1 /* pspp - a program for statistical analysis.
2 Copyright (C) 2012 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/>. */
20 1. "Coding Logistic Regression with Newton-Raphson", James McCaffrey
21 http://msdn.microsoft.com/en-us/magazine/jj618304.aspx
23 2. "SPSS Statistical Algorithms" Chapter LOGISTIC REGRESSION Algorithms
26 The Newton Raphson method finds successive approximations to $\bf b$ where
27 approximation ${\bf b}_t$ is (hopefully) better than the previous ${\bf b}_{t-1}$.
29 $ {\bf b}_t = {\bf b}_{t -1} + ({\bf X}^T{\bf W}_{t-1}{\bf X})^{-1}{\bf X}^T({\bf y} - {\bf \pi}_{t-1})$
32 $\bf X$ is the $n \times p$ design matrix, $n$ being the number of cases,
33 $p$ the number of parameters, \par
34 $\bf W$ is the diagonal matrix whose diagonal elements are
35 $\hat{\pi}_0(1 - \hat{\pi}_0), \, \hat{\pi}_1(1 - \hat{\pi}_2)\dots \hat{\pi}_{n-1}(1 - \hat{\pi}_{n-1})$
42 #include <gsl/gsl_blas.h>
44 #include <gsl/gsl_linalg.h>
45 #include <gsl/gsl_cdf.h>
46 #include <gsl/gsl_matrix.h>
47 #include <gsl/gsl_vector.h>
50 #include "data/case.h"
51 #include "data/casegrouper.h"
52 #include "data/casereader.h"
53 #include "data/dataset.h"
54 #include "data/dictionary.h"
55 #include "data/format.h"
56 #include "data/value.h"
57 #include "language/command.h"
58 #include "language/dictionary/split-file.h"
59 #include "language/lexer/lexer.h"
60 #include "language/lexer/value-parser.h"
61 #include "language/lexer/variable-parser.h"
62 #include "libpspp/assertion.h"
63 #include "libpspp/ll.h"
64 #include "libpspp/message.h"
65 #include "libpspp/misc.h"
66 #include "math/categoricals.h"
67 #include "math/interaction.h"
68 #include "libpspp/hmap.h"
69 #include "libpspp/hash-functions.h"
71 #include "output/tab.h"
74 #define _(msgid) gettext (msgid)
79 #define PRINT_EACH_STEP 0x01
80 #define PRINT_SUMMARY 0x02
81 #define PRINT_CORR 0x04
82 #define PRINT_ITER 0x08
83 #define PRINT_GOODFIT 0x10
87 #define PRINT_DEFAULT (PRINT_SUMMARY | PRINT_EACH_STEP)
90 The constant parameters of the procedure.
91 That is, those which are set by the user.
95 /* The dependent variable */
96 const struct variable *dep_var;
98 /* The predictor variables (excluding categorical ones) */
99 const struct variable **predictor_vars;
100 size_t n_predictor_vars;
102 /* The categorical predictors */
103 struct interaction **cat_predictors;
104 size_t n_cat_predictors;
107 /* The union of the categorical and non-categorical variables */
108 const struct variable **indep_vars;
112 /* Which classes of missing vars are to be excluded */
113 enum mv_class exclude;
115 /* The weight variable */
116 const struct variable *wv;
118 /* The dictionary of the dataset */
119 const struct dictionary *dict;
121 /* True iff the constant (intercept) is to be included in the model */
124 /* Ths maximum number of iterations */
127 /* Other iteration limiting conditions */
132 /* The confidence interval (in percent) */
135 /* What results should be presented */
142 /* The results and intermediate result of the procedure.
143 These are mutated as the procedure runs. Used for
144 temporary variables etc.
