private static double GetLikelihood_Normal(List <RDataRecord> data, double[] beta_hat)
{
int N = data.Count;
int k = beta_hat.Length;
double residual_sum_of_squares = 0;
double[] y = new double[N];
for (int i = 0; i < N; ++i)
{
y[i] = data[i].YValue;
}
double sigma = StdDev.GetStdDev(y, Mean.GetMean(y)) / (N - k - 1);
for (int i = 0; i < N; ++i)
{
double linear_predictor = 0;
RDataRecord rec = data[i];
for (int j = 0; j < k; ++j)
{
linear_predictor += rec.data[j] * beta_hat[j];
}
double residual = rec.YValue - linear_predictor;
residual_sum_of_squares += residual * residual;
}
return(System.Math.Exp(-residual_sum_of_squares / (2 * sigma)) / System.Math.Sqrt(2 * System.Math.PI * sigma));
}
/// <summary>
///
/// </summary>
/// <param name="vcovmat">variance-covariance matrix for the model coefficients</param>
private void UpdateStatistics(IMatrix vcovmat, IMatrix W)
{
int n = vcovmat.RowCount;
int m = b.Dimension;
for (int i = 0; i < n; ++i)
{
mStats.StandardErrors[i] = System.Math.Sqrt(vcovmat[i, i]);
for (int j = 0; j < n; ++j)
{
mStats.VCovMatrix[i][j] = vcovmat[i, j];
}
}
double[] outcomes = new double[m];
for (int i = 0; i < m; i++)
{
double cross_prod = 0;
for (int j = 0; j < n; ++j)
{
cross_prod += A[i, j] * mX[j];
}
mStats.Residuals[i] = b[i] - mLinkFunc.GetInvLink(cross_prod);
outcomes[i] = b[i];
}
mStats.ResidualStdDev = StdDev.GetStdDev(mStats.Residuals, 0);
mStats.ResponseMean = Mean.GetMean(outcomes);
mStats.ResponseVariance = System.Math.Pow(StdDev.GetStdDev(outcomes, mStats.ResponseMean), 2);
mStats.R2 = 1 - mStats.ResidualStdDev * mStats.ResidualStdDev / mStats.ResponseVariance;
mStats.AdjustedR2 = 1 - mStats.ResidualStdDev * mStats.ResidualStdDev / mStats.ResponseVariance * (n - 1) / (n - mX.Length - 1);
}
/// <summary>
/// Calculate the adjusted R^2 (the explained variablity by the regression model)
/// The higher the adjusted R^2, the better the fitted regression model
/// </summary>
/// <param name="residuals">the residuals {y_i - X_i * beta_hat }_i</param>
/// <param name="y">The outcomes (i.e. sample values of the response variable)</param>
/// <param name="k">The number of parameters (i.e. the predictor coefficients in the regression model)</param>
/// <param name="n">The number of sample data points (i.e., the number records in the training data)</param>
/// <returns></returns>
public static double CalcAdjustedRSquare(double[] residuals, double[] y, int k, int n)
{
double Var_e = 0;
for (int i = 0; i < residuals.Length; ++i)
{
Var_e = residuals[i] * residuals[i];
}
double Var_y = System.Math.Pow(StdDev.GetStdDev(y, Mean.GetMean(y)), 2);
return(1 - (Var_e / (n - k - 1)) / (Var_y / (n - 1)));
}
protected void UpdateStatistics(double[] W)
{
IMatrix AtWA = At.ScalarMultiply(W).Multiply(A);
IMatrix AtWAInv = QRSolver.Invert(AtWA);
int n = AtWAInv.RowCount;
int m = b.Dimension;
for (int i = 0; i < n; ++i)
{
mStats.StandardErrors[i] = System.Math.Sqrt(AtWAInv[i, i]);
for (int j = 0; j < n; ++j)
{
mStats.VCovMatrix[i][j] = AtWAInv[i, j];
}
}
double[] outcomes = new double[m];
for (int i = 0; i < m; i++)
{
double cross_prod = 0;
for (int j = 0; j < n; ++j)
{
cross_prod += A[i, j] * mX[j];
}
mStats.Residuals[i] = b[i] - mLinkFunc.GetInvLink(cross_prod);
outcomes[i] = b[i];
}
mStats.ResidualStdDev = StdDev.GetStdDev(mStats.Residuals, 0);
mStats.ResponseMean = Mean.GetMean(outcomes);
mStats.ResponseVariance = System.Math.Pow(StdDev.GetStdDev(outcomes, mStats.ResponseMean), 2);
mStats.R2 = 1 - mStats.ResidualStdDev * mStats.ResidualStdDev / mStats.ResponseVariance;
mStats.AdjustedR2 = 1 - mStats.ResidualStdDev * mStats.ResidualStdDev / mStats.ResponseVariance * (n - 1) / (n - mX.Length - 1);
}
/// <summary>
/// In this particular instance, it is assumed that W = sigma^(-2) I, that is e is identical and uncorrelated
/// </summary>
/// <param name="A"></param>
/// <param name="b"></param>
/// <param name="x"></param>
public GlmStatistics(double[][] A, double[] b, double[] x)
{
int m = A.GetLength(0);
int n = A.GetLength(1);
mResiduals = new double[m];
for (int i = 0; i < m; ++i)
{
double cross_prod = 0;
for (int j = 0; j < n; ++j)
{
cross_prod += A[i][j] * x[j];
}
mResiduals[i] = b[i] - cross_prod;
}
double residual_mu = 0;
mResidualStdDev = StdDev.GetStdDev(mResiduals, residual_mu);
mResponseMean = Mean.GetMean(b);
mResponseVariance = System.Math.Pow(StdDev.GetStdDev(b, mResponseMean), 2);
// (A.transpose * A).inverse * sigma^2
IMatrix AtA = new SparseMatrix(n, n);
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < n; ++j)
{
double cross_prod = 0;
for (int k = 0; k < m; ++k)
{
cross_prod += A[i][k] * A[k][j];
}
AtA[i, j] = cross_prod;
}
}
IMatrix AtAInv = QRSolver.Invert(AtA);
double sigmaSq = mResidualStdDev * mResidualStdDev;
mVcovMatrix = new double[n][];
for (int i = 0; i < n; ++i)
{
mVcovMatrix[i] = new double[n];
for (int j = 0; j < n; ++j)
{
mVcovMatrix[i][j] = AtAInv[i, j] * sigmaSq;
}
}
mStandardErrors = new double[n];
for (int i = 0; i < n; ++i)
{
mStandardErrors[i] = System.Math.Sqrt(mVcovMatrix[i][i]);
}
mR2 = 1 - sigmaSq / mResponseVariance;
mAdjustedR2 = 1 - sigmaSq / mResponseVariance * (n - 1) / (n - x.Length - 1);
}
