Springer. 1998. ISBN 0-387-98542-5.
*/
+struct linreg
+{
+ double n_obs; /* Number of observations. */
+ int n_indeps; /* Number of independent variables. */
+ int n_coeffs; /* The intercept is not considered a
+ coefficient here. */
+
+ /*
+ Pointers to the variables.
+ */
+ const struct variable *depvar;
+ const struct variable **indep_vars;
+
+ double *coeff;
+ double intercept;
+ /*
+ Means and standard deviations of the variables.
+ If these pointers are null when pspp_linreg() is
+ called, pspp_linreg() will compute their values.
+
+ Entry i of indep_means is the mean of independent
+ variable i, whose observations are stored in the ith
+ column of the design matrix.
+ */
+ double depvar_mean;
+ gsl_vector *indep_means;
+ gsl_vector *indep_std;
+
+ /*
+ Sums of squares.
+ */
+ double ssm; /* Sums of squares for the overall model. */
+ double sst; /* Sum of squares total. */
+ double sse; /* Sum of squares error. */
+ double mse; /* Mean squared error. This is just sse /
+ dfe, but since it is the best unbiased
+ estimate of the population variance, it
+ has its own entry here. */
+ /*
+ Covariance matrix of the parameter estimates.
+ */
+ gsl_matrix *cov;
+ /*
+ Degrees of freedom.
+ */
+ double dft;
+ double dfe;
+ double dfm;
+
+ int dependent_column; /* Column containing the dependent variable. Defaults to last column. */
+ int refcnt;
+
+ bool origin;
+};
const struct variable **
-linreg_get_vars (const linreg *c)
+linreg_get_vars (const struct linreg *c)
{
return c->indep_vars;
}
Allocate a linreg and return a pointer to it. n is the number of
cases, p is the number of independent variables.
*/
-linreg *
+struct linreg *
linreg_alloc (const struct variable *depvar, const struct variable **indep_vars,
double n, size_t p, bool origin)
{
- linreg *c;
+ struct linreg *c;
size_t i;
c = xmalloc (sizeof (*c));
/*
Default settings.
*/
- c->method = LINREG_SWEEP;
c->refcnt = 1;
void
-linreg_ref (linreg *c)
+linreg_ref (struct linreg *c)
{
c->refcnt++;
}
void
-linreg_unref (linreg *c)
+linreg_unref (struct linreg *c)
{
if (--c->refcnt == 0)
{
}
static void
-post_sweep_computations (linreg *l, gsl_matrix *sw)
+post_sweep_computations (struct linreg *l, gsl_matrix *sw)
{
double m;
size_t i;
order of the coefficients in the linreg struct.
*/
double
-linreg_predict (const linreg *c, const double *vals, size_t n_vals)
+linreg_predict (const struct linreg *c, const double *vals, size_t n_vals)
{
size_t j;
double result;
}
double
-linreg_residual (const linreg *c, double obs, const double *vals, size_t n_vals)
+linreg_residual (const struct linreg *c, double obs, const double *vals, size_t n_vals)
{
if (vals == NULL || c == NULL)
{
/*
Mean of the independent variable.
*/
-double linreg_get_indep_variable_mean (const linreg *c, size_t j)
+double
+linreg_get_indep_variable_mean (const struct linreg *c, size_t j)
{
assert (c != NULL);
return gsl_vector_get (c->indep_means, j);
}
-void linreg_set_indep_variable_mean (linreg *c, size_t j, double m)
+void
+linreg_set_indep_variable_mean (struct linreg *c, size_t j, double m)
{
assert (c != NULL);
gsl_vector_set (c->indep_means, j, m);
}
static void
-linreg_fit_qr (const gsl_matrix *cov, linreg *l)
+linreg_fit_qr (const gsl_matrix *cov, struct linreg *l)
{
double intcpt_coef = 0.0;
double intercept_variance = 0.0;
gsl_matrix_set (q, i, j, gsl_matrix_get (q, j, i));
}
}
- l->intercept = linreg_get_depvar_mean (l);
- for (i = 0; i < l->n_indeps; i++)
- {
- double tmp = linreg_get_indep_variable_mean (l, i);
- l->intercept -= l->coeff[i] * tmp;
- intercept_variance += tmp * tmp * gsl_matrix_get (q, i, i);
- }
- /* Covariances related to the intercept. */
- intercept_variance += linreg_mse (l) / linreg_n_obs (l);
- gsl_matrix_set (l->cov, 0, 0, intercept_variance);
- for (i = 0; i < q->size1; i++)
+ if (!l->origin)
{
- for (j = 0; j < q->size2; j++)
+ l->intercept = linreg_get_depvar_mean (l);
+ for (i = 0; i < l->n_indeps; i++)
{
- intcpt_coef -= gsl_matrix_get (q, i, j)
- * linreg_get_indep_variable_mean (l, j);
+ double tmp = linreg_get_indep_variable_mean (l, i);
+ l->intercept -= l->coeff[i] * tmp;
+ intercept_variance += tmp * tmp * gsl_matrix_get (q, i, i);
+ }
+
+ /* Covariances related to the intercept. */
+ intercept_variance += linreg_mse (l) / linreg_n_obs (l);
+ gsl_matrix_set (l->cov, 0, 0, intercept_variance);
+ for (i = 0; i < q->size1; i++)
+ {
+ for (j = 0; j < q->size2; j++)
+ {
+ intcpt_coef -= gsl_matrix_get (q, i, j)
+ * linreg_get_indep_variable_mean (l, j);
+ }
+ gsl_matrix_set (l->cov, 0, i + 1, intcpt_coef);
+ gsl_matrix_set (l->cov, i + 1, 0, intcpt_coef);
+ intcpt_coef = 0.0;
}
- gsl_matrix_set (l->cov, 0, i + 1, intcpt_coef);
- gsl_matrix_set (l->cov, i + 1, 0, intcpt_coef);
- intcpt_coef = 0.0;
}
gsl_matrix_free (q);
gsl_vector_free (params);
}
+#define REG_LARGE_DATA 1000
+
/*
Estimate the model parameters from the covariance matrix. This
function assumes the covariance entries corresponding to the
matrix.
