1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2006, 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 - Pearson's R (but not Spearman!) is off a little.
20 - T values for Spearman's R and Pearson's R are wrong.
21 - How to calculate significance of symmetric and directional measures?
22 - Asymmetric ASEs and T values for lambda are wrong.
23 - ASE of Goodman and Kruskal's tau is not calculated.
24 - ASE of symmetric somers' d is wrong.
25 - Approx. T of uncertainty coefficient is wrong.
32 #include <gsl/gsl_cdf.h>
36 #include <data/case.h>
37 #include <data/casegrouper.h>
38 #include <data/casereader.h>
39 #include <data/data-out.h>
40 #include <data/dictionary.h>
41 #include <data/format.h>
42 #include <data/procedure.h>
43 #include <data/value-labels.h>
44 #include <data/variable.h>
45 #include <language/command.h>
46 #include <language/dictionary/split-file.h>
47 #include <language/lexer/lexer.h>
48 #include <language/lexer/variable-parser.h>
49 #include <libpspp/array.h>
50 #include <libpspp/assertion.h>
51 #include <libpspp/compiler.h>
52 #include <libpspp/hash.h>
53 #include <libpspp/hmap.h>
54 #include <libpspp/hmapx.h>
55 #include <libpspp/message.h>
56 #include <libpspp/misc.h>
57 #include <libpspp/pool.h>
58 #include <libpspp/str.h>
59 #include <output/output.h>
60 #include <output/table.h>
67 #define _(msgid) gettext (msgid)
68 #define N_(msgid) msgid
76 missing=miss:!table/include/report;
77 +write[wr_]=none,cells,all;
78 +format=fmt:!labels/nolabels/novallabs,
81 tabl:!tables/notables,
84 +cells[cl_]=count,expected,row,column,total,residual,sresidual,
86 +statistics[st_]=chisq,phi,cc,lambda,uc,none,btau,ctau,risk,gamma,d,
92 /* Number of chi-square statistics. */
95 /* Number of symmetric statistics. */
98 /* Number of directional statistics. */
99 #define N_DIRECTIONAL 13
101 /* A single table entry for general mode. */
104 struct hmap_node node; /* Entry in hash table. */
105 double freq; /* Frequency count. */
106 union value values[1]; /* Values. */
110 table_entry_size (size_t n_values)
112 return (offsetof (struct table_entry, values)
113 + n_values * sizeof (union value));
116 /* Indexes into the 'vars' member of struct pivot_table and
117 struct crosstab member. */
120 ROW_VAR = 0, /* Row variable. */
121 COL_VAR = 1 /* Column variable. */
122 /* Higher indexes cause multiple tables to be output. */
125 /* A crosstabulation of 2 or more variables. */
128 struct fmt_spec weight_format; /* Format for weight variable. */
129 double missing; /* Weight of missing cases. */
131 /* Variables (2 or more). */
133 const struct variable **vars;
135 /* Constants (0 or more). */
137 const struct variable **const_vars;
138 union value *const_values;
142 struct table_entry **entries;
145 /* Column values, number of columns. */
149 /* Row values, number of rows. */
153 /* Number of statistically interesting columns/rows
154 (columns/rows with data in them). */
155 int ns_cols, ns_rows;
157 /* Matrix contents. */
158 double *mat; /* Matrix proper. */
159 double *row_tot; /* Row totals. */
160 double *col_tot; /* Column totals. */
161 double total; /* Grand total. */
164 /* Integer mode variable info. */
167 int min; /* Minimum value. */
168 int max; /* Maximum value + 1. */
169 int count; /* max - min. */
172 static inline struct var_range *
173 get_var_range (const struct variable *v)
175 return var_get_aux (v);
178 struct crosstabs_proc
180 enum { INTEGER, GENERAL } mode;
181 enum mv_class exclude;
184 struct fmt_spec weight_format;
186 /* Variables specifies on VARIABLES. */
187 const struct variable **variables;
191 struct pivot_table *pivots;
195 int n_cells; /* Number of cells requested. */
196 unsigned int cells; /* Bit k is 1 if cell k is requested. */
197 int a_cells[CRS_CL_count]; /* 0...n_cells-1 are the requested cells. */
200 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
203 /* Auxiliary data structure for tab_dim. */
204 struct crosstabs_dim_aux
206 enum mv_class exclude;
210 init_proc (struct crosstabs_proc *proc, struct dataset *ds)
212 const struct variable *wv = dict_get_weight (dataset_dict (ds));
213 proc->bad_warn = true;
214 proc->variables = NULL;
215 proc->n_variables = 0;
218 proc->weight_format = wv ? *var_get_print_format (wv) : F_8_0;
222 free_proc (struct crosstabs_proc *proc)
224 struct pivot_table *pt;
226 free (proc->variables);
227 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
230 free (pt->const_vars);
231 /* We must not call value_destroy on const_values because
232 it is a wild pointer; it never pointed to anything owned
235 The rest of the data was allocated and destroyed at a
236 lower level already. */
241 static int internal_cmd_crosstabs (struct lexer *lexer, struct dataset *ds,
242 struct crosstabs_proc *);
243 static bool should_tabulate_case (const struct pivot_table *,
244 const struct ccase *, enum mv_class exclude);
245 static void tabulate_general_case (struct pivot_table *, const struct ccase *,
247 static void tabulate_integer_case (struct pivot_table *, const struct ccase *,
249 static void postcalc (struct crosstabs_proc *);
250 static void submit (struct crosstabs_proc *, struct pivot_table *,
253 /* Parse and execute CROSSTABS, then clean up. */
255 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
257 struct crosstabs_proc proc;
260 init_proc (&proc, ds);
261 result = internal_cmd_crosstabs (lexer, ds, &proc);
267 /* Parses and executes the CROSSTABS procedure. */
269 internal_cmd_crosstabs (struct lexer *lexer, struct dataset *ds,
270 struct crosstabs_proc *proc)
272 struct casegrouper *grouper;
273 struct casereader *input, *group;
274 struct cmd_crosstabs cmd;
275 struct pivot_table *pt;
279 if (!parse_crosstabs (lexer, ds, &cmd, proc))
282 proc->mode = proc->n_variables ? INTEGER : GENERAL;
286 proc->cells = 1u << CRS_CL_COUNT;
287 else if (cmd.a_cells[CRS_CL_ALL])
288 proc->cells = UINT_MAX;
292 for (i = 0; i < CRS_CL_count; i++)
294 proc->cells |= 1u << i;
295 if (proc->cells == 0)
296 proc->cells = ((1u << CRS_CL_COUNT)
298 | (1u << CRS_CL_COLUMN)
299 | (1u << CRS_CL_TOTAL));
301 proc->cells &= ((1u << CRS_CL_count) - 1);
302 proc->cells &= ~((1u << CRS_CL_NONE) | (1u << CRS_CL_ALL));
304 for (i = 0; i < CRS_CL_count; i++)
305 if (proc->cells & (1u << i))
306 proc->a_cells[proc->n_cells++] = i;
309 if (cmd.a_statistics[CRS_ST_ALL])
310 proc->statistics = UINT_MAX;
311 else if (cmd.sbc_statistics)
315 proc->statistics = 0;
316 for (i = 0; i < CRS_ST_count; i++)
317 if (cmd.a_statistics[i])
318 proc->statistics |= 1u << i;
319 if (proc->statistics == 0)
320 proc->statistics |= 1u << CRS_ST_CHISQ;
323 proc->statistics = 0;
326 proc->exclude = (cmd.miss == CRS_TABLE ? MV_ANY
327 : cmd.miss == CRS_INCLUDE ? MV_SYSTEM
329 if (proc->mode == GENERAL && proc->mode == MV_NEVER)
331 msg (SE, _("Missing mode REPORT not allowed in general mode. "
332 "Assuming MISSING=TABLE."));
337 proc->pivot = cmd.pivot == CRS_PIVOT;
339 input = casereader_create_filter_weight (proc_open (ds), dataset_dict (ds),
341 grouper = casegrouper_create_splits (input, dataset_dict (ds));
342 while (casegrouper_get_next_group (grouper, &group))
346 /* Output SPLIT FILE variables. */
347 c = casereader_peek (group, 0);
350 output_split_file_values (ds, c);
355 for (; (c = casereader_read (group)) != NULL; case_unref (c))
356 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
358 double weight = dict_get_case_weight (dataset_dict (ds), c,
360 if (should_tabulate_case (pt, c, proc->exclude))
362 if (proc->mode == GENERAL)
363 tabulate_general_case (pt, c, weight);
365 tabulate_integer_case (pt, c, weight);
368 pt->missing += weight;
370 casereader_destroy (group);
375 ok = casegrouper_destroy (grouper);
376 ok = proc_commit (ds) && ok;
378 return ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
381 /* Parses the TABLES subcommand. */
383 crs_custom_tables (struct lexer *lexer, struct dataset *ds,
384 struct cmd_crosstabs *cmd UNUSED, void *proc_)
386 struct crosstabs_proc *proc = proc_;
387 struct const_var_set *var_set;
389 const struct variable ***by = NULL;
391 size_t *by_nvar = NULL;
396 /* Ensure that this is a TABLES subcommand. */
397 if (!lex_match_id (lexer, "TABLES")
398 && (lex_token (lexer) != T_ID ||
