1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 2005, 2009 Free Software Foundation, Inc.
4 This program is free software: you can redistribute it and/or modify
5 it under the terms of the GNU General Public License as published by
6 the Free Software Foundation, either version 3 of the License, or
7 (at your option) any later version.
9 This program is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 GNU General Public License for more details.
14 You should have received a copy of the GNU General Public License
15 along with this program. If not, see <http://www.gnu.org/licenses/>. */
19 #include <gsl/gsl_cdf.h>
20 #include <gsl/gsl_matrix.h>
21 #include <gsl/gsl_vector.h>
24 #include <data/case.h>
25 #include <data/casegrouper.h>
26 #include <data/casereader.h>
27 #include <data/category.h>
28 #include <data/dictionary.h>
29 #include <data/missing-values.h>
30 #include <data/procedure.h>
31 #include <data/transformations.h>
32 #include <data/value-labels.h>
33 #include <data/variable.h>
34 #include <language/command.h>
35 #include <language/dictionary/split-file.h>
36 #include <language/data-io/file-handle.h>
37 #include <language/lexer/lexer.h>
38 #include <libpspp/compiler.h>
39 #include <libpspp/message.h>
40 #include <libpspp/taint.h>
41 #include <math/covariance.h>
42 #include <math/linreg.h>
43 #include <math/moments.h>
44 #include <output/table.h>
49 #define _(msgid) gettext (msgid)
51 #define REG_LARGE_DATA 1000
56 "REGRESSION" (regression_):
76 +save[sv_]=resid,pred;
81 static struct cmd_regression cmd;
84 Moments for each of the variables used.
89 const struct variable *v;
93 Transformations for saving predicted values
98 int n_trns; /* Number of transformations. */
99 int trns_id; /* Which trns is this one? */
100 linreg *c; /* Linear model for this trns. */
103 Variables used (both explanatory and response).
105 static const struct variable **v_variables;
110 static size_t n_variables;
112 static bool run_regression (struct casereader *, struct cmd_regression *,
113 struct dataset *, linreg **);
116 STATISTICS subcommand output functions.
118 static void reg_stats_r (linreg *);
119 static void reg_stats_coeff (linreg *);
120 static void reg_stats_anova (linreg *);
121 static void reg_stats_outs (linreg *);
122 static void reg_stats_zpp (linreg *);
123 static void reg_stats_label (linreg *);
124 static void reg_stats_sha (linreg *);
125 static void reg_stats_ci (linreg *);
126 static void reg_stats_f (linreg *);
127 static void reg_stats_bcov (linreg *);
128 static void reg_stats_ses (linreg *);
129 static void reg_stats_xtx (linreg *);
130 static void reg_stats_collin (linreg *);
131 static void reg_stats_tol (linreg *);
132 static void reg_stats_selection (linreg *);
133 static void statistics_keyword_output (void (*)(linreg *),
137 reg_stats_r (linreg * c)
147 rsq = c->ssm / c->sst;
148 adjrsq = 1.0 - (1.0 - rsq) * (c->n_obs - 1.0) / (c->n_obs - c->n_indeps);
149 std_error = sqrt (linreg_mse (c));
150 t = tab_create (n_cols, n_rows, 0);
151 tab_dim (t, tab_natural_dimensions, NULL);
152 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1);
153 tab_hline (t, TAL_2, 0, n_cols - 1, 1);
154 tab_vline (t, TAL_2, 2, 0, n_rows - 1);
155 tab_vline (t, TAL_0, 1, 0, 0);
157 tab_text (t, 1, 0, TAB_CENTER | TAT_TITLE, _("R"));
158 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("R Square"));
159 tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("Adjusted R Square"));
160 tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Std. Error of the Estimate"));
161 tab_double (t, 1, 1, TAB_RIGHT, sqrt (rsq), NULL);
162 tab_double (t, 2, 1, TAB_RIGHT, rsq, NULL);
163 tab_double (t, 3, 1, TAB_RIGHT, adjrsq, NULL);
164 tab_double (t, 4, 1, TAB_RIGHT, std_error, NULL);
165 tab_title (t, _("Model Summary"));
