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Statsample::Regression::Multiple::MatrixEngine

Pure Ruby Class for Multiple Regression Analysis, based on a covariance or correlation matrix.

Use Statsample::Regression::Multiple::RubyEngine if you have a Dataset, to avoid setting all details.

Remember: NEVER use a Covariance data if you have missing data. Use only correlation matrix on that case.

Example:

matrix=[[1.0, 0.5, 0.2], [0.5, 1.0, 0.7], [0.2, 0.7, 1.0]]

lr=Statsample::Regression::Multiple::MatrixEngine.new(matrix,2)

Attributes

x_sd[RW]

Hash of standard deviation of predictors. Only useful for Correlation Matrix, because by default is set to 1

y_sd[RW]

Standard deviation of criterion Only useful for Correlation Matrix, because by default is set to 1

x_mean[RW]

Hash of mean for predictors. By default, set to 0

y_mean[RW]

Mean for criteria. By default, set to 0

cases[W]

Number of cases

digits[W]

Public Class Methods

new(matrix,y_var, opts=Hash.new) click to toggle source

Create object

# File lib/statsample/regression/multiple/matrixengine.rb, line 36
def initialize(matrix,y_var, opts=Hash.new)
  matrix.extend Statsample::CovariateMatrix
  raise "#{y_var} variable should be on data" unless matrix.fields.include? y_var
  if matrix._type==:covariance
    @matrix_cov=matrix
    @matrix_cor=matrix.correlation
    @no_covariance=false
  else
    @matrix_cor=matrix
    @matrix_cov=matrix
    @no_covariance=true
  end
  
  @y_var=y_var
  @fields=matrix.fields-[y_var]
  
  @n_predictors=@fields.size
  @predictors_n=@n_predictors
  @matrix_x= @matrix_cor.submatrix(@fields)
  @matrix_x_cov= @matrix_cov.submatrix(@fields)
  raise LinearDependency, "Regressors are linearly dependent" if @matrix_x.determinant<1e-15

  
  @matrix_y = @matrix_cor.submatrix(@fields, [y_var])
  @matrix_y_cov = @matrix_cov.submatrix(@fields, [y_var])
  

  
  @y_sd=Math::sqrt(@matrix_cov.submatrix([y_var])[0,0])
  
  @x_sd=@n_predictors.times.inject({}) {|ac,i|
    ac[@matrix_x_cov.fields[i]]=Math::sqrt(@matrix_x_cov[i,i])
    ac;
  }
  
  @cases=nil
  @x_mean=@fields.inject({}) {|ac,f|
    ac[f]=0.0
    ac;
  }
  
  @y_mean=0.0
  @name=_("Multiple reggresion of %s on %s") % [@fields.join(","), @y_var]
  
  opts_default={:digits=>3}
  opts=opts_default.merge opts
  opts.each{|k,v|
      self.send("#{k}=",v) if self.respond_to? k
  }
    result_matrix=@matrix_x_cov.inverse * @matrix_y_cov

  if matrix._type==:covariance
    @coeffs=result_matrix.column(0).to_a
    @coeffs_stan=coeffs.collect {|k,v|
      coeffs[k]*@x_sd[k].quo(@y_sd)
    }
  else
    @coeffs_stan=result_matrix.column(0).to_a
    @coeffs=standarized_coeffs.collect {|k,v|
      standarized_coeffs[k]*@y_sd.quo(@x_sd[k])
    } 
  end
  @total_cases=@valid_cases=@cases
end

Public Instance Methods

cases() click to toggle source
# File lib/statsample/regression/multiple/matrixengine.rb, line 100
def cases
  raise "You should define the number of valid cases first" if @cases.nil?
  @cases
end
coeffs() click to toggle source

Hash of b or raw coefficients

# File lib/statsample/regression/multiple/matrixengine.rb, line 123
def coeffs
  assign_names(@coeffs)    
end
coeffs_se() click to toggle source

