Example 2

In this example, a two-way analysis of covariance model containing all the interaction terms is fit. First, RegressorsForGLM is used to produce a matrix of regressors, regressors , from the data x . Then, regressors is used as the input matrix into Regression to produce the final fit. The mapping from effects to columns in the matrix regressors is given by the jagged array returned by getEffectsColumns . Each row in this matrix gives the column number for the corresponding effect.

The regressors, generated using the dummy method LEAVE_OUT_LAST , are the model whose mean function is

 \mu + \alpha_i + \beta_j + \gamma_{ij} + \delta x_{ij} +\zeta_i x_{ij} +\eta x_{ij} + \theta_i x_{ij} \mbox{~~~} i = 1, 2;~ j=1, 2, 3
where \alpha_2 = \beta_3 = \gamma_{21} + \gamma_{22} + \gamma{23} + \zeta_2 + \eta_3 + \theta_{21} + \theta_{22} + \theta_{23} = 0.

import java.text.*;
import com.imsl.stat.*;
import com.imsl.math.PrintMatrix;
import com.imsl.math.PrintMatrixFormat;
import java.text.MessageFormat;

public class RegressorsForGLMEx2 {
    static MessageFormat mf = new MessageFormat("{0}  {1,number,#0.0000}");

    static public void main(String arg[]) {
        double x[][] = {
            {1.0, 1.0, 1.11},
            {1.0, 1.0, 2.22},
            {1.0, 1.0, 3.33},
            {1.0, 2.0, 1.11},
            {1.0, 2.0, 2.22},
            {1.0, 2.0, 3.33},
            {1.0, 3.0, 1.11},
            {1.0, 3.0, 2.22},
            {1.0, 3.0, 3.33},
            {2.0, 1.0, 1.11},
            {2.0, 1.0, 2.22},
            {2.0, 1.0, 3.33},
            {2.0, 2.0, 1.11},
            {2.0, 2.0, 2.22},
            {2.0, 2.0, 3.33},
            {2.0, 3.0, 1.11},
            {2.0, 3.0, 2.22},
            {2.0, 3.0, 3.33}
        };
        double y[] = {
            1.0, 2.0, 2.0, 4.0, 4.0, 6.0,
            3.0, 3.5, 4.0, 4.5, 5.0, 5.5,
            2.0, 3.0, 4.0, 5.0, 6.0, 7.0
        };
        int effects[][] = {
            {0},
            {1},
            {0, 1},
            {2},
            {0, 2},
            {1, 2},
            {0, 1, 2}};
        
        int nClassVariables = 2;
        
        RegressorsForGLM r = new RegressorsForGLM(x, nClassVariables);
        r.setDummyMethod(RegressorsForGLM.LEAVE_OUT_LAST);
        r.setEffects(effects);
        
        System.out.println("Mapping of Effects to Regressor Columns");
        int col[][] = r.getEffectsColumns();
        for (int iEffect = 0;  iEffect < effects.length;  iEffect++) {
            System.out.print("Effect {");
            for (int j = 0;  j < effects[iEffect].length;  j++) {
                if (j > 0)  System.out.print(", ");
                System.out.print(effects[iEffect][j]);
            }
            System.out.print("} is in regressor column(s) {");
            for (int j = 0;  j < col[iEffect].length;  j++) {
                if (j > 0)  System.out.print(", ");
                System.out.print(col[iEffect][j]);
            }
            System.out.println("}");
        }
        System.out.println();

        double regressors[][] = r.getRegressors();
        
        PrintMatrixFormat pmf = new PrintMatrixFormat();
        pmf.setColumnLabels(new String[]{"Alpha1", "Beta1", "Beta2",
            "Gamma11", "Gamma12", "Delta", "Zeta1", "Eta1", "Eta2",
            "Theta11", "Theta12"});
        new PrintMatrix("Regressors").print(pmf,regressors);
        
        int nRegressors = r.getNumberOfRegressors();
        LinearRegression regression = new LinearRegression(nRegressors, true);
        regression.update(regressors, y);
        
        System.out.println("        * * * Analysis of Variance * * *");
        ANOVA anova = regression.getANOVA();
        
