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 */
138 /* Inverse logit of the cut point */
139 double ilogit_cut_point;
143 /* The results and intermediate result of the procedure.
144 These are mutated as the procedure runs. Used for
145 temporary variables etc.
149 /* Used to indicate if a pass should flag a warning when
150 invalid (ie negative or missing) weight values are encountered */
151 bool warn_bad_weight;
153 /* The two values of the dependent variable. */
158 /* The sum of caseweights */
161 /* The number of missing and nonmissing cases */
162 casenumber n_missing;
163 casenumber n_nonmissing;
168 /* The categoricals and their payload. Null if the analysis has no
169 categorical predictors */
170 struct categoricals *cats;
174 /* The estimates of the predictor coefficients */
175 gsl_vector *beta_hat;
177 /* The predicted classifications:
178 True Negative, True Positive, False Negative, False Positive */
179 double tn, tp, fn, fp;
184 Convert INPUT into a dichotomous scalar, according to how the dependent variable's
186 For simple cases, this is a 1:1 mapping
187 The return value is always either 0 or 1
190 map_dependent_var (const struct lr_spec *cmd, const struct lr_result *res, const union value *input)
192 const int width = var_get_width (cmd->dep_var);
193 if (value_equal (input, &res->y0, width))
196 if (value_equal (input, &res->y1, width))
199 /* This should never happen. If it does, then y0 and/or y1 have probably not been set */
205 static void output_classification_table (const struct lr_spec *cmd, const struct lr_result *res);
207 static void output_categories (const struct lr_spec *cmd, const struct lr_result *res);
209 static void output_depvarmap (const struct lr_spec *cmd, const struct lr_result *);
211 static void output_variables (const struct lr_spec *cmd,
212 const struct lr_result *);
214 static void output_model_summary (const struct lr_result *,
215 double initial_likelihood, double likelihood);
217 static void case_processing_summary (const struct lr_result *);
220 /* Return the value of case C corresponding to the INDEX'th entry in the
223 predictor_value (const struct ccase *c,
224 const struct variable **x, size_t n_x,
225 const struct categoricals *cats,
228 /* Values of the scalar predictor variables */
230 return case_data (c, x[index])->f;
232 /* Coded values of categorical predictor variables (or interactions) */
233 if (cats && index - n_x < categoricals_df_total (cats))
235 double x = categoricals_get_dummy_code_for_case (cats, index - n_x, c);
239 /* The constant term */
245 Return the probability beta_hat (that is the estimator logit(y) )
246 corresponding to the coefficient estimator for case C
249 pi_hat (const struct lr_spec *cmd,
250 const struct lr_result *res,
251 const struct variable **x, size_t n_x,
252 const struct ccase *c)
256 size_t n_coeffs = res->beta_hat->size;
260 pi += gsl_vector_get (res->beta_hat, res->beta_hat->size - 1);
264 for (v0 = 0; v0 < n_coeffs; ++v0)
266 pi += gsl_vector_get (res->beta_hat, v0) *
267 predictor_value (c, x, n_x, res->cats, v0);
270 pi = 1.0 / (1.0 + exp(-pi));
277 Calculates the Hessian matrix X' V X,
278 where: X is the n by N_X matrix comprising the n cases in INPUT
279 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})}
280 (the partial derivative of the predicted values)
282 If ALL predicted values derivatives are close to zero or one, then CONVERGED
286 hessian (const struct lr_spec *cmd,
287 struct lr_result *res,
288 struct casereader *input,
289 const struct variable **x, size_t n_x,
292 struct casereader *reader;
295 double max_w = -DBL_MAX;
297 gsl_matrix_set_zero (res->hessian);
299 for (reader = casereader_clone (input);
300 (c = casereader_read (reader)) != NULL; case_unref (c))
303 double pi = pi_hat (cmd, res, x, n_x, c);
305 double weight = dict_get_case_weight (cmd->dict, c, &res->warn_bad_weight);
306 double w = pi * (1 - pi);
311 for (v0 = 0; v0 < res->beta_hat->size; ++v0)
313 double in0 = predictor_value (c, x, n_x, res->cats, v0);
314 for (v1 = 0; v1 < res->beta_hat->size; ++v1)
316 double in1 = predictor_value (c, x, n_x, res->cats, v1);
317 double *o = gsl_matrix_ptr (res->hessian, v0, v1);
322 casereader_destroy (reader);
324 if ( max_w < cmd->min_epsilon)
327 msg (MN, _("All predicted values are either 1 or 0"));
332 /* Calculates the value X' (y - pi)
333 where X is the design model,
334 y is the vector of observed independent variables
335 pi is the vector of estimates for y
338 the likelihood is stored in LIKELIHOOD;
339 the predicted values are placed in the respective tn, fn, tp fp values in RES
342 xt_times_y_pi (const struct lr_spec *cmd,
343 struct lr_result *res,
344 struct casereader *input,
345 const struct variable **x, size_t n_x,
346 const struct variable *y_var,
349 struct casereader *reader;
351 gsl_vector *output = gsl_vector_calloc (res->beta_hat->size);
354 res->tn = res->tp = res->fn = res->fp = 0;
355 for (reader = casereader_clone (input);
356 (c = casereader_read (reader)) != NULL; case_unref (c))
360 double pi = pi_hat (cmd, res, x, n_x, c);
361 double weight = dict_get_case_weight (cmd->dict, c, &res->warn_bad_weight);
364 double y = map_dependent_var (cmd, res, case_data (c, y_var));
366 *likelihood *= pow (pi, weight * y) * pow (1 - pi, weight * (1 - y));
368 for (v0 = 0; v0 < res->beta_hat->size; ++v0)
370 double in0 = predictor_value (c, x, n_x, res->cats, v0);
371 double *o = gsl_vector_ptr (output, v0);
372 *o += in0 * (y - pi) * weight;
373 pred_y += gsl_vector_get (res->beta_hat, v0) * in0;
376 /* Count the number of cases which would be correctly/incorrectly classified by this
378 if (pred_y <= cmd->ilogit_cut_point)
394 casereader_destroy (reader);
401 /* "payload" functions for the categoricals.
