independent variables.
*/
pspp_linreg_cache *
-pspp_linreg_cache_alloc (size_t n, size_t p)
+pspp_linreg_cache_alloc (const struct variable *depvar, const struct variable **indep_vars,
+ size_t n, size_t p)
{
+ size_t i;
pspp_linreg_cache *c;
c = (pspp_linreg_cache *) malloc (sizeof (pspp_linreg_cache));
- c->depvar = NULL;
+ c->depvar = depvar;
+ c->indep_vars = indep_vars;
c->indep_means = gsl_vector_alloc (p);
c->indep_std = gsl_vector_alloc (p);
c->ssx = gsl_vector_alloc (p); /* Sums of squares for the
c->ss_indeps = gsl_vector_alloc (p); /* Sums of squares for the
model parameters.
*/
- c->cov = gsl_matrix_alloc (p + 1, p + 1); /* Covariance matrix. */
c->n_obs = n;
c->n_indeps = p;
+ c->n_coeffs = 0;
+ for (i = 0; i < p; i++)
+ {
+ if (var_is_numeric (indep_vars[i]))
+ {
+ c->n_coeffs++;
+ }
+ else
+ {
+ c->n_coeffs += cat_get_n_categories (indep_vars[i]) - 1;
+ }
+ }
+
+ c->cov = gsl_matrix_alloc (c->n_coeffs + 1, c->n_coeffs + 1);
/*
Default settings.
*/
}
return true;
}
+static void
+cache_init (pspp_linreg_cache *cache)
+{
+ assert (cache != NULL);
+ cache->dft = cache->n_obs - 1;
+ cache->dfm = cache->n_indeps;
+ cache->dfe = cache->dft - cache->dfm;
+ cache->intercept = 0.0;
+}
+static void
+post_sweep_computations (pspp_linreg_cache *cache, const struct design_matrix *dm,
+ gsl_matrix *sw)
+{
+ gsl_matrix *xm;
+ gsl_matrix_view xtx;
+ gsl_matrix_view xmxtx;
+ double m;
+ double tmp;
+ size_t i;
+ size_t j;
+ int rc;
+
+ assert (sw != NULL);
+ assert (cache != NULL);
+
+ cache->sse = gsl_matrix_get (sw, cache->n_indeps, cache->n_indeps);
+ cache->mse = cache->sse / cache->dfe;
+ /*
+ Get the intercept.
+ */
+ m = cache->depvar_mean;
+ for (i = 0; i < cache->n_indeps; i++)
+ {
+ tmp = gsl_matrix_get (sw, i, cache->n_indeps);
+ cache->coeff[i]->estimate = tmp;
+ m -= tmp * pspp_linreg_get_indep_variable_mean (cache, design_matrix_col_to_var (dm, i));
+ }
+ /*
+ Get the covariance matrix of the parameter estimates.
+ Only the upper triangle is necessary.
+ */
+
+ /*
+ The loops below do not compute the entries related
+ to the estimated intercept.
+ */
+ for (i = 0; i < cache->n_indeps; i++)
+ for (j = i; j < cache->n_indeps; j++)
+ {
+ tmp = -1.0 * cache->mse * gsl_matrix_get (sw, i, j);
+ gsl_matrix_set (cache->cov, i + 1, j + 1, tmp);
+ }
+ /*
+ Get the covariances related to the intercept.
