Class: Statsample::Bivariate::Polychoric

Inherits:
Object
  • Object
show all
Includes:
DirtyMemoize, Summarizable
Defined in:
lib/statsample/bivariate/polychoric.rb,
lib/statsample/bivariate/polychoric/processor.rb

Defined Under Namespace

Classes: Processor

Constant Summary collapse

METHOD =

Default method

:two_step
MAX_ITERATIONS =

Max number of iteratios

300
EPSILON =

Epsilon

1e-6
MINIMIZER_TYPE_TWO_STEP =

GSL unidimensional minimizer

"brent"
MINIMIZER_TYPE_JOINT_DERIVATIVE =

GSL multidimensional minimizer, derivative based

"conjugate_pr"
MINIMIZER_TYPE_JOINT_NO_DERIVATIVE =

GSL multidimensional minimizer, non derivative based

"nmsimplex"

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(matrix, opts = Hash.new) ⇒ Polychoric

Params:

  • matrix: Contingence table

  • opts: Hash with options. Could be any

accessable attribute of object



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# File 'lib/statsample/bivariate/polychoric.rb', line 168

def initialize(matrix, opts=Hash.new)
  @matrix=matrix
  @n=matrix.column_size
  @m=matrix.row_size
  raise "row size <1" if @m<=1
  raise "column size <1" if @n<=1
  
  @method=METHOD
  @name=_("Polychoric correlation")
  @max_iterations=MAX_ITERATIONS
  @epsilon=EPSILON
  @minimizer_type_two_step=MINIMIZER_TYPE_TWO_STEP
  @minimizer_type_joint_no_derivative=MINIMIZER_TYPE_JOINT_NO_DERIVATIVE
  @minimizer_type_joint_derivative=MINIMIZER_TYPE_JOINT_DERIVATIVE
  
  @debug=false
  @iteration=nil
  opts.each{|k,v|
    self.send("#{k}=",v) if self.respond_to? k
  }
  @r=nil
  @pd=nil
  @failed=false
  compute_basic_parameters
end

Instance Attribute Details

#alpha ⇒ Object (readonly) Also known as: threshold_x

Returns the rows thresholds



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# File 'lib/statsample/bivariate/polychoric.rb', line 139

def alpha
  @alpha
end

#beta ⇒ Object (readonly) Also known as: threshold_y

Returns the columns thresholds



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# File 'lib/statsample/bivariate/polychoric.rb', line 141

def beta
  @beta
end

#debug ⇒ Object

Debug algorithm (See iterations, for example)



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# File 'lib/statsample/bivariate/polychoric.rb', line 102

def debug
  @debug
end

#epsilon ⇒ Object

Absolute error for iteration.



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# File 'lib/statsample/bivariate/polychoric.rb', line 125

def epsilon
  @epsilon
end

#failed ⇒ Object (readonly)

Returns the value of attribute failed.



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# File 'lib/statsample/bivariate/polychoric.rb', line 143

def failed
  @failed
end

#iteration ⇒ Object (readonly)

Number of iterations



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# File 'lib/statsample/bivariate/polychoric.rb', line 128

def iteration
  @iteration
end

#log ⇒ Object (readonly)

Log of algorithm



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# File 'lib/statsample/bivariate/polychoric.rb', line 131

def log
  @log
end

#loglike_model ⇒ Object (readonly)

Model ll



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# File 'lib/statsample/bivariate/polychoric.rb', line 134

def loglike_model
  @loglike_model
end

#max_iterations ⇒ Object

Max number of iterations used on iterative methods. Default to MAX_ITERATIONS



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# File 'lib/statsample/bivariate/polychoric.rb', line 100

def max_iterations
  @max_iterations
end

#method ⇒ Object

Method of calculation of polychoric series. :two_step used by default.

:two_step

two-step ML, based on code by J.Fox

:polychoric_series

polychoric series estimate, using algorithm AS87 by Martinson and Hamdan (1975).

:joint

one-step ML, usign derivatives by Olsson (1979)



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# File 'lib/statsample/bivariate/polychoric.rb', line 123

def method
  @method
end

#minimizer_type_joint_derivative ⇒ Object

Minimizer type for joint estimate, using derivative. Default “conjugate_pr”. See rb-gsl.rubyforge.org/min.html for reference.