170 Table showing estimated regression coefficients.
173 reg_stats_coeff (linreg * c)
185 const struct variable *v;
189 n_rows = c->n_coeffs + 3;
191 t = tab_create (n_cols, n_rows, 0);
192 tab_headers (t, 2, 0, 1, 0);
193 tab_dim (t, tab_natural_dimensions, NULL);
194 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1);
195 tab_hline (t, TAL_2, 0, n_cols - 1, 1);
196 tab_vline (t, TAL_2, 2, 0, n_rows - 1);
197 tab_vline (t, TAL_0, 1, 0, 0);
199 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("B"));
200 tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("Std. Error"));
201 tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Beta"));
202 tab_text (t, 5, 0, TAB_CENTER | TAT_TITLE, _("t"));
203 tab_text (t, 6, 0, TAB_CENTER | TAT_TITLE, _("Significance"));
204 tab_text (t, 1, 1, TAB_LEFT | TAT_TITLE, _("(Constant)"));
205 tab_double (t, 2, 1, 0, linreg_intercept (c), NULL);
206 std_err = sqrt (gsl_matrix_get (linreg_cov (c), 0, 0));
207 tab_double (t, 3, 1, 0, std_err, NULL);
208 tab_double (t, 4, 1, 0, 0.0, NULL);
209 t_stat = linreg_intercept (c) / std_err;
210 tab_double (t, 5, 1, 0, t_stat, NULL);
211 pval = 2 * gsl_cdf_tdist_Q (fabs (t_stat), 1.0);
212 tab_double (t, 6, 1, 0, pval, NULL);
213 for (j = 0; j < linreg_n_coeffs (c); j++)
216 ds_init_empty (&tstr);
219 v = linreg_indep_var (c, j);
220 label = var_to_string (v);
221 /* Do not overwrite the variable's name. */
222 ds_put_cstr (&tstr, label);
223 tab_text (t, 1, this_row, TAB_CENTER, ds_cstr (&tstr));
225 Regression coefficients.
227 tab_double (t, 2, this_row, 0, linreg_coeff (c, j), NULL);
229 Standard error of the coefficients.
231 std_err = sqrt (gsl_matrix_get (linreg_cov (c), j + 1, j + 1));
232 tab_double (t, 3, this_row, 0, std_err, NULL);
234 Standardized coefficient, i.e., regression coefficient
235 if all variables had unit variance.
237 beta = sqrt (gsl_matrix_get (linreg_cov (c), j, j));
238 beta *= linreg_coeff (c, j) / c->depvar_std;
239 tab_double (t, 4, this_row, 0, beta, NULL);
242 Test statistic for H0: coefficient is 0.
244 t_stat = linreg_coeff (c, j) / std_err;
245 tab_double (t, 5, this_row, 0, t_stat, NULL);
247 P values for the test statistic above.
250 2 * gsl_cdf_tdist_Q (fabs (t_stat),
251 (double) (linreg_n_obs (c) - linreg_n_coeffs (c)));
252 tab_double (t, 6, this_row, 0, pval, NULL);
255 tab_title (t, _("Coefficients"));
