Class: Statsample::Reliability::ScaleAnalysis

Inherits:
Object
  • Object
show all
Includes:
Summarizable
Defined in:
lib/statsample/reliability/scaleanalysis.rb

Overview

Analysis of a Scale. Analoge of Scale Reliability analysis on SPSS. Returns several statistics for complete scale and each item

Usage

@x1 = Daru::Vector.new([1,1,1,1,2,2,2,2,3,3,3,30])
@x2 = Daru::Vector.new([1,1,1,2,2,3,3,3,3,4,4,50])
@x3 = Daru::Vector.new([2,2,1,1,1,2,2,2,3,4,5,40])
@x4 = Daru::Vector.new([1,2,3,4,4,4,4,3,4,4,5,30])
ds  = Daru::DataFrame.new({:x1 => @x1,:x2 => @x2,:x3 => @x3,:x4 => @x4})
ia  = Statsample::Reliability::ScaleAnalysis.new(ds)
puts ia.summary

Instance Attribute Summary collapse

Instance Method Summary collapse

Methods included from Summarizable

#summary

Constructor Details

#initialize(ds, opts = Hash.new) ⇒ ScaleAnalysis

Returns a new instance of ScaleAnalysis.



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# File 'lib/statsample/reliability/scaleanalysis.rb', line 18

def initialize(ds, opts=Hash.new)
  @dumped=ds.vectors.to_a.find_all {|f|
    ds[f].variance == 0
  }
  
  @ods = ds
  @ds  = ds.reject_values(*Daru::MISSING_VALUES).dup(ds.vectors.to_a - @dumped)
  @ds.rename ds.name
  
  @k     = @ds.ncols
  @total = @ds.vector_sum
  @o_total=@dumped.size > 0 ? @ods.vector_sum : nil
  
  @vector_mean = @ds.vector_mean
  @item_mean   = @vector_mean.mean
  @item_sd     = @vector_mean.sd
  
  @mean     = @total.mean
  @median   = @total.median
  @skew     = @total.skew
  @kurtosis = @total.kurtosis
  @sd       = @total.sd
  @variance = @total.variance
  @valid_n  = @total.size

  opts_default = {
    :name => _("Reliability Analysis"),
    :summary_histogram => true
  }
  @opts = opts_default.merge(opts)
  @opts.each{ |k,v| self.send("#{k}=",v) if self.respond_to? k }
  
  @cov_m=Statsample::Bivariate.covariance_matrix(@ds)
  # Mean for covariances and variances
  @variances = Daru::Vector.new(@k.times.map { |i| @cov_m[i,i] })
  @variances_mean=@variances.mean
  @covariances_mean=(@variance-@variances.sum).quo(@k**2-@k)
  #begin
    @alpha = Statsample::Reliability.cronbach_alpha(@ds)
    @alpha_standarized = Statsample::Reliability.cronbach_alpha_standarized(@ds)
  #rescue => e
  #  raise DatasetException.new(@ds,e), "Error calculating alpha"
  #end
end

Instance Attribute Details

#alpha ⇒ Object (readonly)

Returns the value of attribute alpha.



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# File 'lib/statsample/reliability/scaleanalysis.rb', line 15

def alpha
  @alpha
end

#alpha_standarized ⇒ Object (readonly)

Returns the value of attribute alpha_standarized.



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# File 'lib/statsample/reliability/scaleanalysis.rb', line 15

def alpha_standarized
  @alpha_standarized
end

#cov_m ⇒ Object (readonly)

Returns the value of attribute cov_m.



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# File 'lib/statsample/reliability/scaleanalysis.rb', line 15

def cov_m
  @cov_m
end

#covariances_mean ⇒ Object (readonly)

Returns the value of attribute covariances_mean.



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# File 'lib/statsample/reliability/scaleanalysis.rb', line 15

def covariances_mean
  @covariances_mean
end

#ds ⇒ Object (readonly)

Returns the value of attribute ds.



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# File 'lib/statsample/reliability/scaleanalysis.rb', line 15

def ds
  @ds
end

#mean ⇒ Object (readonly)

Returns the value of attribute mean.



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# File 'lib/statsample/reliability/scaleanalysis.rb', line 15

def mean
  @mean
end

#name ⇒ Object

Returns the value of attribute name.



