsample::Factor::PCA

    • Statsample::Factor::PrincipalAxis

  • Classes for Rotation of factors:

    • Statsample::Factor::Varimax

    • Statsample::Factor::Equimax

    • Statsample::Factor::Quartimax

  • Classes for determining the number of components

    • Statsample::Factor::MAP

    • Statsample::Factor::ParallelAnalysis

About number of components, O’Connor(2000) said:

The two procedures [PA and MAP ] complement each other nicely,
in that the MAP tends to err (when it does err) in the direction
of underextraction, whereas parallel analysis tends to err
(when it does err) in the direction of overextraction.
Optimal decisions are thus likely to be made after considering
the results of both analytic procedures. (p.10)

Defined Under Namespace

Classes: Equimax, MAP, PCA, ParallelAnalysis, PrincipalAxis, Quartimax, Rotation, Varimax

Class Method Summary collapse

Class Method Details

.anti_image_correlation_matrix(matrix) ⇒ Object 



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# File 'lib/statsample/factor.rb', line 43

def self.anti_image_correlation_matrix(matrix)
  matrix=matrix.to_matrix
  s=Matrix.diagonal(*(matrix.inverse.diagonal)).sqrt.inverse
  aicm=s*matrix.inverse*s
  
  aicm.extend(Statsample::CovariateMatrix)
  aicm.fields=matrix.fields if matrix.respond_to? :fields
  aicm
end

.anti_image_covariance_matrix(matrix) ⇒ Object

Anti-image covariance matrix. Useful for inspection of desireability of data for factor analysis. According to Dziuban & Shirkey (1974, p.359): 

"If this matrix does not exhibit many zero off-diagonal elements,
the investigator has evidence that the correlation
matrix is not appropriate for factor analysis."



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# File 'lib/statsample/factor.rb', line 36

def self.anti_image_covariance_matrix(matrix)
  s2=Matrix.diagonal(*(matrix.inverse.diagonal)).inverse
  aicm=(s2)*matrix.inverse*(s2)
  aicm.extend(Statsample::CovariateMatrix)
  aicm.fields=matrix.fields if matrix.respond_to? :fields
  aicm
end

.kmo(matrix) ⇒ Object

Kaiser-Meyer-Olkin measure of sampling adequacy for correlation matrix.

Kaiser’s (1974, cited on Dziuban & Shirkey, 1974) present calibration of the index is as follows :

  • .90s—marvelous

  • .80s— meritorious

  • .70s—middling

  • .60s—mediocre

  • .50s—miserable

  • .50 •—unacceptable



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# File 'lib/statsample/factor.rb', line 62

def self.kmo(matrix)
  q=anti_image_correlation_matrix(matrix)
  n=matrix.row_size
  sum_r,sum_q=0,0
  n.times do |j|
    n.times do |k|
      if j!=k
        sum_r+=matrix[j,k]**2
        sum_q+=q[j,k]**2
      end
    end
  end
  sum_r.quo(sum_r+sum_q)
end

.kmo_univariate(matrix, var) ⇒ Object

Kaiser-Meyer-Olkin measure of sampling adequacy for one variable.



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# File 'lib/statsample/factor.rb', line 78

def self.kmo_univariate(matrix, var)
  if var.is_a? String
    if matrix.respond_to? :fields
      j=matrix.fields.index(var)
      raise "Matrix doesn't have field #{var}" if j.nil?
    else
      raise "Matrix doesn't respond to fields"
    end
  else
    j=var
  end
  
  q=anti_image_correlation_matrix(matrix)
  n=matrix.row_size
  
  sum_r,sum_q=0,0
  
  n.times do |k|
    if j!=k
      sum_r+=matrix[j,k]**2
      sum_q+=q[j,k]**2
    end
  end
  sum_r.quo(sum_r+sum_q)
end