?  search:
summary | log | graphiclog1 | graphiclog2 | commit | commitdiff | tree | refs | edit | fork
blame | history | raw | HEAD
CROSSTABS: Implement COUNT subcommand to round case or cell weights.
[pspp.git] / src / language / stats / crosstabs.q
blob6e87c0260b856173bb4debbcd07dbabbd6036f7f
1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2006, 2009, 2010, 2011, 2012, 2013, 2014, 2016 Free Software Foundation, Inc.
3
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.
8
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.
13
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/>. */
16
17 /* FIXME:
18
19 - How to calculate significance of some symmetric and directional measures?
20 - How to calculate ASE for symmetric Somers ' d?
21 - How to calculate ASE for Goodman and Kruskal's tau?
22 - How to calculate approx. T of symmetric uncertainty coefficient?
23
24 */
25
26 #include <config.h>
27
28 #include <ctype.h>
29 #include <float.h>
30 #include <gsl/gsl_cdf.h>
31 #include <stdlib.h>
32 #include <stdio.h>
33
34 #include "data/case.h"
35 #include "data/casegrouper.h"
36 #include "data/casereader.h"
37 #include "data/data-out.h"
38 #include "data/dataset.h"
39 #include "data/dictionary.h"
40 #include "data/format.h"
41 #include "data/value-labels.h"
42 #include "data/variable.h"
43 #include "language/command.h"
44 #include "language/stats/freq.h"
45 #include "language/dictionary/split-file.h"
46 #include "language/lexer/lexer.h"
47 #include "language/lexer/variable-parser.h"
48 #include "libpspp/array.h"
49 #include "libpspp/assertion.h"
50 #include "libpspp/compiler.h"
51 #include "libpspp/hash-functions.h"
52 #include "libpspp/hmap.h"
53 #include "libpspp/hmapx.h"
54 #include "libpspp/message.h"
55 #include "libpspp/misc.h"
56 #include "libpspp/pool.h"
57 #include "libpspp/str.h"
58 #include "output/tab.h"
59 #include "output/chart-item.h"
60 #include "output/charts/barchart.h"
61
62 #include "gl/minmax.h"
63 #include "gl/xalloc.h"
64 #include "gl/xsize.h"
65
66 #include "gettext.h"
67 #define _(msgid) gettext (msgid)
68 #define N_(msgid) msgid
69
70 /* (headers) */
71
72 /* (specification)
73 crosstabs (crs_):
74 *^tables=custom;
75 +variables=custom;
76 missing=miss:!table/include/report;
77 count=roundwhat:asis/case/!cell,
78 roundhow:!round/truncate;
79 +write[wr_]=none,cells,all;
80 +format=val:!avalue/dvalue,
81 indx:!noindex/index,
82 tabl:!tables/notables,
83 box:!box/nobox,
84 pivot:!pivot/nopivot;
85 +barchart=;
86 +cells[cl_]=count,expected,row,column,total,residual,sresidual,
87 asresidual,all,none;
88 +statistics[st_]=chisq,phi,cc,lambda,uc,none,btau,ctau,risk,gamma,d,
89 kappa,eta,corr,all.
90 */
91 /* (declarations) */
92 /* (functions) */
93
94 /* Number of chi-square statistics. */
95 #define N_CHISQ 5
96
97 /* Number of symmetric statistics. */
98 #define N_SYMMETRIC 9
99
100 /* Number of directional statistics. */
101 #define N_DIRECTIONAL 13
102
103
104 /* Indexes into the 'vars' member of struct pivot_table and
105 struct crosstab member. */
106 enum
107 {
108 ROW_VAR = 0, /* Row variable. */
109 COL_VAR = 1 /* Column variable. */
110 /* Higher indexes cause multiple tables to be output. */
111 };
112
113 /* A crosstabulation of 2 or more variables. */
114 struct pivot_table
115 {
116 struct crosstabs_proc *proc;
117 struct fmt_spec weight_format; /* Format for weight variable. */
118 double missing; /* Weight of missing cases. */
119
120 /* Variables (2 or more). */
121 int n_vars;
122 const struct variable **vars;
123
124 /* Constants (0 or more). */
125 int n_consts;
126 const struct variable **const_vars;
127 union value *const_values;
128
129 /* Data. */
130 struct hmap data;
131 struct freq **entries;
132 size_t n_entries;
133
134 /* Column values, number of columns. */
135 union value *cols;
136 int n_cols;
137
138 /* Row values, number of rows. */
139 union value *rows;
140 int n_rows;
141
142 /* Number of statistically interesting columns/rows
143 (columns/rows with data in them). */
144 int ns_cols, ns_rows;
145
146 /* Matrix contents. */
147 double *mat; /* Matrix proper. */
148 double *row_tot; /* Row totals. */
149 double *col_tot; /* Column totals. */
150 double total; /* Grand total. */
151 };
152
153 /* Integer mode variable info. */
154 struct var_range
155 {
156 struct hmap_node hmap_node; /* In struct crosstabs_proc var_ranges map. */
157 const struct variable *var; /* The variable. */
158 int min; /* Minimum value. */
159 int max; /* Maximum value + 1. */
160 int count; /* max - min. */
161 };
162
163 struct crosstabs_proc
164 {
165 const struct dictionary *dict;
166 enum { INTEGER, GENERAL } mode;
167 enum mv_class exclude;
168 bool pivot;
169 bool barchart;
170 bool bad_warn;
171 struct fmt_spec weight_format;
172
173 /* Variables specifies on VARIABLES. */
174 const struct variable **variables;
175 size_t n_variables;
176 struct hmap var_ranges;
177
178 /* TABLES. */
179 struct pivot_table *pivots;
180 int n_pivots;
181
182 /* CELLS. */
183 int n_cells; /* Number of cells requested. */
184 unsigned int cells; /* Bit k is 1 if cell k is requested. */
185 int a_cells[CRS_CL_count]; /* 0...n_cells-1 are the requested cells. */
186
187 /* Rounding of cells. */
188 bool round_case_weights; /* Round case weights? */
189 bool round_cells; /* If !round_case_weights, round cells? */
190 bool round_down; /* Round down? (otherwise to nearest) */
191
192 /* STATISTICS. */
193 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
194
195 bool descending; /* True if descending sort order is requested. */
196 };
197
198 const struct var_range *get_var_range (const struct crosstabs_proc *,
199 const struct variable *);
200
201 static bool should_tabulate_case (const struct pivot_table *,
202 const struct ccase *, enum mv_class exclude);
203 static void tabulate_general_case (struct pivot_table *, const struct ccase *,
204 double weight);
205 static void tabulate_integer_case (struct pivot_table *, const struct ccase *,
206 double weight);
207 static void postcalc (struct crosstabs_proc *);
208 static void submit (struct pivot_table *, struct tab_table *);
209
210 static double
211 round_weight (const struct crosstabs_proc *proc, double weight)
212 {
213 return proc->round_down ? floor (weight) : floor (weight + 0.5);
214 }
215
216 /* Parses and executes the CROSSTABS procedure. */
217 int
218 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
219 {
220 const struct variable *wv = dict_get_weight (dataset_dict (ds));
221 struct var_range *range, *next_range;
222 struct crosstabs_proc proc;
223 struct casegrouper *grouper;
224 struct casereader *input, *group;
225 struct cmd_crosstabs cmd;
226 struct pivot_table *pt;
227 int result;
228 bool ok;
229 int i;
230
231 proc.dict = dataset_dict (ds);
232 proc.bad_warn = true;
233 proc.variables = NULL;
234 proc.n_variables = 0;
235 hmap_init (&proc.var_ranges);
236 proc.pivots = NULL;
237 proc.n_pivots = 0;
238 proc.descending = false;
239 proc.weight_format = wv ? *var_get_print_format (wv) : F_8_0;
240
241 if (!parse_crosstabs (lexer, ds, &cmd, &proc))
242 {
243 result = CMD_FAILURE;
244 goto exit;
245 }
246
247 proc.mode = proc.n_variables ? INTEGER : GENERAL;
248 proc.barchart = cmd.sbc_barchart > 0;
249
250 proc.descending = cmd.val == CRS_DVALUE;
251
252 proc.round_case_weights = cmd.sbc_count && cmd.roundwhat == CRS_CASE;
253 proc.round_cells = cmd.sbc_count && cmd.roundwhat == CRS_CELL;
254 proc.round_down = cmd.roundhow == CRS_TRUNCATE;
255
256 /* CELLS. */
257 if (!cmd.sbc_cells)
258 proc.cells = 1u << CRS_CL_COUNT;
259 else if (cmd.a_cells[CRS_CL_ALL])
260 proc.cells = UINT_MAX;
261 else
262 {
263 proc.cells = 0;
264 for (i = 0; i < CRS_CL_count; i++)
265 if (cmd.a_cells[i])
266 proc.cells |= 1u << i;
267 if (proc.cells == 0)
268 proc.cells = ((1u << CRS_CL_COUNT)
269 | (1u << CRS_CL_ROW)
270 | (1u << CRS_CL_COLUMN)
271 | (1u << CRS_CL_TOTAL));
272 }
273 proc.cells &= ((1u << CRS_CL_count) - 1);
274 proc.cells &= ~((1u << CRS_CL_NONE) | (1u << CRS_CL_ALL));
275 proc.n_cells = 0;
276 for (i = 0; i < CRS_CL_count; i++)
277 if (proc.cells & (1u << i))
278 proc.a_cells[proc.n_cells++] = i;
279
280 /* STATISTICS. */
281 if (cmd.a_statistics[CRS_ST_ALL])
282 proc.statistics = UINT_MAX;
283 else if (cmd.sbc_statistics)
284 {
285 int i;
286
287 proc.statistics = 0;
288 for (i = 0; i < CRS_ST_count; i++)
289 if (cmd.a_statistics[i])
290 proc.statistics |= 1u << i;
291 if (proc.statistics == 0)
292 proc.statistics |= 1u << CRS_ST_CHISQ;
293 }
294 else
295 proc.statistics = 0;
296
297 /* MISSING. */
298 proc.exclude = (cmd.miss == CRS_TABLE ? MV_ANY
299 : cmd.miss == CRS_INCLUDE ? MV_SYSTEM
300 : MV_NEVER);
301 if (proc.mode == GENERAL && proc.exclude == MV_NEVER)
302 {
303 msg (SE, _("Missing mode %s not allowed in general mode. "
304 "Assuming %s."), "REPORT", "MISSING=TABLE");
305 proc.exclude = MV_ANY;
306 }
307
308 /* PIVOT. */
309 proc.pivot = cmd.pivot == CRS_PIVOT;
310
311 input = casereader_create_filter_weight (proc_open (ds), dataset_dict (ds),
312 NULL, NULL);
313 grouper = casegrouper_create_splits (input, dataset_dict (ds));
314 while (casegrouper_get_next_group (grouper, &group))
315 {
316 struct ccase *c;
317
318 /* Output SPLIT FILE variables. */
319 c = casereader_peek (group, 0);
320 if (c != NULL)
321 {
322 output_split_file_values (ds, c);
323 case_unref (c);
324 }
325
326 /* Initialize hash tables. */
327 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
328 hmap_init (&pt->data);
329
330 /* Tabulate. */
331 for (; (c = casereader_read (group)) != NULL; case_unref (c))
332 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
333 {
334 double weight = dict_get_case_weight (dataset_dict (ds), c,
335 &proc.bad_warn);
336 if (cmd.roundwhat == CRS_CASE)
337 {
338 weight = round_weight (&proc, weight);
339 if (weight == 0.)