402 The only function is to accumulate the frequency of each
407 frq_create (const void *aux1 UNUSED, void *aux2 UNUSED)
409 return xzalloc (sizeof (double));
413 frq_update (const void *aux1 UNUSED, void *aux2 UNUSED,
414 void *ud, const struct ccase *c UNUSED , double weight)
421 frq_destroy (const void *aux1 UNUSED, void *aux2 UNUSED, void *user_data UNUSED)
429 Makes an initial pass though the data, doing the following:
431 * Checks that the dependent variable is dichotomous,
432 * Creates and initialises the categoricals,
433 * Accumulates summary results,
434 * Calculates necessary initial values.
435 * Creates an initial value for \hat\beta the vector of beta_hats of \beta
437 Returns true if successful
440 initial_pass (const struct lr_spec *cmd, struct lr_result *res, struct casereader *input)
442 const int width = var_get_width (cmd->dep_var);
445 struct casereader *reader;
454 size_t n_coefficients = cmd->n_predictor_vars;
458 /* Create categoricals if appropriate */
459 if (cmd->n_cat_predictors > 0)
461 res->cp.create = frq_create;
462 res->cp.update = frq_update;
463 res->cp.calculate = NULL;
464 res->cp.destroy = frq_destroy;
466 res->cats = categoricals_create (cmd->cat_predictors, cmd->n_cat_predictors,
467 cmd->wv, cmd->exclude, MV_ANY);
469 categoricals_set_payload (res->cats, &res->cp, cmd, res);
473 for (reader = casereader_clone (input);
474 (c = casereader_read (reader)) != NULL; case_unref (c))
477 bool missing = false;
478 double weight = dict_get_case_weight (cmd->dict, c, &res->warn_bad_weight);
479 const union value *depval = case_data (c, cmd->dep_var);
481 for (v = 0; v < cmd->n_indep_vars; ++v)
483 const union value *val = case_data (c, cmd->indep_vars[v]);
484 if (var_is_value_missing (cmd->indep_vars[v], val, cmd->exclude))
491 /* Accumulate the missing and non-missing counts */
499 /* Find the values of the dependent variable */
502 value_clone (&res->y0, depval, width);
507 if ( !value_equal (&res->y0, depval, width))
509 value_clone (&res->y1, depval, width);
515 if (! value_equal (&res->y0, depval, width)
517 ! value_equal (&res->y1, depval, width)
520 msg (ME, _("Dependent variable's values are not dichotomous."));
525 if (v0set && value_equal (&res->y0, depval, width))
528 if (v1set && value_equal (&res->y1, depval, width))
534 categoricals_update (res->cats, c);
536 casereader_destroy (reader);
538 categoricals_done (res->cats);
542 /* Ensure that Y0 is less than Y1. Otherwise the mapping gets
543 inverted, which is confusing to users */
544 if (var_is_numeric (cmd->dep_var) && value_compare_3way (&res->y0, &res->y1, width) > 0)
547 value_clone (&tmp, &res->y0, width);
548 value_copy (&res->y0, &res->y1, width);
549 value_copy (&res->y1, &tmp, width);
550 value_destroy (&tmp, width);
554 n_coefficients += categoricals_df_total (res->cats);
555 res->beta_hat = gsl_vector_calloc (n_coefficients);
559 double mean = sum / res->cc;
560 gsl_vector_set (res->beta_hat, res->beta_hat->size - 1, log (mean / (1 - mean)));
566 casereader_destroy (reader);
572 /* Start of the logistic regression routine proper */
574 run_lr (const struct lr_spec *cmd, struct casereader *input,
575 const struct dataset *ds UNUSED)
579 bool converged = false;
581 /* Set the likelihoods to a negative sentinel value */
582 double likelihood = -1;
583 double prev_likelihood = -1;
584 double initial_likelihood = -1;
586 struct lr_result work;
588 work.n_nonmissing = 0;
589 work.warn_bad_weight = true;
591 work.beta_hat = NULL;
593 /* Get the initial estimates of \beta and their standard errors.