399 dict_lookup_var (dataset_dict (ds), lex_tokid (lexer)) == NULL)
400 && lex_token (lexer) != T_ALL)
402 lex_match (lexer, '=');
404 if (proc->variables != NULL)
405 var_set = const_var_set_create_from_array (proc->variables,
408 var_set = const_var_set_create_from_dict (dataset_dict (ds));
409 assert (var_set != NULL);
413 by = xnrealloc (by, n_by + 1, sizeof *by);
414 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
415 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
416 PV_NO_DUPLICATE | PV_NO_SCRATCH))
418 if (xalloc_oversized (nx, by_nvar[n_by]))
420 msg (SE, _("Too many cross-tabulation variables or dimensions."));
426 if (!lex_match (lexer, T_BY))
430 lex_error (lexer, _("expecting BY"));
438 by_iter = xcalloc (n_by, sizeof *by_iter);
439 proc->pivots = xnrealloc (proc->pivots,
440 proc->n_pivots + nx, sizeof *proc->pivots);
441 for (i = 0; i < nx; i++)
443 struct pivot_table *pt = &proc->pivots[proc->n_pivots++];
446 pt->weight_format = proc->weight_format;
449 pt->vars = xmalloc (n_by * sizeof *pt->vars);
451 pt->const_vars = NULL;
452 pt->const_values = NULL;
453 hmap_init (&pt->data);
457 for (j = 0; j < n_by; j++)
458 pt->vars[j] = by[j][by_iter[j]];
460 for (j = n_by - 1; j >= 0; j--)
462 if (++by_iter[j] < by_nvar[j])
471 /* All return paths lead here. */
472 for (i = 0; i < n_by; i++)
477 const_var_set_destroy (var_set);
482 /* Parses the VARIABLES subcommand. */
484 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
485 struct cmd_crosstabs *cmd UNUSED, void *proc_)
487 struct crosstabs_proc *proc = proc_;
490 msg (SE, _("VARIABLES must be specified before TABLES."));
494 lex_match (lexer, '=');
498 size_t orig_nv = proc->n_variables;
503 if (!parse_variables_const (lexer, dataset_dict (ds),
504 &proc->variables, &proc->n_variables,
505 (PV_APPEND | PV_NUMERIC
506 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
509 if (lex_token (lexer) != '(')
511 lex_error (lexer, "expecting `('");
516 if (!lex_force_int (lexer))
518 min = lex_integer (lexer);
521 lex_match (lexer, ',');
523 if (!lex_force_int (lexer))
525 max = lex_integer (lexer);
528 msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
534 if (lex_token (lexer) != ')')
536 lex_error (lexer, "expecting `)'");
541 for (i = orig_nv; i < proc->n_variables; i++)
543 struct var_range *vr = xmalloc (sizeof *vr);
546 vr->count = max - min + 1;
547 var_attach_aux (proc->variables[i], vr, var_dtor_free);
550 if (lex_token (lexer) == '/')
557 free (proc->variables);
558 proc->variables = NULL;
559 proc->n_variables = 0;
563 /* Data file processing. */
566 should_tabulate_case (const struct pivot_table *pt, const struct ccase *c,
567 enum mv_class exclude)
570 for (j = 0; j < pt->n_vars; j++)
572 const struct variable *var = pt->vars[j];
573 struct var_range *range = get_var_range (var);
575 if (var_is_value_missing (var, case_data (c, var), exclude))
580 double num = case_num (c, var);
581 if (num < range->min || num > range->max)
589 tabulate_integer_case (struct pivot_table *pt, const struct ccase *c,
592 struct table_entry *te;
597 for (j = 0; j < pt->n_vars; j++)
599 /* Throw away fractional parts of values. */
600 hash = hash_int (case_num (c, pt->vars[j]), hash);
603 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
605 for (j = 0; j < pt->n_vars; j++)
606 if ((int) case_num (c, pt->vars[j]) != (int) te->values[j].f)
609 /* Found an existing entry. */
616 /* No existing entry. Create a new one. */
617 te = xmalloc (table_entry_size (pt->n_vars));
619 for (j = 0; j < pt->n_vars; j++)
620 te->values[j].f = (int) case_num (c, pt->vars[j]);
621 hmap_insert (&pt->data, &te->node, hash);
625 tabulate_general_case (struct pivot_table *pt, const struct ccase *c,
628 struct table_entry *te;
633 for (j = 0; j < pt->n_vars; j++)
635 const struct variable *var = pt->vars[j];
636 hash = value_hash (case_data (c, var), var_get_width (var), hash);
639 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
641 for (j = 0; j < pt->n_vars; j++)
643 const struct variable *var = pt->vars[j];
644 if (!value_equal (case_data (c, var), &te->values[j],
645 var_get_width (var)))
649 /* Found an existing entry. */
656 /* No existing entry. Create a new one. */
657 te = xmalloc (table_entry_size (pt->n_vars));
659 for (j = 0; j < pt->n_vars; j++)
661 const struct variable *var = pt->vars[j];
662 int width = var_get_width (var);
663 value_init (&te->values[j], width);
664 value_copy (&te->values[j], case_data (c, var), width);
666 hmap_insert (&pt->data, &te->node, hash);
669 /* Post-data reading calculations. */
671 static int compare_table_entry_vars_3way (const struct table_entry *a,
672 const struct table_entry *b,
673 const struct pivot_table *pt,
675 static int compare_table_entry_3way (const void *ap_, const void *bp_,
677 static void enum_var_values (const struct pivot_table *, int var_idx,
678 union value **valuesp, int *n_values);
679 static void output_pivot_table (struct crosstabs_proc *,
680 struct pivot_table *);
681 static void make_pivot_table_subset (struct pivot_table *pt,
682 size_t row0, size_t row1,
683 struct pivot_table *subset);
684 static void make_summary_table (struct crosstabs_proc *);
685 static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
688 postcalc (struct crosstabs_proc *proc)
690 struct pivot_table *pt;
692 /* Convert hash tables into sorted arrays of entries. */
693 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
695 struct table_entry *e;
698 pt->n_entries = hmap_count (&pt->data);
699 pt->entries = xnmalloc (pt->n_entries, sizeof *pt->entries);
701 HMAP_FOR_EACH (e, struct table_entry, node, &pt->data)
702 pt->entries[i++] = e;
703 hmap_destroy (&pt->data);
705 sort (pt->entries, pt->n_entries, sizeof *pt->entries,
706 compare_table_entry_3way, pt);
709 make_summary_table (proc);
711 /* Output each pivot table. */
712 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
714 if (proc->pivot || pt->n_vars == 2)
715 output_pivot_table (proc, pt);
718 size_t row0 = 0, row1 = 0;
719 while (find_crosstab (pt, &row0, &row1))
721 struct pivot_table subset;
722 make_pivot_table_subset (pt, row0, row1, &subset);
723 output_pivot_table (proc, &subset);
728 /* Free output and prepare for next split file. */
729 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
735 /* Free only the members that were allocated in this
736 function. The other pointer members are either both
737 allocated and destroyed at a lower level (in
738 output_pivot_table), or both allocated and destroyed at
739 a higher level (in crs_custom_tables and free_proc,
741 for (i = 0; i < pt->n_entries; i++)
742 free (pt->entries[i]);
748 make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
749 struct pivot_table *subset)
754 assert (pt->n_consts == 0);
755 subset->missing = pt->missing;
757 subset->vars = pt->vars;
758 subset->n_consts = pt->n_vars - 2;
759 subset->const_vars = pt->vars + 2;
760 subset->const_values = &pt->entries[row0]->values[2];
762 subset->entries = &pt->entries[row0];
763 subset->n_entries = row1 - row0;
767 compare_table_entry_var_3way (const struct table_entry *a,
768 const struct table_entry *b,
769 const struct pivot_table *pt,
772 return value_compare_3way (&a->values[idx], &b->values[idx],
773 var_get_width (pt->vars[idx]));
777 compare_table_entry_vars_3way (const struct table_entry *a,
778 const struct table_entry *b,
779 const struct pivot_table *pt,
784 for (i = idx1 - 1; i >= idx0; i--)
786 int cmp = compare_table_entry_var_3way (a, b, pt, i);
793 /* Compare the struct table_entry at *AP to the one at *BP and
794 return a strcmp()-type result. */
796 compare_table_entry_3way (const void *ap_, const void *bp_, const void *pt_)
798 const struct table_entry *const *ap = ap_;
799 const struct table_entry *const *bp = bp_;
800 const struct table_entry *a = *ap;
801 const struct table_entry *b = *bp;
802 const struct pivot_table *pt = pt_;
805 cmp = compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars);
809 cmp = compare_table_entry_var_3way (a, b, pt, ROW_VAR);
813 return compare_table_entry_var_3way (a, b, pt, COL_VAR);
817 find_first_difference (const struct pivot_table *pt, size_t row)
820 return pt->n_vars - 1;
823 const struct table_entry *a = pt->entries[row];
