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.

import java.text.*;
import com.imsl.stat.*;
import com.imsl.math.*;

public class FactorAnalysisEx2 {

    public static void main(String args[]) throws Exception {
        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.VARIANCE_COVARIANCE_MATRIX, 3);
        fl.setConvergenceCriterion1(.000001);
        fl.setConvergenceCriterion2(.01);
        fl.setFactorLoadingEstimationMethod(FactorAnalysis.MAXIMUM_LIKELIHOOD);
        fl.setVarianceEstimationMethod(0);
        fl.setMaxStep(10);
        fl.setDegreesOfFreedom(210);
        NumberFormat nf = NumberFormat.getInstance();
        nf.setMinimumFractionDigits(4);
        PrintMatrixFormat pmf = new PrintMatrixFormat();
        pmf.setNumberFormat(nf);
        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