340 continue;
341 }
342 if (should_tabulate_case (pt, c, proc.exclude))
343 {
344 if (proc.mode == GENERAL)
345 tabulate_general_case (pt, c, weight);
346 else
347 tabulate_integer_case (pt, c, weight);
348 }
349 else
350 pt->missing += weight;
351 }
352 casereader_destroy (group);
353
354 /* Output. */
355 postcalc (&proc);
356 }
357 ok = casegrouper_destroy (grouper);
358 ok = proc_commit (ds) && ok;
359
360 result = ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
361
362 exit:
363 free (proc.variables);
364 HMAP_FOR_EACH_SAFE (range, next_range, struct var_range, hmap_node,
365 &proc.var_ranges)
366 {
367 hmap_delete (&proc.var_ranges, &range->hmap_node);
368 free (range);
369 }
370 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
371 {
372 free (pt->vars);
373 free (pt->const_vars);
374 /* We must not call value_destroy on const_values because
375 it is a wild pointer; it never pointed to anything owned
376 by the pivot_table.
377
378 The rest of the data was allocated and destroyed at a
379 lower level already. */
380 }
381 free (proc.pivots);
382
383 return result;
384 }
385
386 /* Parses the TABLES subcommand. */
387 static int
388 crs_custom_tables (struct lexer *lexer, struct dataset *ds,
389 struct cmd_crosstabs *cmd UNUSED, void *proc_)
390 {
391 struct crosstabs_proc *proc = proc_;
392 struct const_var_set *var_set;
393 int n_by;
394 const struct variable ***by = NULL;
395 int *by_iter;
396 size_t *by_nvar = NULL;
397 size_t nx = 1;
398 bool ok = false;
399 int i;
400
401 /* Ensure that this is a TABLES subcommand. */
402 if (!lex_match_id (lexer, "TABLES")
403 && (lex_token (lexer) != T_ID ||
404 dict_lookup_var (dataset_dict (ds), lex_tokcstr (lexer)) == NULL)
405 && lex_token (lexer) != T_ALL)
406 return 2;
407 lex_match (lexer, T_EQUALS);
408
409 if (proc->variables != NULL)
410 var_set = const_var_set_create_from_array (proc->variables,
411 proc->n_variables);
412 else
413 var_set = const_var_set_create_from_dict (dataset_dict (ds));
414 assert (var_set != NULL);
415
416 for (n_by = 0; ;)
417 {
418 by = xnrealloc (by, n_by + 1, sizeof *by);
419 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
420 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
421 PV_NO_DUPLICATE | PV_NO_SCRATCH))
422 goto done;
423 if (xalloc_oversized (nx, by_nvar[n_by]))
424 {
425 msg (SE, _("Too many cross-tabulation variables or dimensions."));
426 goto done;
427 }
428 nx *= by_nvar[n_by];
429 n_by++;
430
431 if (!lex_match (lexer, T_BY))
432 {
433 if (n_by < 2)
434 goto done;
435 else
436 break;
437 }
438 }
439
440 by_iter = xcalloc (n_by, sizeof *by_iter);
441 proc->pivots = xnrealloc (proc->pivots,
442 proc->n_pivots + nx, sizeof *proc->pivots);
443 for (i = 0; i < nx; i++)
444 {
445 struct pivot_table *pt = &proc->pivots[proc->n_pivots++];
446 int j;
447
448 pt->proc = proc;
449 pt->weight_format = proc->weight_format;
450 pt->missing = 0.;
451 pt->n_vars = n_by;
452 pt->vars = xmalloc (n_by * sizeof *pt->vars);
453 pt->n_consts = 0;
454 pt->const_vars = NULL;
455 pt->const_values = NULL;
456
457 for (j = 0; j < n_by; j++)
458 pt->vars[j] = by[j][by_iter[j]];
459
460 for (j = n_by - 1; j >= 0; j--)
461 {
462 if (++by_iter[j] < by_nvar[j])
463 break;
464 by_iter[j] = 0;
465 }
466 }
467 free (by_iter);
468 ok = true;
469
470 done:
471 /* All return paths lead here. */
472 for (i = 0; i < n_by; i++)
473 free (by[i]);
474 free (by);
475 free (by_nvar);
476
477 const_var_set_destroy (var_set);
478
479 return ok;
480 }
481
482 /* Parses the VARIABLES subcommand. */
483 static int
484 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
485 struct cmd_crosstabs *cmd UNUSED, void *proc_)
486 {
487 struct crosstabs_proc *proc = proc_;
488 if (proc->n_pivots)
489 {
490 msg (SE, _("%s must be specified before %s."), "VARIABLES", "TABLES");
491 return 0;
492 }
493
494 lex_match (lexer, T_EQUALS);
495
496 for (;;)
497 {
498 size_t orig_nv = proc->n_variables;
499 size_t i;
500
501 long min, max;
502
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)))
507 return 0;
508
509 if (!lex_force_match (lexer, T_LPAREN))
510 goto lossage;
511
512 if (!lex_force_int (lexer))
513 goto lossage;
514 min = lex_integer (lexer);
515 lex_get (lexer);
516
517 lex_match (lexer, T_COMMA);
518
519 if (!lex_force_int (lexer))
520 goto lossage;
521 max = lex_integer (lexer);
522 if (max < min)
523 {
524 msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
525 max, min);
526 goto lossage;
527 }
528 lex_get (lexer);
529
530 if (!lex_force_match (lexer, T_RPAREN))
531 goto lossage;
532
533 for (i = orig_nv; i < proc->n_variables; i++)
534 {
535 const struct variable *var = proc->variables[i];
536 struct var_range *vr = xmalloc (sizeof *vr);
537
538 vr->var = var;
539 vr->min = min;
540 vr->max = max;
541 vr->count = max - min + 1;
542 hmap_insert (&proc->var_ranges, &vr->hmap_node,
543 hash_pointer (var, 0));
544 }
545
546 if (lex_token (lexer) == T_SLASH)
547 break;
548 }
549
550 return 1;
551
552 lossage:
553 free (proc->variables);
554 proc->variables = NULL;
555 proc->n_variables = 0;
556 return 0;
557 }
558 \f
559 /* Data file processing. */
560
561 const struct var_range *
562 get_var_range (const struct crosstabs_proc *proc, const struct variable *var)
563 {
564 if (!hmap_is_empty (&proc->var_ranges))
565 {
566 const struct var_range *range;
567
568 HMAP_FOR_EACH_IN_BUCKET (range, struct var_range, hmap_node,
569 hash_pointer (var, 0), &proc->var_ranges)
570 if (range->var == var)
571 return range;
572 }
573
574 return NULL;
575 }
576
577 static bool
578 should_tabulate_case (const struct pivot_table *pt, const struct ccase *c,
579 enum mv_class exclude)
580 {
581 int j;
582 for (j = 0; j < pt->n_vars; j++)
583 {
584 const struct variable *var = pt->vars[j];
585 const struct var_range *range = get_var_range (pt->proc, var);
586
587 if (var_is_value_missing (var, case_data (c, var), exclude))
588 return false;
589
590 if (range != NULL)
591 {
592 double num = case_num (c, var);
593 if (num < range->min || num >= range->max + 1.)
594 return false;
595 }
596 }
597 return true;
598 }
599
600 static void
601 tabulate_integer_case (struct pivot_table *pt, const struct ccase *c,
602 double weight)
603 {
604 struct freq *te;
605 size_t hash;
606 int j;
607
608 hash = 0;
609 for (j = 0; j < pt->n_vars; j++)
610 {
611 /* Throw away fractional parts of values. */
612 hash = hash_int (case_num (c, pt->vars[j]), hash);
613 }
614
615 HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &pt->data)
616 {
617 for (j = 0; j < pt->n_vars; j++)
618 if ((int) case_num (c, pt->vars[j]) != (int) te->values[j].f)
619 goto no_match;
620
621 /* Found an existing entry. */
622 te->count += weight;
623 return;
624
625 no_match: ;
626 }
627
628 /* No existing entry. Create a new one. */
629 te = xmalloc (table_entry_size (pt->n_vars));
630 te->count = weight;
631 for (j = 0; j < pt->n_vars; j++)
632 te->values[j].f = (int) case_num (c, pt->vars[j]);
633 hmap_insert (&pt->data, &te->node, hash);
634 }
635
636 static void
637 tabulate_general_case (struct pivot_table *pt, const struct ccase *c,
638 double weight)
639 {
640 struct freq *te;
641 size_t hash;
642 int j;
643
644 hash = 0;
645 for (j = 0; j < pt->n_vars; j++)
646 {
647 const struct variable *var = pt->vars[j];
648 hash = value_hash (case_data (c, var), var_get_width (var), hash);
649 }
650
651 HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &pt->data)
652 {
653 for (j = 0; j < pt->n_vars; j++)
654 {
655 const struct variable *var = pt->vars[j];
656 if (!value_equal (case_data (c, var), &te->values[j],
657 var_get_width (var)))
658 goto no_match;
659 }
660
661 /* Found an existing entry. */
662 te->count += weight;
663 return;
664
665 no_match: ;
666 }
667
668 /* No existing entry. Create a new one. */
669 te = xmalloc (table_entry_size (pt->n_vars));
670 te->count = weight;
671 for (j = 0; j < pt->n_vars; j++)
672 {
673 const struct variable *var = pt->vars[j];
674 value_clone (&te->values[j], case_data (c, var), var_get_width (var));
675 }
676 hmap_insert (&pt->data, &te->node, hash);
677 }
678 \f
679 /* Post-data reading calculations. */
680
681 static int compare_table_entry_vars_3way (const struct freq *a,
682 const struct freq *b,
683 const struct pivot_table *pt,
684 int idx0, int idx1);
685 static int compare_table_entry_3way (const void *ap_, const void *bp_,
686 const void *pt_);
687 static int compare_table_entry_3way_inv (const void *ap_, const void *bp_,
688 const void *pt_);
689
690 static void enum_var_values (const struct pivot_table *, int var_idx,
691 union value **valuesp, int *n_values, bool descending);
692 static void output_pivot_table (struct crosstabs_proc *,
693 struct pivot_table *);
694 static void make_pivot_table_subset (struct pivot_table *pt,
695 size_t row0, size_t row1,
696 struct pivot_table *subset);
697 static void make_summary_table (struct crosstabs_proc *);
698 static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
699
700 static void
701 postcalc (struct crosstabs_proc *proc)
702 {
703
704 /* Round hash table entries, if requested
705
706 If this causes any of the cell counts to fall to zero, delete those
707 cells. */
708 if (proc->round_cells)
709 for (struct pivot_table *pt = proc->pivots;
710 pt < &proc->pivots[proc->n_pivots]; pt++)
711 {
712 struct freq *e, *next;
713 HMAP_FOR_EACH_SAFE (e, next, struct freq, node, &pt->data)
714 {
715 e->count = round_weight (proc, e->count);
716 if (e->count == 0.0)
717 {
718 hmap_delete (&pt->data, &e->node);
719 free (e);
720 }
721 }
722 }
723
724 /* Convert hash tables into sorted arrays of entries. */
725 for (struct pivot_table *pt = proc->pivots;
726 pt < &proc->pivots[proc->n_pivots]; pt++)
727 {
728 struct freq *e;
729
730 pt->n_entries = hmap_count (&pt->data);
731 pt->entries = xnmalloc (pt->n_entries, sizeof *pt->entries);
732 size_t i = 0;
733 HMAP_FOR_EACH (e, struct freq, node, &pt->data)
734 pt->entries[i++] = e;
735 hmap_destroy (&pt->data);
736
737 sort (pt->entries, pt->n_entries, sizeof *pt->entries,
738 proc->descending ? compare_table_entry_3way_inv : compare_table_entry_3way,
739 pt);
740
741 }
742
743 make_summary_table (proc);
744
745 /* Output each pivot table. */
746 for (struct pivot_table *pt = proc->pivots;
747 pt < &proc->pivots[proc->n_pivots]; pt++)
748 {
749 if (proc->pivot || pt->n_vars == 2)
750 output_pivot_table (proc, pt);
751 else
752 {
753 size_t row0 = 0, row1 = 0;
754 while (find_crosstab (pt, &row0, &row1))
755 {
756 struct pivot_table subset;
757 make_pivot_table_subset (pt, row0, row1, &subset);
758 output_pivot_table (proc, &subset);
759 }
760 }
761 if (proc->barchart)
762 chart_item_submit
763 (barchart_create (pt->vars, pt->n_vars, _("Count"), false, pt->entries, pt->n_entries));
764 }
765
766 /* Free output and prepare for next split file. */
767 for (struct pivot_table *pt = proc->pivots;
768 pt < &proc->pivots[proc->n_pivots]; pt++)
769 {
770 pt->missing = 0.0;
771
772 /* Free the members that were allocated in this function(and the values
773 owned by the entries.
