#include <math/coefficient.h>
#include <math/linreg.h>
#include <math/coefficient.h>
+#include <math/design-matrix.h>
+#include <src/data/category.h>
#include <src/data/variable.h>
#include <src/data/value.h>
#include <gl/xalloc.h>
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
values as indicated by opts.
*/
int
-pspp_linreg (const gsl_vector * Y, const gsl_matrix * X,
+pspp_linreg (const gsl_vector * Y, const struct design_matrix *dm,
const pspp_linreg_opts * opts, pspp_linreg_cache * cache)
{
int rc;
gsl_matrix *design = NULL;
gsl_matrix_view xtx;
- gsl_matrix_view xm;
- gsl_matrix_view xmxtx;
gsl_vector_view xty;
gsl_vector_view xi;
gsl_vector_view xj;
gsl_vector *param_estimates;
+ struct pspp_coeff *coef;
+ const struct variable *v;
+ const union value *val;
size_t i;
size_t j;
cache->depvar_std = s;
cache->sst = ss;
}
- for (i = 0; i < cache->n_indeps; i++)
+ cache_init (cache);
+ cache->n_coeffs = dm->m->size2;
+ for (i = 0; i < dm->m->size2; i++)
{
if (opts->get_indep_mean_std[i])
{
- linreg_mean_std (gsl_matrix_const_column (X, i), &m, &s, &ss);
- gsl_vector_set (cache->indep_means, i, m);
- gsl_vector_set (cache->indep_std, i, s);
+ linreg_mean_std (gsl_matrix_const_column (dm->m, i), &m, &s, &ss);
+ v = design_matrix_col_to_var (dm, i);
+ val = NULL;
+ if (var_is_alpha (v))
+ {
+ j = i - design_matrix_var_to_column (dm, v);
+ val = cat_subscript_to_value (j, v);
+ }
+ coef = pspp_linreg_get_coeff (cache, v, val);
+ pspp_coeff_set_mean (coef, m);
+ pspp_coeff_set_sd (coef, s);
gsl_vector_set (cache->ssx, i, ss);
+
}
}
- cache->dft = cache->n_obs - 1;
- cache->dfm = cache->n_indeps;
- cache->dfe = cache->dft - cache->dfm;
- cache->n_coeffs = X->size2;
- cache->intercept = 0.0;
if (cache->method == PSPP_LINREG_SWEEP)
{
gsl_matrix *sw;
/*
Subtract the means to improve the condition of the design
- matrix. This requires copying X and Y. We do not divide by the
+ matrix. This requires copying dm->m and Y. We do not divide by the
standard deviations of the independent variables here since doing
so would cause a miscalculation of the residual sums of
squares. Dividing by the standard deviation is done GSL's linear
(i.e., a column of 1's). If using PSPP_LINREG_QR, we need that column,
so design is allocated here when sweeping, or below if using QR.
*/
- design = gsl_matrix_alloc (X->size1, X->size2);
- for (i = 0; i < X->size2; i++)
+ design = gsl_matrix_alloc (dm->m->size1, dm->m->size2);
+ for (i = 0; i < dm->m->size2; i++)
{
- m = gsl_vector_get (cache->indep_means, i);
- for (j = 0; j < X->size1; j++)
+ v = design_matrix_col_to_var (dm, i);
+ m = pspp_linreg_get_indep_variable_mean (cache, v);
+ for (j = 0; j < dm->m->size1; j++)
{
- tmp = (gsl_matrix_get (X, j, i) - m);
+ tmp = (gsl_matrix_get (dm->m, j, i) - m);
gsl_matrix_set (design, j, i, tmp);
}
}
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 * gsl_vector_get (cache->indep_means, 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_view_vector (cache->indep_means, 1, cache->n_indeps);
- rc = gsl_blas_dsymm (CblasRight, CblasUpper, cache->mse,
- &xtx.matrix, &xm.matrix, 0.0, &xmxtx.matrix);
- 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)
- * gsl_vector_get (cache->indep_means, 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)
Use QR decomposition via GSL.
*/
- param_estimates = gsl_vector_alloc (1 + X->size2);
- design = gsl_matrix_alloc (X->size1, 1 + X->size2);
+ param_estimates = gsl_vector_alloc (1 + dm->m->size2);
+ design = gsl_matrix_alloc (dm->m->size1, 1 + dm->m->size2);
- for (j = 0; j < X->size1; j++)
+ for (j = 0; j < dm->m->size1; j++)
{
gsl_matrix_set (design, j, 0, 1.0);
- for (i = 0; i < X->size2; i++)
+ for (i = 0; i < dm->m->size2; i++)
{
- tmp = gsl_matrix_get (X, j, i);
+ tmp = gsl_matrix_get (dm->m, j, i);
gsl_matrix_set (design, j, i + 1, tmp);
}
}
}
pred = pspp_linreg_predict (predictors, vals, c, n_vals);
- result = gsl_isnan (pred) ? GSL_NAN : (obs->f - pred);
+ result = isnan (pred) ? GSL_NAN : (obs->f - pred);
return result;
}
Which coefficient is associated with V? The VAL argument is relevant
only to categorical variables.
