lib/statsample/factor/parallelanalysis.rb
module Statsample
module Factor
# Performs Horn's 'parallel analysis' to a principal components analysis
# to adjust for sample bias in the retention of components.
# Can create the bootstrap samples using random data, using number
# of cases and variables, parameters for actual data (mean and standard
# deviation of each variable) or bootstrap sampling for actual data.
# == Description
# "PA involves the construction of a number of correlation matrices of random variables based on the same sample size and number of variables in the real data set. The average eigenvalues from the random correlation matrices are then compared to the eigenvalues from the real data correlation matrix, such that the first observed eigenvalue is compared to the first random eigenvalue, the second observed eigenvalue is compared to the second random eigenvalue, and so on." (Hayton, Allen & Scarpello, 2004, p.194)
# == Usage
# *With real dataset*
# # ds should be any valid dataset
# pa=Statsample::Factor::ParallelAnalysis.new(ds, :iterations=>100, :bootstrap_method=>:data)
#
# *With number of cases and variables*
# pa=Statsample::Factor::ParallelAnalysis.with_random_data(100,8)
#
# == Reference
# * Hayton, J., Allen, D. & Scarpello, V.(2004). Factor Retention Decisions in Exploratory Factor Analysis: a Tutorial on Parallel Analysis. <i>Organizational Research Methods, 7</i> (2), 191-205.
# * O'Connor, B. (2000). SPSS and SAS programs for determining the number of components using parallel analysis and Velicer's MAP test. Behavior Research Methods, Instruments, & Computers, 32(3), 396-402.
# * Liu, O., & Rijmen, F. (2008). A modified procedure for parallel analysis of ordered categorical data. Behavior Research Methods, 40(2), 556-562.
class ParallelAnalysis
def self.with_random_data(cases,vars,opts=Hash.new)
ds= Daru::DataFrame.new({},
order: vars.times.map {|i| "v#{i+1}".to_sym},
index: cases )
opts=opts.merge({:bootstrap_method=> :random, :no_data=>true})
new(ds, opts)
end
include DirtyMemoize
include Summarizable
# Number of random sets to produce. 50 by default
attr_accessor :iterations
# Name of analysis
attr_accessor :name
# Dataset. You could use mock vectors when use bootstrap method
attr_reader :ds
# Bootstrap method. <tt>:random</tt> used by default
# * <tt>:random</tt>: uses number of variables and cases for the dataset
# * <tt>:data</tt> : sample with replacement from actual data.
attr_accessor :bootstrap_method
# Uses smc on diagonal of matrixes, to perform simulation
# of a Principal Axis analysis.
# By default, false.
attr_accessor :smc
# Percentil over bootstrap eigenvalue should be accepted. 95 by default
attr_accessor :percentil
# Correlation matrix used with :raw_data . <tt>:correlation_matrix</tt> used by default
attr_accessor :matrix_method
# Number of eigenvalues to calculate. Should be set for
# Principal Axis Analysis.
attr_accessor :n_variables
# Dataset with bootstrapped eigenvalues
attr_reader :ds_eigenvalues
# Perform analysis without actual data.
attr_accessor :no_data
# Show extra information if true
attr_accessor :debug
attr_accessor :use_gsl
def initialize(ds, opts=Hash.new)
@ds=ds
@fields=@ds.vectors.to_a
@n_variables=@fields.size
@n_cases=ds.nrows
opts_default={
:name=>_("Parallel Analysis"),
:iterations=>50, # See Liu and Rijmen (2008)
:bootstrap_method => :random,
:smc=>false,
:percentil=>95,
:debug=>false,
:no_data=>false,
:matrix_method=>:correlation_matrix
}
@use_gsl=Statsample.has_gsl?
@opts=opts_default.merge(opts)
@opts[:matrix_method]==:correlation_matrix if @opts[:bootstrap_method]==:parameters
opts_default.keys.each {|k| send("#{k}=", @opts[k]) }
end
# Number of factor to retent
def number_of_factors
total=0
ds_eigenvalues.vectors.to_a.each_with_index do |f,i|
if (@original[i]>0 and @original[i]>ds_eigenvalues[f].percentil(percentil))
total+=1
else
break
end
end
total
end
def report_building(g) #:nodoc:
g.section(:name=>@name) do |s|
s.text _("Bootstrap Method: %s") % bootstrap_method
s.text _("Uses SMC: %s") % (smc ? _("Yes") : _("No"))
s.text _("Correlation Matrix type : %s") % matrix_method
s.text _("Number of variables: %d") % @n_variables
s.text _("Number of cases: %d") % @n_cases
s.text _("Number of iterations: %d") % @iterations
if @no_data
s.table(:name=>_("Eigenvalues"), :header=>[_("n"), _("generated eigenvalue"), "p.#{percentil}"]) do |t|
ds_eigenvalues.vectors.to_a.each_with_index do |f,i|
v=ds_eigenvalues[f]
t.row [i+1, "%0.4f" % v.mean, "%0.4f" % v.percentil(percentil), ]
end
end
else
s.text _("Number or factors to preserve: %d") % number_of_factors
s.table(:name=>_("Eigenvalues"), :header=>[_("n"), _("data eigenvalue"), _("generated eigenvalue"),"p.#{percentil}",_("preserve?")]) do |t|
ds_eigenvalues.vectors.to_a.each_with_index do |f,i|
v=ds_eigenvalues[f]
t.row [i+1, "%0.4f" % @original[i], "%0.4f" % v.mean, "%0.4f" % v.percentil(percentil), (v.percentil(percentil)>0 and @original[i] > v.percentil(percentil)) ? "Yes":""]
end
end
end
end
end
# Perform calculation. Shouldn't be called directly for the user
def compute
@original=Statsample::Bivariate.send(matrix_method, @ds).eigenvalues unless no_data
@ds_eigenvalues=Daru::DataFrame.new({}, order: (1..@n_variables).map{|v| ("ev_%05d" % v).to_sym})
if bootstrap_method==:parameter or bootstrap_method==:random
rng = Distribution::Normal.rng
end
@iterations.times do |i|
begin
puts "#{@name}: Iteration #{i}" if $DEBUG or debug
# Create a dataset of dummy values
ds_bootstrap = Daru::DataFrame.new({}, order: @ds.vectors, index: @n_cases)
@fields.each do |f|
if bootstrap_method==:random
ds_bootstrap[f] = Daru::Vector.new(@n_cases.times.map {|c| rng.call})
elsif bootstrap_method==:data
ds_bootstrap[f] = ds[f].sample_with_replacement(@n_cases)
else
raise "bootstrap_method doesn't recogniced"
end
end
matrix=Statsample::Bivariate.send(matrix_method, ds_bootstrap)
matrix=matrix.to_gsl if @use_gsl
if smc
smc_v=matrix.inverse.diagonal.map{|ii| 1-(1.quo(ii))}
smc_v.each_with_index do |v,ii|
matrix[ii,ii]=v
end
end
ev=matrix.eigenvalues
@ds_eigenvalues.add_row(ev)
rescue Statsample::Bivariate::Tetrachoric::RequerimentNotMeet => e
puts "Error: #{e}" if $DEBUG
redo
end
end
end
dirty_memoize :number_of_factors, :ds_eigenvalues
dirty_writer :iterations, :bootstrap_method, :percentil, :smc
end
end
end