148 /* Used to indicate if a pass should flag a warning when
149 invalid (ie negative or missing) weight values are encountered */
150 bool warn_bad_weight;
152 /* The two values of the dependent variable. */
157 /* The sum of caseweights */
160 /* The number of missing and nonmissing cases */
161 casenumber n_missing;
162 casenumber n_nonmissing;
167 /* The categoricals and their payload. Null if the analysis has no
168 categorical predictors */
169 struct categoricals *cats;
175 Convert INPUT into a dichotomous scalar, according to how the dependent variable's
177 For simple cases, this is a 1:1 mapping
178 The return value is always either 0 or 1
181 map_dependent_var (const struct lr_spec *cmd, const struct lr_result *res, const union value *input)
183 const int width = var_get_width (cmd->dep_var);
184 if (value_equal (input, &res->y0, width))
187 if (value_equal (input, &res->y1, width))
190 /* This should never happen. If it does, then y0 and/or y1 have probably not been set */
197 static void output_categories (const struct lr_spec *cmd, const struct lr_result *res);
199 static void output_depvarmap (const struct lr_spec *cmd, const struct lr_result *);
201 static void output_variables (const struct lr_spec *cmd,
202 const struct lr_result *,
205 static void output_model_summary (const struct lr_result *,
206 double initial_likelihood, double likelihood);
208 static void case_processing_summary (const struct lr_result *);
211 /* Return the value of case C corresponding to the INDEX'th entry in the
214 predictor_value (const struct ccase *c,
215 const struct variable **x, size_t n_x,
216 const struct categoricals *cats,
219 /* Values of the scalar predictor variables */
221 return case_data (c, x[index])->f;
223 /* Coded values of categorical predictor variables (or interactions) */
224 if (cats && index - n_x < categoricals_df_total (cats))
226 double x = categoricals_get_dummy_code_for_case (cats, index - n_x, c);
230 /* The constant term */
236 Return the probability estimator (that is the estimator of logit(y) )
237 corresponding to the coefficient estimator beta_hat for case C
240 pi_hat (const struct lr_spec *cmd,
241 struct lr_result *res,
242 const gsl_vector *beta_hat,
243 const struct variable **x, size_t n_x,
244 const struct ccase *c)
248 size_t n_coeffs = beta_hat->size;
252 pi += gsl_vector_get (beta_hat, beta_hat->size - 1);
256 for (v0 = 0; v0 < n_coeffs; ++v0)
258 pi += gsl_vector_get (beta_hat, v0) *
259 predictor_value (c, x, n_x, res->cats, v0);
262 pi = 1.0 / (1.0 + exp(-pi));
269 Calculates the Hessian matrix X' V X,
270 where: X is the n by N_X matrix comprising the n cases in INPUT
271 V is a diagonal matrix { (pi_hat_0)(1 - pi_hat_0), (pi_hat_1)(1 - pi_hat_1), ... (pi_hat_{N-1})(1 - pi_hat_{N-1})}
272 (the partial derivative of the predicted values)
274 If ALL predicted values derivatives are close to zero or one, then CONVERGED
278 hessian (const struct lr_spec *cmd,
279 struct lr_result *res,
280 struct casereader *input,
281 const struct variable **x, size_t n_x,
282 const gsl_vector *beta_hat,
285 struct casereader *reader;
288 double max_w = -DBL_MAX;
290 gsl_matrix_set_zero (res->hessian);
292 for (reader = casereader_clone (input);
293 (c = casereader_read (reader)) != NULL; case_unref (c))
296 double pi = pi_hat (cmd, res, beta_hat, x, n_x, c);
298 double weight = dict_get_case_weight (cmd->dict, c, &res->warn_bad_weight);
299 double w = pi * (1 - pi);
304 for (v0 = 0; v0 < beta_hat->size; ++v0)
306 double in0 = predictor_value (c, x, n_x, res->cats, v0);
307 for (v1 = 0; v1 < beta_hat->size; ++v1)
309 double in1 = predictor_value (c, x, n_x, res->cats, v1);
310 double *o = gsl_matrix_ptr (res->hessian, v0, v1);
315 casereader_destroy (reader);
317 if ( max_w < cmd->min_epsilon)
320 msg (MN, _("All predicted values are either 1 or 0"));
325 /* Calculates the value X' (y - pi)
326 where X is the design model,
327 y is the vector of observed independent variables
328 pi is the vector of estimates for y
330 As a side effect, the likelihood is stored in LIKELIHOOD
333 xt_times_y_pi (const struct lr_spec *cmd,
334 struct lr_result *res,
335 struct casereader *input,
336 const struct variable **x, size_t n_x,
337 const struct variable *y_var,
338 const gsl_vector *beta_hat,
341 struct casereader *reader;
343 gsl_vector *output = gsl_vector_calloc (beta_hat->size);
346 for (reader = casereader_clone (input);
347 (c = casereader_read (reader)) != NULL; case_unref (c))
350 double pi = pi_hat (cmd, res, beta_hat, x, n_x, c);
351 double weight = dict_get_case_weight (cmd->dict, c, &res->warn_bad_weight);
354 double y = map_dependent_var (cmd, res, case_data (c, y_var));
356 *likelihood *= pow (pi, weight * y) * pow (1 - pi, weight * (1 - y));
358 for (v0 = 0; v0 < beta_hat->size; ++v0)
360 double in0 = predictor_value (c, x, n_x, res->cats, v0);
361 double *o = gsl_vector_ptr (output, v0);
362 *o += in0 * (y - pi) * weight;
366 casereader_destroy (reader);
373 /* "payload" functions for the categoricals.
