lib/statsample/factor.rb in statsample-0.14.0 vs lib/statsample/factor.rb in statsample-0.14.1

@@ -13,7 +13,81 @@
   #   * Statsample::Factor::Varimax
   #   * Statsample::Factor::Equimax
   #   * Statsample::Factor::Quartimax
   # See documentation of each class to use it
   module Factor
+    # Anti-image covariance matrix.
+    # Useful for inspection of desireability of data for factor analysis.
+    # According to Dziuban  & Shirkey (1974, p.359): 
+    #   "If this matrix does not exhibit many zero off-diagonal elements,
+    #   the investigator has evidence that the correlation
+    #   matrix is not appropriate for factor analysis."
+    # 
+    def self.anti_image_covariance_matrix(matrix)
+      s2=Matrix.diag(*(matrix.inverse.diagonal)).inverse
+      aicm=(s2)*matrix.inverse*(s2)
+      aicm.extend(Statsample::CovariateMatrix)
+      aicm.fields=matrix.fields if matrix.respond_to? :fields
+      aicm
+    end
+    def self.anti_image_correlation_matrix(matrix)
+      s=Matrix.diag(*(matrix.inverse.diagonal)).sqrt.inverse
+      aicm=s*matrix.inverse*s
+      aicm.extend(Statsample::CovariateMatrix)
+      aicm.fields=matrix.fields if matrix.respond_to? :fields
+      aicm
+      
+    end
+      
+    # Kaiser-Meyer-Olkin measure of sampling adequacy for correlation matrix.
+    # 
+    # Kaiser's (1974, cited on Dziuban  & Shirkey, 1974) present calibration of the index is as follows :
+    # * .90s—marvelous
+    # * .80s— meritorious
+    # * .70s—middling
+    # * .60s—mediocre
+    # * .50s—miserable
+    # * .50 •—unacceptable
+    def self.kmo(matrix)
+      q=anti_image_correlation_matrix(matrix)
+      n=matrix.row_size
+      sum_r,sum_q=0,0
+      n.times do |j|
+        n.times do |k|
+          if j!=k
+            sum_r+=matrix[j,k]**2
+            sum_q+=q[j,k]**2
+          end
+        end
+      end
+      sum_r.quo(sum_r+sum_q)
+    end
+    # Kaiser-Meyer-Olkin measure of sampling adequacy for one variable.
+    # 
+    def self.kmo_univariate(matrix, var)
+      if var.is_a? String
+        if matrix.respond_to? :fields
+          j=matrix.fields.index(var)
+          raise "Matrix doesn't have field #{var}" if j.nil?
+        else
+          raise "Matrix doesn't respond to fields"
+        end
+      else
+        j=var
+      end
+      
+      q=anti_image_correlation_matrix(matrix)
+      n=matrix.row_size
+      
+      sum_r,sum_q=0,0
+      
+      n.times do |k|
+        if j!=k
+          sum_r+=matrix[j,k]**2
+          sum_q+=q[j,k]**2
+        end
+      end
+      sum_r.quo(sum_r+sum_q)
+    end
+    
   end
 end