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>
30 #include "dictionary.h"
32 #include "file-handle.h"
35 #include <linreg/pspp_linreg.h>
36 #include "missing-values.h"
45 "REGRESSION" (regression_):
69 static struct cmd_regression cmd;
72 Array holding the subscripts of the independent variables.
77 Return value for the procedure.
79 int pspp_reg_rc = CMD_SUCCESS;
81 static void run_regression (const struct casefile *, void *);
83 STATISTICS subcommand output functions.
85 static void reg_stats_r (pspp_linreg_cache *);
86 static void reg_stats_coeff (pspp_linreg_cache *);
87 static void reg_stats_anova (pspp_linreg_cache *);
88 static void reg_stats_outs (pspp_linreg_cache *);
89 static void reg_stats_zpp (pspp_linreg_cache *);
90 static void reg_stats_label (pspp_linreg_cache *);
91 static void reg_stats_sha (pspp_linreg_cache *);
92 static void reg_stats_ci (pspp_linreg_cache *);
93 static void reg_stats_f (pspp_linreg_cache *);
94 static void reg_stats_bcov (pspp_linreg_cache *);
95 static void reg_stats_ses (pspp_linreg_cache *);
96 static void reg_stats_xtx (pspp_linreg_cache *);
97 static void reg_stats_collin (pspp_linreg_cache *);
98 static void reg_stats_tol (pspp_linreg_cache *);
99 static void reg_stats_selection (pspp_linreg_cache *);
100 static void statistics_keyword_output (void (*)(pspp_linreg_cache *),
101 int, pspp_linreg_cache *);
104 reg_stats_r (pspp_linreg_cache * c)
114 rsq = c->ssm / c->sst;
115 adjrsq = 1.0 - (1.0 - rsq) * (c->n_obs - 1.0) / (c->n_obs - c->n_indeps);
116 std_error = sqrt ((c->n_indeps - 1.0) / (c->n_obs - 1.0));
117 t = tab_create (n_cols, n_rows, 0);
118 tab_dim (t, tab_natural_dimensions);
119 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1);
120 tab_hline (t, TAL_2, 0, n_cols - 1, 1);
121 tab_vline (t, TAL_2, 2, 0, n_rows - 1);
122 tab_vline (t, TAL_0, 1, 0, 0);
124 tab_text (t, 1, 0, TAB_CENTER | TAT_TITLE, _("R"));
125 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("R Square"));
126 tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("Adjusted R Square"));
127 tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Std. Error of the Estimate"));
128 tab_float (t, 1, 1, TAB_RIGHT, sqrt (rsq), 10, 2);
129 tab_float (t, 2, 1, TAB_RIGHT, rsq, 10, 2);
130 tab_float (t, 3, 1, TAB_RIGHT, adjrsq, 10, 2);
131 tab_float (t, 4, 1, TAB_RIGHT, std_error, 10, 2);
132 tab_title (t, 0, _("Model Summary"));
137 Table showing estimated regression coefficients.
140 reg_stats_coeff (pspp_linreg_cache * c)
155 n_rows = c->n_coeffs + 2;
157 t = tab_create (n_cols, n_rows, 0);
158 tab_headers (t, 2, 0, 1, 0);
159 tab_dim (t, tab_natural_dimensions);
160 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1);
161 tab_hline (t, TAL_2, 0, n_cols - 1, 1);
162 tab_vline (t, TAL_2, 2, 0, n_rows - 1);
163 tab_vline (t, TAL_0, 1, 0, 0);
165 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("B"));
166 tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("Std. Error"));
167 tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Beta"));
168 tab_text (t, 5, 0, TAB_CENTER | TAT_TITLE, _("t"));
169 tab_text (t, 6, 0, TAB_CENTER | TAT_TITLE, _("Significance"));
170 tab_text (t, 1, 1, TAB_LEFT | TAT_TITLE, _("(Constant)"));
171 coeff = c->coeff[0].estimate;
172 tab_float (t, 2, 1, 0, coeff, 10, 2);
173 std_err = sqrt (gsl_matrix_get (c->cov, 0, 0));
174 tab_float (t, 3, 1, 0, std_err, 10, 2);
175 beta = coeff / c->depvar_std;
176 tab_float (t, 4, 1, 0, beta, 10, 2);
177 t_stat = coeff / std_err;
178 tab_float (t, 5, 1, 0, t_stat, 10, 2);
179 pval = 2 * gsl_cdf_tdist_Q (fabs (t_stat), 1.0);
180 tab_float (t, 6, 1, 0, pval, 10, 2);
181 for (j = 1; j <= c->n_indeps; j++)
184 label = var_to_string (c->coeff[j].v);
185 tab_text (t, 1, j + 1, TAB_CENTER, label);