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# File 'lib/statsample/bivariate/polychoric.rb', line 113

def minimizer_type_joint_derivative
  @minimizer_type_joint_derivative
end

#minimizer_type_joint_no_derivative ⇒ Object

Minimizer type for joint estimate, no derivative. Default “nmsimplex”. See rb-gsl.rubyforge.org/min.html for reference.



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# File 'lib/statsample/bivariate/polychoric.rb', line 109

def minimizer_type_joint_no_derivative
  @minimizer_type_joint_no_derivative
end

#minimizer_type_two_step ⇒ Object

Minimizer type for two step. Default “brent” See rb-gsl.rubyforge.org/min.html for reference.



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# File 'lib/statsample/bivariate/polychoric.rb', line 105

def minimizer_type_two_step
  @minimizer_type_two_step
end

#name ⇒ Object

Name of the analysis



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# File 'lib/statsample/bivariate/polychoric.rb', line 98

def name
  @name
end

#r ⇒ Object (readonly)

Returns the polychoric correlation



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# File 'lib/statsample/bivariate/polychoric.rb', line 137

def r
  @r
end

Class Method Details

.new_with_vectors(v1, v2) ⇒ Object

Create a Polychoric object, based on two vectors



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# File 'lib/statsample/bivariate/polychoric.rb', line 161

def self.new_with_vectors(v1,v2)
  Polychoric.new(Crosstab.new(v1,v2).to_matrix)
end

Instance Method Details

#chi_square ⇒ Object

Chi Square of model



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# File 'lib/statsample/bivariate/polychoric.rb', line 230

def chi_square
  if @loglike_model.nil?
    compute
  end
  -2*(@loglike_model-loglike_data)
end

#chi_square_df ⇒ Object 



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# File 'lib/statsample/bivariate/polychoric.rb', line 237

def chi_square_df
  (@nr*@nc)-@nc-@nr
end

#compute ⇒ Object

Start the computation of polychoric correlation based on attribute method.



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# File 'lib/statsample/bivariate/polychoric.rb', line 201

def compute
  if @method==:two_step
    compute_two_step_mle
  elsif @method==:joint
    compute_one_step_mle
  elsif @method==:polychoric_series
    compute_polychoric_series
  else
    raise "Not implemented"
  end
end

#compute_basic_parameters ⇒ Object 



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# File 'lib/statsample/bivariate/polychoric.rb', line 244

def compute_basic_parameters
  @nr=@matrix.row_size
  @nc=@matrix.column_size
  @sumr=[0]*@matrix.row_size
  @sumrac=[0]*@matrix.row_size
  @sumc=[0]*@matrix.column_size
  @sumcac=[0]*@matrix.column_size
  @alpha=[0]*(@nr-1)
  @beta=[0]*(@nc-1)
  @total=0
  @nr.times do |i|
    @nc.times do |j|
      @sumr[i]+=@matrix[i,j]
      @sumc[j]+=@matrix[i,j]
      @total+=@matrix[i,j]
    end
  end
  ac=0
  (@nr-1).times do |i|
    @sumrac[i]=@sumr[i]+ac
    @alpha[i]=Distribution::Normal.p_value(@sumrac[i] / @total.to_f)
    ac=@sumrac[i]
  end
  ac=0
  (@nc-1).times do |i|
    @sumcac[i]=@sumc[i]+ac
    @beta[i]=Distribution::Normal.p_value(@sumcac[i] / @total.to_f)
    ac=@sumcac[i]
  end
end

#compute_derivatives_vector(v, df) ⇒ Object

:nodoc:



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# File 'lib/statsample/bivariate/polychoric.rb', line 362

def compute_derivatives_vector(v,df) # :nodoc:
  new_rho=v[0]
  new_alpha=v[1, @nr-1]
  new_beta=v[@nr, @nc-1]
  if new_rho.abs>0.9999
    new_rho= (new_rho>0) ? 0.9999 : -0.9999
  end
  pr=Processor.new(new_alpha,new_beta,new_rho,@matrix)
  
  df[0]=-pr.fd_loglike_rho
  new_alpha.to_a.each_with_index {|v,i|
    df[i+1]=-pr.fd_loglike_a(i)  
  }
  offset=new_alpha.size+1
  new_beta.to_a.each_with_index {|v,i|
    df[offset+i]=-pr.fd_loglike_b(i)  
  }
end

#compute_one_step_mle ⇒ Object

Compute joint ML estimation. Uses compute_one_step_mle_with_derivatives() by default.



