Example: Factor Analysis

This example illustrates the use of the FactorAnalysis class. The following data were originally analyzed by Emmett(1949). There are 211 observations on 9 variables. Following Lawley and Maxwell (1971), three factors will be obtained by the method of maximum likelihood.

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

public class FactorAnalysisEx2
{
    public static void  Main(String[] args)
    {
        double[,] cov = {
                             {1.0, 0.523, 0.395, 0.471, 
                                    0.346, 0.426, 0.576, 0.434, 0.639},
                             {0.523, 1.0, 0.479, 0.506,
                                    0.418, 0.462, 0.547, 0.283, 0.645},
                             {0.395, 0.479, 1.0, 0.355, 
                                    0.27, 0.254, 0.452, 0.219, 0.504},
                             {0.471, 0.506, 0.355, 1.0, 
                                    0.691, 0.791, 0.443, 0.285, 0.505},
                             {0.346, 0.418, 0.27, 0.691, 
                                    1.0, 0.679, 0.383, 0.149, 0.409},
                             {0.426, 0.462, 0.254, 0.791, 
                                    0.679, 1.0, 0.372, 0.314, 0.472},
                             {0.576, 0.547, 0.452, 0.443, 
                                    0.383, 0.372, 1.0, 0.385, 0.68},
                             {0.434, 0.283, 0.219, 0.285,
                                    0.149, 0.314, 0.385, 1.0, 0.47},
                             {0.639, 0.645, 0.504, 0.505, 
                                    0.409, 0.472, 0.68, 0.47, 1.0}};
        FactorAnalysis fl = new FactorAnalysis(cov, 
            FactorAnalysis.MatrixType.VarianceCovariance, 3);
        fl.ConvergenceCriterion1 = .000001;
        fl.ConvergenceCriterion2 = .01;
        fl.FactorLoadingEstimationMethod = 
            FactorAnalysis.Model.MaximumLikelihood;
        fl.VarianceEstimationMethod = 0;
        fl.MaxStep = 10;
        fl.DegreesOfFreedom = 210;

        PrintMatrixFormat pmf = new PrintMatrixFormat();
        pmf.NumberFormat = "0.0000";
        new PrintMatrix
            ("Unique Error Variances").Print(pmf, fl.GetVariances());
        new PrintMatrix
            ("Unrotated Factor Loadings").Print(pmf, fl.GetFactorLoadings());
        new PrintMatrix("Eigenvalues").Print(pmf, fl.GetValues());
        new PrintMatrix("Statistics").Print(pmf, fl.GetStatistics());
    }
}

Output

Unique Error Variances
     0     
0  0.4505  
1  0.4271  
2  0.6166  
3  0.2123  
4  0.3805  
5  0.1769  
6  0.3995  
7  0.4615  
8  0.2309  

  Unrotated Factor Loadings
     0        1        2     
0  0.6642  -0.3209   0.0735  
1  0.6888  -0.2471  -0.1933  
2  0.4926  -0.3022  -0.2224  
3  0.8372   0.2924  -0.0354  
4  0.7050   0.3148  -0.1528  
5  0.8187   0.3767   0.1045  
6  0.6615  -0.3960  -0.0777  
7  0.4579  -0.2955   0.4913  
8  0.7657  -0.4274  -0.0117  

Eigenvalues
     0     
0  0.0626  
1  0.2295  
2  0.5413  
3  0.8650  
4  0.8937  
5  0.9736  
6  1.0802  
7  1.1172  
8  1.1401  

 Statistics
      0     
0  0.0350   
1  1.0000   
2  7.1494   
3  12.0000  
4  0.8476   
5  5.0000