594 And perform other auxilliary initialisation. */
595 if (! initial_pass (cmd, &work, input))
598 for (i = 0; i < cmd->n_cat_predictors; ++i)
600 if (1 >= categoricals_n_count (work.cats, i))
603 ds_init_empty (&str);
605 interaction_to_string (cmd->cat_predictors[i], &str);
607 msg (ME, _("Category %s does not have at least two distinct values. Logistic regression will not be run."),
614 output_depvarmap (cmd, &work);
616 case_processing_summary (&work);
619 input = casereader_create_filter_missing (input,
627 work.hessian = gsl_matrix_calloc (work.beta_hat->size, work.beta_hat->size);
629 /* Start the Newton Raphson iteration process... */
630 for( i = 0 ; i < cmd->max_iter ; ++i)
636 hessian (cmd, &work, input,
637 cmd->predictor_vars, cmd->n_predictor_vars,
640 gsl_linalg_cholesky_decomp (work.hessian);
641 gsl_linalg_cholesky_invert (work.hessian);
643 v = xt_times_y_pi (cmd, &work, input,
644 cmd->predictor_vars, cmd->n_predictor_vars,
650 gsl_vector *delta = gsl_vector_alloc (v->size);
651 gsl_blas_dgemv (CblasNoTrans, 1.0, work.hessian, v, 0, delta);
655 gsl_vector_add (work.beta_hat, delta);
657 gsl_vector_minmax (delta, &min, &max);
659 if ( fabs (min) < cmd->bcon && fabs (max) < cmd->bcon)
661 msg (MN, _("Estimation terminated at iteration number %d because parameter estimates changed by less than %g"),
666 gsl_vector_free (delta);
669 if ( prev_likelihood >= 0)
671 if (-log (likelihood) > -(1.0 - cmd->lcon) * log (prev_likelihood))
673 msg (MN, _("Estimation terminated at iteration number %d because Log Likelihood decreased by less than %g%%"), i + 1, 100 * cmd->lcon);
678 initial_likelihood = likelihood;
679 prev_likelihood = likelihood;
684 casereader_destroy (input);
685 assert (initial_likelihood >= 0);
688 msg (MW, _("Estimation terminated at iteration number %d because maximum iterations has been reached"), i );
691 output_model_summary (&work, initial_likelihood, likelihood);
694 output_categories (cmd, &work);
696 output_classification_table (cmd, &work);
697 output_variables (cmd, &work);
699 gsl_matrix_free (work.hessian);
700 gsl_vector_free (work.beta_hat);
702 categoricals_destroy (work.cats);
709 struct hmap_node node; /* Node in hash map. */
710 const struct variable *var; /* The variable */
713 static struct variable_node *
714 lookup_variable (const struct hmap *map, const struct variable *var, unsigned int hash)
716 struct variable_node *vn = NULL;
717 HMAP_FOR_EACH_WITH_HASH (vn, struct variable_node, node, hash, map)
722 fprintf (stderr, "Warning: Hash table collision\n");
729 /* Parse the LOGISTIC REGRESSION command syntax */
731 cmd_logistic (struct lexer *lexer, struct dataset *ds)
733 /* Temporary location for the predictor variables.