774
775 The other pointer members are either both allocated and destroyed at a
776 lower level (in output_pivot_table), or both allocated and destroyed
777 at a higher level (in crs_custom_tables and free_proc,
778 respectively). */
779 for (size_t i = 0; i < pt->n_vars; i++)
780 {
781 int width = var_get_width (pt->vars[i]);
782 if (value_needs_init (width))
783 {
784 size_t j;
785
786 for (j = 0; j < pt->n_entries; j++)
787 value_destroy (&pt->entries[j]->values[i], width);
788 }
789 }
790
791 for (size_t i = 0; i < pt->n_entries; i++)
792 free (pt->entries[i]);
793 free (pt->entries);
794 }
795 }
796
797 static void
798 make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
799 struct pivot_table *subset)
800 {
801 *subset = *pt;
802 if (pt->n_vars > 2)
803 {
804 assert (pt->n_consts == 0);
805 subset->missing = pt->missing;
806 subset->n_vars = 2;
807 subset->vars = pt->vars;
808 subset->n_consts = pt->n_vars - 2;
809 subset->const_vars = pt->vars + 2;
810 subset->const_values = &pt->entries[row0]->values[2];
811 }
812 subset->entries = &pt->entries[row0];
813 subset->n_entries = row1 - row0;
814 }
815
816 static int
817 compare_table_entry_var_3way (const struct freq *a,
818 const struct freq *b,
819 const struct pivot_table *pt,
820 int idx)
821 {
822 return value_compare_3way (&a->values[idx], &b->values[idx],
823 var_get_width (pt->vars[idx]));
824 }
825
826 static int
827 compare_table_entry_vars_3way (const struct freq *a,
828 const struct freq *b,
829 const struct pivot_table *pt,
830 int idx0, int idx1)
831 {
832 int i;
833
834 for (i = idx1 - 1; i >= idx0; i--)
835 {
836 int cmp = compare_table_entry_var_3way (a, b, pt, i);
837 if (cmp != 0)
838 return cmp;
839 }
840 return 0;
841 }
842
843 /* Compare the struct freq at *AP to the one at *BP and
844 return a strcmp()-type result. */
845 static int
846 compare_table_entry_3way (const void *ap_, const void *bp_, const void *pt_)
847 {
848 const struct freq *const *ap = ap_;
849 const struct freq *const *bp = bp_;
850 const struct freq *a = *ap;
851 const struct freq *b = *bp;
852 const struct pivot_table *pt = pt_;
853 int cmp;
854
855 cmp = compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars);
856 if (cmp != 0)
857 return cmp;
858
859 cmp = compare_table_entry_var_3way (a, b, pt, ROW_VAR);
860 if (cmp != 0)
861 return cmp;
862
863 return compare_table_entry_var_3way (a, b, pt, COL_VAR);
864 }
865
866 /* Inverted version of compare_table_entry_3way */
867 static int
868 compare_table_entry_3way_inv (const void *ap_, const void *bp_, const void *pt_)
869 {
870 return -compare_table_entry_3way (ap_, bp_, pt_);
871 }
872
873 static int
874 find_first_difference (const struct pivot_table *pt, size_t row)
875 {
876 if (row == 0)
877 return pt->n_vars - 1;
878 else
879 {
880 const struct freq *a = pt->entries[row];
881 const struct freq *b = pt->entries[row - 1];
882 int col;
883
884 for (col = pt->n_vars - 1; col >= 0; col--)
885 if (compare_table_entry_var_3way (a, b, pt, col))
886 return col;
887 NOT_REACHED ();
888 }
889 }
890
891 /* Output a table summarizing the cases processed. */
892 static void
893 make_summary_table (struct crosstabs_proc *proc)
894 {
895 struct tab_table *summary;
896 struct pivot_table *pt;
897 struct string name;
898 int i;
899
900 summary = tab_create (7, 3 + proc->n_pivots);
901 tab_set_format (summary, RC_WEIGHT, &proc->weight_format);
902 tab_title (summary, _("Summary."));
903 tab_headers (summary, 1, 0, 3, 0);
904 tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
905 tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
906 tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
907 tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
908 tab_hline (summary, TAL_1, 1, 6, 1);
909 tab_hline (summary, TAL_1, 1, 6, 2);
910 tab_vline (summary, TAL_1, 3, 1, 1);
911 tab_vline (summary, TAL_1, 5, 1, 1);
912 for (i = 0; i < 3; i++)
913 {
914 tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
915 tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
916 }
917 tab_offset (summary, 0, 3);
918
919 ds_init_empty (&name);
920 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
921 {
922 double valid;
923 double n[3];
924 size_t i;
925
926 tab_hline (summary, TAL_1, 0, 6, 0);
927
928 ds_clear (&name);
929 for (i = 0; i < pt->n_vars; i++)
930 {
931 if (i > 0)
932 ds_put_cstr (&name, " * ");
933 ds_put_cstr (&name, var_to_string (pt->vars[i]));
934 }
935 tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
936
937 valid = 0.;
938 for (i = 0; i < pt->n_entries; i++)
939 valid += pt->entries[i]->count;
940
941 n[0] = valid;
942 n[1] = pt->missing;
943 n[2] = n[0] + n[1];
944 for (i = 0; i < 3; i++)
945 {
946 tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i], NULL, RC_WEIGHT);
947 tab_text_format (summary, i * 2 + 2, 0, TAB_RIGHT, "%.1f%%",
948 n[i] / n[2] * 100.);
949 }
950
951 tab_next_row (summary);
952 }
953 ds_destroy (&name);
954
955 submit (NULL, summary);
956 }
957 \f
958 /* Output. */
959
960 static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
961 struct pivot_table *);
962 static struct tab_table *create_chisq_table (struct crosstabs_proc *proc, struct pivot_table *);
963 static struct tab_table *create_sym_table (struct crosstabs_proc *proc, struct pivot_table *);
964 static struct tab_table *create_risk_table (struct crosstabs_proc *proc, struct pivot_table *);
965 static struct tab_table *create_direct_table (struct crosstabs_proc *proc, struct pivot_table *);
966 static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
967 struct tab_table *, int first_difference);
968 static void display_crosstabulation (struct crosstabs_proc *,
969 struct pivot_table *,
970 struct tab_table *);
971 static void display_chisq (struct pivot_table *, struct tab_table *,
972 bool *showed_fisher);
973 static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
974 struct tab_table *);
975 static void display_risk (struct pivot_table *, struct tab_table *);
976 static void display_directional (struct crosstabs_proc *, struct pivot_table *,
977 struct tab_table *);
978 static void table_value_missing (struct crosstabs_proc *proc,
979 struct tab_table *table, int c, int r,
980 unsigned char opt, const union value *v,
981 const struct variable *var);
982 static void delete_missing (struct pivot_table *);
983 static void build_matrix (struct pivot_table *);
984
985 /* Output pivot table PT in the context of PROC. */
986 static void
987 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
988 {
989 struct tab_table *table = NULL; /* Crosstabulation table. */
990 struct tab_table *chisq = NULL; /* Chi-square table. */
991 bool showed_fisher = false;
992 struct tab_table *sym = NULL; /* Symmetric measures table. */
993 struct tab_table *risk = NULL; /* Risk estimate table. */
994 struct tab_table *direct = NULL; /* Directional measures table. */
995 size_t row0, row1;
996
997 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols, proc->descending);
998
999 if (pt->n_cols == 0)
1000 {
1001 struct string vars;
1002 int i;
1003
1004 ds_init_cstr (&vars, var_to_string (pt->vars[0]));
1005 for (i = 1; i < pt->n_vars; i++)
1006 ds_put_format (&vars, " * %s", var_to_string (pt->vars[i]));
1007
1008 /* TRANSLATORS: The %s here describes a crosstabulation. It takes the
1009 form "var1 * var2 * var3 * ...". */
1010 msg (SW, _("Crosstabulation %s contained no non-missing cases."),
1011 ds_cstr (&vars));
1012
1013 ds_destroy (&vars);
1014 free (pt->cols);
1015 return;
1016 }
1017
1018 if (proc->cells)
1019 table = create_crosstab_table (proc, pt);
1020 if (proc->statistics & (1u << CRS_ST_CHISQ))
1021 chisq = create_chisq_table (proc, pt);
1022 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
1023 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
1024 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
1025 | (1u << CRS_ST_KAPPA)))
1026 sym = create_sym_table (proc, pt);
1027 if (proc->statistics & (1u << CRS_ST_RISK))
1028 risk = create_risk_table (proc, pt);
1029 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
1030 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
1031 direct = create_direct_table (proc, pt);
1032
1033 row0 = row1 = 0;
1034 while (find_crosstab (pt, &row0, &row1))
1035 {
1036 struct pivot_table x;
1037 int first_difference;
1038
1039 make_pivot_table_subset (pt, row0, row1, &x);
1040
1041 /* Find all the row variable values. */
1042 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows, proc->descending);
1043
1044 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
1045 sizeof (double))))
1046 xalloc_die ();
1047 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
1048 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
1049 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
1050
1051 /* Allocate table space for the matrix. */
1052 if (table
1053 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
1054 tab_realloc (table, -1,
1055 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
1056 tab_nr (table) * pt->n_entries / x.n_entries));
1057
1058 build_matrix (&x);
1059
1060 /* Find the first variable that differs from the last subtable. */
1061 first_difference = find_first_difference (pt, row0);
1062 if (table)
1063 {
1064 display_dimensions (proc, &x, table, first_difference);
1065 display_crosstabulation (proc, &x, table);
1066 }
1067
1068 if (proc->exclude == MV_NEVER)
1069 delete_missing (&x);
1070
1071 if (chisq)
1072 {
1073 display_dimensions (proc, &x, chisq, first_difference);
1074 display_chisq (&x, chisq, &showed_fisher);
1075 }
1076 if (sym)
1077 {
1078 display_dimensions (proc, &x, sym, first_difference);
1079 display_symmetric (proc, &x, sym);
1080 }
1081 if (risk)
1082 {
1083 display_dimensions (proc, &x, risk, first_difference);
1084 display_risk (&x, risk);
1085 }
1086 if (direct)
1087 {
1088 display_dimensions (proc, &x, direct, first_difference);
1089 display_directional (proc, &x, direct);
1090 }
1091
1092 /* Free the parts of x that are not owned by pt. In
1093 particular we must not free x.cols, which is the same as
1094 pt->cols, which is freed at the end of this function. */
1095 free (x.rows);
1096
1097 free (x.mat);
1098 free (x.row_tot);
1099 free (x.col_tot);
1100 }
1101
1102 submit (NULL, table);
1103
1104 if (chisq)
1105 {
1106 if (!showed_fisher)
1107 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
1108 submit (pt, chisq);
1109 }
1110
1111 submit (pt, sym);
1112 submit (pt, risk);
1113 submit (pt, direct);
1114
1115 free (pt->cols);
1116 }
1117
1118 static void
1119 build_matrix (struct pivot_table *x)
1120 {
1121 const int col_var_width = var_get_width (x->vars[COL_VAR]);
1122 const int row_var_width = var_get_width (x->vars[ROW_VAR]);
1123 int col, row;
1124 double *mp;
1125 struct freq **p;
1126
1127 mp = x->mat;
1128 col = row = 0;
1129 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1130 {
1131 const struct freq *te = *p;
1132
1133 while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
1134 {
1135 for (; col < x->n_cols; col++)
1136 *mp++ = 0.0;
1137 col = 0;
1138 row++;
