private void compute_coefficients(Linalg.Matrix A, double[] y, double[] w)
{
Linalg.Matrix b = new Linalg.Matrix(y, false);
Linalg.Matrix coeffs;
Linalg.Matrix cov;
Linalg.SvDecomposition sv;
if (A.Rows > A.Columns)
{
sv = new Linalg.SvDecomposition(A);
coeffs = sv.Solve(b, false);
}
else
{
sv = new Linalg.SvDecomposition(A.Transpose());
coeffs = sv.Solve(b, true);
}
cov = sv.Cov();
Linalg.Matrix fit = A * coeffs;
Linalg.Matrix residuals = fit - b;
double mss = m_intercept ? Math.Stats.SumOfSquaredDev(fit.RowPackedData(), w) : Math.Stats.SumOfSquares(fit.RowPackedData());
double tss = m_intercept ? Math.Stats.SumOfSquaredDev(y, w) : Math.Stats.SumOfSquares(y);
double rss = Math.Stats.SumOfSquares(residuals.RowPackedData()); //without intercept residuals dont add up to zero
m_observations = A.Rows;
m_coeffs = coeffs.RowPackedData();
int p = m_coeffs.Length;
int n = m_observations;
int dof = n - p;
int dof_intercept = m_intercept ? 1 : 0;
m_coeffs_stderr = new double[p]; //coefficient standard errors
double stderr = System.Math.Sqrt(rss / dof); //residual sum of squares
for (int i = 0; i < p; i++)
{
m_coeffs_stderr[i] = stderr * System.Math.Sqrt(cov[i, i]);
}
double r2 = mss / (mss + rss);
double r2_adj = 1.0 - (n - dof_intercept) * (1.0 - r2) / dof;
double fvalue = (mss / (p - dof_intercept)) / (rss / dof);
double aic = n + n * System.Math.Log(2 * System.Math.PI) + n * System.Math.Log(rss / n) + 2 * (m_coeffs.Length + 1); // sum(log(w))
//generate summary
m_summary = new Dictionary <string, double>();
m_summary["n"] = m_observations;
m_summary["p"] = m_coeffs.Length;
m_summary["dof"] = dof;
m_summary["stderr"] = stderr;
m_summary["rss"] = rss;
m_summary["tss"] = tss;
m_summary["mss"] = mss;
m_summary["r2"] = r2;
m_summary["r2_adj"] = r2_adj;
m_summary["fvalue"] = fvalue;
m_summary["aic"] = aic;
for (int i = 0; i < p; i++)
{
double coef = m_coeffs[i];
double coef_std = m_coeffs_stderr[i];
double tvalue = coef / coef_std;
double pvalue = Math.Special.incbet(0.5 * dof, 0.5, dof / (dof + tvalue * tvalue));
m_summary[m_names[i]] = coef;
m_summary[m_names[i] + "_se"] = coef_std;
m_summary[m_names[i] + "_tvalue"] = tvalue;
m_summary[m_names[i] + "_pvalue"] = pvalue;
}
m_summary["intercept"] = m_intercept ? 1.0 : 0.0;
}
private void compute_coefficients(Linalg.Matrix A, double[] y, double[] w)
{
Linalg.Matrix b = new Linalg.Matrix(y, false);
double[] w_sqrt = null;
if (m_weighted)
{
w_sqrt = new double[b.Rows];
for (int i = 0; i < b.Rows; i++)
{
w_sqrt[i] = System.Math.Sqrt(w[i]);
b[i, 0] = b[i, 0] * w_sqrt[i]; //here we assume that specified weights are sigmas (i.e. not sigma square)
for (int j = 0; j < A.Columns; j++)
{
A[i, j] = A[i, j] * w_sqrt[i];
}
}
}
Linalg.Matrix coeffs;
Linalg.Matrix cov;
Linalg.SvDecomposition sv;
if (A.Rows > A.Columns)
{
sv = new Linalg.SvDecomposition(A);
coeffs = sv.Solve(b, false);
}
else
{
sv = new Linalg.SvDecomposition(A.Transpose());
coeffs = sv.Solve(b, true);
}
cov = sv.Cov();
Linalg.Matrix fit = A * coeffs;
Linalg.Matrix residuals = fit - b;
double aic_weight_correction = 0;
double weight_sum = fit.Rows;
if (m_weighted)
{
for (int i = 0; i < fit.Rows; i++)
{
fit[i, 0] = fit[i, 0] / w_sqrt[i];
residuals[i, 0] = fit[i, 0] - b[i, 0] / w_sqrt[i];
aic_weight_correction += System.Math.Log(w[i]);
}
weight_sum = Math.Stats.Utils.Sum(w);
}
double mss = Math.Stats.Utils.SumOfSquaredDev(fit.RowPackedData(), w);
double rss = Math.Stats.Utils.SumOfSquares(residuals.RowPackedData(), w); //without intercept residuals dont add up to zero
double tss = Math.Stats.Utils.SumOfSquaredDev(y, w);
m_observations = A.Rows;
m_coeffs = coeffs.RowPackedData();
int p = m_coeffs.Length;
int n = m_observations;
int dof = n - p;
int dof_intercept = m_intercept ? 1 : 0;
m_coeffs_stderr = new double[p]; //coefficient standard errors
double stderr = System.Math.Sqrt(rss / dof); //residual sum of squares
for (int i = 0; i < p; i++)
{
m_coeffs_stderr[i] = stderr * System.Math.Sqrt(cov[i, i]);
}
double r2 = mss / (mss + rss);
double r2_adj = 1.0 - (n - dof_intercept) * (1.0 - r2) / dof;
double fvalue = (mss / (p - dof_intercept)) / (rss / dof);
double aic_bic = n + n * System.Math.Log(2 * System.Math.PI) + n * System.Math.Log(rss / n) - aic_weight_correction;
double aic = aic_bic + 2 * (m_coeffs.Length + 1);
double bic = aic_bic + System.Math.Log(m_observations) * (m_coeffs.Length + 1);
//generate summary
m_summary = new Dictionary <string, double>();
m_summary["n"] = m_observations;
m_summary["p"] = m_coeffs.Length;
m_summary["dof"] = dof;
m_summary["stderr"] = stderr;
m_summary["rss"] = rss;
m_summary["tss"] = tss;
m_summary["mss"] = mss;
m_summary["r2"] = r2;
m_summary["r2_adj"] = r2_adj;
m_summary["fvalue"] = fvalue;
m_summary["aic"] = aic;
m_summary["bic"] = bic;
for (int i = 0; i < p; i++)
{
double coef = m_coeffs[i];
double coef_std = m_coeffs_stderr[i];
double tvalue = coef / coef_std;
double pvalue = Math.Special.incbet(0.5 * dof, 0.5, dof / (dof + tvalue * tvalue));
m_summary[m_names[i]] = coef;
m_summary[m_names[i] + "_se"] = coef_std;
m_summary[m_names[i] + "_tvalue"] = tvalue;
m_summary[m_names[i] + "_pvalue"] = pvalue;
}
m_summary["intercept"] = m_intercept ? 1.0 : 0.0;
}