260 Display the ANOVA table.
263 reg_stats_anova (linreg * c)
267 const double msm = linreg_ssreg (c) / linreg_dfmodel (c);
268 const double mse = linreg_mse (c);
269 const double F = msm / mse;
270 const double pval = gsl_cdf_fdist_Q (F, c->dfm, c->dfe);
275 t = tab_create (n_cols, n_rows, 0);
276 tab_headers (t, 2, 0, 1, 0);
277 tab_dim (t, tab_natural_dimensions, NULL);
279 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1);
281 tab_hline (t, TAL_2, 0, n_cols - 1, 1);
282 tab_vline (t, TAL_2, 2, 0, n_rows - 1);
283 tab_vline (t, TAL_0, 1, 0, 0);
285 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("Sum of Squares"));
286 tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("df"));
287 tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Mean Square"));
288 tab_text (t, 5, 0, TAB_CENTER | TAT_TITLE, _("F"));
289 tab_text (t, 6, 0, TAB_CENTER | TAT_TITLE, _("Significance"));
291 tab_text (t, 1, 1, TAB_LEFT | TAT_TITLE, _("Regression"));
292 tab_text (t, 1, 2, TAB_LEFT | TAT_TITLE, _("Residual"));
293 tab_text (t, 1, 3, TAB_LEFT | TAT_TITLE, _("Total"));
295 /* Sums of Squares */
296 tab_double (t, 2, 1, 0, c->ssm, NULL);
297 tab_double (t, 2, 3, 0, c->sst, NULL);
298 tab_double (t, 2, 2, 0, c->sse, NULL);
301 /* Degrees of freedom */
302 tab_text_format (t, 3, 1, TAB_RIGHT, "%g", c->dfm);
303 tab_text_format (t, 3, 2, TAB_RIGHT, "%g", c->dfe);
304 tab_text_format (t, 3, 3, TAB_RIGHT, "%g", c->dft);
307 tab_double (t, 4, 1, TAB_RIGHT, msm, NULL);
308 tab_double (t, 4, 2, TAB_RIGHT, mse, NULL);
310 tab_double (t, 5, 1, 0, F, NULL);
312 tab_double (t, 6, 1, 0, pval, NULL);
314 tab_title (t, _("ANOVA"));
319 reg_stats_outs (linreg * c)
325 reg_stats_zpp (linreg * c)
331 reg_stats_label (linreg * c)
337 reg_stats_sha (linreg * c)
342 reg_stats_ci (linreg * c)
347 reg_stats_f (linreg * c)
352 reg_stats_bcov (linreg * c)
364 n_cols = c->n_indeps + 1 + 2;
365 n_rows = 2 * (c->n_indeps + 1);
366 t = tab_create (n_cols, n_rows, 0);
367 tab_headers (t, 2, 0, 1, 0);
368 tab_dim (t, tab_natural_dimensions, NULL);
369 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1);
370 tab_hline (t, TAL_2, 0, n_cols - 1, 1);
371 tab_vline (t, TAL_2, 2, 0, n_rows - 1);
372 tab_vline (t, TAL_0, 1, 0, 0);
373 tab_text (t, 0, 0, TAB_CENTER | TAT_TITLE, _("Model"));
374 tab_text (t, 1, 1, TAB_CENTER | TAT_TITLE, _("Covariances"));
375 for (i = 0; i < linreg_n_coeffs (c); i++)
377 const struct variable *v = linreg_indep_var (c, i);
378 label = var_to_string (v);
379 tab_text (t, 2, i, TAB_CENTER, label);
380 tab_text (t, i + 2, 0, TAB_CENTER, label);
381 for (k = 1; k < linreg_n_coeffs (c); k++)
383 col = (i <= k) ? k : i;
384 row = (i <= k) ? i : k;
385 tab_double (t, k + 2, i, TAB_CENTER,
386 gsl_matrix_get (c->cov, row, col), NULL);
389 tab_title (t, _("Coefficient Correlations"));
393 reg_stats_ses (linreg * c)
398 reg_stats_xtx (linreg * c)
403 reg_stats_collin (linreg * c)
408 reg_stats_tol (linreg * c)
413 reg_stats_selection (linreg * c)
419 statistics_keyword_output (void (*function) (linreg *),
420 int keyword, linreg * c)
429 subcommand_statistics (int *keywords, linreg * c)
432 The order here must match the order in which the STATISTICS
433 keywords appear in the specification section above.
