public static MANOVA RunMANOVA(double[][] y, int[] grpCat, double signficance_level = 0.05)
{
MANOVA output = new MANOVA();
RunMANOVA(y, grpCat, output, signficance_level);
return(output);
}
public static void RunMANOVA(double[][] y, int[] grpCat, MANOVA output, double signficance_level = 0.05)
{
output.GrandMeansY = GetGrandMeans(y);
int N = grpCat.Length; // number of data points
int p = y[0].Length; // number of variables
Dictionary <int, List <double[]> > groupped_y = new Dictionary <int, List <double[]> >();
for (int i = 0; i < N; ++i)
{
int grpId = grpCat[i];
double[] y_i = y[i];
List <double[]> group_y = null;
if (groupped_y.ContainsKey(grpId))
{
group_y = groupped_y[grpId];
}
else
{
group_y = new List <double[]>();
groupped_y[grpId] = group_y;
}
group_y.Add(y_i);
}
output.SampleMeans = GetSampleMeans(groupped_y);
output.T = GetT(groupped_y, output.GrandMeansY, p);
output.E = GetE(groupped_y, output.SampleMeans, p);
output.H = GetH(output.SampleMeans, output.GrandMeansY, p);
int g = output.SampleMeans.Count;
output.dfT = N - 1;
output.dfH = g - 1;
output.dfE = N - g;
output.pValue = GetWilksLambda(output.H, output.E, N, p, g, out output.F_crit);
}
public static void RunMANCOVA(double[][] X, double[][] Y, int[] grpCat, out MANCOVA output, double significance_level = 0.05)
{
output = new MANCOVA();
int Dx = X[0].Length;
int Dy = Y[0].Length;
int N = Y.Length;
Dictionary <int, List <double> >[] groupped_x_at_dim = new Dictionary <int, List <double> > [Dx];
Dictionary <int, List <double> >[] groupped_y_at_dim = new Dictionary <int, List <double> > [Dy];
for (int l = 0; l < Dx; ++l)
{
groupped_x_at_dim[l] = new Dictionary <int, List <double> >();
}
for (int l = 0; l < Dy; ++l)
{
groupped_y_at_dim[l] = new Dictionary <int, List <double> >();
}
double[][] X_transpose = new double[Dx][];
for (int i = 0; i < N; ++i)
{
double[] X_i = X[i];
X_transpose[i] = new double[Dx];
for (int d = 0; d < Dx; ++d)
{
X_transpose[d][i] = X_i[d];
}
}
double[][] Y_transpose = new double[Dy][];
for (int i = 0; i < N; ++i)
{
double[] Y_i = Y[i];
Y_transpose[i] = new double[Dy];
for (int d = 0; d < Dx; ++d)
{
Y_transpose[d][i] = Y_i[d];
}
}
for (int i = 0; i < N; ++i)
{
int grpId = grpCat[i];
for (int d = 0; d < Dx; ++d)
{
List <double> group_x = null;
if (groupped_x_at_dim[d].ContainsKey(grpId))
{
group_x = groupped_x_at_dim[d][grpId];
}
else
{
group_x = new List <double>();
groupped_x_at_dim[d][grpId] = group_x;
}
group_x.Add(X_transpose[d][i]);
}
for (int d = 0; d < Dy; ++d)
{
List <double> group_y = null;
if (groupped_y_at_dim[d].ContainsKey(grpId))
{
group_y = groupped_y_at_dim[d][grpId];
}
else
{
group_y = new List <double>();
groupped_y_at_dim[d][grpId] = group_y;
}
group_y.Add(Y_transpose[d][i]);
}
}
int k = groupped_x_at_dim[0].Count;
output.GrandMeansX = new double[Dx];
output.GrandMeansY = new double[Dy];
output.SSTx = new double[Dx];
for (int d = 0; d < Dx; ++d)
{
output.SSTx[d] = GetSST(X_transpose[d], out output.GrandMeansX[d]);
}
output.SSTy = new double[Dy];
for (int d = 0; d < Dy; ++d)
{
output.SSTy[d] = GetSST(Y_transpose[d], out output.GrandMeansY[d]);
}
output.SSBGx = new double[Dx];
for (int d = 0; d < Dx; ++d)
{
output.SSBGx[d] = GetSSG(groupped_x_at_dim[d], output.GrandMeansX[d]);
}
output.SSBGy = new double[Dy];
for (int d = 0; d < Dy; ++d)
{
output.SSBGy[d] = GetSSG(groupped_y_at_dim[d], output.GrandMeansY[d]);
}
output.SSWGx = new double[Dx];
for (int d = 0; d < Dx; ++d)
{
output.SSWGx[d] = output.SSTx[d] - output.SSBGx[d];
}
output.SSWGy = new double[Dy];
for (int d = 0; d < Dy; ++d)
{
output.SSWGy[d] = output.SSTy[d] - output.SSBGy[d];
}
output.SCT = new double[Dy][];
for (int dy = 0; dy < Dy; ++dy)
{
output.SCT[dy] = new double[Dx];
for (int dx = 0; dx < Dx; ++dx)
{
output.SCT[dy][dx] = GetCovariance(X_transpose[dx], Y_transpose[dy]);
}
}
output.SCWG = new double[Dy][];
for (int dy = 0; dy < Dy; ++dy)
{
output.SCWG[dy] = new double[Dx];
for (int dx = 0; dx < Dx; ++dx)
{
output.SCWG[dy][dx] = GetCovarianceWithinGroup(groupped_x_at_dim[dx], groupped_y_at_dim[dy]);
}
}
output.rT = new double[Dy][];
for (int dy = 0; dy < Dy; ++dy)
{
output.rT[dy] = new double[Dx];
for (int dx = 0; dx < Dx; ++dx)
{
output.rT[dy][dx] = output.SCT[dy][dx] / System.Math.Sqrt(output.SSTx[dx] * output.SSTy[dy]);
}
}
output.rWG = new double[Dy][];
for (int dy = 0; dy < Dy; ++dy)
{
output.rWG[dy] = new double[Dx];
for (int dx = 0; dx < Dx; ++dx)
{
output.rWG[dy][dx] = output.SCWG[dy][dx] / System.Math.Sqrt(output.SSWGx[dx] * output.SSWGy[dy]);
}
}
output.Slope = new double[Dy][]; //b[i][k] where i is the number of columns in X and k is the number of columns in Y
for (int dy = 0; dy < Dy; ++dy)
{
output.Slope[dy] = new double[Dx];
for (int dx = 0; dx < Dx; ++dx)
{
output.Slope[dy][dx] = output.SCWG[dx][dy] / output.SSWGx[dx];
}
}
output.MeanWithinGroups_x = GetMeanWithinGroup(groupped_x_at_dim);
output.MeanWithinGroups_y = GetMeanWithinGroup(groupped_y_at_dim);
output.Intercepts = GetIntercepts(output.MeanWithinGroups_x, output.MeanWithinGroups_y, output.GrandMeansX, output.Slope);
double[][] Y_adj = new double[N][];
for (int i = 0; i < N; ++i)
{
Y_adj[i] = new double[Dy];
for (int dy = 0; dy < Dy; ++dy)
{
Y_adj[i][dy] = Y[i][dy] - DotProduct(output.Slope[dy], X[i]);
}
}
MANOVA.RunMANOVA(Y_adj, grpCat, output, significance_level);
}