1139 }
1140
1141 while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
1142 {
1143 *mp++ = 0.0;
1144 col++;
1145 }
1146
1147 *mp++ = te->count;
1148 if (++col >= x->n_cols)
1149 {
1150 col = 0;
1151 row++;
1152 }
1153 }
1154 while (mp < &x->mat[x->n_cols * x->n_rows])
1155 *mp++ = 0.0;
1156 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1157
1158 /* Column totals, row totals, ns_rows. */
1159 mp = x->mat;
1160 for (col = 0; col < x->n_cols; col++)
1161 x->col_tot[col] = 0.0;
1162 for (row = 0; row < x->n_rows; row++)
1163 x->row_tot[row] = 0.0;
1164 x->ns_rows = 0;
1165 for (row = 0; row < x->n_rows; row++)
1166 {
1167 bool row_is_empty = true;
1168 for (col = 0; col < x->n_cols; col++)
1169 {
1170 if (*mp != 0.0)
1171 {
1172 row_is_empty = false;
1173 x->col_tot[col] += *mp;
1174 x->row_tot[row] += *mp;
1175 }
1176 mp++;
1177 }
1178 if (!row_is_empty)
1179 x->ns_rows++;
1180 }
1181 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1182
1183 /* ns_cols. */
1184 x->ns_cols = 0;
1185 for (col = 0; col < x->n_cols; col++)
1186 for (row = 0; row < x->n_rows; row++)
1187 if (x->mat[col + row * x->n_cols] != 0.0)
1188 {
1189 x->ns_cols++;
1190 break;
1191 }
1192
1193 /* Grand total. */
1194 x->total = 0.0;
1195 for (col = 0; col < x->n_cols; col++)
1196 x->total += x->col_tot[col];
1197 }
1198
1199 static struct tab_table *
1200 create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1201 {
1202 struct tuple
1203 {
1204 int value;
1205 const char *name;
1206 };
1207 static const struct tuple names[] =
1208 {
1209 {CRS_CL_COUNT, N_("count")},
1210 {CRS_CL_ROW, N_("row %")},
1211 {CRS_CL_COLUMN, N_("column %")},
1212 {CRS_CL_TOTAL, N_("total %")},
1213 {CRS_CL_EXPECTED, N_("expected")},
1214 {CRS_CL_RESIDUAL, N_("residual")},
1215 {CRS_CL_SRESIDUAL, N_("std. resid.")},
1216 {CRS_CL_ASRESIDUAL, N_("adj. resid.")},
1217 };
1218 const int n_names = sizeof names / sizeof *names;
1219 const struct tuple *t;
1220
1221 struct tab_table *table;
1222 struct string title;
1223 struct pivot_table x;
1224
1225 int i;
1226
1227 make_pivot_table_subset (pt, 0, 0, &x);
1228
1229 table = tab_create (x.n_consts + 1 + x.n_cols + 1,
1230 (x.n_entries / x.n_cols) * 3 / 2 * proc->n_cells + 10);
1231 tab_headers (table, x.n_consts + 1, 0, 2, 0);
1232 tab_set_format (table, RC_WEIGHT, &proc->weight_format);
1233
1234 /* First header line. */
1235 tab_joint_text (table, x.n_consts + 1, 0,
1236 (x.n_consts + 1) + (x.n_cols - 1), 0,
1237 TAB_CENTER | TAT_TITLE, var_to_string (x.vars[COL_VAR]));
1238
1239 tab_hline (table, TAL_1, x.n_consts + 1,
1240 x.n_consts + 2 + x.n_cols - 2, 1);
1241
1242 /* Second header line. */
1243 for (i = 2; i < x.n_consts + 2; i++)
1244 tab_joint_text (table, x.n_consts + 2 - i - 1, 0,
1245 x.n_consts + 2 - i - 1, 1,
1246 TAB_RIGHT | TAT_TITLE, var_to_string (x.vars[i]));
1247 tab_text (table, x.n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1248 var_to_string (x.vars[ROW_VAR]));
1249 for (i = 0; i < x.n_cols; i++)
1250 table_value_missing (proc, table, x.n_consts + 2 + i - 1, 1, TAB_RIGHT,
1251 &x.cols[i], x.vars[COL_VAR]);
1252 tab_text (table, x.n_consts + 2 + x.n_cols - 1, 1, TAB_CENTER, _("Total"));
1253
1254 tab_hline (table, TAL_1, 0, x.n_consts + 2 + x.n_cols - 1, 2);
1255 tab_vline (table, TAL_1, x.n_consts + 2 + x.n_cols - 1, 0, 1);
1256
1257 /* Title. */
1258 ds_init_empty (&title);
1259 for (i = 0; i < x.n_consts + 2; i++)
1260 {
1261 if (i)
1262 ds_put_cstr (&title, " * ");
1263 ds_put_cstr (&title, var_to_string (x.vars[i]));
1264 }
1265 for (i = 0; i < pt->n_consts; i++)
1266 {
1267 const struct variable *var = pt->const_vars[i];
1268 char *s;
1269
1270 ds_put_format (&title, ", %s=", var_to_string (var));
1271
1272 /* Insert the formatted value of VAR without any leading spaces. */
1273 s = data_out (&pt->const_values[i], var_get_encoding (var),
1274 var_get_print_format (var));
1275 ds_put_cstr (&title, s + strspn (s, " "));
1276 free (s);
1277 }
1278
1279 ds_put_cstr (&title, " [");
1280 i = 0;
1281 for (t = names; t < &names[n_names]; t++)
1282 if (proc->cells & (1u << t->value))
1283 {
1284 if (i++)
1285 ds_put_cstr (&title, ", ");
1286 ds_put_cstr (&title, gettext (t->name));
1287 }
1288 ds_put_cstr (&title, "].");
1289
1290 tab_title (table, "%s", ds_cstr (&title));
1291 ds_destroy (&title);
1292
1293 tab_offset (table, 0, 2);
1294 return table;
1295 }
1296
1297 static struct tab_table *
1298 create_chisq_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1299 {
1300 struct tab_table *chisq;
1301
1302 chisq = tab_create (6 + (pt->n_vars - 2),
1303 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10);
1304 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1305 tab_set_format (chisq, RC_WEIGHT, &proc->weight_format);
1306
1307 tab_title (chisq, _("Chi-square tests."));
1308
1309 tab_offset (chisq, pt->n_vars - 2, 0);
1310 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1311 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1312 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1313 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1314 _("Asymp. Sig. (2-tailed)"));
1315 tab_text_format (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1316 _("Exact Sig. (%d-tailed)"), 2);
1317 tab_text_format (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1318 _("Exact Sig. (%d-tailed)"), 1);
1319 tab_offset (chisq, 0, 1);
1320
1321 return chisq;
1322 }
1323
1324 /* Symmetric measures. */
1325 static struct tab_table *
1326 create_sym_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1327 {
1328 struct tab_table *sym;
1329
1330 sym = tab_create (6 + (pt->n_vars - 2),
1331 pt->n_entries / pt->n_cols * 7 + 10);
1332
1333 tab_set_format (sym, RC_WEIGHT, &proc->weight_format);
1334
1335 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1336 tab_title (sym, _("Symmetric measures."));
1337
1338 tab_offset (sym, pt->n_vars - 2, 0);
1339 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1340 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1341 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1342 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1343 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1344 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1345 tab_offset (sym, 0, 1);
1346
1347 return sym;
1348 }
1349
1350 /* Risk estimate. */
1351 static struct tab_table *
1352 create_risk_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1353 {
1354 struct tab_table *risk;
1355
1356 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10);
1357 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1358 tab_title (risk, _("Risk estimate."));
1359 tab_set_format (risk, RC_WEIGHT, &proc->weight_format);
1360
1361 tab_offset (risk, pt->n_vars - 2, 0);
1362 tab_joint_text_format (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE,
1363 _("95%% Confidence Interval"));
1364 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1365 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1366 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1367 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1368 tab_hline (risk, TAL_1, 2, 3, 1);
1369 tab_vline (risk, TAL_1, 2, 0, 1);
1370 tab_offset (risk, 0, 2);
1371
1372 return risk;
1373 }
1374
1375 /* Directional measures. */
1376 static struct tab_table *
1377 create_direct_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1378 {
1379 struct tab_table *direct;
1380
1381 direct = tab_create (7 + (pt->n_vars - 2),
1382 pt->n_entries / pt->n_cols * 7 + 10);
1383 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1384 tab_title (direct, _("Directional measures."));
1385 tab_set_format (direct, RC_WEIGHT, &proc->weight_format);
1386
1387 tab_offset (direct, pt->n_vars - 2, 0);
1388 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1389 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1390 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1391 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1392 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1393 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1394 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1395 tab_offset (direct, 0, 1);
1396
1397 return direct;
1398 }
1399
1400
1401 /* Delete missing rows and columns for statistical analysis when
1402 /MISSING=REPORT. */
1403 static void
1404 delete_missing (struct pivot_table *pt)
1405 {
1406 int r, c;
1407
1408 for (r = 0; r < pt->n_rows; r++)
1409 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1410 {
1411 for (c = 0; c < pt->n_cols; c++)
1412 pt->mat[c + r * pt->n_cols] = 0.;
1413 pt->ns_rows--;
1414 }
1415
1416
1417 for (c = 0; c < pt->n_cols; c++)
1418 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1419 {
1420 for (r = 0; r < pt->n_rows; r++)
1421 pt->mat[c + r * pt->n_cols] = 0.;
1422 pt->ns_cols--;
1423 }
1424 }
1425
1426 /* Prepare table T for submission, and submit it. */
1427 static void
1428 submit (struct pivot_table *pt, struct tab_table *t)
1429 {
1430 int i;
1431
1432 if (t == NULL)
1433 return;
1434
1435 tab_resize (t, -1, 0);
1436 if (tab_nr (t) == tab_t (t))
1437 {
1438 table_unref (&t->table);
1439 return;
1440 }
1441 tab_offset (t, 0, 0);
1442 if (pt != NULL)
1443 for (i = 2; i < pt->n_vars; i++)
1444 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1445 var_to_string (pt->vars[i]));
1446 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1447 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1448 tab_nr (t) - 1);
1449 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1450 tab_nr (t) - 1);
1451 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1452
1453 tab_submit (t);
1454 }
1455
1456 static bool
1457 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1458 {
1459 size_t row0 = *row1p;
1460 size_t row1;
1461
1462 if (row0 >= pt->n_entries)
1463 return false;
1464
1465 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1466 {
1467 struct freq *a = pt->entries[row0];
1468 struct freq *b = pt->entries[row1];
1469 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1470 break;
1471 }
1472 *row0p = row0;
1473 *row1p = row1;
1474 return true;
1475 }
1476
1477 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1478 result. WIDTH_ points to an int which is either 0 for a
1479 numeric value or a string width for a string value. */
1480 static int
1481 compare_value_3way (const void *a_, const void *b_, const void *width_)
1482 {
1483 const union value *a = a_;
1484 const union value *b = b_;
1485 const int *width = width_;
1486
1487 return value_compare_3way (a, b, *width);
1488 }
1489
1490 /* Inverted version of the above */
1491 static int
1492 compare_value_3way_inv (const void *a_, const void *b_, const void *width_)
1493 {
1494 return -compare_value_3way (a_, b_, width_);
1495 }
1496
1497
1498 /* Given an array of ENTRY_CNT table_entry structures starting at
1499 ENTRIES, creates a sorted list of the values that the variable
1500 with index VAR_IDX takes on. The values are returned as a
1501 malloc()'d array stored in *VALUES, with the number of values
1502 stored in *VALUE_CNT.
