Class: Statsample::Regression::Multiple::MatrixEngine

Inherits:
BaseEngine
  • Object
show all
Defined in:
lib/statsample/regression/multiple/matrixengine.rb

Overview

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

Direct Known Subclasses

RubyEngine

Instance Attribute Summary collapse

Attributes inherited from BaseEngine

#name

Instance Method Summary collapse

Methods inherited from BaseEngine

#assign_names, #coeffs_t, #coeffs_tolerances, #estimated_variance_covariance_matrix, #f, #mse, #msr, #predicted, #process, #residuals, #se_r2, #significance, #sse, #sse_direct, #ssr, #ssr_direct, #standarized_predicted, #summary, univariate?

Constructor Details

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

Create object



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# File 'lib/statsample/regression/multiple/matrixengine.rb', line 35

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
  
  @matrix_x= @matrix_cor.submatrix(@fields)
  @matrix_x_cov= @matrix_cov.submatrix(@fields)
  
  @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.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

end

Instance Attribute Details

#cases ⇒ Object 



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# File 'lib/statsample/regression/multiple/matrixengine.rb', line 97

def cases
  raise "You should define the number of valid cases first" if @cases.nil?
  @cases
end

#x_mean ⇒ Object

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



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# File 'lib/statsample/regression/multiple/matrixengine.rb', line 24

def x_mean
  @x_mean
end

#x_sd ⇒ Object

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



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# File 'lib/statsample/regression/multiple/matrixengine.rb', line 17

def x_sd
  @x_sd
end

#y_mean ⇒ Object

Mean for criteria. By default, set to 0



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# File 'lib/statsample/regression/multiple/matrixengine.rb', line 28

def y_mean
  @y_mean
end

#y_sd ⇒ Object

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



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# File 'lib/statsample/regression/multiple/matrixengine.rb', line 21

def y_sd
  @y_sd
end

Instance Method Details

#coeffs ⇒ Object

Hash of b or raw coefficients



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# File 'lib/statsample/regression/multiple/matrixengine.rb', line 117

def coeffs
  assign_names(@coeffs)    
end

#coeffs_se ⇒ Object

Reference:

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



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# File 'lib/statsample/regression/multiple/matrixengine.rb', line 157

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 ⇒ Object 



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# File 'lib/statsample/regression/multiple/matrixengine.rb', line 112

def constant
  c=coeffs
  @y_mean - @fields.inject(0){|a,k| a + (c[k] * @x_mean[k])}
end

#constant_se ⇒ Object

Standard error for constant. Recreate the estimaded variance-covariance matrix using means, standard deviation and covariance matrix



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# File 'lib/statsample/regression/multiple/matrixengine.rb', line 172

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]
  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 ⇒ Object 



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# File 'lib/statsample/regression/multiple/matrixengine.rb', line 165

def constant_t
  return nil if constant_se.nil?
  constant.to_f/constant_se
end

#df_e ⇒ Object

Degrees of freedom for error



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# File 'lib/statsample/regression/multiple/matrixengine.rb', line 135

def df_e
  cases-@n_predictors-1
end

#df_r ⇒ Object

Degrees of freedom for regression



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# File 'lib/statsample/regression/multiple/matrixengine.rb', line 131

def df_r
  @n_predictors
end

#r ⇒ Object 



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# File 'lib/statsample/regression/multiple/matrixengine.rb', line 108

def r
  Math::sqrt(r2)
end

#r2 ⇒ Object

Get R^2 for the regression Equal to

  • 1-(|R| / |R_x|) or

  • Sum(b_i*r_yi) <- used



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# File 'lib/statsample/regression/multiple/matrixengine.rb', line 105

def r2
  @n_predictors.times.inject(0) {|ac,i| ac+@coeffs_stan[i]* @matrix_y[i,0]} 
end

#report_building(builder) ⇒ Object

:nodoc:



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# File 'lib/statsample/regression/multiple/matrixengine.rb', line 197

def report_building(builder) # :nodoc:
  builder.section(:name=>_("Multiple Regression: ")+@name) do |g|
    c=coeffs
    g.text(_("Engine: %s") % self.class)
    g.text(_("Cases=%d") % [@cases])
    g.text("R=#{sprintf('%0.3f',r)}")
    g.text("R^2=#{sprintf('%0.3f',r2)}")
    
    g.text(_("Equation")+"="+ sprintf('%0.3f',constant) +" + "+ @fields.collect {|k| sprintf('%0.3f%s',c[k],k)}.join(' + ') )
    
    g.table(:name=>"ANOVA", :header=>%w{source ss df ms f s}) do |t|
      t.row([_("Regression"), sprintf("%0.3f",ssr), df_r, sprintf("%0.3f",msr), sprintf("%0.3f",f), sprintf("%0.3f", significance)])
      t.row([_("Error"), sprintf("%0.3f",sse), df_e, sprintf("%0.3f",mse),"",""])
    
      t.row([_("Total"), sprintf("%0.3f",sst), df_r+df_e,"","",""])
    end
    sc=standarized_coeffs
    cse=coeffs_se
    g.table(:name=>"Beta coefficients", :header=>%w{coeff b beta se t}.collect{|field| _(field)} ) do |t|
      if (constant_se.nil?)
        t.row([_("Constant"), sprintf("%0.3f", constant),"--","?","?"])
      else
        t.row([_("Constant"), sprintf("%0.3f", constant), "-", sprintf("%0.3f", constant_se), sprintf("%0.3f", constant_t)])
      end
      
      @fields.each do |f|
        t.row([f, sprintf("%0.3f", c[f]), sprintf("%0.3f", sc[f]), sprintf("%0.3f", cse[f]), sprintf("%0.3f", c[f].quo(cse[f]))])
      end  
    end
  end    
end

#sst ⇒ Object

Total sum of squares



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# File 'lib/statsample/regression/multiple/matrixengine.rb', line 126

def sst
  @y_sd**2*(cases-1.0)
end

#standarized_coeffs ⇒ Object

Hash of beta or standarized coefficients



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# File 'lib/statsample/regression/multiple/matrixengine.rb', line 122

def standarized_coeffs
  assign_names(@coeffs_stan)
end

#tolerance(var) ⇒ Object

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



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# File 'lib/statsample/regression/multiple/matrixengine.rb', line 145

def tolerance(var)
  lr=Statsample::Regression::Multiple::MatrixEngine.new(@matrix_x, var)
  1-lr.r2
end