        Object table[][] = new Object[15][2];
        table[0][0] = "Degrees of freedom for the model       ";
        table[0][1] = anova.getDegreesOfFreedomForModel();
        table[1][0] = "Degrees of freedom for the error       ";
        table[1][1] = anova.getDegreesOfFreedomForError();
        table[2][0] = "Total degrees of freedom               ";
        table[2][1] = anova.getTotalDegreesOfFreedom();
        table[3][0] = "Sum of squares for the model           ";
        table[3][1] = anova.getSumOfSquaresForModel();
        table[4][0] = "Sum of squares for error               ";
        table[4][1] = anova.getSumOfSquaresForError();
        table[5][0] = "Total sum of squares                   ";
        table[5][1] = anova.getTotalSumOfSquares();
        table[6][0] = "Model mean square                      ";
        table[6][1] = anova.getModelMeanSquare();
        table[7][0] = "Error mean square                      ";
        table[7][1] = anova.getErrorMeanSquare();
        table[8][0] = "F-statistic                            ";
        table[8][1] = anova.getF();
        table[9][0] = "p-value                                ";
        table[9][1] = anova.getP();
        table[10][0] = "R-squared                             ";
        table[10][1] = anova.getRSquared();
        table[11][0] = "Adjusted R-squared                    ";
        table[11][1] = anova.getAdjustedRSquared();
        table[12][0] = "Standard deviation for the model error";
        table[12][1] = anova.getModelErrorStdev();
        table[13][0] = "Overall mean of y                     ";
        table[13][1] = anova.getMeanOfY();
        table[14][0] = "Coefficient of variation              ";
        table[14][1] = anova.getCoefficientOfVariation();
        pmf = new PrintMatrixFormat();
        pmf.setNoColumnLabels();
        pmf.setNoRowLabels();
        pmf.setNumberFormat(new java.text.DecimalFormat("0.0000"));
        new PrintMatrix().print(pmf, table);
    }
}

Output

Mapping of Effects to Regressor Columns
Effect {0} is in regressor column(s) {0}
Effect {1} is in regressor column(s) {1, 2}
Effect {0, 1} is in regressor column(s) {3, 4}
Effect {2} is in regressor column(s) {5}
Effect {0, 2} is in regressor column(s) {6}
Effect {1, 2} is in regressor column(s) {7, 8}
Effect {0, 1, 2} is in regressor column(s) {9, 10}

                                       Regressors
    Alpha1  Beta1  Beta2  Gamma11  Gamma12  Delta  Zeta1  Eta1  Eta2  Theta11  Theta12  
 0    1       1      0       1        0     1.11   1.11   1.11  0      1.11     0       
 1    1       1      0       1        0     2.22   2.22   2.22  0      2.22     0       
 2    1       1      0       1        0     3.33   3.33   3.33  0      3.33     0       
 3    1       0      1       0        1     1.11   1.11   0     1.11   0        1.11    
 4    1       0      1       0        1     2.22   2.22   0     2.22   0        2.22    
 5    1       0      1       0        1     3.33   3.33   0     3.33   0        3.33    
 6    1       0      0       0        0     1.11   1.11   0     0      0        0       
 7    1       0      0       0        0     2.22   2.22   0     0      0        0       
 8    1       0      0       0        0     3.33   3.33   0     0      0        0       
 9    0       1      0       0        0     1.11   0      1.11  0      0        0       
10    0       1      0       0        0     2.22   0      2.22  0      0        0       
11    0       1      0       0        0     3.33   0      3.33  0      0        0       
12    0       0      1       0        0     1.11   0      0     1.11   0        0       
13    0       0      1       0        0     2.22   0      0     2.22   0        0       
14    0       0      1       0        0     3.33   0      0     3.33   0        0       
15    0       0      0       0        0     1.11   0      0     0      0        0       
16    0       0      0       0        0     2.22   0      0     0      0        0       
17    0       0      0       0        0     3.33   0      0     0      0        0       

        * * * Analysis of Variance * * *
                                                    
Degrees of freedom for the model         11.0000  
Degrees of freedom for the error          6.0000  
Total degrees of freedom                 17.0000  
Sum of squares for the model             43.9028  
Sum of squares for error                  0.8333  
Total sum of squares                     44.7361  
Model mean square                         3.9912  
Error mean square                         0.1389  
F-statistic                              28.7364  
p-value                                   0.0003  
R-squared                                98.1372  
Adjusted R-squared                       94.7221  
Standard deviation for the model error    0.3727  
Overall mean of y                         3.9722  
Coefficient of variation                  9.3821  

Link to Java source.