順位を使った回帰

nag_rank_regsn (g08rac) Example Program Data
 1 2 2 0.00001
 20
 1.0 1.0 23.0
 1.0 1.0 32.0
 3.0 1.0 37.0
 4.0 1.0 41.0
 2.0 1.0 41.0
 4.0 1.0 48.0
 1.0 1.0 48.0
 5.0 1.0 55.0
 4.0 1.0 55.0
 4.0 0.0 56.0
 4.0 1.0 57.0
 4.0 1.0 57.0
 4.0 1.0 57.0
 1.0 0.0 58.0
 4.0 1.0 59.0
 5.0 0.0 59.0
 5.0 0.0 60.0
 4.0 1.0 61.0
 4.0 1.0 62.0
 3.0 1.0 62.0

nag_rank_regsn (g08rac) Example Program Results

Number of samples = 1
Number of parameters fitted = 2
Distribution = 2
Tolerance for ties = 0.00001

Score statistic
   -1.048    64.333

Covariance matrix of score statistic
    0.673
   -4.159   533.670

Parameter estimates
   -0.852     0.114

Covariance matrix of parameter estimates
     1.560
     0.012     0.002

Chi-squared statistic =    8.221 with 2 d.f.

Standard errors of estimates and
approximate z-statistics
    1.249        -0.682
    0.044         2.567

/* nag_rank_regsn (g08rac) Example Program.
 *
 * CLL6I261D/CLL6I261DL Version.
 *
 * Copyright 2017 Numerical Algorithms Group.
 *
 * Mark 26.1, 2017.
 */

#include <stdio.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagg08.h>

int main(void)
{

  /* Scalars */
  double tol;
  Integer exit_status, i, idist, p, j, nmax, ns, nsum;
  Integer pdx, pdparvar;
  NagError fail;
  Nag_OrderType order;

  /* Arrays */
  double *eta = 0, *parest = 0, *parvar = 0, *vapvec = 0, *x = 0;
  double *y = 0, *zin = 0;
  Integer *irank = 0, *nv = 0;

#ifdef nAG_COLUMN_MAJOR
#define X(I, J)      x[(J-1)*pdx + I - 1]
#define PARVAR(I, J) parvar[(J-1)*pdparvar + I - 1]
  order = Nag_ColMajor;
#else
#define X(I, J)      x[(I-1)*pdx + J - 1]
#define PARVAR(I, J) parvar[(I-1)*pdparvar + J - 1]
  order = Nag_RowMajor;
#endif

  INIT_FAIL(fail);

  exit_status = 0;
  printf("nag_rank_regsn (g08rac) Example Program Results\n");

  /* Skip heading in data file */
  scanf("%*[^\n] ");

  /* Read number of samples, number of parameters to be fitted,
   * error distribution parameter and tolerance criterion for ties.
   */
  scanf("%ld%ld%ld%lf%*[^\n] ", &ns, &p, &idist,
        &tol);

  /* Allocate memory to nv only */
  if (!(nv = nAG_ALLOC(ns, Integer)))
  {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  printf("\n");
  printf("Number of samples =%2ld\n", ns);
  printf("Number of parameters fitted =%2ld\n", p);
  printf("Distribution =%2ld\n", idist);
  printf("Tolerance for ties =%8.5f\n", tol);

  /* Read the number of observations in each sample. */

  for (i = 1; i <= ns; ++i)
    scanf("%ld", &nv[i - 1]);
  scanf("%*[^\n] ");

  nmax = 0;
  nsum = 0;
  for (i = 1; i <= ns; ++i) {
    nsum += nv[i - 1];
    nmax = MAX(nmax, nv[i - 1]);
  }
  if (nmax > 0 && nmax <= 100 && nsum > 0 && nsum <= 100) {
    /* Allocate memory */
    if (!(eta = nAG_ALLOC(nmax, double)) ||
        !(parest = nAG_ALLOC(4 * p + 1, double)) ||
        !(parvar = nAG_ALLOC((p + 1) * p, double)) ||
        !(vapvec = nAG_ALLOC(nmax * (nmax + 1) / 2, double)) ||
        !(x = nAG_ALLOC(nsum * p, double)) ||
        !(y = nAG_ALLOC(nsum, double)) ||
        !(zin = nAG_ALLOC(nmax, double)) ||
        !(irank = nAG_ALLOC(nmax, Integer)))
    {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }
#ifdef nAG_COLUMN_MAJOR
    pdx = nsum;
    pdparvar = p + 1;
#else
    pdx = p;
    pdparvar = p;
#endif

    /* Read in observations and design matrices for each sample. */
    for (i = 1; i <= nsum; ++i) {
      scanf("%lf", &y[i - 1]);
      for (j = 1; j <= p; ++j)
        scanf("%lf", &X(i, j));
    }
    scanf("%*[^\n] ");

    /* nag_rank_regsn (g08rac).
     * Regression using ranks, uncensored data
     */
    nag_rank_regsn(order, ns, nv, y, p, x, pdx, idist, nmax, tol,
                   parvar, pdparvar, irank, zin, eta, vapvec, parest, &fail);
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_rank_regsn (g08rac).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

    printf("\n");
    printf("Score statistic\n");
    for (i = 1; i <= p; ++i)
      printf("%9.3f%s", parest[i - 1], i % 2 == 0 || i == p ? "\n" : " ");
    printf("\n");

    printf("Covariance matrix of score statistic\n");
    for (j = 1; j <= p; ++j) {
      for (i = 1; i <= j; ++i)
        printf("%9.3f%s", PARVAR(i, j), i % 2 == 0 || i == j ? "\n" : " ");
    }
    printf("\n");

    printf("Parameter estimates\n");
    for (i = 1; i <= p; ++i)
      printf("%9.3f%s", parest[p + i - 1], i % 2 == 0 || i == p ? "\n" : " ");
    printf("\n");

    printf("Covariance matrix of parameter estimates\n");
    for (i = 1; i <= p; ++i)
    {
      printf(" ");

      for (j = 1; j <= i; ++j)
        printf("%9.3f%s", PARVAR(i + 1, j),
               j % 2 == 0 || j == i ? "\n" : " ");
    }
    printf("\n");

    printf("Chi-squared statistic =%9.3f with%2ld d.f.\n",
           parest[p * 2], p);
    printf("\n");
    printf("Standard errors of estimates and\n");
    printf("approximate z-statistics\n");
    for (i = 1; i <= p; ++i)
      printf("%9.3f%14.3f\n", parest[2 * p + 1 + i - 1],
             parest[p * 3 + 1 + i - 1]);
    printf("\n");
  }
END:
  nAG_FREE(eta);
  nAG_FREE(parest);
  nAG_FREE(parvar);
  nAG_FREE(vapvec);
  nAG_FREE(x);
  nAG_FREE(y);
  nAG_FREE(zin);
  nAG_FREE(irank);
  nAG_FREE(nv);

  return exit_status;
}