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# File 'lib/statsample/reliability/scaleanalysis.rb', line 16

def name
  @name
end

#sd ⇒ Object (readonly)

Returns the value of attribute sd.



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# File 'lib/statsample/reliability/scaleanalysis.rb', line 15

def sd
  @sd
end

#summary_histogram ⇒ Object

Returns the value of attribute summary_histogram.



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# File 'lib/statsample/reliability/scaleanalysis.rb', line 17

def summary_histogram
  @summary_histogram
end

#valid_n ⇒ Object (readonly)

Returns the value of attribute valid_n.



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# File 'lib/statsample/reliability/scaleanalysis.rb', line 15

def valid_n
  @valid_n
end

#variances_mean ⇒ Object (readonly)

Returns the value of attribute variances_mean.



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# File 'lib/statsample/reliability/scaleanalysis.rb', line 15

def variances_mean
  @variances_mean
end

Instance Method Details

#item_characteristic_curve ⇒ Object

Returns a hash with structure



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# File 'lib/statsample/reliability/scaleanalysis.rb', line 63

def item_characteristic_curve
  i=0
  out={}
  total={}
  @ds.each do |row|
    tot=@total[i]
    @ds.vectors.each do |f|
      out[f]||= {}
      total[f]||={}
      out[f][tot]||= 0
      total[f][tot]||=0
      out[f][tot]+= row[f]
      total[f][tot]+=1
    end
    i+=1
  end
  total.each do |f,var|
    var.each do |tot,v|
      out[f][tot]=out[f][tot].quo(total[f][tot])
    end
  end
  out
end

#item_difficulty_analysis ⇒ Object

Returns a dataset with cases ordered by score and variables ordered by difficulty



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# File 'lib/statsample/reliability/scaleanalysis.rb', line 109

def item_difficulty_analysis
  dif={}
  @ds.vectors.each{|f| dif[f]=@ds[f].mean }
  dif_sort = dif.sort { |a,b| -(a[1]<=>b[1]) }
  scores_sort={}
  scores=@ds.vector_mean
  scores.each_index{ |i| scores_sort[i]=scores[i] }
  scores_sort=scores_sort.sort{|a,b| a[1]<=>b[1]}
  ds_new = Daru::DataFrame.new({}, order: ([:case,:score] + dif_sort.collect{|a,b| a.to_sym}))
  scores_sort.each do |i,score|
    row = [i, score]
    case_row = @ds.row[i].to_h
    dif_sort.each{ |variable,dif_value| row.push(case_row[variable]) }
    ds_new.add_row(row)
  end
  ds_new
end

#item_statistics ⇒ Object 



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# File 'lib/statsample/reliability/scaleanalysis.rb', line 100

def item_statistics
  @is||=@ds.vectors.to_a.inject({}) do |a,v|
    a[v]={:mean=>@ds[v].mean, :sds=>Math::sqrt(@cov_m.variance(v))}
    a
  end
end

#item_total_correlation ⇒ Object

Adjusted R.P.B. for each item

Adjusted RPB(Point biserial-correlation) for each item



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# File 'lib/statsample/reliability/scaleanalysis.rb', line 89

def item_total_correlation
  vecs = @ds.vectors.to_a
  @itc ||= vecs.inject({}) do |a,v|
    total=@ds.vector_sum(vecs - [v])
    a[v]=Statsample::Bivariate.pearson(@ds[v],total)
    a
  end
end

#mean_rpb ⇒ Object 



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# File 'lib/statsample/reliability/scaleanalysis.rb', line 97

def mean_rpb
  Daru::Vector.new(item_total_correlation.values).mean
end

#report_building(builder) ⇒ Object

:nodoc:



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# File 'lib/statsample/reliability/scaleanalysis.rb', line 149

def report_building(builder) #:nodoc:
  builder.section(:name=>@name) do |s|
    
    if @dumped.size>0
      s.section(:name=>"Items with variance=0") do |s1|
        s.table(:name=>_("Summary for %s with all items") % @name) do |t|
          t.row [_("Items"), @ods.ncols]
          t.row [_("Sum mean"),     "%0.4f" % @o_total.mean]
          t.row [_("S.d. mean"),     "%0.4f" % @o_total.sd]
        end
        s.table(:name=>_("Deleted items"), :header=>['item','mean']) do |t|
          @dumped.each do |f|
            t.row(["#{@ods[f].name}(#{f})", "%0.5f" % @ods[f].mean])
          end
        end
        s.parse_element(Statsample::Graph::Histogram.new(@o_total, :name=>"Histogram (complete data) for %s" % @name)) if @summary_histogram
      end
    end
    