734 These may or may not include the categorical predictors */
735 const struct variable **pred_vars;
741 lr.dict = dataset_dict (ds);
742 lr.n_predictor_vars = 0;
743 lr.predictor_vars = NULL;
745 lr.wv = dict_get_weight (lr.dict);
749 lr.min_epsilon = 0.00000001;
752 lr.print = PRINT_DEFAULT;
753 lr.cat_predictors = NULL;
754 lr.n_cat_predictors = 0;
755 lr.indep_vars = NULL;
758 if (lex_match_id (lexer, "VARIABLES"))
759 lex_match (lexer, T_EQUALS);
761 if (! (lr.dep_var = parse_variable_const (lexer, lr.dict)))
764 lex_force_match (lexer, T_WITH);
766 if (!parse_variables_const (lexer, lr.dict,
767 &pred_vars, &n_pred_vars,
772 while (lex_token (lexer) != T_ENDCMD)
774 lex_match (lexer, T_SLASH);
776 if (lex_match_id (lexer, "MISSING"))
778 lex_match (lexer, T_EQUALS);
779 while (lex_token (lexer) != T_ENDCMD
780 && lex_token (lexer) != T_SLASH)
782 if (lex_match_id (lexer, "INCLUDE"))
784 lr.exclude = MV_SYSTEM;
786 else if (lex_match_id (lexer, "EXCLUDE"))
792 lex_error (lexer, NULL);
797 else if (lex_match_id (lexer, "ORIGIN"))
801 else if (lex_match_id (lexer, "NOORIGIN"))
805 else if (lex_match_id (lexer, "NOCONST"))
809 else if (lex_match_id (lexer, "EXTERNAL"))
811 /* This is for compatibility. It does nothing */
813 else if (lex_match_id (lexer, "CATEGORICAL"))
815 lex_match (lexer, T_EQUALS);
818 lr.cat_predictors = xrealloc (lr.cat_predictors,
819 sizeof (*lr.cat_predictors) * ++lr.n_cat_predictors);
820 lr.cat_predictors[lr.n_cat_predictors - 1] = 0;
822 while (parse_design_interaction (lexer, lr.dict,
823 lr.cat_predictors + lr.n_cat_predictors - 1));
824 lr.n_cat_predictors--;
826 else if (lex_match_id (lexer, "PRINT"))
828 lex_match (lexer, T_EQUALS);
829 while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
831 if (lex_match_id (lexer, "DEFAULT"))
833 lr.print |= PRINT_DEFAULT;
835 else if (lex_match_id (lexer, "SUMMARY"))
837 lr.print |= PRINT_SUMMARY;
840 else if (lex_match_id (lexer, "CORR"))
842 lr.print |= PRINT_CORR;
844 else if (lex_match_id (lexer, "ITER"))
846 lr.print |= PRINT_ITER;
848 else if (lex_match_id (lexer, "GOODFIT"))
850 lr.print |= PRINT_GOODFIT;
853 else if (lex_match_id (lexer, "CI"))
855 lr.print |= PRINT_CI;
856 if (lex_force_match (lexer, T_LPAREN))
858 if (! lex_force_int (lexer))
860 lex_error (lexer, NULL);
863 lr.confidence = lex_integer (lexer);
865 if ( ! lex_force_match (lexer, T_RPAREN))
867 lex_error (lexer, NULL);
872 else if (lex_match_id (lexer, "ALL"))
878 lex_error (lexer, NULL);
883 else if (lex_match_id (lexer, "CRITERIA"))
885 lex_match (lexer, T_EQUALS);
886 while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
888 if (lex_match_id (lexer, "BCON"))
890 if (lex_force_match (lexer, T_LPAREN))
892 if (! lex_force_num (lexer))
894 lex_error (lexer, NULL);
897 lr.bcon = lex_number (lexer);
899 if ( ! lex_force_match (lexer, T_RPAREN))
901 lex_error (lexer, NULL);
906 else if (lex_match_id (lexer, "ITERATE"))
908 if (lex_force_match (lexer, T_LPAREN))
910 if (! lex_force_int (lexer))
912 lex_error (lexer, NULL);
915 lr.max_iter = lex_integer (lexer);
917 if ( ! lex_force_match (lexer, T_RPAREN))
919 lex_error (lexer, NULL);
924 else if (lex_match_id (lexer, "LCON"))
926 if (lex_force_match (lexer, T_LPAREN))
928 if (! lex_force_num (lexer))
930 lex_error (lexer, NULL);
933 lr.lcon = lex_number (lexer);
935 if ( ! lex_force_match (lexer, T_RPAREN))
937 lex_error (lexer, NULL);
942 else if (lex_match_id (lexer, "EPS"))
944 if (lex_force_match (lexer, T_LPAREN))
946 if (! lex_force_num (lexer))
948 lex_error (lexer, NULL);
951 lr.min_epsilon = lex_number (lexer);
953 if ( ! lex_force_match (lexer, T_RPAREN))
955 lex_error (lexer, NULL);
960 else if (lex_match_id (lexer, "CUT"))
962 if (lex_force_match (lexer, T_LPAREN))
964 if (! lex_force_num (lexer))
966 lex_error (lexer, NULL);
969 cp = lex_number (lexer);
971 if (cp < 0 || cp > 1.0)
973 msg (ME, _("Cut point value must be in the range [0,1]"));
977 if ( ! lex_force_match (lexer, T_RPAREN))
979 lex_error (lexer, NULL);
986 lex_error (lexer, NULL);
993 lex_error (lexer, NULL);
998 lr.ilogit_cut_point = - log (1/cp - 1);
1001 /* Copy the predictor variables from the temporary location into the
1002 final one, dropping any categorical variables which appear there.