187 Regression coefficients.
189 coeff = c->coeff[j].estimate;
190 tab_float (t, 2, j + 1, 0, coeff, 10, 2);
192 Standard error of the coefficients.
194 std_err = sqrt (gsl_matrix_get (c->cov, j, j));
195 tab_float (t, 3, j + 1, 0, std_err, 10, 2);
197 'Standardized' coefficient, i.e., regression coefficient
198 if all variables had unit variance.
200 beta = gsl_vector_get (c->indep_std, j);
201 beta *= coeff / c->depvar_std;
202 tab_float (t, 4, j + 1, 0, beta, 10, 2);
205 Test statistic for H0: coefficient is 0.
207 t_stat = coeff / std_err;
208 tab_float (t, 5, j + 1, 0, t_stat, 10, 2);
210 P values for the test statistic above.
212 pval = 2 * gsl_cdf_tdist_Q (fabs (t_stat), 1.0);
213 tab_float (t, 6, j + 1, 0, pval, 10, 2);
215 tab_title (t, 0, _("Coefficients"));
220 Display the ANOVA table.
223 reg_stats_anova (pspp_linreg_cache * c)
227 const double msm = c->ssm / c->dfm;
228 const double mse = c->sse / c->dfe;
229 const double F = msm / mse;
230 const double pval = gsl_cdf_fdist_Q (F, c->dfm, c->dfe);
235 t = tab_create (n_cols, n_rows, 0);
236 tab_headers (t, 2, 0, 1, 0);
237 tab_dim (t, tab_natural_dimensions);
239 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1);
241 tab_hline (t, TAL_2, 0, n_cols - 1, 1);
242 tab_vline (t, TAL_2, 2, 0, n_rows - 1);
243 tab_vline (t, TAL_0, 1, 0, 0);
245 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("Sum of Squares"));
246 tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("df"));
247 tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Mean Square"));
248 tab_text (t, 5, 0, TAB_CENTER | TAT_TITLE, _("F"));
249 tab_text (t, 6, 0, TAB_CENTER | TAT_TITLE, _("Significance"));
251 tab_text (t, 1, 1, TAB_LEFT | TAT_TITLE, _("Regression"));
252 tab_text (t, 1, 2, TAB_LEFT | TAT_TITLE, _("Residual"));
253 tab_text (t, 1, 3, TAB_LEFT | TAT_TITLE, _("Total"));
255 /* Sums of Squares */
256 tab_float (t, 2, 1, 0, c->ssm, 10, 2);
257 tab_float (t, 2, 3, 0, c->sst, 10, 2);
258 tab_float (t, 2, 2, 0, c->sse, 10, 2);
261 /* Degrees of freedom */
262 tab_float (t, 3, 1, 0, c->dfm, 4, 0);
263 tab_float (t, 3, 2, 0, c->dfe, 4, 0);
264 tab_float (t, 3, 3, 0, c->dft, 4, 0);
268 tab_float (t, 4, 1, TAB_RIGHT, msm, 8, 3);
269 tab_float (t, 4, 2, TAB_RIGHT, mse, 8, 3);
271 tab_float (t, 5, 1, 0, F, 8, 3);
273 tab_float (t, 6, 1, 0, pval, 8, 3);
275 tab_title (t, 0, _("ANOVA"));
279 reg_stats_outs (pspp_linreg_cache * c)
284 reg_stats_zpp (pspp_linreg_cache * c)
289 reg_stats_label (pspp_linreg_cache * c)
294 reg_stats_sha (pspp_linreg_cache * c)
299 reg_stats_ci (pspp_linreg_cache * c)
304 reg_stats_f (pspp_linreg_cache * c)
309 reg_stats_bcov (pspp_linreg_cache * c)
322 n_cols = c->n_indeps + 1 + 2;
323 n_rows = 2 * (c->n_indeps + 1);