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# File 'lib/statsample/bivariate/polychoric.rb', line 382

def compute_one_step_mle
  compute_one_step_mle_with_derivatives
end

#compute_one_step_mle_with_derivatives ⇒ Object

Compute Polychoric correlation with joint estimate, usign derivative based minimization method.

Much faster than method without derivatives.



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# File 'lib/statsample/bivariate/polychoric.rb', line 390

def compute_one_step_mle_with_derivatives
  # Get initial values with two-step aproach
  compute_two_step_mle
  # Start iteration with past values
  rho=@r
  cut_alpha=@alpha
  cut_beta=@beta
  parameters=[rho]+cut_alpha+cut_beta
  np=@nc-1+@nr
  
  
  loglike_f = Proc.new { |v, params|
    new_rho=v[0]
    new_alpha=v[1, @nr-1]
    new_beta=v[@nr, @nc-1]
    pr=Processor.new(new_alpha,new_beta,new_rho,@matrix)
    pr.loglike
  }
  
  loglike_df = Proc.new {|v, params, df |
    compute_derivatives_vector(v,df)
  }
    
  
  my_func = GSL::MultiMin::Function_fdf.alloc(loglike_f,loglike_df, np)
  my_func.set_params(parameters)      # parameters
  
  x = GSL::Vector.alloc(parameters.dup)
  minimizer = GSL::MultiMin::FdfMinimizer.alloc(minimizer_type_joint_derivative,np)
  minimizer.set(my_func, x, 1, 1e-3)
  
  iter = 0
  message=""
  begin_time=Time.new
  begin
    iter += 1
    status = minimizer.iterate()
    #p minimizer.f
    #p minimizer.gradient
    status = minimizer.test_gradient(1e-3)
    if status == GSL::SUCCESS
      total_time=Time.new-begin_time
      message+="Joint MLE converged to minimum on %0.3f seconds at\n" % total_time
    end
    x = minimizer.x
    message+= sprintf("%5d iterations", iter)+"\n";
    message+= "args="
    for i in 0...np do
      message+=sprintf("%10.3e ", x[i])
    end
    message+=sprintf("f() = %7.3f\n"  , minimizer.f)+"\n";
  rescue => e
    @failed=true
  end while status == GSL::CONTINUE and iter < @max_iterations
  
  @iteration=iter
  @log+=message        
  @r=minimizer.x[0]
  @alpha=minimizer.x[1,@nr-1].to_a
  @beta=minimizer.x[@nr,@nc-1].to_a
  @loglike_model= -minimizer.minimum
  
  pr=Processor.new(@alpha,@beta,@r,@matrix)
  
end

#compute_one_step_mle_without_derivatives ⇒ Object

Compute Polychoric correlation with joint estimate, usign derivative-less minimization method.

Rho and thresholds are estimated at same time. Code based on R package “polycor”, by J.Fox.



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# File 'lib/statsample/bivariate/polychoric.rb', line 463

def compute_one_step_mle_without_derivatives
  # Get initial values with two-step aproach
  compute_two_step_mle
  # Start iteration with past values
  rho=@r
  cut_alpha=@alpha
  cut_beta=@beta
  parameters=[rho]+cut_alpha+cut_beta
  np=@nc-1+@nr

  minimization = Proc.new { |v, params|
    new_rho=v[0]
   new_alpha=v[1, @nr-1]
   new_beta=v[@nr, @nc-1]
   
   #puts "f'rho=#{fd_loglike_rho(alpha,beta,rho)}"
   #(@nr-1).times {|k|
   #  puts "f'a(#{k}) = #{fd_loglike_a(alpha,beta,rho,k)}"         
   #  puts "f'a(#{k}) v2 = #{fd_loglike_a2(alpha,beta,rho,k)}"         
   #
   #}
   #(@nc-1).times {|k|
   #  puts "f'b(#{k}) = #{fd_loglike_b(alpha,beta,rho,k)}"         
   #}
   pr=Processor.new(new_alpha,new_beta,new_rho,@matrix)
   