824 const struct table_entry *b = pt->entries[row - 1];
827 for (col = pt->n_vars - 1; col >= 0; col--)
828 if (compare_table_entry_var_3way (a, b, pt, col))
834 /* Output a table summarizing the cases processed. */
836 make_summary_table (struct crosstabs_proc *proc)
838 struct tab_table *summary;
839 struct pivot_table *pt;
843 summary = tab_create (7, 3 + proc->n_pivots, 1);
844 tab_title (summary, _("Summary."));
845 tab_headers (summary, 1, 0, 3, 0);
846 tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
847 tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
848 tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
849 tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
850 tab_hline (summary, TAL_1, 1, 6, 1);
851 tab_hline (summary, TAL_1, 1, 6, 2);
852 tab_vline (summary, TAL_1, 3, 1, 1);
853 tab_vline (summary, TAL_1, 5, 1, 1);
854 for (i = 0; i < 3; i++)
856 tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
857 tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
859 tab_offset (summary, 0, 3);
861 ds_init_empty (&name);
862 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
868 tab_hline (summary, TAL_1, 0, 6, 0);
871 for (i = 0; i < pt->n_vars; i++)
874 ds_put_cstr (&name, " * ");
875 ds_put_cstr (&name, var_to_string (pt->vars[i]));
877 tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
880 for (i = 0; i < pt->n_entries; i++)
881 valid += pt->entries[i]->freq;
886 for (i = 0; i < 3; i++)
888 tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i],
889 &proc->weight_format);
890 tab_text (summary, i * 2 + 2, 0, TAB_RIGHT | TAT_PRINTF, "%.1f%%",
894 tab_next_row (summary);
898 submit (proc, NULL, summary);
903 static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
904 struct pivot_table *);
905 static struct tab_table *create_chisq_table (struct pivot_table *);
906 static struct tab_table *create_sym_table (struct pivot_table *);
907 static struct tab_table *create_risk_table (struct pivot_table *);
908 static struct tab_table *create_direct_table (struct pivot_table *);
909 static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
910 struct tab_table *, int first_difference);
911 static void display_crosstabulation (struct crosstabs_proc *,
912 struct pivot_table *,
914 static void display_chisq (struct pivot_table *, struct tab_table *,
915 bool *showed_fisher);
916 static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
918 static void display_risk (struct pivot_table *, struct tab_table *);
919 static void display_directional (struct crosstabs_proc *, struct pivot_table *,
921 static void crosstabs_dim (struct tab_rendering *, void *aux);
922 static void crosstabs_dim_free (void *aux);
923 static void table_value_missing (struct crosstabs_proc *proc,
924 struct tab_table *table, int c, int r,
925 unsigned char opt, const union value *v,
926 const struct variable *var);
927 static void delete_missing (struct pivot_table *);
928 static void build_matrix (struct pivot_table *);
930 /* Output pivot table beginning at PB and continuing until PE,
931 exclusive. For efficiency, *MATP is a pointer to a matrix that can
932 hold *MAXROWS entries. */
934 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
936 struct tab_table *table = NULL; /* Crosstabulation table. */
937 struct tab_table *chisq = NULL; /* Chi-square table. */
938 bool showed_fisher = false;
939 struct tab_table *sym = NULL; /* Symmetric measures table. */
940 struct tab_table *risk = NULL; /* Risk estimate table. */
941 struct tab_table *direct = NULL; /* Directional measures table. */
944 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols);
947 table = create_crosstab_table (proc, pt);
948 if (proc->statistics & (1u << CRS_ST_CHISQ))
949 chisq = create_chisq_table (pt);
950 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
951 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
952 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
953 | (1u << CRS_ST_KAPPA)))
954 sym = create_sym_table (pt);
955 if (proc->statistics & (1u << CRS_ST_RISK))
956 risk = create_risk_table (pt);
957 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
958 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
959 direct = create_direct_table (pt);
962 while (find_crosstab (pt, &row0, &row1))
964 struct pivot_table x;
965 int first_difference;
967 make_pivot_table_subset (pt, row0, row1, &x);
969 /* Find all the row variable values. */
970 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows);
972 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
975 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
976 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
977 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
979 /* Allocate table space for the matrix. */
981 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
982 tab_realloc (table, -1,
983 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
984 tab_nr (table) * pt->n_entries / x.n_entries));
988 /* Find the first variable that differs from the last subtable. */
989 first_difference = find_first_difference (pt, row0);
992 display_dimensions (proc, &x, table, first_difference);
993 display_crosstabulation (proc, &x, table);
996 if (proc->exclude == MV_NEVER)
1001 display_dimensions (proc, &x, chisq, first_difference);
1002 display_chisq (&x, chisq, &showed_fisher);
1006 display_dimensions (proc, &x, sym, first_difference);
1007 display_symmetric (proc, &x, sym);
1011 display_dimensions (proc, &x, risk, first_difference);
1012 display_risk (&x, risk);
1016 display_dimensions (proc, &x, direct, first_difference);
1017 display_directional (proc, &x, direct);
1020 /* Free the parts of x that are not owned by pt. In
1021 particular we must not free x.cols, which is the same as
1022 pt->cols, which is freed at the end of this function. */
1030 submit (proc, NULL, table);
1035 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
1036 submit (proc, pt, chisq);
1039 submit (proc, pt, sym);
1040 submit (proc, pt, risk);
1041 submit (proc, pt, direct);
1047 build_matrix (struct pivot_table *x)
1049 const int col_var_width = var_get_width (x->vars[COL_VAR]);
1050 const int row_var_width = var_get_width (x->vars[ROW_VAR]);
1053 struct table_entry **p;
1057 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1059 const struct table_entry *te = *p;
1061 while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
1063 for (; col < x->n_cols; col++)
1069 while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
1076 if (++col >= x->n_cols)
1082 while (mp < &x->mat[x->n_cols * x->n_rows])
1084 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1086 /* Column totals, row totals, ns_rows. */
1088 for (col = 0; col < x->n_cols; col++)
1089 x->col_tot[col] = 0.0;
1090 for (row = 0; row < x->n_rows; row++)
1091 x->row_tot[row] = 0.0;
1093 for (row = 0; row < x->n_rows; row++)
1095 bool row_is_empty = true;
1096 for (col = 0; col < x->n_cols; col++)
1100 row_is_empty = false;
1101 x->col_tot[col] += *mp;
1102 x->row_tot[row] += *mp;
1109 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1113 for (col = 0; col < x->n_cols; col++)
1114 for (row = 0; row < x->n_rows; row++)
1115 if (x->mat[col + row * x->n_cols] != 0.0)
1123 for (col = 0; col < x->n_cols; col++)
1124 x->total += x->col_tot[col];
1127 static struct tab_table *
1128 create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1135 static const struct tuple names[] =
1137 {CRS_CL_COUNT, N_("count")},
1138 {CRS_CL_ROW, N_("row %")},
1139 {CRS_CL_COLUMN, N_("column %")},
1140 {CRS_CL_TOTAL, N_("total %")},
1141 {CRS_CL_EXPECTED, N_("expected")},
1142 {CRS_CL_RESIDUAL, N_("residual")},
1143 {CRS_CL_SRESIDUAL, N_("std. resid.")},
1144 {CRS_CL_ASRESIDUAL, N_("adj. resid.")},
1146 const int n_names = sizeof names / sizeof *names;
1147 const struct tuple *t;
1149 struct tab_table *table;
1150 struct string title;
1153 table = tab_create (pt->n_consts + 1 + pt->n_cols + 1,
1154 (pt->n_entries / pt->n_cols) * 3 / 2 * proc->n_cells + 10,
1156 tab_headers (table, pt->n_consts + 1, 0, 2, 0);
1158 /* First header line. */
1159 tab_joint_text (table, pt->n_consts + 1, 0,
1160 (pt->n_consts + 1) + (pt->n_cols - 1), 0,
1161 TAB_CENTER | TAT_TITLE, var_get_name (pt->vars[COL_VAR]));
1163 tab_hline (table, TAL_1, pt->n_consts + 1,