1003 FIXME: This is O(NxM).
1006 struct variable_node *vn, *next;
1007 struct hmap allvars;
1008 hmap_init (&allvars);
1009 for (v = x = 0; v < n_pred_vars; ++v)
1012 const struct variable *var = pred_vars[v];
1015 unsigned int hash = hash_pointer (var, 0);
1016 struct variable_node *vn = lookup_variable (&allvars, var, hash);
1019 vn = xmalloc (sizeof *vn);
1021 hmap_insert (&allvars, &vn->node, hash);
1024 for (cv = 0; cv < lr.n_cat_predictors ; ++cv)
1027 const struct interaction *iact = lr.cat_predictors[cv];
1028 for (iv = 0 ; iv < iact->n_vars ; ++iv)
1030 const struct variable *ivar = iact->vars[iv];
1031 unsigned int hash = hash_pointer (ivar, 0);
1032 struct variable_node *vn = lookup_variable (&allvars, ivar, hash);
1035 vn = xmalloc (sizeof *vn);
1038 hmap_insert (&allvars, &vn->node, hash);
1051 lr.predictor_vars = xrealloc (lr.predictor_vars, sizeof *lr.predictor_vars * (x + 1));
1052 lr.predictor_vars[x++] = var;
1053 lr.n_predictor_vars++;
1057 lr.n_indep_vars = hmap_count (&allvars);
1058 lr.indep_vars = xmalloc (lr.n_indep_vars * sizeof *lr.indep_vars);
1060 /* Interate over each variable and push it into the array */
1062 HMAP_FOR_EACH_SAFE (vn, next, struct variable_node, node, &allvars)
1064 lr.indep_vars[x++] = vn->var;
1067 hmap_destroy (&allvars);
1071 /* logistical regression for each split group */
1073 struct casegrouper *grouper;
1074 struct casereader *group;
1077 grouper = casegrouper_create_splits (proc_open (ds), lr.dict);
1078 while (casegrouper_get_next_group (grouper, &group))
1079 ok = run_lr (&lr, group, ds);
1080 ok = casegrouper_destroy (grouper);
1081 ok = proc_commit (ds) && ok;
1084 free (lr.predictor_vars);
1085 free (lr.cat_predictors);
1086 free (lr.indep_vars);
1092 free (lr.predictor_vars);
1093 free (lr.cat_predictors);
1094 free (lr.indep_vars);
1102 /* Show the Dependent Variable Encoding box.
1103 This indicates how the dependent variable
1104 is mapped to the internal zero/one values.
1107 output_depvarmap (const struct lr_spec *cmd, const struct lr_result *res)
1109 const int heading_columns = 0;
1110 const int heading_rows = 1;
1111 struct tab_table *t;
1115 int nr = heading_rows + 2;
1117 t = tab_create (nc, nr);
1118 tab_title (t, _("Dependent Variable Encoding"));
1120 tab_headers (t, heading_columns, 0, heading_rows, 0);
1122 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, nc - 1, nr - 1);
1124 tab_hline (t, TAL_2, 0, nc - 1, heading_rows);
1125 tab_vline (t, TAL_2, heading_columns, 0, nr - 1);
1127 tab_text (t, 0, 0, TAB_CENTER | TAT_TITLE, _("Original Value"));
1128 tab_text (t, 1, 0, TAB_CENTER | TAT_TITLE, _("Internal Value"));
1132 ds_init_empty (&str);
1133 var_append_value_name (cmd->dep_var, &res->y0, &str);
1134 tab_text (t, 0, 0 + heading_rows, 0, ds_cstr (&str));
1137 var_append_value_name (cmd->dep_var, &res->y1, &str);
1138 tab_text (t, 0, 1 + heading_rows, 0, ds_cstr (&str));
1141 tab_double (t, 1, 0 + heading_rows, 0, map_dependent_var (cmd, res, &res->y0), &F_8_0);
1142 tab_double (t, 1, 1 + heading_rows, 0, map_dependent_var (cmd, res, &res->y1), &F_8_0);
1149 /* Show the Variables in the Equation box */
1151 output_variables (const struct lr_spec *cmd,
1152 const struct lr_result *res)
1155 const int heading_columns = 1;
1156 int heading_rows = 1;
1157 struct tab_table *t;
1163 int idx_correction = 0;
1165 if (cmd->print & PRINT_CI)
1171 nr = heading_rows + cmd->n_predictor_vars;
1176 nr += categoricals_df_total (res->cats) + cmd->n_cat_predictors;
1178 t = tab_create (nc, nr);
