class Statsample::Bivariate::Polychoric::Processor

Provides statistics for a given combination of rho, alpha and beta and contingence table.

Constants

EPSILON

Attributes

alpha[R]
beta[R]
matrix[R]
rho[R]

Public Class Methods

new(alpha,beta,rho,matrix=nil) click to toggle source
# File lib/statsample/bivariate/polychoric/processor.rb, line 8
def initialize(alpha,beta,rho,matrix=nil)
  @alpha=alpha
  @beta=beta
  @matrix=matrix
  @nr=@alpha.size+1
  @nc=@beta.size+1
  @rho=rho
  @pd=nil
end

Public Instance Methods

a(i) click to toggle source
# File lib/statsample/bivariate/polychoric/processor.rb, line 37
def a(i)
  raise "Index #{i} should be <= #{@nr-1}" if i>@nr-1
  i < 0 ? -100 : (i==@nr-1 ? 100 : alpha[i])
end
b(j) click to toggle source
# File lib/statsample/bivariate/polychoric/processor.rb, line 41
def b(j)
  raise "Index #{j} should be <= #{@nc-1}" if j>@nc-1
  j < 0 ? -100 : (j==@nc-1 ? 100 : beta[j])
end
bipdf(i,j) click to toggle source
# File lib/statsample/bivariate/polychoric/processor.rb, line 18
def bipdf(i,j)
   Distribution::BivariateNormal.pdf(a(i), b(j), rho)
end
eq12(u,v) click to toggle source
# File lib/statsample/bivariate/polychoric/processor.rb, line 46
def eq12(u,v)
  Distribution::Normal.pdf(u)*Distribution::Normal.cdf((v-rho*u).quo( Math::sqrt(1-rho**2)))
end
eq12b(u,v) click to toggle source
# File lib/statsample/bivariate/polychoric/processor.rb, line 50
def eq12b(u,v)
  Distribution::Normal.pdf(v) * Distribution::Normal.cdf((u-rho*v).quo( Math::sqrt(1-rho**2)))
  
end
fd_loglike_a(k) click to toggle source

First derivative for alpha_k Uses equation (6)

# File lib/statsample/bivariate/polychoric/processor.rb, line 146
def fd_loglike_a(k)
  fd_loglike_a_eq6(k)
end
fd_loglike_a_eq13(k) click to toggle source

Uses equation(13) from Olsson(1979)

# File lib/statsample/bivariate/polychoric/processor.rb, line 169
def fd_loglike_a_eq13(k)
  rho=@rho
  if rho.abs>0.9999
    rho= (rho>0) ? 0.9999 : -0.9999
  end
  total=0
  a_k=a(k)
  @nc.times do |j|
    #puts "j: #{j}"
    #puts "b #{j} : #{b.call(j)}"
    #puts "b #{j-1} : #{b.call(j-1)}"
  
    e_1=@matrix[k,j].quo(pd[k][j]+EPSILON) - @matrix[k+1,j].quo(pd[k+1][j]+EPSILON)
    e_2=Distribution::Normal.pdf(a_k)
    e_3=Distribution::Normal.cdf((b(j)-rho*a_k).quo(Math::sqrt(1-rho**2))) - Distribution::Normal.cdf((b(j-1)-rho*a_k).quo(Math::sqrt(1-rho**2)))
    #puts "val #{j}: #{e_1} | #{e_2} | #{e_3}"
    total+= e_1*e_2*e_3
  end
  total
end
fd_loglike_a_eq6(k) click to toggle source

Uses equation (6) from Olsson(1979)

# File lib/statsample/bivariate/polychoric/processor.rb, line 153
def fd_loglike_a_eq6(k)
  rho=@rho
  if rho.abs>0.9999
    rho= (rho>0) ? 0.9999 : -0.9999
  end
  total=0
  @nr.times do |i|
    @nc.times  do |j|
      total+=@matrix[i,j].quo(pd[i][j]+EPSILON) * fd_loglike_cell_a(i,j,k)
    end
  end
  total
end
fd_loglike_b(m) click to toggle source

First derivative for beta_m. Uses equation 6 (Olsson,1979)

# File lib/statsample/bivariate/polychoric/processor.rb, line 206
def fd_loglike_b(m)
  fd_loglike_b_eq14(m)
end
fd_loglike_b_eq14(m) click to toggle source

First derivative for beta_m Uses equation(14) from Olsson(1979)

# File lib/statsample/bivariate/polychoric/processor.rb, line 211
def fd_loglike_b_eq14(m)
  rho=@rho
  if rho.abs>0.9999
    rho= (rho>0) ? 0.9999 : -0.9999
  end
  total=0
  b_m=b(m)
  @nr.times do |i|
    e_1=@matrix[i,m].quo(pd[i][m]+EPSILON) - @matrix[i,m+1].quo(pd[i][m+1]+EPSILON)
    e_2=Distribution::Normal.pdf(b_m)
    e_3=Distribution::Normal.cdf((a(i)-rho*b_m).quo(Math::sqrt(1-rho**2))) - Distribution::Normal.cdf((a(i-1)-rho*b_m).quo(Math::sqrt(1-rho**2)))
    #puts "val #{j}: #{e_1} | #{e_2} | #{e_3}"
    
    total+= e_1*e_2*e_3
  end
  total
end
fd_loglike_b_eq6(m) click to toggle source

First derivative for b Uses equation 6 (Olsson, 1979)

# File lib/statsample/bivariate/polychoric/processor.rb, line 191
def fd_loglike_b_eq6(m)
  rho=@rho
  if rho.abs>0.9999
    rho= (rho>0) ? 0.9999 : -0.9999
  end
  total=0
  @nr.times do |i|
    @nc.times  do |j|
      total+=@matrix[i,j].quo(pd[i][j]+EPSILON) * fd_loglike_cell_b(i,j,m)
    end
  end
  total
end
fd_loglike_cell_a(i, j, k) click to toggle source