*/
void
-linreg_fit (const gsl_matrix *cov, linreg *l)
+linreg_fit (const gsl_matrix *cov, struct linreg *l)
{
assert (l != NULL);
assert (cov != NULL);
l->sst = gsl_matrix_get (cov, cov->size1 - 1, cov->size2 - 1);
- if (l->method == LINREG_SWEEP)
+
+ if ((l->n_obs * l->n_obs > l->n_indeps) && (l->n_obs > REG_LARGE_DATA))
{
- gsl_matrix *params;
- params = gsl_matrix_calloc (cov->size1, cov->size2);
+ /*
+ For large data sets, use QR decomposition.
+ */
+ linreg_fit_qr (cov, l);
+ }
+ else
+ {
+ gsl_matrix *params = gsl_matrix_calloc (cov->size1, cov->size2);
gsl_matrix_memcpy (params, cov);
reg_sweep (params, l->dependent_column);
post_sweep_computations (l, params);
gsl_matrix_free (params);
}
- else if (l->method == LINREG_QR)
- {
- linreg_fit_qr (cov, l);
- }
}
-double linreg_mse (const linreg *c)
+double
+linreg_mse (const struct linreg *c)
{
assert (c != NULL);
return (c->sse / c->dfe);
}
-double linreg_intercept (const linreg *c)
+double
+linreg_intercept (const struct linreg *c)
{
return c->intercept;
}
const gsl_matrix *
-linreg_cov (const linreg *c)
+linreg_cov (const struct linreg *c)
{
return c->cov;
}
double
-linreg_coeff (const linreg *c, size_t i)
+linreg_coeff (const struct linreg *c, size_t i)
{
return (c->coeff[i]);
}
const struct variable *
-linreg_indep_var (const linreg *c, size_t i)
+linreg_indep_var (const struct linreg *c, size_t i)
{
return (c->indep_vars[i]);
}
+int
+linreg_n_indeps (const struct linreg *c)
+{
+ return c->n_indeps;
+}
+
+
+const struct variable *
+linreg_dep_var (const struct linreg *c)
+{
+ return c->depvar;
+}
+
+
size_t
-linreg_n_coeffs (const linreg *c)
+linreg_n_coeffs (const struct linreg *c)
{
return c->n_coeffs;
}
double
-linreg_n_obs (const linreg *c)
+linreg_n_obs (const struct linreg *c)
{
return c->n_obs;
}
double
-linreg_sse (const linreg *c)
+linreg_sse (const struct linreg *c)
{
return c->sse;
}
double
-linreg_ssreg (const linreg *c)
+linreg_ssreg (const struct linreg *c)
{
return (c->sst - c->sse);
}
-double linreg_sst (const linreg *c)
+double linreg_sst (const struct linreg *c)
{
return c->sst;
}
double
-linreg_dfmodel ( const linreg *c)
+linreg_dfmodel ( const struct linreg *c)
{
return c->dfm;
}
+double
+linreg_dferror ( const struct linreg *c)
+{
+ return c->dfe;
+}
+
+double
+linreg_dftotal ( const struct linreg *c)
+{
+ return c->dft;
+}
+
void
-linreg_set_depvar_mean (linreg *c, double x)
+linreg_set_depvar_mean (struct linreg *c, double x)
{
c->depvar_mean = x;
}
double
-linreg_get_depvar_mean (const linreg *c)
+linreg_get_depvar_mean (const struct linreg *c)
{
return c->depvar_mean;
}