package com.imsl.test.example.stat;

import java.text.*;
import com.imsl.stat.*;
import com.imsl.math.*;
/**
 * <p>Compute the factors on 9 variables by the method of maximum likelihood. </p>
 * 
 * <p>This example illustrates the use of the <code>FactorAnalysis</code> class. 
 * The following data were originally analyzed by Emmett(1949). There are \(211\) 
 * observations on \(9\) variables. Following Lawley and Maxwell (1971), three 
 * factors are obtained by the method of maximum likelihood.  
</p>

 * 
 * @see <a href="FactorAnalysisEx2.java">Code</a>
 * @see <a href="doc-files/FactorAnalysisEx2.out">Output</a>
 */

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());
    }
}