1503
1504 The caller must eventually free *VALUES, but each pointer in *VALUES points
1505 to existing data not owned by *VALUES itself. */
1506 static void
1507 enum_var_values (const struct pivot_table *pt, int var_idx,
1508 union value **valuesp, int *n_values, bool descending)
1509 {
1510 const struct variable *var = pt->vars[var_idx];
1511 const struct var_range *range = get_var_range (pt->proc, var);
1512 union value *values;
1513 size_t i;
1514
1515 if (range)
1516 {
1517 values = *valuesp = xnmalloc (range->count, sizeof *values);
1518 *n_values = range->count;
1519 for (i = 0; i < range->count; i++)
1520 values[i].f = range->min + i;
1521 }
1522 else
1523 {
1524 int width = var_get_width (var);
1525 struct hmapx_node *node;
1526 const union value *iter;
1527 struct hmapx set;
1528
1529 hmapx_init (&set);
1530 for (i = 0; i < pt->n_entries; i++)
1531 {
1532 const struct freq *te = pt->entries[i];
1533 const union value *value = &te->values[var_idx];
1534 size_t hash = value_hash (value, width, 0);
1535
1536 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1537 if (value_equal (iter, value, width))
1538 goto next_entry;
1539
1540 hmapx_insert (&set, (union value *) value, hash);
1541
1542 next_entry: ;
1543 }
1544
1545 *n_values = hmapx_count (&set);
1546 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1547 i = 0;
1548 HMAPX_FOR_EACH (iter, node, &set)
1549 values[i++] = *iter;
1550 hmapx_destroy (&set);
1551
1552 sort (values, *n_values, sizeof *values,
1553 descending ? compare_value_3way_inv : compare_value_3way,
1554 &width);
1555 }
1556 }
1557
1558 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1559 from V, displayed with print format spec from variable VAR. When
1560 in REPORT missing-value mode, missing values have an M appended. */
1561 static void
1562 table_value_missing (struct crosstabs_proc *proc,
1563 struct tab_table *table, int c, int r, unsigned char opt,
1564 const union value *v, const struct variable *var)
1565 {
1566 const char *label = var_lookup_value_label (var, v);
1567 if (label != NULL)
1568 tab_text (table, c, r, TAB_LEFT, label);
1569 else
1570 {
1571 const struct fmt_spec *print = var_get_print_format (var);
1572 if (proc->exclude == MV_NEVER && var_is_value_missing (var, v, MV_USER))
1573 {
1574 char *s = data_out (v, dict_get_encoding (proc->dict), print);
1575 tab_text_format (table, c, r, opt, "%sM", s + strspn (s, " "));
1576 free (s);
1577 }
1578 else
1579 tab_value (table, c, r, opt, v, var, print);
1580 }
1581 }
1582
1583 /* Draws a line across TABLE at the current row to indicate the most
1584 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1585 that changed, and puts the values that changed into the table. TB
1586 and PT must be the corresponding table_entry and crosstab,
1587 respectively. */
1588 static void
1589 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1590 struct tab_table *table, int first_difference)
1591 {
1592 tab_hline (table, TAL_1, pt->n_consts + pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1593
1594 for (; first_difference >= 2; first_difference--)
1595 table_value_missing (proc, table, pt->n_consts + pt->n_vars - first_difference - 1, 0,
1596 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1597 pt->vars[first_difference]);
1598 }
1599
1600 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1601 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1602 additionally suffixed with a letter `M'. */
1603 static void
1604 format_cell_entry (struct tab_table *table, int c, int r, double value,
1605 char suffix, bool mark_missing, const struct dictionary *dict)
1606 {
1607 union value v;
1608 char suffixes[3];
1609 int suffix_len;
1610 char *s;
1611
1612 v.f = value;
1613 s = data_out (&v, dict_get_encoding (dict), settings_get_format ());
1614
1615 suffix_len = 0;
1616 if (suffix != 0)
1617 suffixes[suffix_len++] = suffix;
1618 if (mark_missing)
1619 suffixes[suffix_len++] = 'M';
1620 suffixes[suffix_len] = '\0';
1621
1622 tab_text_format (table, c, r, TAB_RIGHT, "%s%s",
1623 s + strspn (s, " "), suffixes);
1624
1625 free (s);
1626 }
1627
1628 /* Displays the crosstabulation table. */
1629 static void
1630 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1631 struct tab_table *table)
1632 {
1633 int last_row;
1634 int r, c, i;
1635 double *mp;
1636
1637 for (r = 0; r < pt->n_rows; r++)
1638 table_value_missing (proc, table, pt->n_consts + pt->n_vars - 2,
1639 r * proc->n_cells, TAB_RIGHT, &pt->rows[r],
1640 pt->vars[ROW_VAR]);
1641
1642 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1643 TAB_LEFT, _("Total"));
1644
1645 /* Put in the actual cells. */
1646 mp = pt->mat;
1647 tab_offset (table, pt->n_consts + pt->n_vars - 1, -1);
1648 for (r = 0; r < pt->n_rows; r++)
1649 {
1650 if (proc->n_cells > 1)
1651 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1652 for (c = 0; c < pt->n_cols; c++)
1653 {
1654 bool mark_missing = false;
1655 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1656 if (proc->exclude == MV_NEVER
1657 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1658 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1659 MV_USER)))
1660 mark_missing = true;
1661 for (i = 0; i < proc->n_cells; i++)
1662 {
1663 double v;
1664 int suffix = 0;
1665
1666 switch (proc->a_cells[i])
1667 {
1668 case CRS_CL_COUNT:
1669 v = *mp;
1670 break;
1671 case CRS_CL_ROW:
1672 v = *mp / pt->row_tot[r] * 100.;
1673 suffix = '%';
1674 break;
1675 case CRS_CL_COLUMN:
1676 v = *mp / pt->col_tot[c] * 100.;
1677 suffix = '%';
1678 break;
1679 case CRS_CL_TOTAL:
1680 v = *mp / pt->total * 100.;
1681 suffix = '%';
1682 break;
1683 case CRS_CL_EXPECTED:
1684 v = expected_value;
1685 break;
1686 case CRS_CL_RESIDUAL:
1687 v = *mp - expected_value;
1688 break;
1689 case CRS_CL_SRESIDUAL:
1690 v = (*mp - expected_value) / sqrt (expected_value);
1691 break;
1692 case CRS_CL_ASRESIDUAL:
1693 v = ((*mp - expected_value)
1694 / sqrt (expected_value
1695 * (1. - pt->row_tot[r] / pt->total)
1696 * (1. - pt->col_tot[c] / pt->total)));
1697 break;
1698 default:
1699 NOT_REACHED ();
1700 }
1701 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1702 }
1703
1704 mp++;
1705 }
1706
1707 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1708 }
1709
1710 /* Row totals. */
1711 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1712 for (r = 0; r < pt->n_rows; r++)
1713 {
1714 bool mark_missing = false;
1715
1716 if (proc->exclude == MV_NEVER
1717 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1718 mark_missing = true;
1719
1720 for (i = 0; i < proc->n_cells; i++)
1721 {
1722 char suffix = 0;
1723 double v;
1724
1725 switch (proc->a_cells[i])
1726 {
1727 case CRS_CL_COUNT:
1728 v = pt->row_tot[r];
1729 break;
1730 case CRS_CL_ROW:
1731 v = 100.0;
1732 suffix = '%';
1733 break;
1734 case CRS_CL_COLUMN:
1735 v = pt->row_tot[r] / pt->total * 100.;
1736 suffix = '%';
1737 break;
1738 case CRS_CL_TOTAL:
1739 v = pt->row_tot[r] / pt->total * 100.;
1740 suffix = '%';
1741 break;
1742 case CRS_CL_EXPECTED:
1743 case CRS_CL_RESIDUAL:
1744 case CRS_CL_SRESIDUAL:
1745 case CRS_CL_ASRESIDUAL:
1746 v = 0.;
1747 break;
1748 default:
1749 NOT_REACHED ();
1750 }
1751
1752 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing, proc->dict);
1753 tab_next_row (table);
1754 }
1755 }
1756
1757 /* Column totals, grand total. */
1758 last_row = 0;
1759 if (proc->n_cells > 1)
1760 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1761 for (c = 0; c <= pt->n_cols; c++)
1762 {
1763 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1764 bool mark_missing = false;
1765 int i;
1766
1767 if (proc->exclude == MV_NEVER && c < pt->n_cols
1768 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1769 mark_missing = true;
1770
1771 for (i = 0; i < proc->n_cells; i++)
1772 {
1773 char suffix = 0;
1774 double v;
1775
1776 switch (proc->a_cells[i])
1777 {
1778 case CRS_CL_COUNT:
1779 v = ct;
1780 break;
1781 case CRS_CL_ROW:
1782 v = ct / pt->total * 100.;
1783 suffix = '%';
1784 break;
1785 case CRS_CL_COLUMN:
1786 v = 100.;
1787 suffix = '%';
1788 break;
1789 case CRS_CL_TOTAL:
1790 v = ct / pt->total * 100.;
1791 suffix = '%';
1792 break;
1793 case CRS_CL_EXPECTED:
1794 case CRS_CL_RESIDUAL:
1795 case CRS_CL_SRESIDUAL:
1796 case CRS_CL_ASRESIDUAL:
1797 continue;
1798 default:
1799 NOT_REACHED ();
1800 }
1801
1802 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1803 }
1804 last_row = i;
1805 }
1806
1807 tab_offset (table, -1, tab_row (table) + last_row);
1808 tab_offset (table, 0, -1);
1809 }
1810
1811 static void calc_r (struct pivot_table *,
1812 double *PT, double *Y, double *, double *, double *);
1813 static void calc_chisq (struct pivot_table *,
1814 double[N_CHISQ], int[N_CHISQ], double *, double *);
1815
1816 /* Display chi-square statistics. */
1817 static void
1818 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1819 bool *showed_fisher)
1820 {
1821 static const char *chisq_stats[N_CHISQ] =
1822 {
1823 N_("Pearson Chi-Square"),
1824 N_("Likelihood Ratio"),
1825 N_("Fisher's Exact Test"),
1826 N_("Continuity Correction"),
1827 N_("Linear-by-Linear Association"),
1828 };
1829 double chisq_v[N_CHISQ];
1830 double fisher1, fisher2;
1831 int df[N_CHISQ];
1832
1833 int i;
1834
1835 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1836
1837 tab_offset (chisq, pt->n_consts + pt->n_vars - 2, -1);
1838
1839 for (i = 0; i < N_CHISQ; i++)
1840 {
1841 if ((i != 2 && chisq_v[i] == SYSMIS)
1842 || (i == 2 && fisher1 == SYSMIS))
1843 continue;
1844
1845 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1846 if (i != 2)
1847 {
1848 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL, RC_OTHER);
1849 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], NULL, RC_WEIGHT);
1850 tab_double (chisq, 3, 0, TAB_RIGHT,
1851 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL, RC_PVALUE);
1852 }
1853 else
1854 {
1855 *showed_fisher = true;
1856 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL, RC_PVALUE);
1857 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL, RC_PVALUE);
1858 }
1859 tab_next_row (chisq);
1860 }
1861
1862 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1863 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, NULL, RC_WEIGHT);