460 Set everything but F.
462 for (i = 0; i < f; i++)
469 for (i = 0; i < all; i++)
477 Default output: ANOVA table, parameter estimates,
478 and statistics for variables not entered into model,
481 if (keywords[defaults] | d)
489 statistics_keyword_output (reg_stats_r, keywords[r], c);
490 statistics_keyword_output (reg_stats_anova, keywords[anova], c);
491 statistics_keyword_output (reg_stats_coeff, keywords[coeff], c);
492 statistics_keyword_output (reg_stats_outs, keywords[outs], c);
493 statistics_keyword_output (reg_stats_zpp, keywords[zpp], c);
494 statistics_keyword_output (reg_stats_label, keywords[label], c);
495 statistics_keyword_output (reg_stats_sha, keywords[sha], c);
496 statistics_keyword_output (reg_stats_ci, keywords[ci], c);
497 statistics_keyword_output (reg_stats_f, keywords[f], c);
498 statistics_keyword_output (reg_stats_bcov, keywords[bcov], c);
499 statistics_keyword_output (reg_stats_ses, keywords[ses], c);
500 statistics_keyword_output (reg_stats_xtx, keywords[xtx], c);
501 statistics_keyword_output (reg_stats_collin, keywords[collin], c);
502 statistics_keyword_output (reg_stats_tol, keywords[tol], c);
503 statistics_keyword_output (reg_stats_selection, keywords[selection], c);
507 Free the transformation. Free its linear model if this
508 transformation is the last one.
511 regression_trns_free (void *t_)
514 struct reg_trns *t = t_;
516 if (t->trns_id == t->n_trns)
518 result = linreg_free (t->c);
526 Gets the predicted values.
529 regression_trns_pred_proc (void *t_, struct ccase **c,
530 casenumber case_idx UNUSED)
534 struct reg_trns *trns = t_;
536 union value *output = NULL;
537 const union value *tmp;
539 const struct variable **vars = NULL;
541 assert (trns != NULL);
543 assert (model != NULL);
544 assert (model->depvar != NULL);
545 assert (model->pred != NULL);
547 vars = linreg_get_vars (model);
548 n_vals = linreg_n_coeffs (model);
549 vals = xnmalloc (n_vals, sizeof (*vals));
550 *c = case_unshare (*c);
552 output = case_data_rw (*c, model->pred);
554 for (i = 0; i < n_vals; i++)
556 tmp = case_data (*c, vars[i]);
559 output->f = linreg_predict (model, vals, n_vals);
561 return TRNS_CONTINUE;
568 regression_trns_resid_proc (void *t_, struct ccase **c,
569 casenumber case_idx UNUSED)
573 struct reg_trns *trns = t_;
575 union value *output = NULL;
576 const union value *tmp;
579 const struct variable **vars = NULL;
581 assert (trns != NULL);
583 assert (model != NULL);
584 assert (model->depvar != NULL);
585 assert (model->resid != NULL);
587 vars = linreg_get_vars (model);
588 n_vals = linreg_n_coeffs (model);
590 vals = xnmalloc (n_vals, sizeof (*vals));
591 *c = case_unshare (*c);
592 output = case_data_rw (*c, model->resid);
593 assert (output != NULL);
595 for (i = 0; i < n_vals; i++)
597 tmp = case_data (*c, vars[i]);
600 tmp = case_data (*c, model->depvar);
602 output->f = linreg_residual (model, obs, vals, n_vals);
605 return TRNS_CONTINUE;
