1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2006, 2009, 2010, 2011, 2012, 2013, 2014 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.
33 #include <gsl/gsl_cdf.h>
37 #include "data/case.h"
38 #include "data/casegrouper.h"
39 #include "data/casereader.h"
40 #include "data/data-out.h"
41 #include "data/dataset.h"
42 #include "data/dictionary.h"
43 #include "data/format.h"
44 #include "data/value-labels.h"
45 #include "data/variable.h"
46 #include "language/command.h"
47 #include "language/dictionary/split-file.h"
48 #include "language/lexer/lexer.h"
49 #include "language/lexer/variable-parser.h"
50 #include "libpspp/array.h"
51 #include "libpspp/assertion.h"
52 #include "libpspp/compiler.h"
53 #include "libpspp/hash-functions.h"
54 #include "libpspp/hmap.h"
55 #include "libpspp/hmapx.h"
56 #include "libpspp/message.h"
57 #include "libpspp/misc.h"
58 #include "libpspp/pool.h"
59 #include "libpspp/str.h"
60 #include "output/tab.h"
62 #include "gl/minmax.h"
63 #include "gl/xalloc.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=val:!avalue/dvalue,
80 tabl:!tables/notables,
83 +cells[cl_]=count,expected,row,column,total,residual,sresidual,
85 +statistics[st_]=chisq,phi,cc,lambda,uc,none,btau,ctau,risk,gamma,d,
91 /* Number of chi-square statistics. */
94 /* Number of symmetric statistics. */
97 /* Number of directional statistics. */
98 #define N_DIRECTIONAL 13
100 /* A single table entry for general mode. */
103 struct hmap_node node; /* Entry in hash table. */
104 double freq; /* Frequency count. */
105 union value values[1]; /* Values. */
109 table_entry_size (size_t n_values)
111 return (offsetof (struct table_entry, values)
112 + n_values * sizeof (union value));
115 /* Indexes into the 'vars' member of struct pivot_table and
116 struct crosstab member. */
119 ROW_VAR = 0, /* Row variable. */
120 COL_VAR = 1 /* Column variable. */
121 /* Higher indexes cause multiple tables to be output. */
124 /* A crosstabulation of 2 or more variables. */
127 struct crosstabs_proc *proc;
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 struct hmap_node hmap_node; /* In struct crosstabs_proc var_ranges map. */
168 const struct variable *var; /* The variable. */
169 int min; /* Minimum value. */
170 int max; /* Maximum value + 1. */
171 int count; /* max - min. */
174 struct crosstabs_proc
176 const struct dictionary *dict;
177 enum { INTEGER, GENERAL } mode;
178 enum mv_class exclude;
181 struct fmt_spec weight_format;
183 /* Variables specifies on VARIABLES. */
184 const struct variable **variables;
186 struct hmap var_ranges;
189 struct pivot_table *pivots;
193 int n_cells; /* Number of cells requested. */
194 unsigned int cells; /* Bit k is 1 if cell k is requested. */
195 int a_cells[CRS_CL_count]; /* 0...n_cells-1 are the requested cells. */
198 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
200 bool descending; /* True if descending sort order is requested. */
203 const struct var_range *get_var_range (const struct crosstabs_proc *,
204 const struct variable *);
206 static bool should_tabulate_case (const struct pivot_table *,
207 const struct ccase *, enum mv_class exclude);
208 static void tabulate_general_case (struct pivot_table *, const struct ccase *,
210 static void tabulate_integer_case (struct pivot_table *, const struct ccase *,
212 static void postcalc (struct crosstabs_proc *);
213 static void submit (struct pivot_table *, struct tab_table *);
215 /* Parses and executes the CROSSTABS procedure. */
217 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
219 const struct variable *wv = dict_get_weight (dataset_dict (ds));
220 struct var_range *range, *next_range;
221 struct crosstabs_proc proc;
222 struct casegrouper *grouper;
223 struct casereader *input, *group;
224 struct cmd_crosstabs cmd;
225 struct pivot_table *pt;
230 proc.dict = dataset_dict (ds);
231 proc.bad_warn = true;
232 proc.variables = NULL;
233 proc.n_variables = 0;
234 hmap_init (&proc.var_ranges);
