1 /* PSPP - linear regression.
2 Copyright (C) 2005 Free Software Foundation, Inc.
3 Written by Jason H Stover <jason@sakla.net>.
5 This program is free software; you can redistribute it and/or
6 modify it under the terms of the GNU General Public License as
7 published by the Free Software Foundation; either version 2 of the
8 License, or (at your option) any later version.
10 This program is distributed in the hope that it will be useful, but
11 WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 General Public License for more details.
15 You should have received a copy of the GNU General Public License
16 along with this program; if not, write to the Free Software
17 Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
22 #include <gsl/gsl_cdf.h>
23 #include <gsl/gsl_vector.h>
24 #include <gsl/gsl_matrix.h>
27 #include "dictionary.h"
28 #include "file-handle.h"
35 #include <linreg/pspp_linreg.h>
41 "REGRESSION" (regression_):
65 static struct cmd_regression cmd;
68 Array holding the subscripts of the independent variables.
72 static void run_regression (const struct casefile *, void *);
74 STATISTICS subcommand output functions.
76 static void reg_stats_r (pspp_linreg_cache *);
77 static void reg_stats_coeff (pspp_linreg_cache *);
78 static void reg_stats_anova (pspp_linreg_cache *);
79 static void reg_stats_outs (pspp_linreg_cache *);
80 static void reg_stats_zpp (pspp_linreg_cache *);
81 static void reg_stats_label (pspp_linreg_cache *);
82 static void reg_stats_sha (pspp_linreg_cache *);
83 static void reg_stats_ci (pspp_linreg_cache *);
84 static void reg_stats_f (pspp_linreg_cache *);
85 static void reg_stats_bcov (pspp_linreg_cache *);
86 static void reg_stats_ses (pspp_linreg_cache *);
87 static void reg_stats_xtx (pspp_linreg_cache *);
88 static void reg_stats_collin (pspp_linreg_cache *);
89 static void reg_stats_tol (pspp_linreg_cache *);
90 static void reg_stats_selection (pspp_linreg_cache *);
91 static void statistics_keyword_output (void (*)(pspp_linreg_cache *),
92 int, pspp_linreg_cache *);
95 reg_stats_r (pspp_linreg_cache * c)
101 Table showing estimated regression coefficients.
104 reg_stats_coeff (pspp_linreg_cache * c)
119 n_rows = 2 + c->param_estimates->size;
120 t = tab_create (n_cols, n_rows, 0);
121 tab_headers (t, 2, 0, 1, 0);
122 tab_dim (t, tab_natural_dimensions);
123 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1);
124 tab_hline (t, TAL_2, 0, n_cols - 1, 1);
125 tab_vline (t, TAL_2, 2, 0, n_rows - 1);
126 tab_vline (t, TAL_0, 1, 0, 0);
128 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("B"));
129 tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("Std. Error"));
130 tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Beta"));
131 tab_text (t, 5, 0, TAB_CENTER | TAT_TITLE, _("t"));
132 tab_text (t, 6, 0, TAB_CENTER | TAT_TITLE, _("Significance"));
133 tab_text (t, 1, 1, TAB_LEFT | TAT_TITLE, _("(Constant)"));
134 coeff = gsl_vector_get (c->param_estimates, 0);
135 tab_float (t, 2, 1, 0, coeff, 10, 2);
136 std_err = sqrt (gsl_matrix_get (c->cov, 0, 0));
137 tab_float (t, 3, 1, 0, std_err, 10, 2);
138 beta = coeff / c->depvar_std;
139 tab_float (t, 4, 1, 0, beta, 10, 2);
140 t_stat = coeff / std_err;
141 tab_float (t, 5, 1, 0, t_stat, 10, 2);
142 pval = 2 * gsl_cdf_tdist_Q (fabs (t_stat), 1.0);
143 tab_float (t, 6, 1, 0, pval, 10, 2);
144 for (j = 0; j < c->n_indeps; j++)
147 struct variable *v = cmd.v_variables[i];
148 label = var_to_string (v);
149 tab_text (t, 1, j + 2, TAB_CENTER, label);
151 Regression coefficients.
153 coeff = gsl_vector_get (c->param_estimates, j + 1);
154 tab_float (t, 2, j + 2, 0, coeff, 10, 2);
156 Standard error of the coefficients.
158 std_err = sqrt (gsl_matrix_get (c->cov, j + 1, j + 1));
159 tab_float (t, 3, j + 2, 0, std_err, 10, 2);
161 'Standardized' coefficient, i.e., regression coefficient
162 if all variables had unit variance.
