lib/statsample/dominanceanalysis/bootstrap.rb
module Statsample
class DominanceAnalysis
# == Goal
# Generates Bootstrap sample to identity the replicability of a Dominance Analysis. See Azen & Bodescu (2003) for more information.
#
# == Usage
#
# require 'statsample'
# a = Daru::Vector.new(100.times.collect {rand})
# b = Daru::Vector.new(100.times.collect {rand})
# c = Daru::Vector.new(100.times.collect {rand})
# d = Daru::Vector.new(100.times.collect {rand})
# ds = Daru::DataFrame.new({:a => a,:b => b,:c => c,:d => d})
# ds[:y] = ds.collect_rows { |row| row[:a]*5+row[:b]*2+row[:c]*2+row[:d]*2+10*rand() }
# dab=Statsample::DominanceAnalysis::Bootstrap.new(ds, :y, :debug=>true)
# dab.bootstrap(100,nil)
# puts dab.summary
# <strong>Output</strong>
# Sample size: 100
# t: 1.98421693632958
#
# Linear Regression Engine: Statsample::Regression::Multiple::MatrixEngine
# Table: Bootstrap report
# --------------------------------------------------------------------------------------------
# | pairs | sD | Dij | SE(Dij) | Pij | Pji | Pno | Reproducibility |
# --------------------------------------------------------------------------------------------
# | Complete dominance |
# --------------------------------------------------------------------------------------------
# | a - b | 1.0 | 0.6150 | 0.454 | 0.550 | 0.320 | 0.130 | 0.550 |
# | a - c | 1.0 | 0.9550 | 0.175 | 0.930 | 0.020 | 0.050 | 0.930 |
# | a - d | 1.0 | 0.9750 | 0.131 | 0.960 | 0.010 | 0.030 | 0.960 |
# | b - c | 1.0 | 0.8800 | 0.276 | 0.820 | 0.060 | 0.120 | 0.820 |
# | b - d | 1.0 | 0.9250 | 0.193 | 0.860 | 0.010 | 0.130 | 0.860 |
# | c - d | 0.5 | 0.5950 | 0.346 | 0.350 | 0.160 | 0.490 | 0.490 |
# --------------------------------------------------------------------------------------------
# | Conditional dominance |
# --------------------------------------------------------------------------------------------
# | a - b | 1.0 | 0.6300 | 0.458 | 0.580 | 0.320 | 0.100 | 0.580 |
# | a - c | 1.0 | 0.9700 | 0.156 | 0.960 | 0.020 | 0.020 | 0.960 |
# | a - d | 1.0 | 0.9800 | 0.121 | 0.970 | 0.010 | 0.020 | 0.970 |
# | b - c | 1.0 | 0.8850 | 0.283 | 0.840 | 0.070 | 0.090 | 0.840 |
# | b - d | 1.0 | 0.9500 | 0.181 | 0.920 | 0.020 | 0.060 | 0.920 |
# | c - d | 0.5 | 0.5800 | 0.360 | 0.350 | 0.190 | 0.460 | 0.460 |
# --------------------------------------------------------------------------------------------
# | General Dominance |
# --------------------------------------------------------------------------------------------
# | a - b | 1.0 | 0.6500 | 0.479 | 0.650 | 0.350 | 0.000 | 0.650 |
# | a - c | 1.0 | 0.9800 | 0.141 | 0.980 | 0.020 | 0.000 | 0.980 |
# | a - d | 1.0 | 0.9900 | 0.100 | 0.990 | 0.010 | 0.000 | 0.990 |
# | b - c | 1.0 | 0.9000 | 0.302 | 0.900 | 0.100 | 0.000 | 0.900 |
# | b - d | 1.0 | 0.9700 | 0.171 | 0.970 | 0.030 | 0.000 | 0.970 |
# | c - d | 1.0 | 0.5600 | 0.499 | 0.560 | 0.440 | 0.000 | 0.560 |
# --------------------------------------------------------------------------------------------
#
# Table: General averages
# ---------------------------------------
# | var | mean | se | p.5 | p.95 |
# ---------------------------------------
# | a | 0.133 | 0.049 | 0.062 | 0.218 |
# | b | 0.106 | 0.048 | 0.029 | 0.199 |
# | c | 0.035 | 0.032 | 0.002 | 0.106 |
# | d | 0.023 | 0.019 | 0.002 | 0.062 |
# ---------------------------------------
#
# == References:
# * Azen, R. & Budescu, D.V. (2003). The dominance analysis approach for comparing predictors in multiple regression. <em>Psychological Methods, 8</em>(2), 129-148.