1164 pt->n_consts + 2 + pt->n_cols - 2, 1);
1166 /* Second header line. */
1167 for (i = 2; i < pt->n_consts + 2; i++)
1168 tab_joint_text (table, pt->n_consts + 2 - i - 1, 0,
1169 pt->n_consts + 2 - i - 1, 1,
1170 TAB_RIGHT | TAT_TITLE, var_to_string (pt->vars[i]));
1171 tab_text (table, pt->n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1172 var_get_name (pt->vars[ROW_VAR]));
1173 for (i = 0; i < pt->n_cols; i++)
1174 table_value_missing (proc, table, pt->n_consts + 2 + i - 1, 1, TAB_RIGHT,
1175 &pt->cols[i], pt->vars[COL_VAR]);
1176 tab_text (table, pt->n_consts + 2 + pt->n_cols - 1, 1, TAB_CENTER, _("Total"));
1178 tab_hline (table, TAL_1, 0, pt->n_consts + 2 + pt->n_cols - 1, 2);
1179 tab_vline (table, TAL_1, pt->n_consts + 2 + pt->n_cols - 1, 0, 1);
1182 ds_init_empty (&title);
1183 for (i = 0; i < pt->n_consts + 2; i++)
1186 ds_put_cstr (&title, " * ");
1187 ds_put_cstr (&title, var_get_name (pt->vars[i]));
1189 for (i = 0; i < pt->n_consts; i++)
1191 const struct variable *var = pt->const_vars[i];
1194 ds_put_format (&title, ", %s=", var_get_name (var));
1196 /* Insert the formatted value of the variable, then trim
1197 leading spaces in what was just inserted. */
1198 ofs = ds_length (&title);
1199 data_out (&pt->const_values[i], var_get_print_format (var),
1200 ds_put_uninit (&title, var_get_width (var)));
1201 ds_remove (&title, ofs, ss_cspan (ds_substr (&title, ofs, SIZE_MAX),
1205 ds_put_cstr (&title, " [");
1207 for (t = names; t < &names[n_names]; t++)
1208 if (proc->cells & (1u << t->value))
1211 ds_put_cstr (&title, ", ");
1212 ds_put_cstr (&title, gettext (t->name));
1214 ds_put_cstr (&title, "].");
1216 tab_title (table, "%s", ds_cstr (&title));
1217 ds_destroy (&title);
1219 tab_offset (table, 0, 2);
1223 static struct tab_table *
1224 create_chisq_table (struct pivot_table *pt)
1226 struct tab_table *chisq;
1228 chisq = tab_create (6 + (pt->n_vars - 2),
1229 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10,
1231 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1233 tab_title (chisq, _("Chi-square tests."));
1235 tab_offset (chisq, pt->n_vars - 2, 0);
1236 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1237 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1238 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1239 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1240 _("Asymp. Sig. (2-sided)"));
1241 tab_text (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1242 _("Exact. Sig. (2-sided)"));
1243 tab_text (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1244 _("Exact. Sig. (1-sided)"));
1245 tab_offset (chisq, 0, 1);
1250 /* Symmetric measures. */
1251 static struct tab_table *
1252 create_sym_table (struct pivot_table *pt)
1254 struct tab_table *sym;
1256 sym = tab_create (6 + (pt->n_vars - 2),
1257 pt->n_entries / pt->n_cols * 7 + 10, 1);
1258 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1259 tab_title (sym, _("Symmetric measures."));
1261 tab_offset (sym, pt->n_vars - 2, 0);
1262 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1263 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1264 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1265 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1266 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1267 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1268 tab_offset (sym, 0, 1);
1273 /* Risk estimate. */
1274 static struct tab_table *
1275 create_risk_table (struct pivot_table *pt)
1277 struct tab_table *risk;
1279 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10,
1281 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1282 tab_title (risk, _("Risk estimate."));
1284 tab_offset (risk, pt->n_vars - 2, 0);
1285 tab_joint_text (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE | TAT_PRINTF,
1286 _("95%% Confidence Interval"));
1287 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1288 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1289 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1290 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1291 tab_hline (risk, TAL_1, 2, 3, 1);
1292 tab_vline (risk, TAL_1, 2, 0, 1);
1293 tab_offset (risk, 0, 2);
1298 /* Directional measures. */
1299 static struct tab_table *
1300 create_direct_table (struct pivot_table *pt)
1302 struct tab_table *direct;
1304 direct = tab_create (7 + (pt->n_vars - 2),
1305 pt->n_entries / pt->n_cols * 7 + 10, 1);
1306 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1307 tab_title (direct, _("Directional measures."));
1309 tab_offset (direct, pt->n_vars - 2, 0);
1310 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1311 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1312 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1313 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1314 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1315 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1316 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1317 tab_offset (direct, 0, 1);
1323 /* Delete missing rows and columns for statistical analysis when
1326 delete_missing (struct pivot_table *pt)
1330 for (r = 0; r < pt->n_rows; r++)
1331 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1333 for (c = 0; c < pt->n_cols; c++)
1334 pt->mat[c + r * pt->n_cols] = 0.;
1339 for (c = 0; c < pt->n_cols; c++)
1340 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1342 for (r = 0; r < pt->n_rows; r++)
1343 pt->mat[c + r * pt->n_cols] = 0.;
1348 /* Prepare table T for submission, and submit it. */
1350 submit (struct crosstabs_proc *proc, struct pivot_table *pt,
1351 struct tab_table *t)
1353 struct crosstabs_dim_aux *aux;
1359 tab_resize (t, -1, 0);
1360 if (tab_nr (t) == tab_t (t))
1365 tab_offset (t, 0, 0);
1367 for (i = 2; i < pt->n_vars; i++)
1368 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1369 var_to_string (pt->vars[i]));
1370 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1371 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1373 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1375 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1377 aux = xmalloc (sizeof *aux);
1378 aux->exclude = proc->exclude;
1379 tab_dim (t, crosstabs_dim, crosstabs_dim_free, aux);
1384 /* Sets the widths of all the columns and heights of all the rows in
1385 table T for driver D. */
1387 crosstabs_dim (struct tab_rendering *r, void *aux_)
1389 const struct tab_table *t = r->table;
1390 struct outp_driver *d = r->driver;
1391 struct crosstabs_dim_aux *aux = aux_;
1394 /* Width of a numerical column. */
1395 int c = outp_string_width (d, "0.000000", OUTP_PROPORTIONAL);
1396 if (aux->exclude == MV_NEVER)
1397 c += outp_string_width (d, "M", OUTP_PROPORTIONAL);
1399 /* Set width for header columns. */
1405 w = d->width - c * (t->nc - t->l);
1406 for (i = 0; i <= t->nc; i++)
1410 if (w < d->prop_em_width * 8)
1411 w = d->prop_em_width * 8;
1413 if (w > d->prop_em_width * 15)
1414 w = d->prop_em_width * 15;
1416 for (i = 0; i < t->l; i++)
1420 for (i = t->l; i < t->nc; i++)
1423 for (i = 0; i < t->nr; i++)
1424 r->h[i] = tab_natural_height (r, i);
1428 crosstabs_dim_free (void *aux_)
1430 struct crosstabs_dim_aux *aux = aux_;
1435 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1437 size_t row0 = *row1p;
1440 if (row0 >= pt->n_entries)
1443 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1445 struct table_entry *a = pt->entries[row0];
1446 struct table_entry *b = pt->entries[row1];
1447 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1455 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1456 result. WIDTH_ points to an int which is either 0 for a
1457 numeric value or a string width for a string value. */
1459 compare_value_3way (const void *a_, const void *b_, const void *width_)
1461 const union value *a = a_;
1462 const union value *b = b_;
1463 const int *width = width_;
1465 return value_compare_3way (a, b, *width);
1468 /* Given an array of ENTRY_CNT table_entry structures starting at
1469 ENTRIES, creates a sorted list of the values that the variable
1470 with index VAR_IDX takes on. The values are returned as a
1471 malloc()'d array stored in *VALUES, with the number of values
1472 stored in *VALUE_CNT.