324 t = tab_create (n_cols, n_rows, 0);
325 tab_headers (t, 2, 0, 1, 0);
326 tab_dim (t, tab_natural_dimensions);
327 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1);
328 tab_hline (t, TAL_2, 0, n_cols - 1, 1);
329 tab_vline (t, TAL_2, 2, 0, n_rows - 1);
330 tab_vline (t, TAL_0, 1, 0, 0);
331 tab_text (t, 0, 0, TAB_CENTER | TAT_TITLE, _("Model"));
332 tab_text (t, 1, 1, TAB_CENTER | TAT_TITLE, _("Covariances"));
333 for (i = 1; i < c->n_indeps + 1; i++)
335 j = indep_vars[(i - 1)];
336 struct variable *v = cmd.v_variables[j];
337 label = var_to_string (v);
338 tab_text (t, 2, i, TAB_CENTER, label);
339 tab_text (t, i + 2, 0, TAB_CENTER, label);
340 for (k = 1; k < c->n_indeps + 1; k++)
342 col = (i <= k) ? k : i;
343 row = (i <= k) ? i : k;
344 tab_float (t, k + 2, i, TAB_CENTER,
345 gsl_matrix_get (c->cov, row, col), 8, 3);
348 tab_title (t, 0, _("Coefficient Correlations"));
352 reg_stats_ses (pspp_linreg_cache * c)
357 reg_stats_xtx (pspp_linreg_cache * c)
362 reg_stats_collin (pspp_linreg_cache * c)
367 reg_stats_tol (pspp_linreg_cache * c)
372 reg_stats_selection (pspp_linreg_cache * c)
378 statistics_keyword_output (void (*function) (pspp_linreg_cache *),
379 int keyword, pspp_linreg_cache * c)
388 subcommand_statistics (int *keywords, pspp_linreg_cache * c)
391 The order here must match the order in which the STATISTICS
392 keywords appear in the specification section above.
419 Set everything but F.
421 for (i = 0; i < f; i++)
428 for (i = 0; i < all; i++)
436 Default output: ANOVA table, parameter estimates,
437 and statistics for variables not entered into model,
440 if (keywords[defaults] | d)
448 statistics_keyword_output (reg_stats_r, keywords[r], c);
449 statistics_keyword_output (reg_stats_anova, keywords[anova], c);
450 statistics_keyword_output (reg_stats_coeff, keywords[coeff], c);
451 statistics_keyword_output (reg_stats_outs, keywords[outs], c);
452 statistics_keyword_output (reg_stats_zpp, keywords[zpp], c);
453 statistics_keyword_output (reg_stats_label, keywords[label], c);
454 statistics_keyword_output (reg_stats_sha, keywords[sha], c);
455 statistics_keyword_output (reg_stats_ci, keywords[ci], c);
456 statistics_keyword_output (reg_stats_f, keywords[f], c);
457 statistics_keyword_output (reg_stats_bcov, keywords[bcov], c);
458 statistics_keyword_output (reg_stats_ses, keywords[ses], c);
459 statistics_keyword_output (reg_stats_xtx, keywords[xtx], c);
460 statistics_keyword_output (reg_stats_collin, keywords[collin], c);
461 statistics_keyword_output (reg_stats_tol, keywords[tol], c);
462 statistics_keyword_output (reg_stats_selection, keywords[selection], c);
466 cmd_regression (void)
468 if (!parse_regression (&cmd))
472 multipass_procedure_with_splits (run_regression, &cmd);