1179 tab_title (t, _("Variables in the Equation"));
1181 tab_headers (t, heading_columns, 0, heading_rows, 0);
1183 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, nc - 1, nr - 1);
1185 tab_hline (t, TAL_2, 0, nc - 1, heading_rows);
1186 tab_vline (t, TAL_2, heading_columns, 0, nr - 1);
1188 tab_text (t, 0, row + 1, TAB_CENTER | TAT_TITLE, _("Step 1"));
1190 tab_text (t, 2, row, TAB_CENTER | TAT_TITLE, _("B"));
1191 tab_text (t, 3, row, TAB_CENTER | TAT_TITLE, _("S.E."));
1192 tab_text (t, 4, row, TAB_CENTER | TAT_TITLE, _("Wald"));
1193 tab_text (t, 5, row, TAB_CENTER | TAT_TITLE, _("df"));
1194 tab_text (t, 6, row, TAB_CENTER | TAT_TITLE, _("Sig."));
1195 tab_text (t, 7, row, TAB_CENTER | TAT_TITLE, _("Exp(B)"));
1197 if (cmd->print & PRINT_CI)
1199 tab_joint_text_format (t, 8, 0, 9, 0,
1200 TAB_CENTER | TAT_TITLE, _("%d%% CI for Exp(B)"), cmd->confidence);
1202 tab_text (t, 8, row, TAB_CENTER | TAT_TITLE, _("Lower"));
1203 tab_text (t, 9, row, TAB_CENTER | TAT_TITLE, _("Upper"));
1206 for (row = heading_rows ; row < nr; ++row)
1208 const int idx = row - heading_rows - idx_correction;
1210 const double b = gsl_vector_get (res->beta_hat, idx);
1211 const double sigma2 = gsl_matrix_get (res->hessian, idx, idx);
1212 const double wald = pow2 (b) / sigma2;
1213 const double df = 1;
1215 if (idx < cmd->n_predictor_vars)
1217 tab_text (t, 1, row, TAB_LEFT | TAT_TITLE,
1218 var_to_string (cmd->predictor_vars[idx]));
1220 else if (i < cmd->n_cat_predictors)
1223 bool summary = false;
1225 const struct interaction *cat_predictors = cmd->cat_predictors[i];
1226 const int df = categoricals_df (res->cats, i);
1228 ds_init_empty (&str);
1229 interaction_to_string (cat_predictors, &str);
1233 /* Calculate the Wald statistic,
1234 which is \beta' C^-1 \beta .
1235 where \beta is the vector of the coefficient estimates comprising this
1236 categorial variable. and C is the corresponding submatrix of the
1239 gsl_matrix_const_view mv =
1240 gsl_matrix_const_submatrix (res->hessian, idx, idx, df, df);
1241 gsl_matrix *subhessian = gsl_matrix_alloc (mv.matrix.size1, mv.matrix.size2);
1242 gsl_vector_const_view vv = gsl_vector_const_subvector (res->beta_hat, idx, df);
1243 gsl_vector *temp = gsl_vector_alloc (df);
1245 gsl_matrix_memcpy (subhessian, &mv.matrix);
1246 gsl_linalg_cholesky_decomp (subhessian);
1247 gsl_linalg_cholesky_invert (subhessian);
1249 gsl_blas_dgemv (CblasTrans, 1.0, subhessian, &vv.vector, 0, temp);
1250 gsl_blas_ddot (temp, &vv.vector, &wald);
1252 tab_double (t, 4, row, 0, wald, 0);
1253 tab_double (t, 5, row, 0, df, &F_8_0);
1254 tab_double (t, 6, row, 0, gsl_cdf_chisq_Q (wald, df), 0);
1258 gsl_matrix_free (subhessian);
1259 gsl_vector_free (temp);
1263 ds_put_format (&str, "(%d)", ivar);
1266 tab_text (t, 1, row, TAB_LEFT | TAT_TITLE, ds_cstr (&str));
1269 ++i; /* next interaction */
1280 tab_text (t, 1, row, TAB_LEFT | TAT_TITLE, _("Constant"));
1283 tab_double (t, 2, row, 0, b, 0);
1284 tab_double (t, 3, row, 0, sqrt (sigma2), 0);
1285 tab_double (t, 4, row, 0, wald, 0);
1286 tab_double (t, 5, row, 0, df, &F_8_0);
1287 tab_double (t, 6, row, 0, gsl_cdf_chisq_Q (wald, df), 0);
1288 tab_double (t, 7, row, 0, exp (b), 0);
1290 if (cmd->print & PRINT_CI)
1292 double wc = gsl_cdf_ugaussian_Pinv (0.5 + cmd->confidence / 200.0);
1293 wc *= sqrt (sigma2);
1295 if (idx < cmd->n_predictor_vars)
1297 tab_double (t, 8, row, 0, exp (b - wc), 0);
1298 tab_double (t, 9, row, 0, exp (b + wc), 0);
1307 /* Show the model summary box */
1309 output_model_summary (const struct lr_result *res,