1475 enum_var_values (const struct pivot_table *pt, int var_idx,
1476 union value **valuesp, int *n_values)
1478 const struct variable *var = pt->vars[var_idx];
1479 struct var_range *range = get_var_range (var);
1480 union value *values;
1485 values = *valuesp = xnmalloc (range->count, sizeof *values);
1486 *n_values = range->count;
1487 for (i = 0; i < range->count; i++)
1488 values[i].f = range->min + i;
1492 int width = var_get_width (var);
1493 struct hmapx_node *node;
1494 const union value *iter;
1498 for (i = 0; i < pt->n_entries; i++)
1500 const struct table_entry *te = pt->entries[i];
1501 const union value *value = &te->values[var_idx];
1502 size_t hash = value_hash (value, width, 0);
1504 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1505 if (value_equal (iter, value, width))
1508 hmapx_insert (&set, (union value *) value, hash);
1513 *n_values = hmapx_count (&set);
1514 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1516 HMAPX_FOR_EACH (iter, node, &set)
1517 values[i++] = *iter;
1518 hmapx_destroy (&set);
1520 sort (values, *n_values, sizeof *values, compare_value_3way, &width);
1524 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1525 from V, displayed with print format spec from variable VAR. When
1526 in REPORT missing-value mode, missing values have an M appended. */
1528 table_value_missing (struct crosstabs_proc *proc,
1529 struct tab_table *table, int c, int r, unsigned char opt,
1530 const union value *v, const struct variable *var)
1533 const struct fmt_spec *print = var_get_print_format (var);
1535 const char *label = var_lookup_value_label (var, v);
1538 tab_text (table, c, r, TAB_LEFT, label);
1542 s.string = tab_alloc (table, print->w);
1543 data_out (v, print, s.string);
1544 s.length = print->w;
1545 if (proc->exclude == MV_NEVER && var_is_num_missing (var, v->f, MV_USER))
1546 s.string[s.length++] = 'M';
1547 while (s.length && *s.string == ' ')
1552 tab_raw (table, c, r, opt, &s);
1555 /* Draws a line across TABLE at the current row to indicate the most
1556 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1557 that changed, and puts the values that changed into the table. TB
1558 and PT must be the corresponding table_entry and crosstab,
1561 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1562 struct tab_table *table, int first_difference)
1564 tab_hline (table, TAL_1, pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1566 for (; first_difference >= 2; first_difference--)
1567 table_value_missing (proc, table, pt->n_vars - first_difference - 1, 0,
1568 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1569 pt->vars[first_difference]);
1572 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1573 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1574 additionally suffixed with a letter `M'. */
1576 format_cell_entry (struct tab_table *table, int c, int r, double value,
1577 char suffix, bool mark_missing)
1579 const struct fmt_spec f = {FMT_F, 10, 1};
1584 s.string = tab_alloc (table, 16);
1586 data_out (&v, &f, s.string);
1587 while (*s.string == ' ')
1593 s.string[s.length++] = suffix;
1595 s.string[s.length++] = 'M';
1597 tab_raw (table, c, r, TAB_RIGHT, &s);
1600 /* Displays the crosstabulation table. */
1602 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1603 struct tab_table *table)
1609 for (r = 0; r < pt->n_rows; r++)
1610 table_value_missing (proc, table, pt->n_vars - 2, r * proc->n_cells,
1611 TAB_RIGHT, &pt->rows[r], pt->vars[ROW_VAR]);
1613 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1614 TAB_LEFT, _("Total"));
1616 /* Put in the actual cells. */
1618 tab_offset (table, pt->n_vars - 1, -1);
1619 for (r = 0; r < pt->n_rows; r++)
1621 if (proc->n_cells > 1)
1622 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1623 for (c = 0; c < pt->n_cols; c++)
1625 bool mark_missing = false;
1626 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1627 if (proc->exclude == MV_NEVER
1628 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1629 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1631 mark_missing = true;
1632 for (i = 0; i < proc->n_cells; i++)
1637 switch (proc->a_cells[i])
1643 v = *mp / pt->row_tot[r] * 100.;
1647 v = *mp / pt->col_tot[c] * 100.;
1651 v = *mp / pt->total * 100.;
1654 case CRS_CL_EXPECTED:
1657 case CRS_CL_RESIDUAL:
1658 v = *mp - expected_value;
1660 case CRS_CL_SRESIDUAL:
1661 v = (*mp - expected_value) / sqrt (expected_value);
1663 case CRS_CL_ASRESIDUAL:
1664 v = ((*mp - expected_value)
1665 / sqrt (expected_value
1666 * (1. - pt->row_tot[r] / pt->total)
1667 * (1. - pt->col_tot[c] / pt->total)));
1672 format_cell_entry (table, c, i, v, suffix, mark_missing);
1678 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1682 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1683 for (r = 0; r < pt->n_rows; r++)
1685 bool mark_missing = false;
1687 if (proc->exclude == MV_NEVER
1688 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1689 mark_missing = true;
1691 for (i = 0; i < proc->n_cells; i++)
1696 switch (proc->a_cells[i])
1706 v = pt->row_tot[r] / pt->total * 100.;
1710 v = pt->row_tot[r] / pt->total * 100.;
1713 case CRS_CL_EXPECTED:
1714 case CRS_CL_RESIDUAL:
1715 case CRS_CL_SRESIDUAL:
1716 case CRS_CL_ASRESIDUAL:
1723 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing);
1724 tab_next_row (table);
1728 /* Column totals, grand total. */
1730 if (proc->n_cells > 1)
1731 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1732 for (c = 0; c <= pt->n_cols; c++)
1734 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1735 bool mark_missing = false;
1738 if (proc->exclude == MV_NEVER && c < pt->n_cols
1739 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1740 mark_missing = true;
1742 for (i = 0; i < proc->n_cells; i++)
1747 switch (proc->a_cells[i])
1753 v = ct / pt->total * 100.;
1761 v = ct / pt->total * 100.;
1764 case CRS_CL_EXPECTED:
1765 case CRS_CL_RESIDUAL:
1766 case CRS_CL_SRESIDUAL:
1767 case CRS_CL_ASRESIDUAL:
1773 format_cell_entry (table, c, i, v, suffix, mark_missing);
1778 tab_offset (table, -1, tab_row (table) + last_row);
1779 tab_offset (table, 0, -1);
1782 static void calc_r (struct pivot_table *,
1783 double *PT, double *Y, double *, double *, double *);
1784 static void calc_chisq (struct pivot_table *,
1785 double[N_CHISQ], int[N_CHISQ], double *, double *);
1787 /* Display chi-square statistics. */
1789 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1790 bool *showed_fisher)
1792 static const char *chisq_stats[N_CHISQ] =
1794 N_("Pearson Chi-Square"),
1795 N_("Likelihood Ratio"),
1796 N_("Fisher's Exact Test"),
1797 N_("Continuity Correction"),
1798 N_("Linear-by-Linear Association"),
1800 double chisq_v[N_CHISQ];
1801 double fisher1, fisher2;
1806 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1808 tab_offset (chisq, pt->n_vars - 2, -1);
1810 for (i = 0; i < N_CHISQ; i++)
1812 if ((i != 2 && chisq_v[i] == SYSMIS)
1813 || (i == 2 && fisher1 == SYSMIS))
1816 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1819 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL);
1820 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], &pt->weight_format);
1821 tab_double (chisq, 3, 0, TAB_RIGHT,
1822 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL);
1826 *showed_fisher = true;
1827 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL);
1828 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL);
1830 tab_next_row (chisq);
1833 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1834 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1835 tab_next_row (chisq);
1837 tab_offset (chisq, 0, -1);
1840 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1841 double[N_SYMMETRIC], double[N_SYMMETRIC],
1842 double[N_SYMMETRIC],