237 proc.descending = false;
238 proc.weight_format = wv ? *var_get_print_format (wv) : F_8_0;
240 if (!parse_crosstabs (lexer, ds, &cmd, &proc))
242 result = CMD_FAILURE;
246 proc.mode = proc.n_variables ? INTEGER : GENERAL;
249 proc.descending = cmd.val == CRS_DVALUE;
253 proc.cells = 1u << CRS_CL_COUNT;
254 else if (cmd.a_cells[CRS_CL_ALL])
255 proc.cells = UINT_MAX;
259 for (i = 0; i < CRS_CL_count; i++)
261 proc.cells |= 1u << i;
263 proc.cells = ((1u << CRS_CL_COUNT)
265 | (1u << CRS_CL_COLUMN)
266 | (1u << CRS_CL_TOTAL));
268 proc.cells &= ((1u << CRS_CL_count) - 1);
269 proc.cells &= ~((1u << CRS_CL_NONE) | (1u << CRS_CL_ALL));
271 for (i = 0; i < CRS_CL_count; i++)
272 if (proc.cells & (1u << i))
273 proc.a_cells[proc.n_cells++] = i;
276 if (cmd.a_statistics[CRS_ST_ALL])
277 proc.statistics = UINT_MAX;
278 else if (cmd.sbc_statistics)
283 for (i = 0; i < CRS_ST_count; i++)
284 if (cmd.a_statistics[i])
285 proc.statistics |= 1u << i;
286 if (proc.statistics == 0)
287 proc.statistics |= 1u << CRS_ST_CHISQ;
293 proc.exclude = (cmd.miss == CRS_TABLE ? MV_ANY
294 : cmd.miss == CRS_INCLUDE ? MV_SYSTEM
296 if (proc.mode == GENERAL && proc.exclude == MV_NEVER)
298 msg (SE, _("Missing mode %s not allowed in general mode. "
299 "Assuming %s."), "REPORT", "MISSING=TABLE");
300 proc.exclude = MV_ANY;
304 proc.pivot = cmd.pivot == CRS_PIVOT;
306 input = casereader_create_filter_weight (proc_open (ds), dataset_dict (ds),
308 grouper = casegrouper_create_splits (input, dataset_dict (ds));
309 while (casegrouper_get_next_group (grouper, &group))
313 /* Output SPLIT FILE variables. */
314 c = casereader_peek (group, 0);
317 output_split_file_values (ds, c);
321 /* Initialize hash tables. */
322 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
323 hmap_init (&pt->data);
326 for (; (c = casereader_read (group)) != NULL; case_unref (c))
327 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
329 double weight = dict_get_case_weight (dataset_dict (ds), c,
331 if (should_tabulate_case (pt, c, proc.exclude))
333 if (proc.mode == GENERAL)
334 tabulate_general_case (pt, c, weight);
336 tabulate_integer_case (pt, c, weight);
339 pt->missing += weight;
341 casereader_destroy (group);
346 ok = casegrouper_destroy (grouper);
347 ok = proc_commit (ds) && ok;
349 result = ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
352 free (proc.variables);
353 HMAP_FOR_EACH_SAFE (range, next_range, struct var_range, hmap_node,
356 hmap_delete (&proc.var_ranges, &range->hmap_node);
359 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
362 free (pt->const_vars);
363 /* We must not call value_destroy on const_values because
364 it is a wild pointer; it never pointed to anything owned
367 The rest of the data was allocated and destroyed at a
368 lower level already. */
375 /* Parses the TABLES subcommand. */
377 crs_custom_tables (struct lexer *lexer, struct dataset *ds,
378 struct cmd_crosstabs *cmd UNUSED, void *proc_)
380 struct crosstabs_proc *proc = proc_;
381 struct const_var_set *var_set;
383 const struct variable ***by = NULL;
385 size_t *by_nvar = NULL;
390 /* Ensure that this is a TABLES subcommand. */
391 if (!lex_match_id (lexer, "TABLES")
392 && (lex_token (lexer) != T_ID ||
393 dict_lookup_var (dataset_dict (ds), lex_tokcstr (lexer)) == NULL)
394 && lex_token (lexer) != T_ALL)
396 lex_match (lexer, T_EQUALS);
398 if (proc->variables != NULL)
399 var_set = const_var_set_create_from_array (proc->variables,
402 var_set = const_var_set_create_from_dict (dataset_dict (ds));
403 assert (var_set != NULL);
407 by = xnrealloc (by, n_by + 1, sizeof *by);
408 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
409 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
410 PV_NO_DUPLICATE | PV_NO_SCRATCH))
412 if (xalloc_oversized (nx, by_nvar[n_by]))
414 msg (SE, _("Too many cross-tabulation variables or dimensions."));
420 if (!lex_match (lexer, T_BY))
424 lex_force_match (lexer, T_BY);
432 by_iter = xcalloc (n_by, sizeof *by_iter);