374 The only function is to accumulate the frequency of each
379 frq_create (const void *aux1 UNUSED, void *aux2 UNUSED)
381 return xzalloc (sizeof (double));
385 frq_update (const void *aux1 UNUSED, void *aux2 UNUSED,
386 void *ud, const struct ccase *c UNUSED , double weight)
393 frq_destroy (const void *aux1 UNUSED, void *aux2 UNUSED, void *user_data UNUSED)
401 Makes an initial pass though the data, doing the following:
403 * Checks that the dependent variable is dichotomous,
404 * Creates and initialises the categoricals,
405 * Accumulates summary results,
406 * Calculates necessary initial values.
408 Returns an initial value for \hat\beta the vector of estimators of \beta
411 beta_hat_initial (const struct lr_spec *cmd, struct lr_result *res, struct casereader *input)
413 const int width = var_get_width (cmd->dep_var);
416 struct casereader *reader;
425 size_t n_coefficients = cmd->n_predictor_vars;
429 /* Create categoricals if appropriate */
430 if (cmd->n_cat_predictors > 0)
432 res->cp.create = frq_create;
433 res->cp.update = frq_update;
434 res->cp.calculate = NULL;
435 res->cp.destroy = frq_destroy;
437 res->cats = categoricals_create (cmd->cat_predictors, cmd->n_cat_predictors,
438 cmd->wv, cmd->exclude, MV_ANY);
440 categoricals_set_payload (res->cats, &res->cp, cmd, res);
444 for (reader = casereader_clone (input);
445 (c = casereader_read (reader)) != NULL; case_unref (c))
448 bool missing = false;
449 double weight = dict_get_case_weight (cmd->dict, c, &res->warn_bad_weight);
450 const union value *depval = case_data (c, cmd->dep_var);
452 for (v = 0; v < cmd->n_indep_vars; ++v)
454 const union value *val = case_data (c, cmd->indep_vars[v]);
455 if (var_is_value_missing (cmd->indep_vars[v], val, cmd->exclude))
462 /* Accumulate the missing and non-missing counts */
470 /* Find the values of the dependent variable */
473 value_clone (&res->y0, depval, width);
478 if ( !value_equal (&res->y0, depval, width))
480 value_clone (&res->y1, depval, width);
486 if (! value_equal (&res->y0, depval, width)
488 ! value_equal (&res->y1, depval, width)
491 msg (ME, _("Dependent variable's values are not dichotomous."));
496 if (v0set && value_equal (&res->y0, depval, width))
499 if (v1set && value_equal (&res->y1, depval, width))
505 categoricals_update (res->cats, c);
507 casereader_destroy (reader);
509 categoricals_done (res->cats);
513 /* Ensure that Y0 is less than Y1. Otherwise the mapping gets
514 inverted, which is confusing to users */
515 if (var_is_numeric (cmd->dep_var) && value_compare_3way (&res->y0, &res->y1, width) > 0)
518 value_clone (&tmp, &res->y0, width);
519 value_copy (&res->y0, &res->y1, width);
520 value_copy (&res->y1, &tmp, width);
521 value_destroy (&tmp, width);
525 n_coefficients += categoricals_df_total (res->cats);
526 b0 = gsl_vector_calloc (n_coefficients);
530 double mean = sum / res->cc;
531 gsl_vector_set (b0, b0->size - 1, log (mean / (1 - mean)));
537 casereader_destroy (reader);
543 /* Start of the logistic regression routine proper */
545 run_lr (const struct lr_spec *cmd, struct casereader *input,
546 const struct dataset *ds UNUSED)
550 gsl_vector *beta_hat;
552 bool converged = false;
554 /* Set the likelihoods to a negative sentinel value */
555 double likelihood = -1;
556 double prev_likelihood = -1;
557 double initial_likelihood = -1;
559 struct lr_result work;
561 work.n_nonmissing = 0;
562 work.warn_bad_weight = true;
566 /* Get the initial estimates of \beta and their standard errors */
567 beta_hat = beta_hat_initial (cmd, &work, input);
568 if (NULL == beta_hat)
572 for (i = 0; i < cmd->n_cat_predictors; ++i)
574 if (1 >= categoricals_n_count (work.cats, i))
577 ds_init_empty (&str);
579 interaction_to_string (cmd->cat_predictors[i], &str);
581 msg (ME, _("Category %s does not have at least two distinct values. Logistic regression will not be run."),
588 output_depvarmap (cmd, &work);
590 case_processing_summary (&work);