1310 double initial_likelihood, double likelihood)
1312 const int heading_columns = 0;
1313 const int heading_rows = 1;
1314 struct tab_table *t;
1317 int nr = heading_rows + 1;
1320 t = tab_create (nc, nr);
1321 tab_title (t, _("Model Summary"));
1323 tab_headers (t, heading_columns, 0, heading_rows, 0);
1325 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, nc - 1, nr - 1);
1327 tab_hline (t, TAL_2, 0, nc - 1, heading_rows);
1328 tab_vline (t, TAL_2, heading_columns, 0, nr - 1);
1330 tab_text (t, 0, 0, TAB_LEFT | TAT_TITLE, _("Step 1"));
1331 tab_text (t, 1, 0, TAB_CENTER | TAT_TITLE, _("-2 Log likelihood"));
1332 tab_double (t, 1, 1, 0, -2 * log (likelihood), 0);
1335 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("Cox & Snell R Square"));
1336 cox = 1.0 - pow (initial_likelihood /likelihood, 2 / res->cc);
1337 tab_double (t, 2, 1, 0, cox, 0);
1339 tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("Nagelkerke R Square"));
1340 tab_double (t, 3, 1, 0, cox / ( 1.0 - pow (initial_likelihood, 2 / res->cc)), 0);
1346 /* Show the case processing summary box */
1348 case_processing_summary (const struct lr_result *res)
1350 const int heading_columns = 1;
1351 const int heading_rows = 1;
1352 struct tab_table *t;
1355 const int nr = heading_rows + 3;
1358 t = tab_create (nc, nr);
1359 tab_title (t, _("Case Processing Summary"));
1361 tab_headers (t, heading_columns, 0, heading_rows, 0);
1363 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, nc - 1, nr - 1);
1365 tab_hline (t, TAL_2, 0, nc - 1, heading_rows);
1366 tab_vline (t, TAL_2, heading_columns, 0, nr - 1);
1368 tab_text (t, 0, 0, TAB_LEFT | TAT_TITLE, _("Unweighted Cases"));
1369 tab_text (t, 1, 0, TAB_CENTER | TAT_TITLE, _("N"));
1370 tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("Percent"));
1373 tab_text (t, 0, 1, TAB_LEFT | TAT_TITLE, _("Included in Analysis"));
1374 tab_text (t, 0, 2, TAB_LEFT | TAT_TITLE, _("Missing Cases"));
1375 tab_text (t, 0, 3, TAB_LEFT | TAT_TITLE, _("Total"));
1377 tab_double (t, 1, 1, 0, res->n_nonmissing, &F_8_0);
1378 tab_double (t, 1, 2, 0, res->n_missing, &F_8_0);
1380 total = res->n_nonmissing + res->n_missing;
1381 tab_double (t, 1, 3, 0, total , &F_8_0);
1383 tab_double (t, 2, 1, 0, 100 * res->n_nonmissing / (double) total, 0);
1384 tab_double (t, 2, 2, 0, 100 * res->n_missing / (double) total, 0);
1385 tab_double (t, 2, 3, 0, 100 * total / (double) total, 0);
1391 output_categories (const struct lr_spec *cmd, const struct lr_result *res)
1393 const struct fmt_spec *wfmt =
1394 cmd->wv ? var_get_print_format (cmd->wv) : &F_8_0;
1398 const int heading_columns = 2;
1399 const int heading_rows = 2;
1400 struct tab_table *t;
1410 for (i = 0; i < cmd->n_cat_predictors; ++i)
1412 size_t n = categoricals_n_count (res->cats, i);
1413 size_t df = categoricals_df (res->cats, i);
1419 nc = heading_columns + 1 + max_df;
1420 nr = heading_rows + total_cats;
1422 t = tab_create (nc, nr);
1423 tab_title (t, _("Categorical Variables' Codings"));
1425 tab_headers (t, heading_columns, 0, heading_rows, 0);
1427 tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, nc - 1, nr - 1);
1429 tab_hline (t, TAL_2, 0, nc - 1, heading_rows);
1430 tab_vline (t, TAL_2, heading_columns, 0, nr - 1);
1433 tab_text (t, heading_columns, 1, TAB_CENTER | TAT_TITLE, _("Frequency"));
1435 tab_joint_text_format (t, heading_columns + 1, 0, nc - 1, 0,
1436 TAB_CENTER | TAT_TITLE, _("Parameter coding"));
1439 for (i = 0; i < max_df; ++i)
1441 int c = heading_columns + 1 + i;
1442 tab_text_format (t, c, 1, TAB_CENTER | TAT_TITLE, _("(%d)"), i + 1);