609 Returns false if NAME is a duplicate of any existing variable name.
612 try_name (const struct dictionary *dict, const char *name)
614 if (dict_lookup_var (dict, name) != NULL)
621 reg_get_name (const struct dictionary *dict, char name[VAR_NAME_LEN],
622 const char prefix[VAR_NAME_LEN])
626 snprintf (name, VAR_NAME_LEN, "%s%d", prefix, i);
627 while (!try_name (dict, name))
630 snprintf (name, VAR_NAME_LEN, "%s%d", prefix, i);
635 reg_save_var (struct dataset *ds, const char *prefix, trns_proc_func * f,
636 linreg * c, struct variable **v, int n_trns)
638 struct dictionary *dict = dataset_dict (ds);
639 static int trns_index = 1;
640 char name[VAR_NAME_LEN];
641 struct variable *new_var;
642 struct reg_trns *t = NULL;
644 t = xmalloc (sizeof (*t));
645 t->trns_id = trns_index;
648 reg_get_name (dict, name, prefix);
649 new_var = dict_create_var (dict, name, 0);
650 assert (new_var != NULL);
652 add_transformation (ds, f, regression_trns_free, t);
656 subcommand_save (struct dataset *ds, int save, linreg ** models)
662 assert (models != NULL);
666 /* Count the number of transformations we will need. */
667 for (i = 0; i < REGRESSION_SV_count; i++)
674 n_trns *= cmd.n_dependent;
676 for (lc = models; lc < models + cmd.n_dependent; lc++)
680 if ((*lc)->depvar != NULL)
682 if (cmd.a_save[REGRESSION_SV_RESID])
684 reg_save_var (ds, "RES", regression_trns_resid_proc, *lc,
685 &(*lc)->resid, n_trns);
687 if (cmd.a_save[REGRESSION_SV_PRED])
689 reg_save_var (ds, "PRED", regression_trns_pred_proc, *lc,
690 &(*lc)->pred, n_trns);
698 for (lc = models; lc < models + cmd.n_dependent; lc++)
709 cmd_regression (struct lexer *lexer, struct dataset *ds)
711 struct casegrouper *grouper;
712 struct casereader *group;
717 if (!parse_regression (lexer, ds, &cmd, NULL))
722 models = xnmalloc (cmd.n_dependent, sizeof *models);
723 for (i = 0; i < cmd.n_dependent; i++)
729 grouper = casegrouper_create_splits (proc_open (ds), dataset_dict (ds));
730 while (casegrouper_get_next_group (grouper, &group))
731 run_regression (group, &cmd, ds, models);
732 ok = casegrouper_destroy (grouper);
733 ok = proc_commit (ds) && ok;
735 subcommand_save (ds, cmd.sbc_save, models);
738 free_regression (&cmd);
740 return ok ? CMD_SUCCESS : CMD_FAILURE;
744 Is variable k the dependent variable?
747 is_depvar (size_t k, const struct variable *v)
749 return v == v_variables[k];
752 /* Parser for the variables sub command */
754 regression_custom_variables (struct lexer *lexer, struct dataset *ds,
755 struct cmd_regression *cmd UNUSED,
758 const struct dictionary *dict = dataset_dict (ds);
760 lex_match (lexer, '=');
762 if ((lex_token (lexer) != T_ID
763 || dict_lookup_var (dict, lex_tokid (lexer)) == NULL)
764 && lex_token (lexer) != T_ALL)
768 if (!parse_variables_const
769 (lexer, dict, &v_variables, &n_variables, PV_NONE))
774 assert (n_variables);
779 /* Identify the explanatory variables in v_variables. Returns
780 the number of independent variables. */
782 identify_indep_vars (const struct variable **indep_vars,
783 const struct variable *depvar)
785 int n_indep_vars = 0;
788 for (i = 0; i < n_variables; i++)
789 if (!is_depvar (i, depvar))
790 indep_vars[n_indep_vars++] = v_variables[i];
791 if ((n_indep_vars < 1) && is_depvar (0, depvar))
794 There is only one independent variable, and it is the same
795 as the dependent variable. Print a warning and continue.
798 gettext ("The dependent variable is equal to the independent variable."
799 "The least squares line is therefore Y=X."