1864 tab_next_row (chisq);
1865
1866 tab_offset (chisq, 0, -1);
1867 }
1868
1869 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1870 double[N_SYMMETRIC], double[N_SYMMETRIC],
1871 double[N_SYMMETRIC],
1872 double[3], double[3], double[3]);
1873
1874 /* Display symmetric measures. */
1875 static void
1876 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1877 struct tab_table *sym)
1878 {
1879 static const char *categories[] =
1880 {
1881 N_("Nominal by Nominal"),
1882 N_("Ordinal by Ordinal"),
1883 N_("Interval by Interval"),
1884 N_("Measure of Agreement"),
1885 };
1886
1887 static const char *stats[N_SYMMETRIC] =
1888 {
1889 N_("Phi"),
1890 N_("Cramer's V"),
1891 N_("Contingency Coefficient"),
1892 N_("Kendall's tau-b"),
1893 N_("Kendall's tau-c"),
1894 N_("Gamma"),
1895 N_("Spearman Correlation"),
1896 N_("Pearson's R"),
1897 N_("Kappa"),
1898 };
1899
1900 static const int stats_categories[N_SYMMETRIC] =
1901 {
1902 0, 0, 0, 1, 1, 1, 1, 2, 3,
1903 };
1904
1905 int last_cat = -1;
1906 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1907 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1908 int i;
1909
1910 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1911 somers_d_v, somers_d_ase, somers_d_t))
1912 return;
1913
1914 tab_offset (sym, pt->n_consts + pt->n_vars - 2, -1);
1915
1916 for (i = 0; i < N_SYMMETRIC; i++)
1917 {
1918 if (sym_v[i] == SYSMIS)
1919 continue;
1920
1921 if (stats_categories[i] != last_cat)
1922 {
1923 last_cat = stats_categories[i];
1924 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1925 }
1926
1927 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1928 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL, RC_OTHER);
1929 if (sym_ase[i] != SYSMIS)
1930 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL, RC_OTHER);
1931 if (sym_t[i] != SYSMIS)
1932 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL, RC_OTHER);
1933 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL, RC_PVALUE);*/
1934 tab_next_row (sym);
1935 }
1936
1937 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1938 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, NULL, RC_WEIGHT);
1939 tab_next_row (sym);
1940
1941 tab_offset (sym, 0, -1);
1942 }
1943
1944 static int calc_risk (struct pivot_table *,
1945 double[], double[], double[], union value *);
1946
1947 /* Display risk estimate. */
1948 static void
1949 display_risk (struct pivot_table *pt, struct tab_table *risk)
1950 {
1951 char buf[256];
1952 double risk_v[3], lower[3], upper[3];
1953 union value c[2];
1954 int i;
1955
1956 if (!calc_risk (pt, risk_v, upper, lower, c))
1957 return;
1958
1959 tab_offset (risk, pt->n_consts + pt->n_vars - 2, -1);
1960
1961 for (i = 0; i < 3; i++)
1962 {
1963 const struct variable *cv = pt->vars[COL_VAR];
1964 const struct variable *rv = pt->vars[ROW_VAR];
1965 int cvw = var_get_width (cv);
1966 int rvw = var_get_width (rv);
1967
1968 if (risk_v[i] == SYSMIS)
1969 continue;
1970
1971 switch (i)
1972 {
1973 case 0:
1974 if (var_is_numeric (cv))
1975 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1976 var_to_string (cv), c[0].f, c[1].f);
1977 else
1978 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1979 var_to_string (cv),
1980 cvw, value_str (&c[0], cvw),
1981 cvw, value_str (&c[1], cvw));
1982 break;
1983 case 1:
1984 case 2:
1985 if (var_is_numeric (rv))
1986 sprintf (buf, _("For cohort %s = %.*g"),
1987 var_to_string (rv), DBL_DIG + 1, pt->rows[i - 1].f);
1988 else
1989 sprintf (buf, _("For cohort %s = %.*s"),
1990 var_to_string (rv),
1991 rvw, value_str (&pt->rows[i - 1], rvw));
1992 break;
1993 }
1994
1995 tab_text (risk, 0, 0, TAB_LEFT, buf);
1996 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL, RC_OTHER);
1997 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL, RC_OTHER);
1998 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL, RC_OTHER);
1999 tab_next_row (risk);
2000 }
2001
2002 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
2003 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, NULL, RC_WEIGHT);
2004 tab_next_row (risk);
2005
2006 tab_offset (risk, 0, -1);
2007 }
2008
2009 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
2010 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
2011 double[N_DIRECTIONAL], double[N_DIRECTIONAL]);
2012
2013 /* Display directional measures. */
2014 static void
2015 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2016 struct tab_table *direct)
2017 {
2018 static const char *categories[] =
2019 {
2020 N_("Nominal by Nominal"),
2021 N_("Ordinal by Ordinal"),
2022 N_("Nominal by Interval"),
2023 };
2024
2025 static const char *stats[] =
2026 {
2027 N_("Lambda"),
2028 N_("Goodman and Kruskal tau"),
2029 N_("Uncertainty Coefficient"),
2030 N_("Somers' d"),
2031 N_("Eta"),
2032 };
2033
2034 static const char *types[] =
2035 {
2036 N_("Symmetric"),
2037 N_("%s Dependent"),
2038 N_("%s Dependent"),
2039 };
2040
2041 static const int stats_categories[N_DIRECTIONAL] =
2042 {
2043 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
2044 };
2045
2046 static const int stats_stats[N_DIRECTIONAL] =
2047 {
2048 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
2049 };
2050
2051 static const int stats_types[N_DIRECTIONAL] =
2052 {
2053 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
2054 };
2055
2056 static const int *stats_lookup[] =
2057 {
2058 stats_categories,
2059 stats_stats,
2060 stats_types,
2061 };
2062
2063 static const char **stats_names[] =
2064 {
2065 categories,
2066 stats,
2067 types,
2068 };
2069
2070 int last[3] =
2071 {
2072 -1, -1, -1,
2073 };
2074
2075 double direct_v[N_DIRECTIONAL];
2076 double direct_ase[N_DIRECTIONAL];
2077 double direct_t[N_DIRECTIONAL];
2078 double sig[N_DIRECTIONAL];
2079
2080 int i;
2081
2082 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t, sig))
2083 return;
2084
2085 tab_offset (direct, pt->n_consts + pt->n_vars - 2, -1);
2086
2087 for (i = 0; i < N_DIRECTIONAL; i++)
2088 {
2089 if (direct_v[i] == SYSMIS)
2090 continue;
2091
2092 {
2093 int j;
2094
2095 for (j = 0; j < 3; j++)
2096 if (last[j] != stats_lookup[j][i])
2097 {
2098 if (j < 2)
2099 tab_hline (direct, TAL_1, j, 6, 0);
2100
2101 for (; j < 3; j++)
2102 {
2103 const char *string;
2104 int k = last[j] = stats_lookup[j][i];
2105
2106 if (k == 0)
2107 string = NULL;
2108 else if (k == 1)
2109 string = var_to_string (pt->vars[0]);
2110 else
2111 string = var_to_string (pt->vars[1]);
2112
2113 tab_text_format (direct, j, 0, TAB_LEFT,
2114 gettext (stats_names[j][k]), string);
2115 }
2116 }
2117 }
2118
2119 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL, RC_OTHER);
2120 if (direct_ase[i] != SYSMIS)
2121 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL, RC_OTHER);
2122 if (direct_t[i] != SYSMIS)
2123 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL, RC_OTHER);
2124 tab_double (direct, 6, 0, TAB_RIGHT, sig[i], NULL, RC_PVALUE);
2125 tab_next_row (direct);
2126 }
2127
2128 tab_offset (direct, 0, -1);
2129 }
2130 \f
2131 /* Statistical calculations. */
2132
2133 /* Returns the value of the logarithm of gamma (factorial) function for an integer
2134 argument PT. */
2135 static double
2136 log_gamma_int (double pt)
2137 {
2138 double r = 0;
2139 int i;
2140
2141 for (i = 2; i < pt; i++)
2142 r += log(i);
2143
2144 return r;
2145 }
2146
2147 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2148 Appendix 5. */
2149 static inline double
2150 Pr (int a, int b, int c, int d)
2151 {
2152 return exp (log_gamma_int (a + b + 1.) - log_gamma_int (a + 1.)
2153 + log_gamma_int (c + d + 1.) - log_gamma_int (b + 1.)
2154 + log_gamma_int (a + c + 1.) - log_gamma_int (c + 1.)
2155 + log_gamma_int (b + d + 1.) - log_gamma_int (d + 1.)
2156 - log_gamma_int (a + b + c + d + 1.));
2157 }
2158
2159 /* Swap the contents of A and B. */
2160 static inline void
2161 swap (int *a, int *b)
2162 {
2163 int t = *a;
2164 *a = *b;
2165 *b = t;
2166 }
2167
2168 /* Calculate significance for Fisher's exact test as specified in
2169 _SPSS Statistical Algorithms_, Appendix 5. */
2170 static void
2171 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2172 {
2173 int pt;
2174 double pn1;
2175
2176 if (MIN (c, d) < MIN (a, b))
2177 swap (&a, &c), swap (&b, &d);
2178 if (MIN (b, d) < MIN (a, c))
2179 swap (&a, &b), swap (&c, &d);
2180 if (b * c < a * d)
2181 {
2182 if (b < c)
2183 swap (&a, &b), swap (&c, &d);
2184 else
2185 swap (&a, &c), swap (&b, &d);
2186 }
2187
2188 pn1 = Pr (a, b, c, d);
2189 *fisher1 = pn1;
2190 for (pt = 1; pt <= a; pt++)
2191 {
2192 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2193 }
2194
2195 *fisher2 = *fisher1;
2196
2197 for (pt = 1; pt <= b; pt++)
2198 {
2199 double p = Pr (a + pt, b - pt, c - pt, d + pt);
2200 if (p < pn1)
2201 *fisher2 += p;
2202 }
2203 }
2204
2205 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2206 columns with values COLS and N_ROWS rows with values ROWS. Values
2207 in the matrix sum to pt->total. */
2208 static void
2209 calc_chisq (struct pivot_table *pt,
2210 double chisq[N_CHISQ], int df[N_CHISQ],
2211 double *fisher1, double *fisher2)
2212 {
2213 int r, c;
2214
2215 chisq[0] = chisq[1] = 0.;
2216 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2217 *fisher1 = *fisher2 = SYSMIS;
2218
2219 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2220
2221 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2222 {
2223 chisq[0] = chisq[1] = SYSMIS;
2224 return;
2225 }
2226
2227 for (r = 0; r < pt->n_rows; r++)
2228 for (c = 0; c < pt->n_cols; c++)
2229 {
2230 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2231 const double freq = pt->mat[pt->n_cols * r + c];
2232 const double residual = freq - expected;
2233
2234 chisq[0] += residual * residual / expected;
2235 if (freq)
2236 chisq[1] += freq * log (expected / freq);
2237 }
2238
2239 if (chisq[0] == 0.)
2240 chisq[0] = SYSMIS;
2241
2242 if (chisq[1] != 0.)
2243 chisq[1] *= -2.;
2244 else
2245 chisq[1] = SYSMIS;
2246
2247 /* Calculate Yates and Fisher exact test. */
2248 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2249 {
2250 double f11, f12, f21, f22;
2251
2252 {
2253 int nz_cols[2];
2254 int i, j;
2255
2256 for (i = j = 0; i < pt->n_cols; i++)
2257 if (pt->col_tot[i] != 0.)