   df=Array.new(np)
   #compute_derivatives_vector(v,df)
   pr.loglike
  }
  my_func = GSL::MultiMin::Function.alloc(minimization, np)
  my_func.set_params(parameters)      # parameters
  
  x = GSL::Vector.alloc(parameters.dup)
  
  ss = GSL::Vector.alloc(np)
  ss.set_all(1.0)
  
  minimizer = GSL::MultiMin::FMinimizer.alloc(minimizer_type_joint_no_derivative,np)
  minimizer.set(my_func, x, ss)
  
  iter = 0
  message=""
  begin_time=Time.new
  begin
    iter += 1
    status = minimizer.iterate()
    status = minimizer.test_size(@epsilon)
    if status == GSL::SUCCESS
      total_time=Time.new-begin_time
      message="Joint MLE converged to minimum on %0.3f seconds at\n" % total_time
    end
    x = minimizer.x
    message+= sprintf("%5d iterations", iter)+"\n";
    for i in 0...np do
      message+=sprintf("%10.3e ", x[i])
    end
    message+=sprintf("f() = %7.3f size = %.3f\n", minimizer.fval, minimizer.size)+"\n";
  end while status == GSL::CONTINUE and iter < @max_iterations
  @iteration=iter
  @log+=message        
  @r=minimizer.x[0]
  @alpha=minimizer.x[1,@nr-1].to_a
  @beta=minimizer.x[@nr,@nc-1].to_a
  @loglike_model= -minimizer.minimum
end

#compute_polychoric_series ⇒ Object

Compute polychoric correlation using polychoric series. Algorithm: AS87, by Martinson and Hamdam(1975).

Warning: According to Drasgow(2006), this computation diverges greatly of joint and two-step methods.



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# File 'lib/statsample/bivariate/polychoric.rb', line 577

def compute_polychoric_series 
  @nn=@n-1
  @mm=@m-1
  @nn7=7*@nn
  @mm7=7*@mm
  @mn=@n*@m
  @cont=[nil]
  @n.times {|j|
    @m.times {|i|
      @cont.push(@matrix[i,j])
    }
  }

  pcorl=0
  cont=@cont
  xmean=0.0
  sum=0.0
  row=[]
  colmn=[]
  (1..@m).each do |i|
    row[i]=0.0
    l=i
    (1..@n).each do |j|
      row[i]=row[i]+cont[l]
      l+=@m
    end
    raise "Should not be empty rows" if(row[i]==0.0)
    xmean=xmean+row[i]*i.to_f
    sum+=row[i]
  end
  xmean=xmean/sum.to_f
  ymean=0.0
  (1..@n).each do |j|
    colmn[j]=0.0
    l=(j-1)*@m
    (1..@m).each do |i|
      l=l+1
      colmn[j]=colmn[j]+cont[l] #12
    end
    raise "Should not be empty cols" if colmn[j]==0
    ymean=ymean+colmn[j]*j.to_f
  end
  ymean=ymean/sum.to_f
  covxy=0.0
  (1..@m).each do |i|
    l=i
    (1..@n).each do |j|
      conxy=covxy+cont[l]*(i.to_f-xmean)*(j.to_f-ymean)
      l=l+@m
    end
  end
  
  chisq=0.0
  (1..@m).each do |i|
    l=i
    (1..@n).each do |j|
      chisq=chisq+((cont[l]**2).quo(row[i]*colmn[j]))
      l=l+@m
    end
  end
  
  phisq=chisq-1.0-(@mm*@nn).to_f / sum.to_f
  phisq=0 if(phisq<0.0) 
  # Compute cumulative sum of columns and rows
  sumc=[]
  sumr=[]
  sumc[1]=colmn[1]
  sumr[1]=row[1]
  cum=0
  (1..@nn).each do |i| # goto 17 r20
    cum=cum+colmn[i]
    sumc[i]=cum
  end
  cum=0
  (1..@mm).each do |i| 
    cum=cum+row[i]
    sumr[i]=cum
  end
  alpha=[]
  beta=[]
  # Compute points of polytomy
  (1..@mm).each do |i| #do 21
    alpha[i]=Distribution::Normal.p_value(sumr[i] / sum.to_f)
  end # 21
  (1..@nn).each do |i| #do 22
    beta[i]=Distribution::Normal.p_value(sumc[i] / sum.to_f)
  end # 21
  @alpha=alpha[1,alpha.size] 
  @beta=beta[1,beta.size]
  @sumr=row[1,row.size]
  @sumc=colmn[1,colmn.size]
  @total=sum
  