433 proc->pivots = xnrealloc (proc->pivots,
434 proc->n_pivots + nx, sizeof *proc->pivots);
435 for (i = 0; i < nx; i++)
437 struct pivot_table *pt = &proc->pivots[proc->n_pivots++];
441 pt->weight_format = proc->weight_format;
444 pt->vars = xmalloc (n_by * sizeof *pt->vars);
446 pt->const_vars = NULL;
447 pt->const_values = NULL;
449 for (j = 0; j < n_by; j++)
450 pt->vars[j] = by[j][by_iter[j]];
452 for (j = n_by - 1; j >= 0; j--)
454 if (++by_iter[j] < by_nvar[j])
463 /* All return paths lead here. */
464 for (i = 0; i < n_by; i++)
469 const_var_set_destroy (var_set);
474 /* Parses the VARIABLES subcommand. */
476 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
477 struct cmd_crosstabs *cmd UNUSED, void *proc_)
479 struct crosstabs_proc *proc = proc_;
482 msg (SE, _("%s must be specified before %s."), "VARIABLES", "TABLES");
486 lex_match (lexer, T_EQUALS);
490 size_t orig_nv = proc->n_variables;
495 if (!parse_variables_const (lexer, dataset_dict (ds),
496 &proc->variables, &proc->n_variables,
497 (PV_APPEND | PV_NUMERIC
498 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
501 if (!lex_force_match (lexer, T_LPAREN))
504 if (!lex_force_int (lexer))
506 min = lex_integer (lexer);
509 lex_match (lexer, T_COMMA);
511 if (!lex_force_int (lexer))
513 max = lex_integer (lexer);
516 msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
522 if (!lex_force_match (lexer, T_RPAREN))
525 for (i = orig_nv; i < proc->n_variables; i++)
527 const struct variable *var = proc->variables[i];
528 struct var_range *vr = xmalloc (sizeof *vr);
533 vr->count = max - min + 1;
534 hmap_insert (&proc->var_ranges, &vr->hmap_node,
535 hash_pointer (var, 0));
538 if (lex_token (lexer) == T_SLASH)
545 free (proc->variables);
546 proc->variables = NULL;
547 proc->n_variables = 0;
551 /* Data file processing. */
553 const struct var_range *
554 get_var_range (const struct crosstabs_proc *proc, const struct variable *var)
556 if (!hmap_is_empty (&proc->var_ranges))
558 const struct var_range *range;
560 HMAP_FOR_EACH_IN_BUCKET (range, struct var_range, hmap_node,
561 hash_pointer (var, 0), &proc->var_ranges)
562 if (range->var == var)
570 should_tabulate_case (const struct pivot_table *pt, const struct ccase *c,
571 enum mv_class exclude)
574 for (j = 0; j < pt->n_vars; j++)
576 const struct variable *var = pt->vars[j];
577 const struct var_range *range = get_var_range (pt->proc, var);
579 if (var_is_value_missing (var, case_data (c, var), exclude))
584 double num = case_num (c, var);
585 if (num < range->min || num > range->max)
593 tabulate_integer_case (struct pivot_table *pt, const struct ccase *c,
596 struct table_entry *te;
601 for (j = 0; j < pt->n_vars; j++)
603 /* Throw away fractional parts of values. */
604 hash = hash_int (case_num (c, pt->vars[j]), hash);
607 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
609 for (j = 0; j < pt->n_vars; j++)
610 if ((int) case_num (c, pt->vars[j]) != (int) te->values[j].f)
613 /* Found an existing entry. */
620 /* No existing entry. Create a new one. */
621 te = xmalloc (table_entry_size (pt->n_vars));
623 for (j = 0; j < pt->n_vars; j++)
624 te->values[j].f = (int) case_num (c, pt->vars[j]);
625 hmap_insert (&pt->data, &te->node, hash);
629 tabulate_general_case (struct pivot_table *pt, const struct ccase *c,
632 struct table_entry *te;
637 for (j = 0; j < pt->n_vars; j++)
639 const struct variable *var = pt->vars[j];
640 hash = value_hash (case_data (c, var), var_get_width (var), hash);
643 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
645 for (j = 0; j < pt->n_vars; j++)
647 const struct variable *var = pt->vars[j];
648 if (!value_equal (case_data (c, var), &te->values[j],
649 var_get_width (var)))
653 /* Found an existing entry. */
660 /* No existing entry. Create a new one. */
661 te = xmalloc (table_entry_size (pt->n_vars));
663 for (j = 0; j < pt->n_vars; j++)
665 const struct variable *var = pt->vars[j];