+ */
+ xtx = gsl_matrix_submatrix (sw, 0, 0, cache->n_indeps, cache->n_indeps);
+ xmxtx = gsl_matrix_submatrix (cache->cov, 0, 1, 1, cache->n_indeps);
+ xm = gsl_matrix_calloc (1, cache->n_indeps);
+ for (i = 0; i < xm->size2; i++)
+ {
+ gsl_matrix_set (xm, 0, i,
+ pspp_linreg_get_indep_variable_mean (cache, design_matrix_col_to_var (dm, i)));
+ }
+ rc = gsl_blas_dsymm (CblasRight, CblasUpper, cache->mse,
+ &xtx.matrix, xm, 0.0, &xmxtx.matrix);
+ gsl_matrix_free (xm);
+ if (rc == GSL_SUCCESS)
+ {
+ tmp = cache->mse / cache->n_obs;
+ for (i = 1; i < 1 + cache->n_indeps; i++)
+ {
+ tmp -= gsl_matrix_get (cache->cov, 0, i)
+ * pspp_linreg_get_indep_variable_mean (cache, design_matrix_col_to_var (dm, i - 1));
+ }
+ gsl_matrix_set (cache->cov, 0, 0, tmp);
+
+ cache->intercept = m;
+ }
+ else
+ {
+ fprintf (stderr, "%s:%d:gsl_blas_dsymm: %s\n",
+ __FILE__, __LINE__, gsl_strerror (rc));
+ exit (rc);
+ }
+}
+
/*
Fit the linear model via least squares. All pointers passed to pspp_linreg
are assumed to be allocated to the correct size and initialized to the
int rc;
gsl_matrix *design = NULL;
gsl_matrix_view xtx;
- gsl_matrix *xm;
- gsl_matrix_view xmxtx;
gsl_vector_view xty;
gsl_vector_view xi;
gsl_vector_view xj;
cache->depvar_std = s;
cache->sst = ss;
}
-
- cache->dft = cache->n_obs - 1;
- cache->dfm = cache->n_indeps;
- cache->dfe = cache->dft - cache->dfm;
+ cache_init (cache);
cache->n_coeffs = dm->m->size2;
- cache->intercept = 0.0;
-
for (i = 0; i < dm->m->size2; i++)
{
if (opts->get_indep_mean_std[i])
Sweep on the matrix sw, which contains XtX, XtY and YtY.
*/
reg_sweep (sw);
- cache->sse = gsl_matrix_get (sw, cache->n_indeps, cache->n_indeps);
- cache->mse = cache->sse / cache->dfe;
- /*
- Get the intercept.
- */
- m = cache->depvar_mean;
- for (i = 0; i < cache->n_indeps; i++)
- {
- tmp = gsl_matrix_get (sw, i, cache->n_indeps);
- cache->coeff[i]->estimate = tmp;
- m -= tmp * pspp_linreg_get_indep_variable_mean (cache, design_matrix_col_to_var (dm, i));
- }
- /*
- Get the covariance matrix of the parameter estimates.
- Only the upper triangle is necessary.
- */
-
- /*
- The loops below do not compute the entries related
- to the estimated intercept.
- */
- for (i = 0; i < cache->n_indeps; i++)
- for (j = i; j < cache->n_indeps; j++)
- {
- tmp = -1.0 * cache->mse * gsl_matrix_get (sw, i, j);
- gsl_matrix_set (cache->cov, i + 1, j + 1, tmp);
- }
- /*
- Get the covariances related to the intercept.
- */
- xtx = gsl_matrix_submatrix (sw, 0, 0, cache->n_indeps, cache->n_indeps);
- xmxtx = gsl_matrix_submatrix (cache->cov, 0, 1, 1, cache->n_indeps);
- xm = gsl_matrix_calloc (1, cache->n_indeps);
- for (i = 0; i < xm->size2; i++)
- {
- gsl_matrix_set (xm, 0, i,
- pspp_linreg_get_indep_variable_mean (cache, design_matrix_col_to_var (dm, i)));
- }
- rc = gsl_blas_dsymm (CblasRight, CblasUpper, cache->mse,
- &xtx.matrix, xm, 0.0, &xmxtx.matrix);
- gsl_matrix_free (xm);
- if (rc == GSL_SUCCESS)
- {
- tmp = cache->mse / cache->n_obs;
- for (i = 1; i < 1 + cache->n_indeps; i++)
- {
- tmp -= gsl_matrix_get (cache->cov, 0, i)
- * pspp_linreg_get_indep_variable_mean (cache, design_matrix_col_to_var (dm, i - 1));
- }
- gsl_matrix_set (cache->cov, 0, 0, tmp);
-
- cache->intercept = m;
- }
- else
- {
- fprintf (stderr, "%s:%d:gsl_blas_dsymm: %s\n",
- __FILE__, __LINE__, gsl_strerror (rc));
- exit (rc);
- }
+ post_sweep_computations (cache, dm, sw);
gsl_matrix_free (sw);
}
else if (cache->method == PSPP_LINREG_CONDITIONAL_INVERSE)
coef = pspp_linreg_get_coeff (c, v, NULL);
return pspp_coeff_get_mean (coef);
}
- return GSL_NAN;
+ return 0.0;
}
void pspp_linreg_set_indep_variable_mean (pspp_linreg_cache *c, const struct variable *v,
only variables in the model are in the covariance matrix.