1843 double[3], double[3], double[3]);
1845 /* Display symmetric measures. */
1847 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1848 struct tab_table *sym)
1850 static const char *categories[] =
1852 N_("Nominal by Nominal"),
1853 N_("Ordinal by Ordinal"),
1854 N_("Interval by Interval"),
1855 N_("Measure of Agreement"),
1858 static const char *stats[N_SYMMETRIC] =
1862 N_("Contingency Coefficient"),
1863 N_("Kendall's tau-b"),
1864 N_("Kendall's tau-c"),
1866 N_("Spearman Correlation"),
1871 static const int stats_categories[N_SYMMETRIC] =
1873 0, 0, 0, 1, 1, 1, 1, 2, 3,
1877 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1878 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1881 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1882 somers_d_v, somers_d_ase, somers_d_t))
1885 tab_offset (sym, pt->n_vars - 2, -1);
1887 for (i = 0; i < N_SYMMETRIC; i++)
1889 if (sym_v[i] == SYSMIS)
1892 if (stats_categories[i] != last_cat)
1894 last_cat = stats_categories[i];
1895 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1898 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1899 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL);
1900 if (sym_ase[i] != SYSMIS)
1901 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL);
1902 if (sym_t[i] != SYSMIS)
1903 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL);
1904 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL);*/
1908 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1909 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1912 tab_offset (sym, 0, -1);
1915 static int calc_risk (struct pivot_table *,
1916 double[], double[], double[], union value *);
1918 /* Display risk estimate. */
1920 display_risk (struct pivot_table *pt, struct tab_table *risk)
1923 double risk_v[3], lower[3], upper[3];
1927 if (!calc_risk (pt, risk_v, upper, lower, c))
1930 tab_offset (risk, pt->n_vars - 2, -1);
1932 for (i = 0; i < 3; i++)
1934 const struct variable *cv = pt->vars[COL_VAR];
1935 const struct variable *rv = pt->vars[ROW_VAR];
1936 int cvw = var_get_width (cv);
1937 int rvw = var_get_width (rv);
1939 if (risk_v[i] == SYSMIS)
1945 if (var_is_numeric (cv))
1946 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1947 var_get_name (cv), c[0].f, c[1].f);
1949 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1951 cvw, value_str (&c[0], cvw),
1952 cvw, value_str (&c[1], cvw));
1956 if (var_is_numeric (rv))
1957 sprintf (buf, _("For cohort %s = %g"),
1958 var_get_name (rv), pt->rows[i - 1].f);
1960 sprintf (buf, _("For cohort %s = %.*s"),
1962 rvw, value_str (&pt->rows[i - 1], rvw));
1966 tab_text (risk, 0, 0, TAB_LEFT, buf);
1967 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL);
1968 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL);
1969 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL);
1970 tab_next_row (risk);
1973 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1974 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1975 tab_next_row (risk);
1977 tab_offset (risk, 0, -1);
1980 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1981 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1982 double[N_DIRECTIONAL]);
1984 /* Display directional measures. */
1986 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
1987 struct tab_table *direct)
1989 static const char *categories[] =
1991 N_("Nominal by Nominal"),
1992 N_("Ordinal by Ordinal"),
1993 N_("Nominal by Interval"),
1996 static const char *stats[] =
1999 N_("Goodman and Kruskal tau"),
2000 N_("Uncertainty Coefficient"),
2005 static const char *types[] =
2012 static const int stats_categories[N_DIRECTIONAL] =
2014 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
2017 static const int stats_stats[N_DIRECTIONAL] =
2019 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
2022 static const int stats_types[N_DIRECTIONAL] =
2024 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
2027 static const int *stats_lookup[] =
2034 static const char **stats_names[] =
2046 double direct_v[N_DIRECTIONAL];
2047 double direct_ase[N_DIRECTIONAL];
2048 double direct_t[N_DIRECTIONAL];
2052 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t))
2055 tab_offset (direct, pt->n_vars - 2, -1);
2057 for (i = 0; i < N_DIRECTIONAL; i++)
2059 if (direct_v[i] == SYSMIS)
2065 for (j = 0; j < 3; j++)
2066 if (last[j] != stats_lookup[j][i])
2069 tab_hline (direct, TAL_1, j, 6, 0);
2074 int k = last[j] = stats_lookup[j][i];
2079 string = var_get_name (pt->vars[0]);
2081 string = var_get_name (pt->vars[1]);
2083 tab_text (direct, j, 0, TAB_LEFT | TAT_PRINTF,
2084 gettext (stats_names[j][k]), string);
2089 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL);
2090 if (direct_ase[i] != SYSMIS)
2091 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL);
2092 if (direct_t[i] != SYSMIS)
2093 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL);
2094 /*tab_double (direct, 6, 0, TAB_RIGHT, normal_sig (direct_v[i]), NULL);*/
2095 tab_next_row (direct);
2098 tab_offset (direct, 0, -1);
2101 /* Statistical calculations. */
2103 /* Returns the value of the gamma (factorial) function for an integer
2106 gamma_int (double pt)
2111 for (i = 2; i < pt; i++)
2116 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2118 static inline double
2119 Pr (int a, int b, int c, int d)
2121 return (gamma_int (a + b + 1.) / gamma_int (a + 1.)
2122 * gamma_int (c + d + 1.) / gamma_int (b + 1.)
2123 * gamma_int (a + c + 1.) / gamma_int (c + 1.)
2124 * gamma_int (b + d + 1.) / gamma_int (d + 1.)
2125 / gamma_int (a + b + c + d + 1.));
2128 /* Swap the contents of A and B. */
2130 swap (int *a, int *b)
2137 /* Calculate significance for Fisher's exact test as specified in
2138 _SPSS Statistical Algorithms_, Appendix 5. */
2140 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2144 if (MIN (c, d) < MIN (a, b))
2145 swap (&a, &c), swap (&b, &d);
2146 if (MIN (b, d) < MIN (a, c))
2147 swap (&a, &b), swap (&c, &d);
2151 swap (&a, &b), swap (&c, &d);
2153 swap (&a, &c), swap (&b, &d);
2157 for (pt = 0; pt <= a; pt++)
2158 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2160 *fisher2 = *fisher1;
2161 for (pt = 1; pt <= b; pt++)
2162 *fisher2 += Pr (a + pt, b - pt, c - pt, d + pt);
2165 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2166 columns with values COLS and N_ROWS rows with values ROWS. Values
2167 in the matrix sum to pt->total. */
2169 calc_chisq (struct pivot_table *pt,
2170 double chisq[N_CHISQ], int df[N_CHISQ],
2171 double *fisher1, double *fisher2)
2175 chisq[0] = chisq[1] = 0.;
2176 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2177 *fisher1 = *fisher2 = SYSMIS;
2179 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2181 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2183 chisq[0] = chisq[1] = SYSMIS;
2187 for (r = 0; r < pt->n_rows; r++)
2188 for (c = 0; c < pt->n_cols; c++)
2190 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2191 const double freq = pt->mat[pt->n_cols * r + c];
2192 const double residual = freq - expected;
2194 chisq[0] += residual * residual / expected;
2196 chisq[1] += freq * log (expected / freq);
2207 /* Calculate Yates and Fisher exact test. */
2208 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2210 double f11, f12, f21, f22;
2216 for (i = j = 0; i < pt->n_cols; i++)
2217 if (pt->col_tot[i] != 0.)
2226 f11 = pt->mat[nz_cols[0]];
2227 f12 = pt->mat[nz_cols[1]];
2228 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2229 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2234 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2237 chisq[3] = (pt->total * pow2 (pt_)
2238 / (f11 + f12) / (f21 + f22)
2239 / (f11 + f21) / (f12 + f22));
2247 if (f11 < 5. || f12 < 5. || f21 < 5. || f22 < 5.)