    
    s.table(:name=>_("Summary for %s") % @name) do |t|
      t.row [_("Valid Items"), @ds.ncols]
    
    t.row [_("Valid cases"), @valid_n]
    t.row [_("Sum mean"),     "%0.4f" % @mean]
    t.row [_("Sum sd"),       "%0.4f" % @sd  ]
#          t.row [_("Sum variance"), "%0.4f" % @variance]
    t.row [_("Sum median"),   @median]
    t.hr
    t.row [_("Item mean"),    "%0.4f" % @item_mean]
    t.row [_("Item sd"),    "%0.4f" % @item_sd]
    t.hr
    t.row [_("Skewness"),     "%0.4f" % @skew]
    t.row [_("Kurtosis"),     "%0.4f" % @kurtosis]
    t.hr
    t.row [_("Cronbach's alpha"), @alpha ? ("%0.4f" % @alpha) : "--"]
    t.row [_("Standarized Cronbach's alpha"), @alpha_standarized ? ("%0.4f" % @alpha_standarized) : "--" ]
    t.row [_("Mean rpb"), "%0.4f" % mean_rpb]
    
    t.row [_("Variances mean"),  "%g" % @variances_mean]
    t.row [_("Covariances mean") , "%g" % @covariances_mean]
    end
    
    if (@alpha)
      s.text _("Items for obtain alpha(0.8) : %d" % Statsample::Reliability::n_for_desired_reliability(@alpha, 0.8, @ds.ncols))
      s.text _("Items for obtain alpha(0.9) : %d" % Statsample::Reliability::n_for_desired_reliability(@alpha, 0.9, @ds.ncols))
    end
    
    
    sid=stats_if_deleted
    is=item_statistics
    itc=item_total_correlation
    
    s.table(:name=>_("Items report for %s") % @name, :header=>["item","mean","sd", "mean if deleted", "var if deleted", "sd if deleted"," item-total correl.", "alpha if deleted"]) do |t|
      @ds.vectors.each do |f|
        row=["#{@ds[f].name}(#{f})"]
        if is[f]
          row+=[sprintf("%0.5f",is[f][:mean]), sprintf("%0.5f", is[f][:sds])]
        else
          row+=["-","-"]
        end
        if sid[f]
          row+= [sprintf("%0.5f",sid[f][:mean]), sprintf("%0.5f",sid[f][:variance_sample]), sprintf("%0.5f",sid[f][:sds])]
        else
          row+=%w{- - -}
        end
        if itc[f]
          row+= [sprintf("%0.5f",itc[f])]
        else 
          row+=['-']
        end
        if sid[f] and !sid[f][:alpha].nil?
          row+=[sprintf("%0.5f",sid[f][:alpha])]
        else
          row+=["-"]
        end
        t.row row
      end # end each
    end # table
    s.parse_element(Statsample::Graph::Histogram.new(@total, :name=>"Histogram (valid data) for %s" % @name)) if @summary_histogram
  end # section
end

#stats_if_deleted ⇒ Object 



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# File 'lib/statsample/reliability/scaleanalysis.rb', line 127

def stats_if_deleted
  @sif||=stats_if_deleted_intern
end

#stats_if_deleted_intern ⇒ Object

:nodoc:



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# File 'lib/statsample/reliability/scaleanalysis.rb', line 131

def stats_if_deleted_intern # :nodoc:
  return Hash.new if @ds.ncols == 1
  vecs = @ds.vectors.to_a
  vecs.inject({}) do |a,v|
    cov_2=@cov_m.submatrix(vecs - [v])
    #[email protected]
    #ds2.delete_vector(v)
    #total=ds2.vector_sum
    a[v]={}
    #a[v][:mean]=total.mean
    a[v][:mean]=@mean-item_statistics[v][:mean]
    a[v][:variance_sample]=cov_2.total_sum
    a[v][:sds]=Math::sqrt(a[v][:variance_sample])
    n=cov_2.row_size
    a[v][:alpha] = (n>=2) ? Statsample::Reliability.cronbach_alpha_from_covariance_matrix(cov_2) : nil
    a
  end
end