Equation(10) from Olsson(1979)

# File lib/statsample/bivariate/polychoric/processor.rb, line 59
        def fd_loglike_cell_a(i, j, k)
=begin
          if k==i
            Distribution::NormalBivariate.pd_cdf_x(a(k),b(j), rho) - Distribution::NormalBivariate.pd_cdf_x(a(k),b(j-1),rho)
          elsif k==(i-1)
            -Distribution::NormalBivariate.pd_cdf_x(a(k),b(j),rho) + Distribution::NormalBivariate.pd_cdf_x(a(k),b(j-1),rho)
          else
            0
          end
=end
          if k==i
            eq12(a(k),b(j))-eq12(a(k), b(j-1))
          elsif k==(i-1)
            -eq12(a(k),b(j))+eq12(a(k), b(j-1))
          else
            0
          end          
        end
fd_loglike_cell_b(i, j, m) click to toggle source
# File lib/statsample/bivariate/polychoric/processor.rb, line 78
        def fd_loglike_cell_b(i, j, m)
          if m==j
             eq12b(a(i),b(m))-eq12b(a(i-1),b(m))
          elsif m==(j-1)
            -eq12b(a(i),b(m))+eq12b(a(i-1),b(m))
          else
            0
          end
=begin          
          if m==j
            Distribution::NormalBivariate.pd_cdf_x(a(i),b(m), rho) - Distribution::NormalBivariate.pd_cdf_x(a(i-1),b(m),rho)
          elsif m==(j-1)
            -Distribution::NormalBivariate.pd_cdf_x(a(i),b(m),rho) + Distribution::NormalBivariate.pd_cdf_x(a(i-1),b(m),rho)
          else
            0
          end
=end
          
          
        end
fd_loglike_cell_rho(i, j) click to toggle source

Equation(8) from Olsson(1979)

# File lib/statsample/bivariate/polychoric/processor.rb, line 55
def fd_loglike_cell_rho(i, j)
  bipdf(i,j) - bipdf(i-1,j) - bipdf(i, j-1) + bipdf(i-1, j-1)
end
fd_loglike_rho() click to toggle source

First derivate for rho Uses equation (9) from Olsson(1979)

# File lib/statsample/bivariate/polychoric/processor.rb, line 129
def fd_loglike_rho
  rho=@rho
  if rho.abs>0.9999
    rho= (rho>0) ? 0.9999 : -0.9999
  end
  total=0
  @nr.times do |i|
    @nc.times do |j|
      pi=pd[i][j] + EPSILON
      total+= (@matrix[i,j].quo(pi))  * (bipdf(i,j)-bipdf(i-1,j)-bipdf(i,j-1)+bipdf(i-1,j-1))  
    end
  end
  total
end
im_function(t,i,j) click to toggle source

Returns the derivative correct according to order

# File lib/statsample/bivariate/polychoric/processor.rb, line 229
def im_function(t,i,j)
  if t==0
    fd_loglike_cell_rho(i,j)
  elsif t>=1 and t<=@alpha.size
    fd_loglike_cell_a(i,j,t-1)
  elsif t>=@alpha.size+1 and t<=(@alpha.size+@beta.size)
    fd_loglike_cell_b(i,j,t-@alpha.size-1)
  else
    raise "incorrect #{t}"
  end
end
information_matrix() click to toggle source
# File lib/statsample/bivariate/polychoric/processor.rb, line 240
def information_matrix
  total_n=@matrix.total_sum
  vars=@alpha.size+@beta.size+1
  matrix=vars.times.map { vars.times.map {0}}
  vars.times do |m|
    vars.times do |n|
      total=0
      (@nr-1).times do |i|
        (@nc-1).times do |j|
          total+=(1.quo(pd[i][j]+EPSILON)) * im_function(m,i,j) * im_function(n,i,j)
        end
      end
      matrix[m][n]=total_n*total
    end
  end
  m=::Matrix.rows(matrix)
   
end
loglike() click to toggle source
# File lib/statsample/bivariate/polychoric/processor.rb, line 22
def loglike
  rho=@rho
  if rho.abs>0.9999
    rho= (rho>0) ? 0.9999 : -0.9999
  end
  loglike=0
  @nr.times do |i|
    @nc.times do |j|
      res=pd[i][j]+EPSILON
      loglike+= @matrix[i,j]  * Math::log( res )
    end
  end
  -loglike
end
pd() click to toggle source

phi_ij for each i and j Uses equation(4) from Olsson(1979)

# File lib/statsample/bivariate/polychoric/processor.rb, line 101
def pd
  if @pd.nil?
    @pd=@nr.times.collect{ [0] * @nc}
    pc=@nr.times.collect{ [0] * @nc}
    @nr.times do |i|
    @nc.times do |j|
     
      if i==@nr-1 and j==@nc-1
        @pd[i][j]=1.0
      else
        a=(i==@nr-1) ? 100: alpha[i]
        b=(j==@nc-1) ? 100: beta[j]
        #puts "a:#{a} b:#{b}"
        @pd[i][j]=Distribution::BivariateNormal.cdf(a, b, rho)
      end
      pc[i][j] = @pd[i][j]
      @pd[i][j] = @pd[i][j] - pc[i-1][j] if i>0
      @pd[i][j] = @pd[i][j] - pc[i][j-1] if j>0
      @pd[i][j] = @pd[i][j] + pc[i-1][j-1] if (i>0 and j>0)
    end
    end
  end
  @pd
end