593 input = casereader_create_filter_missing (input,
601 work.hessian = gsl_matrix_calloc (beta_hat->size, beta_hat->size);
603 /* Start the Newton Raphson iteration process... */
604 for( i = 0 ; i < cmd->max_iter ; ++i)
610 hessian (cmd, &work, input,
611 cmd->predictor_vars, cmd->n_predictor_vars,
615 gsl_linalg_cholesky_decomp (work.hessian);
616 gsl_linalg_cholesky_invert (work.hessian);
618 v = xt_times_y_pi (cmd, &work, input,
619 cmd->predictor_vars, cmd->n_predictor_vars,
626 gsl_vector *delta = gsl_vector_alloc (v->size);
627 gsl_blas_dgemv (CblasNoTrans, 1.0, work.hessian, v, 0, delta);
631 gsl_vector_add (beta_hat, delta);
633 gsl_vector_minmax (delta, &min, &max);
635 if ( fabs (min) < cmd->bcon && fabs (max) < cmd->bcon)
637 msg (MN, _("Estimation terminated at iteration number %d because parameter estimates changed by less than %g"),
642 gsl_vector_free (delta);
645 if ( prev_likelihood >= 0)
647 if (-log (likelihood) > -(1.0 - cmd->lcon) * log (prev_likelihood))
649 msg (MN, _("Estimation terminated at iteration number %d because Log Likelihood decreased by less than %g%%"), i + 1, 100 * cmd->lcon);
654 initial_likelihood = likelihood;
655 prev_likelihood = likelihood;
660 casereader_destroy (input);
661 assert (initial_likelihood >= 0);
664 msg (MW, _("Estimation terminated at iteration number %d because maximum iterations has been reached"), i );
667 output_model_summary (&work, initial_likelihood, likelihood);
670 output_categories (cmd, &work);
672 output_variables (cmd, &work, beta_hat);
674 gsl_matrix_free (work.hessian);
675 gsl_vector_free (beta_hat);
677 categoricals_destroy (work.cats);
684 struct hmap_node node; /* Node in hash map. */
685 const struct variable *var; /* The variable */
688 static struct variable_node *
689 lookup_variable (const struct hmap *map, const struct variable *var, unsigned int hash)
691 struct variable_node *vn = NULL;
692 HMAP_FOR_EACH_WITH_HASH (vn, struct variable_node, node, hash, map)
697 fprintf (stderr, "Warning: Hash table collision\n");
704 /* Parse the LOGISTIC REGRESSION command syntax */
706 cmd_logistic (struct lexer *lexer, struct dataset *ds)
708 /* Temporary location for the predictor variables.
709 These may or may not include the categorical predictors */
710 const struct variable **pred_vars;
715 lr.dict = dataset_dict (ds);
716 lr.n_predictor_vars = 0;
717 lr.predictor_vars = NULL;
719 lr.wv = dict_get_weight (lr.dict);
723 lr.min_epsilon = 0.00000001;
727 lr.print = PRINT_DEFAULT;
728 lr.cat_predictors = NULL;
729 lr.n_cat_predictors = 0;
730 lr.indep_vars = NULL;
733 if (lex_match_id (lexer, "VARIABLES"))
734 lex_match (lexer, T_EQUALS);
736 if (! (lr.dep_var = parse_variable_const (lexer, lr.dict)))
739 lex_force_match (lexer, T_WITH);
741 if (!parse_variables_const (lexer, lr.dict,
742 &pred_vars, &n_pred_vars,
747 while (lex_token (lexer) != T_ENDCMD)
749 lex_match (lexer, T_SLASH);
751 if (lex_match_id (lexer, "MISSING"))
753 lex_match (lexer, T_EQUALS);
754 while (lex_token (lexer) != T_ENDCMD
755 && lex_token (lexer) != T_SLASH)
757 if (lex_match_id (lexer, "INCLUDE"))
759 lr.exclude = MV_SYSTEM;
761 else if (lex_match_id (lexer, "EXCLUDE"))
767 lex_error (lexer, NULL);
772 else if (lex_match_id (lexer, "ORIGIN"))
776 else if (lex_match_id (lexer, "NOORIGIN"))
780 else if (lex_match_id (lexer, "NOCONST"))
784 else if (lex_match_id (lexer, "EXTERNAL"))
786 /* This is for compatibility. It does nothing */
788 else if (lex_match_id (lexer, "CATEGORICAL"))
790 lex_match (lexer, T_EQUALS);
793 lr.cat_predictors = xrealloc (lr.cat_predictors,
794 sizeof (*lr.cat_predictors) * ++lr.n_cat_predictors);
795 lr.cat_predictors[lr.n_cat_predictors - 1] = 0;
797 while (parse_design_interaction (lexer, lr.dict,
798 lr.cat_predictors + lr.n_cat_predictors - 1));
799 lr.n_cat_predictors--;
801 else if (lex_match_id (lexer, "PRINT"))
803 lex_match (lexer, T_EQUALS);
804 while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