  # Compute Fourier coefficients a and b. Verified
  h=hermit(alpha,@mm)
  hh=hermit(beta,@nn)
  a=[]
  b=[]
  if @m!=2 # goto 24
    mmm=@m-2
    (1..mmm).each do |i| #do 23
      a1=sum.quo(row[i+1] * sumr[i] * sumr[i+1])
      a2=sumr[i]   * xnorm(alpha[i+1])
      a3=sumr[i+1] * xnorm(alpha[i])
      l=i
      (1..7).each do |j| #do 23
        a[l]=Math::sqrt(a1.quo(j))*(h[l+1] * a2 - h[l] * a3)
        l=l+@mm
      end
    end #23
  end
  # 24
  
  
  if @n!=2 # goto 26
    nnn=@n-2
    (1..nnn).each do |i| #do 25
      a1=sum.quo(colmn[i+1] * sumc[i] * sumc[i+1])
      a2=sumc[i] * xnorm(beta[i+1])
      a3=sumc[i+1] * xnorm(beta[i])
      l=i
      (1..7).each do |j| #do 25
        b[l]=Math::sqrt(a1.quo(j))*(a2 * hh[l+1] - a3*hh[l])
        l=l+@nn
      end # 25
    end # 25
  end
  #26 r20
  l = @mm
  a1 = -sum * xnorm(alpha[@mm])
  a2 = row[@m] * sumr[@mm] 
  (1..7).each do |j| # do 27
    a[l]=a1 * h[l].quo(Math::sqrt(j*a2))
    l=l+@mm
  end # 27
  
  l = @nn
  a1 = -sum * xnorm(beta[@nn])
  a2 = colmn[@n] * sumc[@nn]

  (1..7).each do |j| # do 28
    b[l]=a1 * hh[l].quo(Math::sqrt(j*a2))
    l = l + @nn
  end # 28
  rcof=[]
  # compute coefficients rcof of polynomial of order 8
  rcof[1]=-phisq
  (2..9).each do |i| # do 30
    rcof[i]=0.0
  end #30 
  m1=@mm
  (1..@mm).each do |i| # do 31
    m1=m1+1
    m2=m1+@mm
    m3=m2+@mm
    m4=m3+@mm
    m5=m4+@mm
    m6=m5+@mm
    n1=@nn
    (1..@nn).each do |j| # do 31
      n1=n1+1
      n2=n1+@nn
      n3=n2+@nn
      n4=n3+@nn
      n5=n4+@nn
      n6=n5+@nn
      
      rcof[3] = rcof[3] + a[i]**2 * b[j]**2
      
      rcof[4] = rcof[4] + 2.0 * a[i] * a[m1] * b[j] * b[n1]
      
      rcof[5] = rcof[5] + a[m1]**2 * b[n1]**2 +
        2.0 * a[i] * a[m2] * b[j] * b[n2]
      
      rcof[6] = rcof[6] + 2.0 * (a[i] * a[m3] * b[j] *
        b[n3] + a[m1] * a[m2] * b[n1] * b[n2])
      
      rcof[7] = rcof[7] + a[m2]**2 * b[n2]**2 +
        2.0 * (a[i] * a[m4] * b[j] * b[n4] + a[m1] * a[m3] *
          b[n1] * b[n3])
      
      rcof[8] = rcof[8] + 2.0 * (a[i] * a[m5] * b[j] * b[n5] +
        a[m1] * a[m4] * b[n1] * b[n4] + a[m2] *  a[m3] * b[n2] * b[n3])
      
      rcof[9] = rcof[9] + a[m3]**2 * b[n3]**2 +
        2.0 * (a[i] * a[m6] * b[j] * b[n6] + a[m1] * a[m5] * b[n1] *
        b[n5] + (a[m2] * a[m4] * b[n2] * b[n4]))
    end # 31
  end # 31

  rcof=rcof[1,rcof.size]
  poly = GSL::Poly.alloc(rcof)
  roots=poly.solve
  rootr=[nil]
  rooti=[nil]
  roots.each {|c|
    rootr.push(c.real)
    rooti.push(c.im)
  }
  @rootr=rootr
  @rooti=rooti
  