*/
static struct design_matrix *
-rearrange_covariance_matrix (const struct design_matrix *cov, pspp_linreg_cache *c)
+rearrange_covariance_matrix (const struct covariance_matrix *cm, pspp_linreg_cache *c)
{
- struct variable **v;
- struct variable **model_vars;
- struct variable *tmp;
+ const struct variable **model_vars;
+ struct design_matrix *cov;
struct design_matrix *result;
- int n_vars;
- int found;
- size_t *columns;
+ size_t *permutation;
size_t i;
size_t j;
size_t k;
- size_t dep_col;
+ size_t n_coeffs = 0;
+ assert (cm != NULL);
+ cov = covariance_to_design (cm);
assert (cov != NULL);
assert (c != NULL);
assert (cov->m->size1 > 0);
assert (cov->m->size2 == cov->m->size1);
- v = xnmalloc (c->n_coeffs, sizeof (*v));
- model_vars = xnmalloc (c->n_coeffs, sizeof (*model_vars));
- columns = xnmalloc (cov->m->size2, sizeof (*columns));
- n_vars = pspp_linreg_get_vars (c, v);
- dep_col = 0;
- k = 0;
- for (i = 0; i < cov->m->size2; i++)
- {
- tmp = design_matrix_col_to_var (cov, i);
- found = 0;
- j = 0;
- while (!found && j < n_vars)
- {
- if (tmp == v[j])
- {
- found = 1;
- if (tmp == c->depvar)
- {
- dep_col = j;
- }
- else
- {
- columns[k] = j;
- k++;
- }
- }
- j++;
- }
- }
- k++;
- columns[k] = dep_col;
- /*
- K should now be equal to C->N_INDEPS + 1. If it is not, then
- either the code above is wrong or the caller didn't send us the
- correct values in C.
- */
- assert (k == c->n_indeps + 1);
+ model_vars = xnmalloc (1 + c->n_indeps, sizeof (*model_vars));
+
/*
Put the model variables in the right order in MODEL_VARS.
+ Count the number of coefficients.
*/
- for (i = 0; i < k; i++)
+ for (i = 0; i < c->n_indeps; i++)
{
- model_vars[i] = v[columns[i]];
+ model_vars[i] = c->indep_vars[i];
}
+ model_vars[i] = c->depvar;
+ result = covariance_matrix_create (1 + c->n_indeps, model_vars);
+ permutation = xnmalloc (design_matrix_get_n_cols (result), sizeof (*permutation));
- result = covariance_matrix_create (k, model_vars);
- for (i = 0; i < result->m->size1; i++)
+ for (j = 0; j < cov->m->size2; j++)
{
- for (j = 0; j < result->m->size2; j++)
+ k = 0;
+ while (k < result->m->size2)
{
- gsl_matrix_set (result->m, i, j, gsl_matrix_get (cov->m, columns[i], columns[j]));
+ if (design_matrix_col_to_var (cov, j) == design_matrix_col_to_var (result, k))
+ {
+ permutation[k] = j;
+ }
+ k++;
}
}
- free (columns);
- free (v);
+ for (i = 0; i < result->m->size1; i++)
+ for (j = 0; j < result->m->size2; j++)
+ {
+ gsl_matrix_set (result->m, i, j, gsl_matrix_get (cov->m, permutation[i], permutation[j]));
+ }
+ free (permutation);
+ free (model_vars);
return result;
}
/*
Estimate the model parameters from the covariance matrix only. This
method uses less memory than PSPP_LINREG, which requires the entire
data set to be stored in memory.
+
+ The function assumes FULL_COV may contain columns corresponding to
+ variables that are not in the model. It fixes this in
+ REARRANG_COVARIANCE_MATRIX. This allows the caller to compute a
+ large covariance matrix once before, then pass it to this without
+ having to alter it. The problem is that this means the caller must
+ set CACHE->N_COEFFS.
*/
-int
-pspp_linreg_with_cov (const struct design_matrix *cov,
- const pspp_linreg_opts * opts, pspp_linreg_cache * cache)
+void
+pspp_linreg_with_cov (const struct covariance_matrix *full_cov,
+ pspp_linreg_cache * cache)
{
- assert (cov != NULL);
- assert (opts != NULL);
+ struct design_matrix *cov;
+
+ assert (full_cov != NULL);
assert (cache != NULL);
+
+ cov = rearrange_covariance_matrix (full_cov, cache);
+ cache_init (cache);
+ reg_sweep (cov->m);
+ post_sweep_computations (cache, cov, cov->m);
+ design_matrix_destroy (cov);
}
+double pspp_linreg_mse (const pspp_linreg_cache *c)
+{
+ assert (c != NULL);
+ return (c->sse / c->dfe);
+}
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