2258 {
2259 nz_cols[j++] = i;
2260 if (j == 2)
2261 break;
2262 }
2263
2264 assert (j == 2);
2265
2266 f11 = pt->mat[nz_cols[0]];
2267 f12 = pt->mat[nz_cols[1]];
2268 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2269 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2270 }
2271
2272 /* Yates. */
2273 {
2274 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2275
2276 if (pt_ > 0.)
2277 chisq[3] = (pt->total * pow2 (pt_)
2278 / (f11 + f12) / (f21 + f22)
2279 / (f11 + f21) / (f12 + f22));
2280 else
2281 chisq[3] = 0.;
2282
2283 df[3] = 1.;
2284 }
2285
2286 /* Fisher. */
2287 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2288 }
2289
2290 /* Calculate Mantel-Haenszel. */
2291 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2292 {
2293 double r, ase_0, ase_1;
2294 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2295
2296 chisq[4] = (pt->total - 1.) * r * r;
2297 df[4] = 1;
2298 }
2299 }
2300
2301 /* Calculate the value of Pearson's r. r is stored into R, its T value into
2302 T, and standard error into ERROR. The row and column values must be
2303 passed in PT and Y. */
2304 static void
2305 calc_r (struct pivot_table *pt,
2306 double *PT, double *Y, double *r, double *t, double *error)
2307 {
2308 double SX, SY, S, T;
2309 double Xbar, Ybar;
2310 double sum_XYf, sum_X2Y2f;
2311 double sum_Xr, sum_X2r;
2312 double sum_Yc, sum_Y2c;
2313 int i, j;
2314
2315 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2316 for (j = 0; j < pt->n_cols; j++)
2317 {
2318 double fij = pt->mat[j + i * pt->n_cols];
2319 double product = PT[i] * Y[j];
2320 double temp = fij * product;
2321 sum_XYf += temp;
2322 sum_X2Y2f += temp * product;
2323 }
2324
2325 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2326 {
2327 sum_Xr += PT[i] * pt->row_tot[i];
2328 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2329 }
2330 Xbar = sum_Xr / pt->total;
2331
2332 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2333 {
2334 sum_Yc += Y[i] * pt->col_tot[i];
2335 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2336 }
2337 Ybar = sum_Yc / pt->total;
2338
2339 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2340 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2341 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2342 T = sqrt (SX * SY);
2343 *r = S / T;
2344 *t = *r / sqrt (1 - pow2 (*r)) * sqrt (pt->total - 2);
2345
2346 {
2347 double s, c, y, t;
2348
2349 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2350 for (j = 0; j < pt->n_cols; j++)
2351 {
2352 double Xresid, Yresid;
2353 double temp;
2354
2355 Xresid = PT[i] - Xbar;
2356 Yresid = Y[j] - Ybar;
2357 temp = (T * Xresid * Yresid
2358 - ((S / (2. * T))
2359 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2360 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2361 t = s + y;
2362 c = (t - s) - y;
2363 s = t;
2364 }
2365 *error = sqrt (s) / (T * T);
2366 }
2367 }
2368
2369 /* Calculate symmetric statistics and their asymptotic standard
2370 errors. Returns 0 if none could be calculated. */
2371 static int
2372 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2373 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2374 double t[N_SYMMETRIC],
2375 double somers_d_v[3], double somers_d_ase[3],
2376 double somers_d_t[3])
2377 {
2378 int q, i;
2379
2380 q = MIN (pt->ns_rows, pt->ns_cols);
2381 if (q <= 1)
2382 return 0;
2383
2384 for (i = 0; i < N_SYMMETRIC; i++)
2385 v[i] = ase[i] = t[i] = SYSMIS;
2386
2387 /* Phi, Cramer's V, contingency coefficient. */
2388 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2389 {
2390 double Xp = 0.; /* Pearson chi-square. */
2391 int r, c;
2392
2393 for (r = 0; r < pt->n_rows; r++)
2394 for (c = 0; c < pt->n_cols; c++)
2395 {
2396 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2397 const double freq = pt->mat[pt->n_cols * r + c];
2398 const double residual = freq - expected;
2399
2400 Xp += residual * residual / expected;
2401 }
2402
2403 if (proc->statistics & (1u << CRS_ST_PHI))
2404 {
2405 v[0] = sqrt (Xp / pt->total);
2406 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2407 }
2408 if (proc->statistics & (1u << CRS_ST_CC))
2409 v[2] = sqrt (Xp / (Xp + pt->total));
2410 }
2411
2412 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2413 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2414 {
2415 double *cum;
2416 double Dr, Dc;
2417 double P, Q;
2418 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2419 double btau_var;
2420 int r, c;
2421
2422 Dr = Dc = pow2 (pt->total);
2423 for (r = 0; r < pt->n_rows; r++)
2424 Dr -= pow2 (pt->row_tot[r]);
2425 for (c = 0; c < pt->n_cols; c++)
2426 Dc -= pow2 (pt->col_tot[c]);
2427
2428 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2429 for (c = 0; c < pt->n_cols; c++)
2430 {
2431 double ct = 0.;
2432
2433 for (r = 0; r < pt->n_rows; r++)
2434 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2435 }
2436
2437 /* P and Q. */
2438 {
2439 int i, j;
2440 double Cij, Dij;
2441
2442 P = Q = 0.;
2443 for (i = 0; i < pt->n_rows; i++)
2444 {
2445 Cij = Dij = 0.;
2446
2447 for (j = 1; j < pt->n_cols; j++)
2448 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2449
2450 if (i > 0)
2451 for (j = 1; j < pt->n_cols; j++)
2452 Dij += cum[j + (i - 1) * pt->n_cols];
2453
2454 for (j = 0;;)
2455 {
2456 double fij = pt->mat[j + i * pt->n_cols];
2457 P += fij * Cij;
2458 Q += fij * Dij;
2459
2460 if (++j == pt->n_cols)
2461 break;
2462 assert (j < pt->n_cols);
2463
2464 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2465 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2466
2467 if (i > 0)
2468 {
2469 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2470 Dij -= cum[j + (i - 1) * pt->n_cols];
2471 }
2472 }
2473 }
2474 }
2475
2476 if (proc->statistics & (1u << CRS_ST_BTAU))
2477 v[3] = (P - Q) / sqrt (Dr * Dc);
2478 if (proc->statistics & (1u << CRS_ST_CTAU))
2479 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2480 if (proc->statistics & (1u << CRS_ST_GAMMA))
2481 v[5] = (P - Q) / (P + Q);
2482
2483 /* ASE for tau-b, tau-c, gamma. Calculations could be
2484 eliminated here, at expense of memory. */
2485 {
2486 int i, j;
2487 double Cij, Dij;
2488
2489 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2490 for (i = 0; i < pt->n_rows; i++)
2491 {
2492 Cij = Dij = 0.;
2493
2494 for (j = 1; j < pt->n_cols; j++)
2495 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2496
2497 if (i > 0)
2498 for (j = 1; j < pt->n_cols; j++)
2499 Dij += cum[j + (i - 1) * pt->n_cols];
2500
2501 for (j = 0;;)
2502 {
2503 double fij = pt->mat[j + i * pt->n_cols];
2504
2505 if (proc->statistics & (1u << CRS_ST_BTAU))
2506 {
2507 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2508 + v[3] * (pt->row_tot[i] * Dc
2509 + pt->col_tot[j] * Dr));
2510 btau_cum += fij * temp * temp;
2511 }
2512
2513 {
2514 const double temp = Cij - Dij;
2515 ctau_cum += fij * temp * temp;
2516 }
2517
2518 if (proc->statistics & (1u << CRS_ST_GAMMA))
2519 {
2520 const double temp = Q * Cij - P * Dij;
2521 gamma_cum += fij * temp * temp;
2522 }
2523
2524 if (proc->statistics & (1u << CRS_ST_D))
2525 {
2526 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2527 - (P - Q) * (pt->total - pt->row_tot[i]));
2528 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2529 - (Q - P) * (pt->total - pt->col_tot[j]));
2530 }
2531
2532 if (++j == pt->n_cols)
2533 break;
2534 assert (j < pt->n_cols);
2535
2536 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2537 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2538
2539 if (i > 0)
2540 {
2541 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2542 Dij -= cum[j + (i - 1) * pt->n_cols];
2543 }
2544 }
2545 }
2546 }
2547
2548 btau_var = ((btau_cum
2549 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2550 / pow2 (Dr * Dc));
2551 if (proc->statistics & (1u << CRS_ST_BTAU))
2552 {
2553 ase[3] = sqrt (btau_var);
2554 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2555 / (Dr * Dc)));
2556 }
2557 if (proc->statistics & (1u << CRS_ST_CTAU))
2558 {
2559 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2560 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2561 t[4] = v[4] / ase[4];
2562 }
2563 if (proc->statistics & (1u << CRS_ST_GAMMA))
2564 {
2565 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2566 t[5] = v[5] / (2. / (P + Q)
2567 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2568 }
2569 if (proc->statistics & (1u << CRS_ST_D))
2570 {
2571 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2572 somers_d_ase[0] = SYSMIS;
2573 somers_d_t[0] = (somers_d_v[0]
2574 / (4 / (Dc + Dr)
2575 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2576 somers_d_v[1] = (P - Q) / Dc;
2577 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2578 somers_d_t[1] = (somers_d_v[1]
2579 / (2. / Dc
2580 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2581 somers_d_v[2] = (P - Q) / Dr;
2582 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2583 somers_d_t[2] = (somers_d_v[2]
2584 / (2. / Dr
2585 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2586 }
2587
2588 free (cum);
2589 }
2590
2591 /* Spearman correlation, Pearson's r. */
2592 if (proc->statistics & (1u << CRS_ST_CORR))
2593 {
2594 double *R = xmalloc (sizeof *R * pt->n_rows);
2595 double *C = xmalloc (sizeof *C * pt->n_cols);
2596
2597 {
2598 double y, t, c = 0., s = 0.;
2599 int i = 0;
2600
2601 for (;;)
2602 {
2603 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2604 y = pt->row_tot[i] - c;
2605 t = s + y;
2606 c = (t - s) - y;
2607 s = t;
2608 if (++i == pt->n_rows)
2609 break;
2610 assert (i < pt->n_rows);
2611 }
2612 }
2613
2614 {
2615 double y, t, c = 0., s = 0.;
2616 int j = 0;
2617
2618 for (;;)
2619 {
2620 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2621 y = pt->col_tot[j] - c;
2622 t = s + y;
2623 c = (t - s) - y;
2624 s = t;
2625 if (++j == pt->n_cols)
2626 break;
2627 assert (j < pt->n_cols);
2628 }
2629 }
2630
2631 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2632
2633 free (R);
2634 free (C);
2635
2636 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2637 }
2638
2639 /* Cohen's kappa. */
2640 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2641 {
2642 double ase_under_h0;
2643 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2644 int i, j;
2645
2646 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2647 i < pt->ns_rows; i++, j++)
2648 {
2649 double prod, sum;
2650
2651 while (pt->col_tot[j] == 0.)
2652 j++;
2653
2654 prod = pt->row_tot[i] * pt->col_tot[j];
2655 sum = pt->row_tot[i] + pt->col_tot[j];
2656
2657 sum_fii += pt->mat[j + i * pt->n_cols];
2658 sum_rici += prod;
2659 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2660 sum_riciri_ci += prod * sum;
2661 }
2662 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2663 for (j = 0; j < pt->ns_cols; j++)
2664 {
2665 double sum = pt->row_tot[i] + pt->col_tot[j];
2666 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2667 }
2668
2669 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2670
2671 ase_under_h0 = sqrt ((pow2 (pt->total) * sum_rici
2672 + sum_rici * sum_rici
2673 - pt->total * sum_riciri_ci)
2674 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2675
2676 ase[8] = sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2677 / pow2 (pow2 (pt->total) - sum_rici))
2678 + ((2. * (pt->total - sum_fii)
2679 * (2. * sum_fii * sum_rici
2680 - pt->total * sum_fiiri_ci))
2681 / pow3 (pow2 (pt->total) - sum_rici))
2682 + (pow2 (pt->total - sum_fii)
2683 * (pt->total * sum_fijri_ci2 - 4.