478 Is variable k one of the dependent variables?
484 for (j = 0; j < cmd.n_dependent; j++)
487 compare_var_names returns 0 if the variable
490 if (!compare_var_names (cmd.v_dependent[j], cmd.v_variables[k], NULL))
497 run_regression (const struct casefile *cf, void *cmd_ UNUSED)
507 Keep track of the missing cases.
509 int *is_missing_case;
510 const union value *val;
511 struct casereader *r;
512 struct casereader *r2;
515 struct design_matrix *X;
517 pspp_linreg_cache *lcache;
518 pspp_linreg_opts lopts;
520 n_data = casefile_get_case_cnt (cf);
522 is_missing_case = xnmalloc (n_data, sizeof (*is_missing_case));
523 for (i = 0; i < n_data; i++)
524 is_missing_case[i] = 0;
526 n_indep = cmd.n_variables - cmd.n_dependent;
527 indep_vars = xnmalloc (n_indep, sizeof *indep_vars);
529 lopts.get_depvar_mean_std = 1;
530 lopts.get_indep_mean_std = xnmalloc (n_indep, sizeof (int));
534 Read from the active file. The first pass encodes categorical
535 variables and drops cases with missing values.
537 for (i = 0; i < cmd.n_variables; i++)
539 v = cmd.v_variables[i];
540 if (v->type == ALPHA)
542 /* Make a place to hold the binary vectors
543 corresponding to this variable's values. */
544 cat_stored_values_create (v);
546 for (r = casefile_get_reader (cf);
547 casereader_read (r, &c); case_destroy (&c))
549 row = casereader_cnum (r) - 1;
551 val = case_data (&c, v->fv);
552 cat_value_update (v, val);
553 if (mv_is_value_missing (&v->miss, val))
555 if (!is_missing_case[row])
557 /* Now it is missing. */
559 is_missing_case[row] = 1;
565 Y = gsl_vector_alloc (n_data);
567 design_matrix_create (n_indep, (const struct variable **) cmd.v_variables,
569 lcache = pspp_linreg_cache_alloc (X->m->size1, X->m->size2);
570 lcache->indep_means = gsl_vector_alloc (X->m->size2);
571 lcache->indep_std = gsl_vector_alloc (X->m->size2);
574 The second pass creates the design matrix.
577 for (r2 = casefile_get_reader (cf); casereader_read (r2, &c);
579 /* Iterate over the cases. */
582 case_num = casereader_cnum (r2) - 1;
583 if (!is_missing_case[case_num])
585 for (i = 0; i < cmd.n_variables; ++i) /* Iterate over the variables
586 for the current case.
589 v = cmd.v_variables[i];
590 val = case_data (&c, v->fv);
592 Independent/dependent variable separation. The
593 'variables' subcommand specifies a varlist which contains
594 both dependent and independent variables. The dependent
595 variables are specified with the 'dependent'
596 subcommand. We need to separate the two.
600 if (v->type != NUMERIC)
603 gettext ("Dependent variable must be numeric."));
604 pspp_reg_rc = CMD_FAILURE;
607 lcache->depvar = (const struct var *) v;
608 gsl_vector_set (Y, row, val->f);
612 if (v->type == ALPHA)
614 design_matrix_set_categorical (X, row, v, val);
616 else if (v->type == NUMERIC)
618 design_matrix_set_numeric (X, row, v, val);
623 lopts.get_indep_mean_std[i] = 1;
630 Now that we know the number of coefficients, allocate space
631 and store pointers to the variables that correspond to the
634 lcache->coeff = xnmalloc (X->m->size2 + 1, sizeof (*lcache->coeff));
635 for (i = 0; i < X->m->size2; i++)
637 j = i + 1; /* The first coeff is the intercept. */
639 (const struct variable *) design_matrix_col_to_var (X, i);
640 assert (lcache->coeff[j].v != NULL);
643 Find the least-squares estimates and other statistics.
645 pspp_linreg ((const gsl_vector *) Y, X->m, &lopts, lcache);
646 subcommand_statistics (cmd.a_statistics, lcache);
648 design_matrix_destroy (X);
649 pspp_linreg_cache_free (lcache);
650 free (lopts.get_indep_mean_std);
652 free (is_missing_case);
653 casereader_destroy (r);