806 if (lex_match_id (lexer, "DEFAULT"))
808 lr.print |= PRINT_DEFAULT;
810 else if (lex_match_id (lexer, "SUMMARY"))
812 lr.print |= PRINT_SUMMARY;
815 else if (lex_match_id (lexer, "CORR"))
817 lr.print |= PRINT_CORR;
819 else if (lex_match_id (lexer, "ITER"))
821 lr.print |= PRINT_ITER;
823 else if (lex_match_id (lexer, "GOODFIT"))
825 lr.print |= PRINT_GOODFIT;
828 else if (lex_match_id (lexer, "CI"))
830 lr.print |= PRINT_CI;
831 if (lex_force_match (lexer, T_LPAREN))
833 if (! lex_force_int (lexer))
835 lex_error (lexer, NULL);
838 lr.confidence = lex_integer (lexer);
840 if ( ! lex_force_match (lexer, T_RPAREN))
842 lex_error (lexer, NULL);
847 else if (lex_match_id (lexer, "ALL"))
853 lex_error (lexer, NULL);
858 else if (lex_match_id (lexer, "CRITERIA"))
860 lex_match (lexer, T_EQUALS);
861 while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
863 if (lex_match_id (lexer, "BCON"))
865 if (lex_force_match (lexer, T_LPAREN))
867 if (! lex_force_num (lexer))
869 lex_error (lexer, NULL);
872 lr.bcon = lex_number (lexer);
874 if ( ! lex_force_match (lexer, T_RPAREN))
876 lex_error (lexer, NULL);
881 else if (lex_match_id (lexer, "ITERATE"))
883 if (lex_force_match (lexer, T_LPAREN))
885 if (! lex_force_int (lexer))
887 lex_error (lexer, NULL);
890 lr.max_iter = lex_integer (lexer);
892 if ( ! lex_force_match (lexer, T_RPAREN))
894 lex_error (lexer, NULL);
899 else if (lex_match_id (lexer, "LCON"))
901 if (lex_force_match (lexer, T_LPAREN))
903 if (! lex_force_num (lexer))
905 lex_error (lexer, NULL);
908 lr.lcon = lex_number (lexer);
910 if ( ! lex_force_match (lexer, T_RPAREN))
912 lex_error (lexer, NULL);
917 else if (lex_match_id (lexer, "EPS"))
919 if (lex_force_match (lexer, T_LPAREN))
921 if (! lex_force_num (lexer))
923 lex_error (lexer, NULL);
926 lr.min_epsilon = lex_number (lexer);
928 if ( ! lex_force_match (lexer, T_RPAREN))
930 lex_error (lexer, NULL);
937 lex_error (lexer, NULL);
944 lex_error (lexer, NULL);
949 /* Copy the predictor variables from the temporary location into the
950 final one, dropping any categorical variables which appear there.
951 FIXME: This is O(NxM).
955 struct variable_node *vn, *next;
957 hmap_init (&allvars);
958 for (v = x = 0; v < n_pred_vars; ++v)
961 const struct variable *var = pred_vars[v];
964 unsigned int hash = hash_pointer (var, 0);
965 struct variable_node *vn = lookup_variable (&allvars, var, hash);
968 vn = xmalloc (sizeof *vn);
970 hmap_insert (&allvars, &vn->node, hash);
973 for (cv = 0; cv < lr.n_cat_predictors ; ++cv)
976 const struct interaction *iact = lr.cat_predictors[cv];
977 for (iv = 0 ; iv < iact->n_vars ; ++iv)
979 const struct variable *ivar = iact->vars[iv];
980 unsigned int hash = hash_pointer (ivar, 0);
981 struct variable_node *vn = lookup_variable (&allvars, ivar, hash);
984 vn = xmalloc (sizeof *vn);
987 hmap_insert (&allvars, &vn->node, hash);
1000 lr.predictor_vars = xrealloc (lr.predictor_vars, sizeof *lr.predictor_vars * (x + 1));
1001 lr.predictor_vars[x++] = var;
1002 lr.n_predictor_vars++;
1006 lr.n_indep_vars = hmap_count (&allvars);
1007 lr.indep_vars = xmalloc (lr.n_indep_vars * sizeof *lr.indep_vars);
1009 /* Interate over each variable and push it into the array */
1011 HMAP_FOR_EACH_SAFE (vn, next, struct variable_node, node, &allvars)
1013 lr.indep_vars[x++] = vn->var;
1016 hmap_destroy (&allvars);
1020 /* logistical regression for each split group */
1022 struct casegrouper *grouper;
1023 struct casereader *group;
1026 grouper = casegrouper_create_splits (proc_open (ds), lr.dict);
1027 while (casegrouper_get_next_group (grouper, &group))
1028 ok = run_lr (&lr, group, ds);
1029 ok = casegrouper_destroy (grouper);
1030 ok = proc_commit (ds) && ok;
1033 free (lr.predictor_vars);
1034 free (lr.cat_predictors);
1035 free (lr.indep_vars);
1041 free (lr.predictor_vars);
1042 free (lr.cat_predictors);
1043 free (lr.indep_vars);
1051 /* Show the Dependent Variable Encoding box.