2248 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2251 /* Calculate Mantel-Haenszel. */
2252 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2254 double r, ase_0, ase_1;
2255 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2257 chisq[4] = (pt->total - 1.) * r * r;
2262 /* Calculate the value of Pearson's r. r is stored into R, ase_1 into
2263 ASE_1, and ase_0 into ASE_0. The row and column values must be
2264 passed in PT and Y. */
2266 calc_r (struct pivot_table *pt,
2267 double *PT, double *Y, double *r, double *ase_0, double *ase_1)
2269 double SX, SY, S, T;
2271 double sum_XYf, sum_X2Y2f;
2272 double sum_Xr, sum_X2r;
2273 double sum_Yc, sum_Y2c;
2276 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2277 for (j = 0; j < pt->n_cols; j++)
2279 double fij = pt->mat[j + i * pt->n_cols];
2280 double product = PT[i] * Y[j];
2281 double temp = fij * product;
2283 sum_X2Y2f += temp * product;
2286 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2288 sum_Xr += PT[i] * pt->row_tot[i];
2289 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2291 Xbar = sum_Xr / pt->total;
2293 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2295 sum_Yc += Y[i] * pt->col_tot[i];
2296 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2298 Ybar = sum_Yc / pt->total;
2300 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2301 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2302 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2305 *ase_0 = sqrt ((sum_X2Y2f - pow2 (sum_XYf) / pt->total) / (sum_X2r * sum_Y2c));
2310 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2311 for (j = 0; j < pt->n_cols; j++)
2313 double Xresid, Yresid;
2316 Xresid = PT[i] - Xbar;
2317 Yresid = Y[j] - Ybar;
2318 temp = (T * Xresid * Yresid
2320 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2321 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2326 *ase_1 = sqrt (s) / (T * T);
2330 /* Calculate symmetric statistics and their asymptotic standard
2331 errors. Returns 0 if none could be calculated. */
2333 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2334 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2335 double t[N_SYMMETRIC],
2336 double somers_d_v[3], double somers_d_ase[3],
2337 double somers_d_t[3])
2341 q = MIN (pt->ns_rows, pt->ns_cols);
2345 for (i = 0; i < N_SYMMETRIC; i++)
2346 v[i] = ase[i] = t[i] = SYSMIS;
2348 /* Phi, Cramer's V, contingency coefficient. */
2349 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2351 double Xp = 0.; /* Pearson chi-square. */
2354 for (r = 0; r < pt->n_rows; r++)
2355 for (c = 0; c < pt->n_cols; c++)
2357 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2358 const double freq = pt->mat[pt->n_cols * r + c];
2359 const double residual = freq - expected;
2361 Xp += residual * residual / expected;
2364 if (proc->statistics & (1u << CRS_ST_PHI))
2366 v[0] = sqrt (Xp / pt->total);
2367 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2369 if (proc->statistics & (1u << CRS_ST_CC))
2370 v[2] = sqrt (Xp / (Xp + pt->total));
2373 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2374 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2379 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2383 Dr = Dc = pow2 (pt->total);
2384 for (r = 0; r < pt->n_rows; r++)
2385 Dr -= pow2 (pt->row_tot[r]);
2386 for (c = 0; c < pt->n_cols; c++)
2387 Dc -= pow2 (pt->col_tot[c]);
2389 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2390 for (c = 0; c < pt->n_cols; c++)
2394 for (r = 0; r < pt->n_rows; r++)
2395 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2404 for (i = 0; i < pt->n_rows; i++)
2408 for (j = 1; j < pt->n_cols; j++)
2409 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2412 for (j = 1; j < pt->n_cols; j++)
2413 Dij += cum[j + (i - 1) * pt->n_cols];
2417 double fij = pt->mat[j + i * pt->n_cols];
2421 if (++j == pt->n_cols)
2423 assert (j < pt->n_cols);
2425 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2426 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2430 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2431 Dij -= cum[j + (i - 1) * pt->n_cols];
2437 if (proc->statistics & (1u << CRS_ST_BTAU))
2438 v[3] = (P - Q) / sqrt (Dr * Dc);
2439 if (proc->statistics & (1u << CRS_ST_CTAU))
2440 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2441 if (proc->statistics & (1u << CRS_ST_GAMMA))
2442 v[5] = (P - Q) / (P + Q);
2444 /* ASE for tau-b, tau-c, gamma. Calculations could be
2445 eliminated here, at expense of memory. */
2450 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2451 for (i = 0; i < pt->n_rows; i++)
2455 for (j = 1; j < pt->n_cols; j++)
2456 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2459 for (j = 1; j < pt->n_cols; j++)
2460 Dij += cum[j + (i - 1) * pt->n_cols];
2464 double fij = pt->mat[j + i * pt->n_cols];
2466 if (proc->statistics & (1u << CRS_ST_BTAU))
2468 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2469 + v[3] * (pt->row_tot[i] * Dc
2470 + pt->col_tot[j] * Dr));
2471 btau_cum += fij * temp * temp;
2475 const double temp = Cij - Dij;
2476 ctau_cum += fij * temp * temp;
2479 if (proc->statistics & (1u << CRS_ST_GAMMA))
2481 const double temp = Q * Cij - P * Dij;
2482 gamma_cum += fij * temp * temp;
2485 if (proc->statistics & (1u << CRS_ST_D))
2487 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2488 - (P - Q) * (pt->total - pt->row_tot[i]));
2489 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2490 - (Q - P) * (pt->total - pt->col_tot[j]));
2493 if (++j == pt->n_cols)
2495 assert (j < pt->n_cols);
2497 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2498 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2502 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2503 Dij -= cum[j + (i - 1) * pt->n_cols];
2509 btau_var = ((btau_cum
2510 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2512 if (proc->statistics & (1u << CRS_ST_BTAU))
2514 ase[3] = sqrt (btau_var);
2515 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2518 if (proc->statistics & (1u << CRS_ST_CTAU))
2520 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2521 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2522 t[4] = v[4] / ase[4];
2524 if (proc->statistics & (1u << CRS_ST_GAMMA))
2526 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2527 t[5] = v[5] / (2. / (P + Q)
2528 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2530 if (proc->statistics & (1u << CRS_ST_D))
2532 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2533 somers_d_ase[0] = 2. * btau_var / (Dr + Dc) * sqrt (Dr * Dc);
2534 somers_d_t[0] = (somers_d_v[0]
2536 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2537 somers_d_v[1] = (P - Q) / Dc;
2538 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2539 somers_d_t[1] = (somers_d_v[1]
2541 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2542 somers_d_v[2] = (P - Q) / Dr;
2543 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2544 somers_d_t[2] = (somers_d_v[2]
2546 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2552 /* Spearman correlation, Pearson's r. */
2553 if (proc->statistics & (1u << CRS_ST_CORR))
2555 double *R = xmalloc (sizeof *R * pt->n_rows);
2556 double *C = xmalloc (sizeof *C * pt->n_cols);
2559 double y, t, c = 0., s = 0.;
2564 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2565 y = pt->row_tot[i] - c;
2569 if (++i == pt->n_rows)
2571 assert (i < pt->n_rows);
2576 double y, t, c = 0., s = 0.;
2581 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2582 y = pt->col_tot[j] - c;
2586 if (++j == pt->n_cols)
2588 assert (j < pt->n_cols);
2592 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2598 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2602 /* Cohen's kappa. */
2603 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2605 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2608 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2609 i < pt->ns_rows; i++, j++)
2613 while (pt->col_tot[j] == 0.)
2616 prod = pt->row_tot[i] * pt->col_tot[j];
2617 sum = pt->row_tot[i] + pt->col_tot[j];
2619 sum_fii += pt->mat[j + i * pt->n_cols];
2621 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2622 sum_riciri_ci += prod * sum;
2624 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2625 for (j = 0; j < pt->ns_cols; j++)
2627 double sum = pt->row_tot[i] + pt->col_tot[j];
2628 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2631 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2633 ase[8] = sqrt ((pow2 (pt->total) * sum_rici
2634 + sum_rici * sum_rici
2635 - pt->total * sum_riciri_ci)
2636 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2638 t[8] = v[8] / sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2639 / pow2 (pow2 (pt->total) - sum_rici))
2640 + ((2. * (pt->total - sum_fii)
2641 * (2. * sum_fii * sum_rici
2642 - pt->total * sum_fiiri_ci))
2643 / cube (pow2 (pt->total) - sum_rici))
2644 + (pow2 (pt->total - sum_fii)
2645 * (pt->total * sum_fijri_ci2 - 4.
