class Statsample::Factor::MAP
Velicer's Minimum Average Partial¶ ↑
“Velicer’s (1976) MAP test involves a complete princi pal components analysis followed by the examination of a series of matrices of partial correlations. Specifically, on the first step, the first principal component is par tialed out of the correlations between the variables of in terest, and the average squared coefficient in the off diagonals of the resulting partial correlation matrix is computed. On the second step, the first two principal components are partialed out of the original correlation matrix and the average squared partial correlation is again computed. These computations are conducted for k (the number of variables) minus one steps. The average squared partial correlations from these steps are then lined up, and the number of components is determined by the step number in the analyses that resulted in the lowest average squared partial correlation. The average squared coefficient in the original correlation matrix is also com puted, and if this coefficient happens to be lower than the lowest average squared partial correlation, then no components should be extracted from the correlation ma trix. Statistically, components are retained as long as the variance in the correlation matrix represents systematic variance. Components are no longer retained when there is proportionately more unsystematic variance than sys tematic variance.” (O'Connor, 2000, p.397).
Current algorithm is loosely based on SPSS O'Connor algorithm
Reference¶ ↑

O'Connor, B. (2000). SPSS and SAS programs for determining the number of components using parallel analysis and Velicer's MAP test. Behavior Research Methods, Instruments, & Computers, 32(3), 396402.
Velicer's Minimum Average Partial¶ ↑
“Velicer’s (1976) MAP test involves a complete princi pal components analysis followed by the examination of a series of matrices of partial correlations. Specifically, on the first step, the first principal component is par tialed out of the correlations between the variables of in terest, and the average squared coefficient in the off diagonals of the resulting partial correlation matrix is computed. On the second step, the first two principal components are partialed out of the original correlation matrix and the average squared partial correlation is again computed. These computations are conducted for k (the number of variables) minus one steps. The average squared partial correlations from these steps are then lined up, and the number of components is determined by the step number in the analyses that resulted in the lowest average squared partial correlation. The average squared coefficient in the original correlation matrix is also com puted, and if this coefficient happens to be lower than the lowest average squared partial correlation, then no components should be extracted from the correlation ma trix. Statistically, components are retained as long as the variance in the correlation matrix represents systematic variance. Components are no longer retained when there is proportionately more unsystematic variance than sys tematic variance.” (O'Connor, 2000, p.397).
Current algorithm is loosely based on SPSS O'Connor algorithm
Reference¶ ↑
Attributes
Average squared correlations
Smallest average squared correlation
Name of analysis
Number of factors to retain
Public Class Methods
# File lib/statsample/factor/map.rb, line 56 def initialize(matrix, opts=Hash.new) @matrix=matrix opts_default={ :use_gsl=>true, :name=>_("Velicer's MAP") } @opts=opts_default.merge(opts) opts_default.keys.each {k send("#{k}=", @opts[k]) } end
# File lib/statsample/factor/map.rb, line 53 def self.with_dataset(ds,opts=Hash.new) new(ds.correlation_matrix,opts) end
Public Instance Methods
# File lib/statsample/factor/map.rb, line 65 def compute gsl_m=(use_gsl and Statsample.has_gsl?) ? @matrix.to_gsl : @matrix klass_m=gsl_m.class eigvect,@eigenvalues=gsl_m.eigenvectors_matrix, gsl_m.eigenvalues eigenvalues_sqrt=@eigenvalues.collect {v Math.sqrt(v)} loadings=eigvect*(klass_m.diagonal(*eigenvalues_sqrt)) fm=Array.new(@matrix.row_size) ncol=@matrix.column_size fm[0]=(gsl_m.mssq  ncol).quo(ncol*(ncol1)) (ncol1).times do m puts "MAP:Eigenvalue #{m+1}" if $DEBUG a=loadings[0..(loadings.row_size1),0..m] partcov= gsl_m  (a*a.transpose) d=klass_m.diagonal(*(partcov.diagonal.collect {v Math::sqrt(1/v)})) pr=d*partcov*d fm[m+1]=(pr.mssqncol).quo(ncol*(ncol1)) end minfm=fm[0] nfactors=0 @errors=[] fm.each_with_index do v,s if defined?(Complex) and v.is_a? ::Complex @errors.push(s) else if v < minfm minfm=v nfactors=s end end end @number_of_factors=nfactors @fm=fm @minfm=minfm end