1052 This indicates how the dependent variable
1053 is mapped to the internal zero/one values.
1056 output_depvarmap (const struct lr_spec *cmd, const struct lr_result *res)
1058 const int heading_columns = 0;
1059 const int heading_rows = 1;
1060 struct tab_table *t;
1064 int nr = heading_rows + 2;
1066 t = tab_create (nc, nr);
1067 tab_title (t, _("Dependent Variable Encoding"));
1069 tab_headers (t, heading_columns, 0, heading_rows, 0);
1071 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, nc - 1, nr - 1);
1073 tab_hline (t, TAL_2, 0, nc - 1, heading_rows);
1074 tab_vline (t, TAL_2, heading_columns, 0, nr - 1);
1076 tab_text (t, 0, 0, TAB_CENTER | TAT_TITLE, _("Original Value"));
1077 tab_text (t, 1, 0, TAB_CENTER | TAT_TITLE, _("Internal Value"));
1081 ds_init_empty (&str);
1082 var_append_value_name (cmd->dep_var, &res->y0, &str);
1083 tab_text (t, 0, 0 + heading_rows, 0, ds_cstr (&str));
1086 var_append_value_name (cmd->dep_var, &res->y1, &str);
1087 tab_text (t, 0, 1 + heading_rows, 0, ds_cstr (&str));
1090 tab_double (t, 1, 0 + heading_rows, 0, map_dependent_var (cmd, res, &res->y0), &F_8_0);
1091 tab_double (t, 1, 1 + heading_rows, 0, map_dependent_var (cmd, res, &res->y1), &F_8_0);
1098 /* Show the Variables in the Equation box */
1100 output_variables (const struct lr_spec *cmd,
1101 const struct lr_result *res,
1102 const gsl_vector *beta)
1105 const int heading_columns = 1;
1106 int heading_rows = 1;
1107 struct tab_table *t;
1113 int idx_correction = 0;
1115 if (cmd->print & PRINT_CI)
1121 nr = heading_rows + cmd->n_predictor_vars;
1126 nr += categoricals_df_total (res->cats) + cmd->n_cat_predictors;
1128 t = tab_create (nc, nr);
1129 tab_title (t, _("Variables in the Equation"));
1131 tab_headers (t, heading_columns, 0, heading_rows, 0);
1133 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, nc - 1, nr - 1);
1135 tab_hline (t, TAL_2, 0, nc - 1, heading_rows);
1136 tab_vline (t, TAL_2, heading_columns, 0, nr - 1);
1138 tab_text (t, 0, row + 1, TAB_CENTER | TAT_TITLE, _("Step 1"));
1140 tab_text (t, 2, row, TAB_CENTER | TAT_TITLE, _("B"));
1141 tab_text (t, 3, row, TAB_CENTER | TAT_TITLE, _("S.E."));
1142 tab_text (t, 4, row, TAB_CENTER | TAT_TITLE, _("Wald"));
1143 tab_text (t, 5, row, TAB_CENTER | TAT_TITLE, _("df"));
1144 tab_text (t, 6, row, TAB_CENTER | TAT_TITLE, _("Sig."));
1145 tab_text (t, 7, row, TAB_CENTER | TAT_TITLE, _("Exp(B)"));
1147 if (cmd->print & PRINT_CI)
1149 tab_joint_text_format (t, 8, 0, 9, 0,
1150 TAB_CENTER | TAT_TITLE, _("%d%% CI for Exp(B)"), cmd->confidence);
1152 tab_text (t, 8, row, TAB_CENTER | TAT_TITLE, _("Lower"));
1153 tab_text (t, 9, row, TAB_CENTER | TAT_TITLE, _("Upper"));
1156 for (row = heading_rows ; row < nr; ++row)
1158 const int idx = row - heading_rows - idx_correction;
1160 const double b = gsl_vector_get (beta, idx);
1161 const double sigma2 = gsl_matrix_get (res->hessian, idx, idx);
1162 const double wald = pow2 (b) / sigma2;
1163 const double df = 1;
1165 if (idx < cmd->n_predictor_vars)
1167 tab_text (t, 1, row, TAB_LEFT | TAT_TITLE,
1168 var_to_string (cmd->predictor_vars[idx]));
1170 else if (i < cmd->n_cat_predictors)
1173 bool summary = false;
1175 const struct interaction *cat_predictors = cmd->cat_predictors[i];
1176 const int df = categoricals_df (res->cats, i);
1178 ds_init_empty (&str);
1179 interaction_to_string (cat_predictors, &str);
1183 /* Calculate the Wald statistic,
1184 which is \beta' C^-1 \beta .