2646 * sum_rici * sum_rici)
2647 / pow4 (pow2 (pt->total) - sum_rici))));
2649 t[8] = v[8] / ase[8];
2656 /* Calculate risk estimate. */
2658 calc_risk (struct pivot_table *pt,
2659 double *value, double *upper, double *lower, union value *c)
2661 double f11, f12, f21, f22;
2667 for (i = 0; i < 3; i++)
2668 value[i] = upper[i] = lower[i] = SYSMIS;
2671 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2678 for (i = j = 0; i < pt->n_cols; i++)
2679 if (pt->col_tot[i] != 0.)
2688 f11 = pt->mat[nz_cols[0]];
2689 f12 = pt->mat[nz_cols[1]];
2690 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2691 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2693 c[0] = pt->cols[nz_cols[0]];
2694 c[1] = pt->cols[nz_cols[1]];
2697 value[0] = (f11 * f22) / (f12 * f21);
2698 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2699 lower[0] = value[0] * exp (-1.960 * v);
2700 upper[0] = value[0] * exp (1.960 * v);
2702 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2703 v = sqrt ((f12 / (f11 * (f11 + f12)))
2704 + (f22 / (f21 * (f21 + f22))));
2705 lower[1] = value[1] * exp (-1.960 * v);
2706 upper[1] = value[1] * exp (1.960 * v);
2708 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2709 v = sqrt ((f11 / (f12 * (f11 + f12)))
2710 + (f21 / (f22 * (f21 + f22))));
2711 lower[2] = value[2] * exp (-1.960 * v);
2712 upper[2] = value[2] * exp (1.960 * v);
2717 /* Calculate directional measures. */
2719 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2720 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2721 double t[N_DIRECTIONAL])
2726 for (i = 0; i < N_DIRECTIONAL; i++)
2727 v[i] = ase[i] = t[i] = SYSMIS;
2731 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2733 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2734 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2735 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2736 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2737 double sum_fim, sum_fmj;
2739 int rm_index, cm_index;
2742 /* Find maximum for each row and their sum. */
2743 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2745 double max = pt->mat[i * pt->n_cols];
2748 for (j = 1; j < pt->n_cols; j++)
2749 if (pt->mat[j + i * pt->n_cols] > max)
2751 max = pt->mat[j + i * pt->n_cols];
2755 sum_fim += fim[i] = max;
2756 fim_index[i] = index;
2759 /* Find maximum for each column. */
2760 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2762 double max = pt->mat[j];
2765 for (i = 1; i < pt->n_rows; i++)
2766 if (pt->mat[j + i * pt->n_cols] > max)
2768 max = pt->mat[j + i * pt->n_cols];
2772 sum_fmj += fmj[j] = max;
2773 fmj_index[j] = index;
2776 /* Find maximum row total. */
2777 rm = pt->row_tot[0];
2779 for (i = 1; i < pt->n_rows; i++)
2780 if (pt->row_tot[i] > rm)
2782 rm = pt->row_tot[i];
2786 /* Find maximum column total. */
2787 cm = pt->col_tot[0];
2789 for (j = 1; j < pt->n_cols; j++)
2790 if (pt->col_tot[j] > cm)
2792 cm = pt->col_tot[j];
2796 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2797 v[1] = (sum_fmj - rm) / (pt->total - rm);
2798 v[2] = (sum_fim - cm) / (pt->total - cm);
2800 /* ASE1 for Y given PT. */
2804 for (accum = 0., i = 0; i < pt->n_rows; i++)
2805 for (j = 0; j < pt->n_cols; j++)
2807 const int deltaj = j == cm_index;
2808 accum += (pt->mat[j + i * pt->n_cols]
2809 * pow2 ((j == fim_index[i])
2814 ase[2] = sqrt (accum - pt->total * v[0]) / (pt->total - cm);
2817 /* ASE0 for Y given PT. */
2821 for (accum = 0., i = 0; i < pt->n_rows; i++)
2822 if (cm_index != fim_index[i])
2823 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2824 + pt->mat[i * pt->n_cols + cm_index]);
2825 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2828 /* ASE1 for PT given Y. */
2832 for (accum = 0., i = 0; i < pt->n_rows; i++)
2833 for (j = 0; j < pt->n_cols; j++)
2835 const int deltaj = i == rm_index;
2836 accum += (pt->mat[j + i * pt->n_cols]
2837 * pow2 ((i == fmj_index[j])
2842 ase[1] = sqrt (accum - pt->total * v[0]) / (pt->total - rm);
2845 /* ASE0 for PT given Y. */
2849 for (accum = 0., j = 0; j < pt->n_cols; j++)
2850 if (rm_index != fmj_index[j])
2851 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2852 + pt->mat[j + pt->n_cols * rm_index]);
2853 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2856 /* Symmetric ASE0 and ASE1. */
2861 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2862 for (j = 0; j < pt->n_cols; j++)
2864 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2865 int temp1 = (i == rm_index) + (j == cm_index);
2866 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2867 accum1 += (pt->mat[j + i * pt->n_cols]
2868 * pow2 (temp0 + (v[0] - 1.) * temp1));
2870 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2871 t[0] = v[0] / (sqrt (accum0 - pow2 ((sum_fim + sum_fmj - cm - rm) / pt->total))
2872 / (2. * pt->total - rm - cm));
2881 double sum_fij2_ri, sum_fij2_ci;
2882 double sum_ri2, sum_cj2;
2884 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2885 for (j = 0; j < pt->n_cols; j++)
2887 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2888 sum_fij2_ri += temp / pt->row_tot[i];
2889 sum_fij2_ci += temp / pt->col_tot[j];
2892 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2893 sum_ri2 += pow2 (pt->row_tot[i]);
2895 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2896 sum_cj2 += pow2 (pt->col_tot[j]);
2898 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2899 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2903 if (proc->statistics & (1u << CRS_ST_UC))
2905 double UX, UY, UXY, P;
2906 double ase1_yx, ase1_xy, ase1_sym;
2909 for (UX = 0., i = 0; i < pt->n_rows; i++)
2910 if (pt->row_tot[i] > 0.)
2911 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2913 for (UY = 0., j = 0; j < pt->n_cols; j++)
2914 if (pt->col_tot[j] > 0.)
2915 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2917 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2918 for (j = 0; j < pt->n_cols; j++)
2920 double entry = pt->mat[j + i * pt->n_cols];
2925 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2926 UXY -= entry / pt->total * log (entry / pt->total);
2929 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2930 for (j = 0; j < pt->n_cols; j++)
2932 double entry = pt->mat[j + i * pt->n_cols];
2937 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2938 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2939 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2940 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2941 ase1_sym += entry * pow2 ((UXY
2942 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2943 - (UX + UY) * log (entry / pt->total));
2946 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2947 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2948 t[5] = v[5] / ((2. / (pt->total * (UX + UY)))
2949 * sqrt (P - pow2 (UX + UY - UXY) / pt->total));
2951 v[6] = (UX + UY - UXY) / UX;
2952 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2953 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2955 v[7] = (UX + UY - UXY) / UY;
2956 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2957 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2961 if (proc->statistics & (1u << CRS_ST_D))
2963 double v_dummy[N_SYMMETRIC];
2964 double ase_dummy[N_SYMMETRIC];
2965 double t_dummy[N_SYMMETRIC];
2966 double somers_d_v[3];
2967 double somers_d_ase[3];
2968 double somers_d_t[3];
2970 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2971 somers_d_v, somers_d_ase, somers_d_t))
2974 for (i = 0; i < 3; i++)
2976 v[8 + i] = somers_d_v[i];
2977 ase[8 + i] = somers_d_ase[i];
2978 t[8 + i] = somers_d_t[i];
2984 if (proc->statistics & (1u << CRS_ST_ETA))
2987 double sum_Xr, sum_X2r;
2991 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2993 sum_Xr += pt->rows[i].f * pt->row_tot[i];
2994 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
2996 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2998 for (SXW = 0., j = 0; j < pt->n_cols; j++)
3002 for (cum = 0., i = 0; i < pt->n_rows; i++)
3004 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
3005 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
3008 SXW -= cum * cum / pt->col_tot[j];
3010 v[11] = sqrt (1. - SXW / SX);
3014 double sum_Yc, sum_Y2c;
3018 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
3020 sum_Yc += pt->cols[i].f * pt->col_tot[i];
3021 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
3023 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
3025 for (SYW = 0., i = 0; i < pt->n_rows; i++)
3029 for (cum = 0., j = 0; j < pt->n_cols; j++)
3031 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
3032 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
3035 SYW -= cum * cum / pt->row_tot[i];
3037 v[12] = sqrt (1. - SYW / SY);