164 beta = gsl_vector_get (c->indep_std, j + 1);
165 beta *= coeff / c->depvar_std;
166 tab_float (t, 4, j + 2, 0, beta, 10, 2);
169 Test statistic for H0: coefficient is 0.
171 t_stat = coeff / std_err;
172 tab_float (t, 5, j + 2, 0, t_stat, 10, 2);
174 P values for the test statistic above.
176 pval = 2 * gsl_cdf_tdist_Q (fabs (t_stat), 1.0);
177 tab_float (t, 6, j + 2, 0, pval, 10, 2);
179 tab_title (t, 0, _("Coefficients"));
184 Display the ANOVA table.
187 reg_stats_anova (pspp_linreg_cache * c)
191 const double msm = c->ssm / c->dfm;
192 const double mse = c->sse / c->dfe;
193 const double F = msm / mse;
194 const double pval = gsl_cdf_fdist_Q (F, c->dfm, c->dfe);
199 t = tab_create (n_cols, n_rows, 0);
200 tab_headers (t, 2, 0, 1, 0);
201 tab_dim (t, tab_natural_dimensions);
203 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1);
205 tab_hline (t, TAL_2, 0, n_cols - 1, 1);
206 tab_vline (t, TAL_2, 2, 0, n_rows - 1);
207 tab_vline (t, TAL_0, 1, 0, 0);
209 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("Sum of Squares"));
210 tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("df"));
211 tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Mean Square"));
212 tab_text (t, 5, 0, TAB_CENTER | TAT_TITLE, _("F"));
213 tab_text (t, 6, 0, TAB_CENTER | TAT_TITLE, _("Significance"));
215 tab_text (t, 1, 1, TAB_LEFT | TAT_TITLE, _("Regression"));
216 tab_text (t, 1, 2, TAB_LEFT | TAT_TITLE, _("Residual"));
217 tab_text (t, 1, 3, TAB_LEFT | TAT_TITLE, _("Total"));
219 /* Sums of Squares */
220 tab_float (t, 2, 1, 0, c->ssm, 10, 2);
221 tab_float (t, 2, 3, 0, c->sst, 10, 2);
222 tab_float (t, 2, 2, 0, c->sse, 10, 2);
225 /* Degrees of freedom */
226 tab_float (t, 3, 1, 0, c->dfm, 4, 0);
227 tab_float (t, 3, 2, 0, c->dfe, 4, 0);
228 tab_float (t, 3, 3, 0, c->dft, 4, 0);
232 tab_float (t, 4, 1, TAB_RIGHT, msm, 8, 3);
233 tab_float (t, 4, 2, TAB_RIGHT, mse, 8, 3);
235 tab_float (t, 5, 1, 0, F, 8, 3);
237 tab_float (t, 6, 1, 0, pval, 8, 3);
239 tab_title (t, 0, _("ANOVA"));
243 reg_stats_outs (pspp_linreg_cache * c)
248 reg_stats_zpp (pspp_linreg_cache * c)
253 reg_stats_label (pspp_linreg_cache * c)
258 reg_stats_sha (pspp_linreg_cache * c)
263 reg_stats_ci (pspp_linreg_cache * c)
268 reg_stats_f (pspp_linreg_cache * c)
273 reg_stats_bcov (pspp_linreg_cache * c)
278 reg_stats_ses (pspp_linreg_cache * c)
283 reg_stats_xtx (pspp_linreg_cache * c)
288 reg_stats_collin (pspp_linreg_cache * c)
293 reg_stats_tol (pspp_linreg_cache * c)
298 reg_stats_selection (pspp_linreg_cache * c)
304 statistics_keyword_output (void (*function) (pspp_linreg_cache *),
305 int keyword, pspp_linreg_cache * c)
314 subcommand_statistics (int *keywords, pspp_linreg_cache * c)
317 The order here must match the order in which the STATISTICS
318 keywords appear in the specification section above.