1185 where \beta is the vector of the coefficient estimates comprising this
1186 categorial variable. and C is the corresponding submatrix of the
1189 gsl_matrix_const_view mv =
1190 gsl_matrix_const_submatrix (res->hessian, idx, idx, df, df);
1191 gsl_matrix *subhessian = gsl_matrix_alloc (mv.matrix.size1, mv.matrix.size2);
1192 gsl_vector_const_view vv = gsl_vector_const_subvector (beta, idx, df);
1193 gsl_vector *temp = gsl_vector_alloc (df);
1195 gsl_matrix_memcpy (subhessian, &mv.matrix);
1196 gsl_linalg_cholesky_decomp (subhessian);
1197 gsl_linalg_cholesky_invert (subhessian);
1199 gsl_blas_dgemv (CblasTrans, 1.0, subhessian, &vv.vector, 0, temp);
1200 gsl_blas_ddot (temp, &vv.vector, &wald);
1202 tab_double (t, 4, row, 0, wald, 0);
1203 tab_double (t, 5, row, 0, df, &F_8_0);
1204 tab_double (t, 6, row, 0, gsl_cdf_chisq_Q (wald, df), 0);
1208 gsl_matrix_free (subhessian);
1209 gsl_vector_free (temp);
1213 ds_put_format (&str, "(%d)", ivar);
1216 tab_text (t, 1, row, TAB_LEFT | TAT_TITLE, ds_cstr (&str));
1219 ++i; /* next interaction */
1230 tab_text (t, 1, row, TAB_LEFT | TAT_TITLE, _("Constant"));
1233 tab_double (t, 2, row, 0, b, 0);
1234 tab_double (t, 3, row, 0, sqrt (sigma2), 0);
1235 tab_double (t, 4, row, 0, wald, 0);
1236 tab_double (t, 5, row, 0, df, &F_8_0);
1237 tab_double (t, 6, row, 0, gsl_cdf_chisq_Q (wald, df), 0);
1238 tab_double (t, 7, row, 0, exp (b), 0);
1240 if (cmd->print & PRINT_CI)
1242 double wc = gsl_cdf_ugaussian_Pinv (0.5 + cmd->confidence / 200.0);
1243 wc *= sqrt (sigma2);
1245 if (idx < cmd->n_predictor_vars)
1247 tab_double (t, 8, row, 0, exp (b - wc), 0);
1248 tab_double (t, 9, row, 0, exp (b + wc), 0);
1257 /* Show the model summary box */
1259 output_model_summary (const struct lr_result *res,
1260 double initial_likelihood, double likelihood)
1262 const int heading_columns = 0;
1263 const int heading_rows = 1;
1264 struct tab_table *t;
1267 int nr = heading_rows + 1;
1270 t = tab_create (nc, nr);
1271 tab_title (t, _("Model Summary"));
1273 tab_headers (t, heading_columns, 0, heading_rows, 0);
1275 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, nc - 1, nr - 1);
1277 tab_hline (t, TAL_2, 0, nc - 1, heading_rows);
1278 tab_vline (t, TAL_2, heading_columns, 0, nr - 1);
1280 tab_text (t, 0, 0, TAB_LEFT | TAT_TITLE, _("Step 1"));
1281 tab_text (t, 1, 0, TAB_CENTER | TAT_TITLE, _("-2 Log likelihood"));
1282 tab_double (t, 1, 1, 0, -2 * log (likelihood), 0);
1285 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("Cox & Snell R Square"));
1286 cox = 1.0 - pow (initial_likelihood /likelihood, 2 / res->cc);
1287 tab_double (t, 2, 1, 0, cox, 0);
1289 tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("Nagelkerke R Square"));
1290 tab_double (t, 3, 1, 0, cox / ( 1.0 - pow (initial_likelihood, 2 / res->cc)), 0);
1296 /* Show the case processing summary box */
1298 case_processing_summary (const struct lr_result *res)
1300 const int heading_columns = 1;
1301 const int heading_rows = 1;
1302 struct tab_table *t;
1305 const int nr = heading_rows + 3;
1308 t = tab_create (nc, nr);
1309 tab_title (t, _("Case Processing Summary"));
1311 tab_headers (t, heading_columns, 0, heading_rows, 0);
1313 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, nc - 1, nr - 1);