2684 * sum_rici * sum_rici)
2685 / pow4 (pow2 (pt->total) - sum_rici))));
2686
2687 t[8] = v[8] / ase_under_h0;
2688 }
2689
2690 return 1;
2691 }
2692
2693 /* Calculate risk estimate. */
2694 static int
2695 calc_risk (struct pivot_table *pt,
2696 double *value, double *upper, double *lower, union value *c)
2697 {
2698 double f11, f12, f21, f22;
2699 double v;
2700
2701 {
2702 int i;
2703
2704 for (i = 0; i < 3; i++)
2705 value[i] = upper[i] = lower[i] = SYSMIS;
2706 }
2707
2708 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2709 return 0;
2710
2711 {
2712 int nz_cols[2];
2713 int i, j;
2714
2715 for (i = j = 0; i < pt->n_cols; i++)
2716 if (pt->col_tot[i] != 0.)
2717 {
2718 nz_cols[j++] = i;
2719 if (j == 2)
2720 break;
2721 }
2722
2723 assert (j == 2);
2724
2725 f11 = pt->mat[nz_cols[0]];
2726 f12 = pt->mat[nz_cols[1]];
2727 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2728 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2729
2730 c[0] = pt->cols[nz_cols[0]];
2731 c[1] = pt->cols[nz_cols[1]];
2732 }
2733
2734 value[0] = (f11 * f22) / (f12 * f21);
2735 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2736 lower[0] = value[0] * exp (-1.960 * v);
2737 upper[0] = value[0] * exp (1.960 * v);
2738
2739 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2740 v = sqrt ((f12 / (f11 * (f11 + f12)))
2741 + (f22 / (f21 * (f21 + f22))));
2742 lower[1] = value[1] * exp (-1.960 * v);
2743 upper[1] = value[1] * exp (1.960 * v);
2744
2745 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2746 v = sqrt ((f11 / (f12 * (f11 + f12)))
2747 + (f21 / (f22 * (f21 + f22))));
2748 lower[2] = value[2] * exp (-1.960 * v);
2749 upper[2] = value[2] * exp (1.960 * v);
2750
2751 return 1;
2752 }
2753
2754 /* Calculate directional measures. */
2755 static int
2756 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2757 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2758 double t[N_DIRECTIONAL], double sig[N_DIRECTIONAL])
2759 {
2760 {
2761 int i;
2762
2763 for (i = 0; i < N_DIRECTIONAL; i++)
2764 v[i] = ase[i] = t[i] = sig[i] = SYSMIS;
2765 }
2766
2767 /* Lambda. */
2768 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2769 {
2770 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2771 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2772 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2773 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2774 double sum_fim, sum_fmj;
2775 double rm, cm;
2776 int rm_index, cm_index;
2777 int i, j;
2778
2779 /* Find maximum for each row and their sum. */
2780 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2781 {
2782 double max = pt->mat[i * pt->n_cols];
2783 int index = 0;
2784
2785 for (j = 1; j < pt->n_cols; j++)
2786 if (pt->mat[j + i * pt->n_cols] > max)
2787 {
2788 max = pt->mat[j + i * pt->n_cols];
2789 index = j;
2790 }
2791
2792 sum_fim += fim[i] = max;
2793 fim_index[i] = index;
2794 }
2795
2796 /* Find maximum for each column. */
2797 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2798 {
2799 double max = pt->mat[j];
2800 int index = 0;
2801
2802 for (i = 1; i < pt->n_rows; i++)
2803 if (pt->mat[j + i * pt->n_cols] > max)
2804 {
2805 max = pt->mat[j + i * pt->n_cols];
2806 index = i;
2807 }
2808
2809 sum_fmj += fmj[j] = max;
2810 fmj_index[j] = index;
2811 }
2812
2813 /* Find maximum row total. */
2814 rm = pt->row_tot[0];
2815 rm_index = 0;
2816 for (i = 1; i < pt->n_rows; i++)
2817 if (pt->row_tot[i] > rm)
2818 {
2819 rm = pt->row_tot[i];
2820 rm_index = i;
2821 }
2822
2823 /* Find maximum column total. */
2824 cm = pt->col_tot[0];
2825 cm_index = 0;
2826 for (j = 1; j < pt->n_cols; j++)
2827 if (pt->col_tot[j] > cm)
2828 {
2829 cm = pt->col_tot[j];
2830 cm_index = j;
2831 }
2832
2833 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2834 v[1] = (sum_fmj - rm) / (pt->total - rm);
2835 v[2] = (sum_fim - cm) / (pt->total - cm);
2836
2837 /* ASE1 for Y given PT. */
2838 {
2839 double accum;
2840
2841 accum = 0.;
2842 for (i = 0; i < pt->n_rows; i++)
2843 if (cm_index == fim_index[i])
2844 accum += fim[i];
2845 ase[2] = sqrt ((pt->total - sum_fim) * (sum_fim + cm - 2. * accum)
2846 / pow3 (pt->total - cm));
2847 }
2848
2849 /* ASE0 for Y given PT. */
2850 {
2851 double accum;
2852
2853 for (accum = 0., i = 0; i < pt->n_rows; i++)
2854 if (cm_index != fim_index[i])
2855 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2856 + pt->mat[i * pt->n_cols + cm_index]);
2857 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2858 }
2859
2860 /* ASE1 for PT given Y. */
2861 {
2862 double accum;
2863
2864 accum = 0.;
2865 for (j = 0; j < pt->n_cols; j++)
2866 if (rm_index == fmj_index[j])
2867 accum += fmj[j];
2868 ase[1] = sqrt ((pt->total - sum_fmj) * (sum_fmj + rm - 2. * accum)
2869 / pow3 (pt->total - rm));
2870 }
2871
2872 /* ASE0 for PT given Y. */
2873 {
2874 double accum;
2875
2876 for (accum = 0., j = 0; j < pt->n_cols; j++)
2877 if (rm_index != fmj_index[j])
2878 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2879 + pt->mat[j + pt->n_cols * rm_index]);
2880 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2881 }
2882
2883 /* Symmetric ASE0 and ASE1. */
2884 {
2885 double accum0;
2886 double accum1;
2887
2888 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2889 for (j = 0; j < pt->n_cols; j++)
2890 {
2891 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2892 int temp1 = (i == rm_index) + (j == cm_index);
2893 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2894 accum1 += (pt->mat[j + i * pt->n_cols]
2895 * pow2 (temp0 + (v[0] - 1.) * temp1));
2896 }
2897 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2898 t[0] = v[0] / (sqrt (accum0 - pow2 (sum_fim + sum_fmj - cm - rm) / pt->total)
2899 / (2. * pt->total - rm - cm));
2900 }
2901
2902 for (i = 0; i < 3; i++)
2903 sig[i] = 2 * gsl_cdf_ugaussian_Q (t[i]);
2904
2905 free (fim);
2906 free (fim_index);
2907 free (fmj);
2908 free (fmj_index);
2909
2910 /* Tau. */
2911 {
2912 double sum_fij2_ri, sum_fij2_ci;
2913 double sum_ri2, sum_cj2;
2914
2915 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2916 for (j = 0; j < pt->n_cols; j++)
2917 {
2918 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2919 sum_fij2_ri += temp / pt->row_tot[i];
2920 sum_fij2_ci += temp / pt->col_tot[j];
2921 }
2922
2923 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2924 sum_ri2 += pow2 (pt->row_tot[i]);
2925
2926 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2927 sum_cj2 += pow2 (pt->col_tot[j]);
2928
2929 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2930 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2931 }
2932 }
2933
2934 if (proc->statistics & (1u << CRS_ST_UC))
2935 {
2936 double UX, UY, UXY, P;
2937 double ase1_yx, ase1_xy, ase1_sym;
2938 int i, j;
2939
2940 for (UX = 0., i = 0; i < pt->n_rows; i++)
2941 if (pt->row_tot[i] > 0.)
2942 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2943
2944 for (UY = 0., j = 0; j < pt->n_cols; j++)
2945 if (pt->col_tot[j] > 0.)
2946 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2947
2948 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2949 for (j = 0; j < pt->n_cols; j++)
2950 {
2951 double entry = pt->mat[j + i * pt->n_cols];
2952
2953 if (entry <= 0.)
2954 continue;
2955
2956 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2957 UXY -= entry / pt->total * log (entry / pt->total);
2958 }
2959
2960 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2961 for (j = 0; j < pt->n_cols; j++)
2962 {
2963 double entry = pt->mat[j + i * pt->n_cols];
2964
2965 if (entry <= 0.)
2966 continue;
2967
2968 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2969 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2970 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2971 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2972 ase1_sym += entry * pow2 ((UXY
2973 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2974 - (UX + UY) * log (entry / pt->total));
2975 }
2976
2977 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2978 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2979 t[5] = SYSMIS;
2980
2981 v[6] = (UX + UY - UXY) / UX;
2982 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2983 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2984
2985 v[7] = (UX + UY - UXY) / UY;
2986 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2987 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2988 }
2989
2990 /* Somers' D. */
2991 if (proc->statistics & (1u << CRS_ST_D))
2992 {
2993 double v_dummy[N_SYMMETRIC];
2994 double ase_dummy[N_SYMMETRIC];
2995 double t_dummy[N_SYMMETRIC];
2996 double somers_d_v[3];
2997 double somers_d_ase[3];
2998 double somers_d_t[3];
2999
3000 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
3001 somers_d_v, somers_d_ase, somers_d_t))
3002 {
3003 int i;
3004 for (i = 0; i < 3; i++)
3005 {
3006 v[8 + i] = somers_d_v[i];
3007 ase[8 + i] = somers_d_ase[i];
3008 t[8 + i] = somers_d_t[i];
3009 sig[8 + i] = 2 * gsl_cdf_ugaussian_Q (fabs (somers_d_t[i]));
3010 }
3011 }
3012 }
3013
3014 /* Eta. */
3015 if (proc->statistics & (1u << CRS_ST_ETA))
3016 {
3017 {
3018 double sum_Xr, sum_X2r;
3019 double SX, SXW;
3020 int i, j;
3021
3022 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
3023 {
3024 sum_Xr += pt->rows[i].f * pt->row_tot[i];
3025 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
3026 }
3027 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
3028
3029 for (SXW = 0., j = 0; j < pt->n_cols; j++)
3030 {
3031 double cum;
3032
3033 for (cum = 0., i = 0; i < pt->n_rows; i++)
3034 {
3035 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
3036 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
3037 }
3038
3039 SXW -= cum * cum / pt->col_tot[j];
3040 }
3041 v[11] = sqrt (1. - SXW / SX);
3042 }
3043
3044 {
3045 double sum_Yc, sum_Y2c;
3046 double SY, SYW;
3047 int i, j;
3048
3049 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
3050 {
3051 sum_Yc += pt->cols[i].f * pt->col_tot[i];
3052 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
3053 }
3054 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
3055
3056 for (SYW = 0., i = 0; i < pt->n_rows; i++)
3057 {
3058 double cum;
3059
3060 for (cum = 0., j = 0; j < pt->n_cols; j++)
3061 {
3062 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
3063 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
3064 }
3065
3066 SYW -= cum * cum / pt->row_tot[i];
3067 }
3068 v[12] = sqrt (1. - SYW / SY);
3069 }
3070 }
3071
3072 return 1;
3073 }
3074
3075 /*
3076 Local Variables:
3077 mode: c
3078 End:
3079 */
GNU PSPP