Standard Error for coefficients. Standard error of a coefficients depends on

  • Tolerance of the coeffients: Higher tolerances implies higher error

  • Higher r2 implies lower error

Reference:

  • Cohen et al. (2003). Applied Multiple Reggression / Correlation Analysis for the Behavioral Sciences

# File lib/statsample/regression/multiple/matrixengine.rb, line 161
def coeffs_se
  out={}
  #mse=sse.quo(df_e)
  coeffs.each {|k,v|
    out[k]=@y_sd.quo(@x_sd[k])*Math::sqrt( 1.quo(tolerance(k)))*Math::sqrt((1-r2).quo(df_e))
  }
  out
end
constant() click to toggle source

Value of constant

# File lib/statsample/regression/multiple/matrixengine.rb, line 118
def constant
  c=coeffs
  @y_mean - @fields.inject(0){|a,k| a + (c[k] * @x_mean[k])}
end
constant_se() click to toggle source

Standard error for constant. This method recreates the estimaded variance-covariance matrix using means, standard deviation and covariance matrix. So, needs the covariance matrix.

# File lib/statsample/regression/multiple/matrixengine.rb, line 178
def constant_se
  return nil if @no_covariance
  means=@x_mean
  #means[@y_var]=@y_mean
  means[:constant]=1
  sd=@x_sd
  #sd[@y_var]=@y_sd
  sd[:constant]=0
  fields=[:constant]+@matrix_cov.fields-[@y_var]
  # Recreate X'X using the variance-covariance matrix
  xt_x=Matrix.rows(fields.collect {|i|
    fields.collect {|j|
      if i==:constant or j==:constant
        cov=0
      elsif i==j
        cov=sd[i]**2
      else
        cov=@matrix_cov.submatrix(i..i,j..j)[0,0]
      end
      cov*(@cases-1)+@cases*means[i]*means[j]
    }
  })
  matrix=xt_x.inverse * mse
  matrix.collect {|i| Math::sqrt(i) if i>0 }[0,0]
end
constant_t() click to toggle source

t value for constant

# File lib/statsample/regression/multiple/matrixengine.rb, line 170
def constant_t
  return nil if constant_se.nil?
  constant.to_f / constant_se
end
df_e() click to toggle source

Degrees of freedom for error

# File lib/statsample/regression/multiple/matrixengine.rb, line 141
def df_e
  cases-@n_predictors-1
end
df_r() click to toggle source

Degrees of freedom for regression

# File lib/statsample/regression/multiple/matrixengine.rb, line 137
def df_r
  @n_predictors
end
r() click to toggle source

Multiple correlation, on random models.

# File lib/statsample/regression/multiple/matrixengine.rb, line 114
def r
  Math::sqrt(r2)
end
r2() click to toggle source

Get R^2 for the regression For fixed models is the coefficient of determination. On random models, is the ‘squared-multiple correlation’ Equal to

  • 1-(|R| / |R_x|) or

  • Sum(b_i*r_yi) <- used

# File lib/statsample/regression/multiple/matrixengine.rb, line 110
def r2
  @n_predictors.times.inject(0) {|ac,i| ac+@coeffs_stan[i]* @matrix_y[i,0]} 
end
sst() click to toggle source

Total sum of squares

# File lib/statsample/regression/multiple/matrixengine.rb, line 132
def sst
  @y_sd**2*(cases-1.0)
end
standarized_coeffs() click to toggle source

Hash of beta or standarized coefficients

# File lib/statsample/regression/multiple/matrixengine.rb, line 128
def standarized_coeffs
  assign_names(@coeffs_stan)
end
tolerance(var) click to toggle source

Tolerance for a given variable defined as (1-R^2) of regression of other independent variables over the selected

Reference:

# File lib/statsample/regression/multiple/matrixengine.rb, line 149
def tolerance(var)
  return 1 if @matrix_x.column_size==1
  lr=Statsample::Regression::Multiple::MatrixEngine.new(@matrix_x, var)
  1-lr.r2
end

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