1315 tab_hline (t, TAL_2, 0, nc - 1, heading_rows);
1316 tab_vline (t, TAL_2, heading_columns, 0, nr - 1);
1318 tab_text (t, 0, 0, TAB_LEFT | TAT_TITLE, _("Unweighted Cases"));
1319 tab_text (t, 1, 0, TAB_CENTER | TAT_TITLE, _("N"));
1320 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("Percent"));
1323 tab_text (t, 0, 1, TAB_LEFT | TAT_TITLE, _("Included in Analysis"));
1324 tab_text (t, 0, 2, TAB_LEFT | TAT_TITLE, _("Missing Cases"));
1325 tab_text (t, 0, 3, TAB_LEFT | TAT_TITLE, _("Total"));
1327 tab_double (t, 1, 1, 0, res->n_nonmissing, &F_8_0);
1328 tab_double (t, 1, 2, 0, res->n_missing, &F_8_0);
1330 total = res->n_nonmissing + res->n_missing;
1331 tab_double (t, 1, 3, 0, total , &F_8_0);
1333 tab_double (t, 2, 1, 0, 100 * res->n_nonmissing / (double) total, 0);
1334 tab_double (t, 2, 2, 0, 100 * res->n_missing / (double) total, 0);
1335 tab_double (t, 2, 3, 0, 100 * total / (double) total, 0);
1341 output_categories (const struct lr_spec *cmd, const struct lr_result *res)
1343 const struct fmt_spec *wfmt =
1344 cmd->wv ? var_get_print_format (cmd->wv) : &F_8_0;
1348 const int heading_columns = 2;
1349 const int heading_rows = 2;
1350 struct tab_table *t;
1360 for (i = 0; i < cmd->n_cat_predictors; ++i)
1362 size_t n = categoricals_n_count (res->cats, i);
1363 size_t df = categoricals_df (res->cats, i);
1369 nc = heading_columns + 1 + max_df;
1370 nr = heading_rows + total_cats;
1372 t = tab_create (nc, nr);
1373 tab_title (t, _("Categorical Variables' Codings"));
1375 tab_headers (t, heading_columns, 0, heading_rows, 0);
1377 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, nc - 1, nr - 1);
1379 tab_hline (t, TAL_2, 0, nc - 1, heading_rows);
1380 tab_vline (t, TAL_2, heading_columns, 0, nr - 1);
1383 tab_text (t, heading_columns, 1, TAB_CENTER | TAT_TITLE, _("Frequency"));
1385 tab_joint_text_format (t, heading_columns + 1, 0, nc - 1, 0,
1386 TAB_CENTER | TAT_TITLE, _("Parameter coding"));
1389 for (i = 0; i < max_df; ++i)
1391 int c = heading_columns + 1 + i;
1392 tab_text_format (t, c, 1, TAB_CENTER | TAT_TITLE, _("(%d)"), i + 1);
1396 for (v = 0; v < cmd->n_cat_predictors; ++v)
1399 const struct interaction *cat_predictors = cmd->cat_predictors[v];
1400 int df = categoricals_df (res->cats, v);
1402 ds_init_empty (&str);
1404 interaction_to_string (cat_predictors, &str);
1406 tab_text (t, 0, heading_rows + r, TAB_LEFT | TAT_TITLE, ds_cstr (&str) );
1410 for (cat = 0; cat < categoricals_n_count (res->cats, v) ; ++cat)
1413 const struct ccase *c = categoricals_get_case_by_category_real (res->cats, v, cat);
1414 const double *freq = categoricals_get_user_data_by_category_real (res->cats, v, cat);
1417 ds_init_empty (&str);
1419 for (x = 0; x < cat_predictors->n_vars; ++x)
1421 const union value *val = case_data (c, cat_predictors->vars[x]);
1422 var_append_value_name (cat_predictors->vars[x], val, &str);
1424 if (x < cat_predictors->n_vars - 1)
1425 ds_put_cstr (&str, " ");
1428 tab_text (t, 1, heading_rows + r, 0, ds_cstr (&str));
1430 tab_double (t, 2, heading_rows + r, 0, *freq, wfmt);
1432 for (x = 0; x < df; ++x)
1434 tab_double (t, heading_columns + 1 + x, heading_rows + r, 0, (cat == x), &F_8_0);
1438 cumulative_df += df;