800 "Standard errors and related statistics may be meaningless."));
802 indep_vars[0] = v_variables[0];
807 fill_covariance (gsl_matrix *cov, struct covariance *all_cov,
808 const struct variable **vars,
809 size_t n_vars, const struct variable *dep_var,
810 const struct variable **all_vars, size_t n_all_vars)
815 size_t dep_subscript;
817 const gsl_matrix *ssizes;
818 const gsl_matrix *cm;
821 cm = covariance_calculate (all_cov);
822 rows = xnmalloc (cov->size1 - 1, sizeof (*rows));
824 for (i = 0; i < n_all_vars; i++)
826 for (j = k; j < n_vars; j++)
828 if (vars[j] == all_vars[i])
830 if (vars[j] != dep_var)
843 for (i = 0; i < cov->size1 - 1; i++)
845 for (j = 0; j < cov->size2 - 1; j++)
847 gsl_matrix_set (cov, i, j, gsl_matrix_get (cm, rows[i], rows[j]));
848 gsl_matrix_set (cov, j, i, gsl_matrix_get (cm, rows[j], rows[i]));
851 ssizes = covariance_moments (all_cov, MOMENT_NONE);
852 result = gsl_matrix_get (ssizes, dep_subscript, rows[0]);
853 for (i = 0; i < cov->size1 - 1; i++)
855 gsl_matrix_set (cov, i, cov->size1 - 1,
856 gsl_matrix_get (cm, rows[i], dep_subscript));
857 gsl_matrix_set (cov, cov->size1 - 1, i,
858 gsl_matrix_get (cm, rows[i], dep_subscript));
859 if (result > gsl_matrix_get (ssizes, rows[i], dep_subscript))
861 result = gsl_matrix_get (ssizes, rows[i], dep_subscript);
868 run_regression (struct casereader *input, struct cmd_regression *cmd,
869 struct dataset *ds, linreg **models)
876 struct covariance *cov;
877 const struct variable **vars;
878 const struct variable *dep_var;
879 struct casereader *reader;
880 const struct dictionary *dict;
883 assert (models != NULL);
885 for (i = 0; i < n_variables; i++)
887 if (!var_is_numeric (v_variables[i]))
889 msg (SE, _("REGRESSION requires numeric variables."));
894 c = casereader_peek (input, 0);
897 casereader_destroy (input);
900 output_split_file_values (ds, c);
903 dict = dataset_dict (ds);
906 dict_get_vars (dict, &v_variables, &n_variables, 0);
908 vars = xnmalloc (n_variables, sizeof (*vars));
909 cov = covariance_1pass_create (n_variables, v_variables,
910 dict_get_weight (dict), MV_ANY);
912 reader = casereader_clone (input);
913 reader = casereader_create_filter_missing (reader, v_variables, n_variables,
915 for (; (c = casereader_read (reader)) != NULL; case_unref (c))
917 covariance_accumulate (cov, c);
920 for (k = 0; k < cmd->n_dependent; k++)
922 dep_var = cmd->v_dependent[k];
923 n_indep = identify_indep_vars (vars, dep_var);
925 this_cm = gsl_matrix_alloc (n_indep + 1, n_indep + 1);
926 n_data = fill_covariance (this_cm, cov, vars, n_indep,
927 dep_var, v_variables, n_variables);
928 models[k] = linreg_alloc (dep_var, (const struct variable **) vars,
930 models[k]->depvar = dep_var;
933 For large data sets, use QR decomposition.
935 if (n_data > sqrt (n_indep) && n_data > REG_LARGE_DATA)
937 models[k]->method = LINREG_QR;
943 Find the least-squares estimates and other statistics.
945 linreg_fit (this_cm, models[k]);
947 if (!taint_has_tainted_successor (casereader_get_taint (input)))
949 subcommand_statistics (cmd->a_statistics, models[k]);
955 gettext ("No valid data found. This command was skipped."));
959 casereader_destroy (reader);
961 casereader_destroy (input);
962 covariance_destroy (cov);