1446 for (v = 0; v < cmd->n_cat_predictors; ++v)
1449 const struct interaction *cat_predictors = cmd->cat_predictors[v];
1450 int df = categoricals_df (res->cats, v);
1452 ds_init_empty (&str);
1454 interaction_to_string (cat_predictors, &str);
1456 tab_text (t, 0, heading_rows + r, TAB_LEFT | TAT_TITLE, ds_cstr (&str) );
1460 for (cat = 0; cat < categoricals_n_count (res->cats, v) ; ++cat)
1463 const struct ccase *c = categoricals_get_case_by_category_real (res->cats, v, cat);
1464 const double *freq = categoricals_get_user_data_by_category_real (res->cats, v, cat);
1467 ds_init_empty (&str);
1469 for (x = 0; x < cat_predictors->n_vars; ++x)
1471 const union value *val = case_data (c, cat_predictors->vars[x]);
1472 var_append_value_name (cat_predictors->vars[x], val, &str);
1474 if (x < cat_predictors->n_vars - 1)
1475 ds_put_cstr (&str, " ");
1478 tab_text (t, 1, heading_rows + r, 0, ds_cstr (&str));
1480 tab_double (t, 2, heading_rows + r, 0, *freq, wfmt);
1482 for (x = 0; x < df; ++x)
1484 tab_double (t, heading_columns + 1 + x, heading_rows + r, 0, (cat == x), &F_8_0);
1488 cumulative_df += df;
1497 output_classification_table (const struct lr_spec *cmd, const struct lr_result *res)
1499 const struct fmt_spec *wfmt =
1500 cmd->wv ? var_get_print_format (cmd->wv) : &F_8_0;
1502 const int heading_columns = 3;
1503 const int heading_rows = 3;
1505 struct string sv0, sv1;
1507 const int nc = heading_columns + 3;
1508 const int nr = heading_rows + 3;
1510 struct tab_table *t = tab_create (nc, nr);
1512 ds_init_empty (&sv0);
1513 ds_init_empty (&sv1);
1515 tab_title (t, _("Classification Table"));
1517 tab_headers (t, heading_columns, 0, heading_rows, 0);
1519 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, nc - 1, nr - 1);
1520 tab_box (t, -1, -1, -1, TAL_1, heading_columns, 0, nc - 1, nr - 1);
1522 tab_hline (t, TAL_2, 0, nc - 1, heading_rows);
1523 tab_vline (t, TAL_2, heading_columns, 0, nr - 1);
1525 tab_text (t, 0, heading_rows, TAB_CENTER | TAT_TITLE, _("Step 1"));
1528 tab_joint_text (t, heading_columns, 0, nc - 1, 0,
1529 TAB_CENTER | TAT_TITLE, _("Predicted"));
1531 tab_joint_text (t, heading_columns, 1, heading_columns + 1, 1,
1532 0, var_to_string (cmd->dep_var) );
1534 tab_joint_text (t, 1, 2, 2, 2,
1535 TAB_LEFT | TAT_TITLE, _("Observed"));
1537 tab_text (t, 1, 3, TAB_LEFT, var_to_string (cmd->dep_var) );
1540 tab_joint_text (t, nc - 1, 1, nc - 1, 2,
1541 TAB_CENTER | TAT_TITLE, _("Percentage\nCorrect"));
1544 tab_joint_text (t, 1, nr - 1, 2, nr - 1,
1545 TAB_LEFT | TAT_TITLE, _("Overall Percentage"));
1548 tab_hline (t, TAL_1, 1, nc - 1, nr - 1);
1550 var_append_value_name (cmd->dep_var, &res->y0, &sv0);
1551 var_append_value_name (cmd->dep_var, &res->y1, &sv1);
1553 tab_text (t, 2, heading_rows, TAB_LEFT, ds_cstr (&sv0));
1554 tab_text (t, 2, heading_rows + 1, TAB_LEFT, ds_cstr (&sv1));
1556 tab_text (t, heading_columns, 2, 0, ds_cstr (&sv0));
1557 tab_text (t, heading_columns + 1, 2, 0, ds_cstr (&sv1));
1562 tab_double (t, heading_columns, 3, 0, res->tn, wfmt);
1563 tab_double (t, heading_columns + 1, 4, 0, res->tp, wfmt);
1565 tab_double (t, heading_columns + 1, 3, 0, res->fp, wfmt);
1566 tab_double (t, heading_columns, 4, 0, res->fn, wfmt);
1568 tab_double (t, heading_columns + 2, 3, 0, 100 * res->tn / (res->tn + res->fp), 0);
1569 tab_double (t, heading_columns + 2, 4, 0, 100 * res->tp / (res->tp + res->fn), 0);
1571 tab_double (t, heading_columns + 2, 5, 0,
1572 100 * (res->tp + res->tn) / (res->tp + res->tn + res->fp + res->fn), 0);