  norts=0
  (1..7).each do |i| # do 43
    
    next if rooti[i]!=0.0 
    if (covxy>=0.0)
      next if(rootr[i]<0.0 or rootr[i]>1.0)
      pcorl=rootr[i]
      norts=norts+1
    else
      if (rootr[i]>=-1.0 and rootr[i]<0.0)
        pcorl=rootr[i]
        norts=norts+1              
      end
    end
  end # 43
  raise "Error" if norts==0
  @r=pcorl
  pr=Processor.new(@alpha,@beta,@r,@matrix)
  @loglike_model=-pr.loglike
  
end

#compute_two_step_mle ⇒ Object

Computation of polychoric correlation usign two-step ML estimation.

Two-step ML estimation “first estimates the thresholds from the one-way marginal frequencies, then estimates rho, conditional on these thresholds, via maximum likelihood” (Uebersax, 2006).

The algorithm is based on code by Gegenfurtner(1992).

References:

  • Gegenfurtner, K. (1992). PRAXIS: Brent’s algorithm for function minimization. Behavior Research Methods, Instruments & Computers, 24(4), 560-564. Available on www.allpsych.uni-giessen.de/karl/pdf/03.praxis.pdf

  • Uebersax, J.S. (2006). The tetrachoric and polychoric correlation coefficients. Statistical Methods for Rater Agreement web site. 2006. Available at: john-uebersax.com/stat/tetra.htm . Accessed February, 11, 2010



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# File 'lib/statsample/bivariate/polychoric.rb', line 287

def compute_two_step_mle
  if Statsample.has_gsl?
    compute_two_step_mle_gsl
  else
    compute_two_step_mle_ruby
  end
end

#compute_two_step_mle_gsl ⇒ Object

Compute two step ML estimation using gsl.



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# File 'lib/statsample/bivariate/polychoric.rb', line 319

def compute_two_step_mle_gsl 
  
fn1=GSL::Function.alloc {|rho|
  pr=Processor.new(@alpha,@beta, rho, @matrix)
  pr.loglike
}
@iteration = 0
max_iter = @max_iterations
m = 0             # initial guess
m_expected = 0
a=-0.9999
b=+0.9999
gmf = GSL::Min::FMinimizer.alloc(@minimizer_type_two_step)
gmf.set(fn1, m, a, b)
header=_("Two step minimization using %s method\n") % gmf.name
header+=sprintf("%5s [%9s, %9s] %9s %10s %9s\n", "iter", "lower", "upper", "min",
   "err", "err(est)")
  
header+=sprintf("%5d [%.7f, %.7f] %.7f %+.7f %.7f\n", @iteration, a, b, m, m - m_expected, b - a)
@log=header
puts header if @debug
begin
  @iteration += 1
  status = gmf.iterate
  status = gmf.test_interval(@epsilon, 0.0)
  
  if status == GSL::SUCCESS
    @log+="converged:"
    puts "converged:" if @debug
  end
  a = gmf.x_lower
  b = gmf.x_upper
  m = gmf.x_minimum
  message=sprintf("%5d [%.7f, %.7f] %.7f %+.7f %.7f\n",
    @iteration, a, b, m, m - m_expected, b - a);
  @log+=message
  puts message if @debug
end while status == GSL::CONTINUE and @iteration < @max_iterations
@r=gmf.x_minimum
@loglike_model=-gmf.f_minimum
end

#compute_two_step_mle_ruby ⇒ Object

Compute two step ML estimation using only ruby.



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# File 'lib/statsample/bivariate/polychoric.rb', line 297

def compute_two_step_mle_ruby #:nodoc:
  
  f=proc {|rho|
    pr=Processor.new(@alpha,@beta, rho, @matrix)
    pr.loglike
  }
  
  @log=_("Two step minimization using GSL Brent method (pure ruby)\n")
  min=Minimization::Brent.new(-0.9999,0.9999,f)
  min.epsilon=@epsilon
  min.expected=0
  min.iterate
  @log+=min.log.to_table.to_s
  @r=min.x_minimum
  @loglike_model=-min.f_minimum
  @iteration=min.iterations
  puts @log if @debug
  
end

#expected ⇒ Object

:nodoc:



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# File 'lib/statsample/bivariate/polychoric.rb', line 546

def expected # :nodoc:
  rt=[]
  ct=[]
  t=0
  @matrix.row_size.times {|i|
    @matrix.column_size.times {|j|
      rt[i]=0 if rt[i].nil?
      ct[j]=0 if ct[j].nil?
      rt[i]+=@matrix[i,j]
      ct[j]+=@matrix[i,j]
      t+=@matrix[i,j]
    }
  }
  m=[]
  @matrix.row_size.times {|i|
    row=[]
    @matrix.column_size.times {|j|
      row[j]=(rt[i]*ct[j]).quo(t)
    }
    m.push(row)
  }
  
  Matrix.rows(m)
end

#hermit(s, k) ⇒ Object

Computes vector h(mm7) of orthogonal hermite…



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# File 'lib/statsample/bivariate/polychoric.rb', line 801

def hermit(s,k) # :nodoc:
  h=[]
  (1..k).each do |i| # do 14
    l=i
    ll=i+k
    lll=ll+k
    h[i]=1.0
    h[ll]=s[i]
    v=1.0
    (2..6).each do |j| #do 14
      w=Math::sqrt(j)
      h[lll]=(s[i]*h[ll] - v*h[l]).quo(w)
      v=w
      l=l+k
      ll=ll+k
      lll=lll+k
    end
  end
  h
end

#loglike_data ⇒ Object

:section: LL methods Retrieve log likehood for actual data.



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# File 'lib/statsample/bivariate/polychoric.rb', line 215

def loglike_data
  loglike=0
  @nr.times do |i|
    @nc.times do |j|
      res=@matrix[i,j].quo(@total)
      if (res==0)
        res=1e-16
      end
    loglike+= @matrix[i,j]  * Math::log(res )
    end
  end
  loglike
end

#matrix_for_rho(rho) ⇒ Object

:nodoc:



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# File 'lib/statsample/bivariate/polychoric.rb', line 530

def matrix_for_rho(rho) # :nodoc:
  pd=@nr.times.collect{ [0]*@nc}
  pc=@nr.times.collect{ [0]*@nc}
  @nr.times { |i|
      @nc.times { |j|
        pd[i][j]=Distribution::BivariateNormal.cdf(@alpha[i], @beta[j], rho)
        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)
        res= pd[i][j]
      }
   }
   Matrix.rows(pc)
end

#report_building(generator) ⇒ Object

:nodoc:



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# File 'lib/statsample/bivariate/polychoric.rb', line 825

def report_building(generator) # :nodoc: 
  compute if dirty?
  
  
  section=ReportBuilder::Section.new(:name=>@name)
  
  if @failed
    section.add("Failed to converge")
  else        
    t=ReportBuilder::Table.new(:name=>_("Contingence Table"), :header=>[""]+(@n.times.collect {|i| "Y=#{i}"})+["Total"])
    @m.times do |i|
      t.row(["X = #{i}"]+(@n.times.collect {|j| @matrix[i,j]}) + [@sumr[i]])
    end
    t.hr
    t.row(["T"]+(@n.times.collect {|j| @sumc[j]})+[@total])
    section.add(t)
    section.add(sprintf("r: %0.4f",r))
    t=ReportBuilder::Table.new(:name=>_("Thresholds"), :header=>["","Value"])
    threshold_x.each_with_index {|val,i|
      t.row([_("Threshold X %d") % i, sprintf("%0.4f", val)])
    }
    threshold_y.each_with_index {|val,i|
      t.row([_("Threshold Y %d") % i, sprintf("%0.4f", val)])
    }
    section.add(t)
    section.add(_("Iterations: %d") % @iteration) if @iteration
    section.add(_("Test of bivariate normality: X^2 = %0.3f, df = %d, p= %0.5f" % [ chi_square, chi_square_df, 1-Distribution::ChiSquare.cdf(chi_square, chi_square_df)])) 
    generator.parse_element(section)
  end
  
end

#xnorm(t) ⇒ Object

:nodoc:



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# File 'lib/statsample/bivariate/polychoric.rb', line 821

def xnorm(t) # :nodoc:
  Math::exp(-0.5 * t **2) * (1.0/Math::sqrt(2*Math::PI))
end