*/
-const struct pspp_coeff *
+struct pspp_coeff *
pspp_linreg_get_coeff (const pspp_linreg_cache * c,
const struct variable *v, const union value *val)
{
- int i;
- struct pspp_coeff *result = NULL;
- const struct variable *tmp = NULL;
-
if (c == NULL)
{
return NULL;
{
return NULL;
}
- i = 0;
- result = c->coeff[0];
- tmp = pspp_coeff_get_var (result, 0);
- while (tmp != v && i < c->n_coeffs)
+ return pspp_coeff_var_to_coeff (v, c->coeff, c->n_coeffs, val);
+}
+/*
+ Return the standard deviation of the independent variable.
+ */
+double pspp_linreg_get_indep_variable_sd (pspp_linreg_cache *c, const struct variable *v)
+{
+ if (var_is_numeric (v))
{
- result = c->coeff[i];
- tmp = pspp_coeff_get_var (result, 0);
- i++;
+ const struct pspp_coeff *coef;
+ coef = pspp_linreg_get_coeff (c, v, NULL);
+ return pspp_coeff_get_sd (coef);
}
- if (tmp != v)
+ return GSL_NAN;
+}
+
+void pspp_linreg_set_indep_variable_sd (pspp_linreg_cache *c, const struct variable *v,
+ double s)
+{
+ if (var_is_numeric (v))
{
- /*
- Not found.
- */
- return NULL;
+ struct pspp_coeff *coef;
+ coef = pspp_linreg_get_coeff (c, v, NULL);
+ pspp_coeff_set_sd (coef, s);
+ }
+}
+
+/*
+ Mean of the independent variable.
+ */
+double pspp_linreg_get_indep_variable_mean (pspp_linreg_cache *c, const struct variable *v)
+{
+ if (var_is_numeric (v))
+ {
+ struct pspp_coeff *coef;
+ coef = pspp_linreg_get_coeff (c, v, NULL);
+ return pspp_coeff_get_mean (coef);
}
+ return GSL_NAN;
+}
+
+void pspp_linreg_set_indep_variable_mean (pspp_linreg_cache *c, const struct variable *v,
+ double m)
+{
if (var_is_numeric (v))
{
- return result;
+ struct pspp_coeff *coef;
+ coef = pspp_linreg_get_coeff (c, v, NULL);
+ pspp_coeff_set_mean (coef, m);
}
- else if (val != NULL)
+}
+
+/*
+ Make sure the dependent variable is at the last column, and that
+ only variables in the model are in the covariance matrix.
+ */
+static struct design_matrix *
+rearrange_covariance_matrix (const struct covariance_matrix *cm, pspp_linreg_cache *c)
+{
+ const struct variable **model_vars;
+ struct design_matrix *cov;
+ struct design_matrix *result;
+ size_t *permutation;
+ size_t i;
+ size_t j;
+ size_t k;
+
+ 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);
+ permutation = xnmalloc (1 + c->n_indeps, sizeof (*permutation));
+ model_vars = xnmalloc (1 + c->n_indeps, sizeof (*model_vars));
+
+ /*
+ Put the model variables in the right order in MODEL_VARS.
+ */
+ for (i = 0; i < c->n_indeps; i++)
{
- /*
- If v is categorical, we need to ensure the coefficient
- matches the VAL.
- */
- while (tmp != v && i < c->n_coeffs
- && compare_values (pspp_coeff_get_value (result, tmp),
- val, var_get_width (v)))
- { /* FIX THIS */
- i++;
- result = c->coeff[i];
- tmp = pspp_coeff_get_var (result, 0);
- }
- if (i == c->n_coeffs && tmp != v)
+ model_vars[i] = c->indep_vars[i];
+ }
+ model_vars[i] = c->depvar;
+ result = covariance_matrix_create (1 + c->n_indeps, model_vars);
+ for (j = 0; j < cov->m->size2; j++)
+ {
+ k = 0;
+ while (k < result->m->size2)
{
- return NULL;
+ if (design_matrix_col_to_var (cov, j) == design_matrix_col_to_var (result, k))
+ {
+ permutation[k] = j;
+ }
+ k++;
}
- return result;
}
- return NULL;
+ 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.
+*/
+void
+pspp_linreg_with_cov (const struct covariance_matrix *full_cov,
+ pspp_linreg_cache * cache)
+{
+ 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);
}