Partial Covariances

Example 2

This example computes partial correlations from a 9 variable correlation matrix originally given by Emmett (1949). The partial correlations between the remaining variables, after adjusting for variables 1, 3 and 9, are computed. Note in the output that the row and column labels are numbers, not variable numbers. The corresponding variable numbers would be 2, 4, 5, 6, 7 and 8, respectively.

using System;
using PartialCovariances = Imsl.Stat.PartialCovariances;
using PrintMatrix = Imsl.Math.PrintMatrix;
using PrintMatrixFormat = Imsl.Math.PrintMatrixFormat;

public class PartialCovariancesEx2
{

   static public void Main(String[] arg)
   {
      double[,] sigma = 
      { 
      { 1.000, 0.523, 0.395, 0.471, 0.346, 0.426, 0.576, 0.434, 0.639 }, 
      { 0.523, 1.000, 0.479, 0.506, 0.418, 0.462, 0.547, 0.283, 0.645 }, 
      { 0.395, 0.479, 1.000, 0.355, 0.270, 0.254, 0.452, 0.219, 0.504 }, 
      { 0.471, 0.506, 0.355, 1.000, 0.691, 0.791, 0.443, 0.285, 0.505 }, 
      { 0.346, 0.418, 0.270, 0.691, 1.000, 0.679, 0.383, 0.149, 0.409 }, 
      { 0.426, 0.462, 0.254, 0.791, 0.679, 1.000, 0.372, 0.314, 0.472 }, 
      { 0.576, 0.547, 0.452, 0.443, 0.383, 0.372, 1.000, 0.385, 0.680 }, 
      { 0.434, 0.283, 0.219, 0.285, 0.149, 0.314, 0.385, 1.000, 0.470 }, 
      { 0.639, 0.645, 0.504, 0.505, 0.409, 0.472, 0.680, 0.470, 1.000 } 
      };

      int[] xIndices = { 1, 0, 1, 0, 0, 0, 0, 0, 1 };
      int df = 30;

      PartialCovariances pcov = new PartialCovariances(xIndices, sigma, df);

      double[,] correl = pcov.GetPartialCorrelationMatrix();
      PrintMatrixFormat pmf = new PrintMatrixFormat();
      pmf.NumberFormat = "0.0000";
      new PrintMatrix("Partial Correlations").Print(pmf, correl);

      double[,] pValues = pcov.GetPValues();
      new PrintMatrix("P-Values").Print(pmf, pValues);
   }
}

Output

                 Partial Correlations
      0       1        2       3       4        5     
0   1.0000  0.2235   0.1936  0.2113  0.1253  -0.0610  
1   0.2235  1.0000   0.6054  0.7198  0.0919   0.0249  
2   0.1936  0.6054   1.0000  0.5977  0.1230  -0.0766  
3   0.2113  0.7198   0.5977  1.0000  0.0349   0.0856  
4   0.1253  0.0919   0.1230  0.0349  1.0000   0.0622  
5  -0.0610  0.0249  -0.0766  0.0856  0.0622   1.0000  

                     P-Values
     0       1       2       3       4       5     
0  0.0000  0.2525  0.3232  0.2801  0.5249  0.7576  
1  0.2525  0.0000  0.0006  0.0000  0.6417  0.9000  
2  0.3232  0.0006  0.0000  0.0007  0.5328  0.6982  
3  0.2801  0.0000  0.0007  0.0000  0.8602  0.6650  
4  0.5249  0.6417  0.5328  0.8602  0.0000  0.7532  
5  0.7576  0.9000  0.6982  0.6650  0.7532  0.0000

Link to C# source.