345 Set everything but F.
347 for (i = 0; i < f; i++)
354 for (i = 0; i < all; i++)
362 Default output: ANOVA table, parameter estimates,
363 and statistics for variables not entered into model,
366 if (keywords[defaults] | d)
368 *(keywords + anova) = 1;
369 *(keywords + outs) = 1;
370 *(keywords + coeff) = 1;
374 statistics_keyword_output (reg_stats_r, keywords[r], c);
375 statistics_keyword_output (reg_stats_anova, keywords[anova], c);
376 statistics_keyword_output (reg_stats_coeff, keywords[coeff], c);
377 statistics_keyword_output (reg_stats_outs, keywords[outs], c);
378 statistics_keyword_output (reg_stats_zpp, keywords[zpp], c);
379 statistics_keyword_output (reg_stats_label, keywords[label], c);
380 statistics_keyword_output (reg_stats_sha, keywords[sha], c);
381 statistics_keyword_output (reg_stats_ci, keywords[ci], c);
382 statistics_keyword_output (reg_stats_f, keywords[f], c);
383 statistics_keyword_output (reg_stats_bcov, keywords[bcov], c);
384 statistics_keyword_output (reg_stats_ses, keywords[ses], c);
385 statistics_keyword_output (reg_stats_xtx, keywords[xtx], c);
386 statistics_keyword_output (reg_stats_collin, keywords[collin], c);
387 statistics_keyword_output (reg_stats_tol, keywords[tol], c);
388 statistics_keyword_output (reg_stats_selection, keywords[selection], c);
392 cmd_regression (void)
394 if (!parse_regression (&cmd))
398 multipass_procedure_with_splits (run_regression, &cmd);
404 Is variable k one of the dependent variables?
410 for (j = 0; j < cmd.n_dependent; j++)
413 compare_var_names returns 0 if the variable
416 if (!compare_var_names (cmd.v_dependent[j], cmd.v_variables[k], NULL))
423 run_regression (const struct casefile *cf, void *cmd_)
430 const union value *val;
431 struct casereader *r;
432 struct casereader *r2;
434 const struct variable *v;
435 struct recoded_categorical_array *ca;
436 struct recoded_categorical *rc;
437 struct design_matrix *X;
439 pspp_linreg_cache *lcache;
440 pspp_linreg_opts lopts;
442 n_data = casefile_get_case_cnt (cf);
443 n_indep = cmd.n_variables - cmd.n_dependent;
444 indep_vars = (size_t *) malloc (n_indep * sizeof (*indep_vars));
446 Y = gsl_vector_alloc (n_data);
447 lopts.get_depvar_mean_std = 1;
448 lopts.get_indep_mean_std = (int *) malloc (n_indep * sizeof (int));
450 lcache = pspp_linreg_cache_alloc (n_data, n_indep);
451 lcache->indep_means = gsl_vector_alloc (n_indep);
452 lcache->indep_std = gsl_vector_alloc (n_indep);
455 Read from the active file. The first pass encodes categorical
458 ca = cr_recoded_cat_ar_create (cmd.n_variables, cmd.v_variables);
459 for (r = casefile_get_reader (cf);
460 casereader_read (r, &c); case_destroy (&c))
462 for (i = 0; i < ca->n_vars; i++)
464 v = (*(ca->a + i))->v;
465 val = case_data (&c, v->fv);
466 cr_value_update (*(ca->a + i), val);
470 cr_create_value_matrices (ca);
472 design_matrix_create (n_indep, (const struct variable **) cmd.v_variables,
476 The second pass creates the design matrix.
478 for (r2 = casefile_get_reader (cf); casereader_read (r2, &c);
480 /* Iterate over the cases. */
483 row = casereader_cnum (r2) - 1;
484 for (i = 0; i < cmd.n_variables; ++i) /* Iterate over the variables
485 for the current case.
488 v = cmd.v_variables[i];
489 val = case_data (&c, v->fv);
491 Independent/dependent variable separation. The
492 'variables' subcommand specifies a varlist which contains
493 both dependent and independent variables. The dependent
494 variables are specified with the 'dependent'
495 subcommand. We need to separate the two.
499 if (v->type == NUMERIC)
501 gsl_vector_set (Y, row, val->f);
507 "%s:%d: Dependent variable should be numeric: %s\n",
508 __FILE__, __LINE__, strerror (errno));
514 if (v->type == ALPHA)
516 rc = cr_var_to_recoded_categorical (v, ca);
517 design_matrix_set_categorical (X, row, v, val, rc);
519 else if (v->type == NUMERIC)
521 design_matrix_set_numeric (X, row, v, val);
526 lopts.get_indep_mean_std[i] = 1;
531 Find the least-squares estimates and other statistics.
533 pspp_linreg ((const gsl_vector *) Y, X->m, &lopts, lcache);
534 subcommand_statistics (cmd.a_statistics, lcache);
536 design_matrix_destroy (X);
537 pspp_linreg_cache_free (lcache);
538 free (lopts.get_indep_mean_std);
540 casereader_destroy (r);