class Bootstrap
include Writable
include Summarizable
# Total Dominance results
attr_reader :samples_td
# Conditional Dominance results
attr_reader :samples_cd
# General Dominance results
attr_reader :samples_gd
# General average results
attr_reader :samples_ga
# Name of fields
attr_reader :fields
# Regression class used for analysis
attr_accessor :regression_class
# Dataset
attr_accessor :ds
# Name of analysis
attr_accessor :name
# Alpha level of confidence. Default: ALPHA
attr_accessor :alpha
# Debug?
attr_accessor :debug
# Default level of confidence for t calculation
ALPHA=0.95
# Create a new Dominance Analysis Bootstrap Object
#
# * ds: A Daru::DataFrame object
# * y_var: Name of dependent variable
# * opts: Any other attribute of the class
def initialize(ds,y_var, opts=Hash.new)
@ds = ds
@y_var = y_var.respond_to?(:to_sym) ? y_var.to_sym : y_var
@n = ds.nrows
@n_samples=0
@alpha=ALPHA
@debug=false
if y_var.is_a? Array
@fields=ds.vectors.to_a - y_var
@regression_class=Regression::Multiple::MultipleDependent
else
@fields=ds.vectors.to_a - [y_var]
@regression_class=Regression::Multiple::MatrixEngine
end
@samples_ga=@fields.inject({}) { |a,v| a[v]=[]; a }
@name=_("Bootstrap dominance Analysis: %s over %s") % [ ds.vectors.to_a.join(",") , @y_var]
opts.each{|k,v|
self.send("#{k}=",v) if self.respond_to? k
}
create_samples_pairs
end
# lr_class deprecated
alias_method :lr_class, :regression_class
def da
if @da.nil?
@da=DominanceAnalysis.new(@ds,@y_var, :regression_class => @regression_class)
end
@da
end
# Creates n re-samples from original dataset and store result of
# each sample on @samples_td, @samples_cd, @samples_gd, @samples_ga
#
# * number_samples: Number of new samples to add
# * n: size of each new sample. If nil, equal to original sample size
def bootstrap(number_samples,n=nil)
number_samples.times{ |t|
@n_samples+=1
puts _("Bootstrap %d of %d") % [t+1, number_samples] if @debug
ds_boot=@ds.bootstrap(n)
da_1=DominanceAnalysis.new(ds_boot, @y_var, :regression_class => @regression_class)
da_1.total_dominance.each{|k,v|
@samples_td[k].push(v)
}
da_1.conditional_dominance.each{|k,v|
@samples_cd[k].push(v)
}
da_1.general_dominance.each{|k,v|
@samples_gd[k].push(v)
}
da_1.general_averages.each{|k,v|
@samples_ga[k].push(v)
}
}
end
def create_samples_pairs
@samples_td={}
@samples_cd={}
@samples_gd={}
@pairs=[]
c=(0...@fields.size).to_a.combination(2)
c.each do |data|
p data
convert=data.collect {|i| @fields[i] }
@pairs.push(convert)
[@samples_td, @samples_cd, @samples_gd].each{|s|
s[convert]=[]
}
end
end
def t
Distribution::T.p_value(1-((1-@alpha) / 2), @n_samples - 1)
end
def report_building(builder) # :nodoc:
raise "You should bootstrap first" if @n_samples==0
builder.section(:name=>@name) do |generator|
generator.text _("Sample size: %d\n") % @n_samples
generator.text "t: #{t}\n"
generator.text _("Linear Regression Engine: %s") % @regression_class.name
table=ReportBuilder::Table.new(:name=>"Bootstrap report", :header => [_("pairs"), "sD","Dij", _("SE(Dij)"), "Pij", "Pji", "Pno", _("Reproducibility")])
table.row([_("Complete dominance"),"","","","","","",""])
table.hr
@pairs.each{|pair|
std=Daru::Vector.new(@samples_td[pair])
ttd=da.total_dominance_pairwise(pair[0],pair[1])
table.row(summary_pairs(pair,std,ttd))
}
table.hr
table.row([_("Conditional dominance"),"","","","","","",""])
table.hr
@pairs.each{|pair|
std=Daru::Vector.new(@samples_cd[pair])
ttd=da.conditional_dominance_pairwise(pair[0],pair[1])
table.row(summary_pairs(pair,std,ttd))
}
table.hr
table.row([_("General Dominance"),"","","","","","",""])
table.hr
@pairs.each{|pair|
std=Daru::Vector.new(@samples_gd[pair])
ttd=da.general_dominance_pairwise(pair[0],pair[1])
table.row(summary_pairs(pair,std,ttd))
}
generator.parse_element(table)
table=ReportBuilder::Table.new(:name=>_("General averages"), :header=>[_("var"), _("mean"), _("se"), _("p.5"), _("p.95")])
@fields.each{|f|
v=Daru::Vector.new(@samples_ga[f])
row=[@ds[f].name, sprintf("%0.3f",v.mean), sprintf("%0.3f",v.sd), sprintf("%0.3f",v.percentil(5)),sprintf("%0.3f",v.percentil(95))]
table.row(row)
}
generator.parse_element(table)
end
end
def summary_pairs(pair,std,ttd)
freqs=std.proportions
[0, 0.5, 1].each{|n|
freqs[n]=0 if freqs[n].nil?
}
name="%s - %s" % [@ds[pair[0]].name, @ds[pair[1]].name]
[name,f(ttd,1),f(std.mean,4),f(std.sd),f(freqs[1]), f(freqs[0]), f(freqs[0.5]), f(freqs[ttd])]
end
def f(v,n=3)
prec="%0.#{n}f"
sprintf(prec,v)
end
end
end
end