/// <summary>
/// Approximate Wilk's lambda by F statistics
/// </summary>
/// <param name="H">Hypothesis Sum of Squares and Cross Products.</param>
/// <param name="E">Error Sum of Squares and Cross Products</param>
/// <param name="N">number of data points</param>
/// <param name="p">number of variables</param>
/// <param name="g">number of groups</param>
/// <param name="F_crit">The F critical value</param>
/// <returns>The p-value</returns>
public static double GetWilksLambda(double[][] H, double[][] E, int N, int p, int g, out double F_crit)
{
double[][] H_plus_E = Add(H, E);
double E_determinant = MatrixOp.GetDeterminant(E);
double H_plus_E_determinant = MatrixOp.GetDeterminant(H_plus_E);
double lambda = E_determinant / H_plus_E_determinant;
double a = N - g - (p - g + 2) / 2.0;
int b_threshold = p * p + (g - 1) * (g - 1) - 5;
double b = 1;
if (b_threshold > 0)
{
b = System.Math.Sqrt((p * p * (g - 1) - 4) / b_threshold);
}
double c = (p * (g - 1) - 2) / 2.0;
F_crit = ((1 - System.Math.Pow(lambda, 1 / b)) / (System.Math.Pow(lambda, 1 / b))) * ((a * b - c) / (p * (g - 1)));
double DF1 = p * (g - 1);
double DF2 = a * b - c;
double pValue = 1 - FDistribution.GetPercentile(F_crit, DF1, DF2);
return(pValue);
}
public static void RunExample(double[][] A)
{
Console.WriteLine("A = {0}", MatrixOp.Summary(A));
double[][] C = MatrixOp.GetUpperTriangularMatrix(A);
Console.WriteLine("C = {0}", MatrixOp.Summary(C));
double detA = MatrixOp.GetDeterminant(A);
Console.WriteLine("det(A) = {0}", detA);
}