666 value_clone (&te->values[j], case_data (c, var), var_get_width (var));
668 hmap_insert (&pt->data, &te->node, hash);
671 /* Post-data reading calculations. */
673 static int compare_table_entry_vars_3way (const struct table_entry *a,
674 const struct table_entry *b,
675 const struct pivot_table *pt,
677 static int compare_table_entry_3way (const void *ap_, const void *bp_,
679 static int compare_table_entry_3way_inv (const void *ap_, const void *bp_,
682 static void enum_var_values (const struct pivot_table *, int var_idx,
683 union value **valuesp, int *n_values, bool descending);
684 static void output_pivot_table (struct crosstabs_proc *,
685 struct pivot_table *);
686 static void make_pivot_table_subset (struct pivot_table *pt,
687 size_t row0, size_t row1,
688 struct pivot_table *subset);
689 static void make_summary_table (struct crosstabs_proc *);
690 static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
693 postcalc (struct crosstabs_proc *proc)
695 struct pivot_table *pt;
697 /* Convert hash tables into sorted arrays of entries. */
698 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
700 struct table_entry *e;
703 pt->n_entries = hmap_count (&pt->data);
704 pt->entries = xnmalloc (pt->n_entries, sizeof *pt->entries);
706 HMAP_FOR_EACH (e, struct table_entry, node, &pt->data)
707 pt->entries[i++] = e;
708 hmap_destroy (&pt->data);
710 sort (pt->entries, pt->n_entries, sizeof *pt->entries,
711 proc->descending ? compare_table_entry_3way_inv : compare_table_entry_3way,
715 make_summary_table (proc);
717 /* Output each pivot table. */
718 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
720 if (proc->pivot || pt->n_vars == 2)
721 output_pivot_table (proc, pt);
724 size_t row0 = 0, row1 = 0;
725 while (find_crosstab (pt, &row0, &row1))
727 struct pivot_table subset;
728 make_pivot_table_subset (pt, row0, row1, &subset);
729 output_pivot_table (proc, &subset);
734 /* Free output and prepare for next split file. */
735 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
741 /* Free the members that were allocated in this function(and the values
742 owned by the entries.
744 The other pointer members are either both allocated and destroyed at a
745 lower level (in output_pivot_table), or both allocated and destroyed
746 at a higher level (in crs_custom_tables and free_proc,
748 for (i = 0; i < pt->n_vars; i++)
750 int width = var_get_width (pt->vars[i]);
751 if (value_needs_init (width))
755 for (j = 0; j < pt->n_entries; j++)
756 value_destroy (&pt->entries[j]->values[i], width);
760 for (i = 0; i < pt->n_entries; i++)
761 free (pt->entries[i]);
767 make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
768 struct pivot_table *subset)
773 assert (pt->n_consts == 0);
774 subset->missing = pt->missing;
776 subset->vars = pt->vars;
777 subset->n_consts = pt->n_vars - 2;
778 subset->const_vars = pt->vars + 2;
779 subset->const_values = &pt->entries[row0]->values[2];
781 subset->entries = &pt->entries[row0];
782 subset->n_entries = row1 - row0;
786 compare_table_entry_var_3way (const struct table_entry *a,
787 const struct table_entry *b,
788 const struct pivot_table *pt,
791 return value_compare_3way (&a->values[idx], &b->values[idx],
792 var_get_width (pt->vars[idx]));
796 compare_table_entry_vars_3way (const struct table_entry *a,
797 const struct table_entry *b,
798 const struct pivot_table *pt,
803 for (i = idx1 - 1; i >= idx0; i--)
805 int cmp = compare_table_entry_var_3way (a, b, pt, i);
812 /* Compare the struct table_entry at *AP to the one at *BP and
813 return a strcmp()-type result. */
815 compare_table_entry_3way (const void *ap_, const void *bp_, const void *pt_)
817 const struct table_entry *const *ap = ap_;
818 const struct table_entry *const *bp = bp_;
819 const struct table_entry *a = *ap;
820 const struct table_entry *b = *bp;
821 const struct pivot_table *pt = pt_;
824 cmp = compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars);
828 cmp = compare_table_entry_var_3way (a, b, pt, ROW_VAR);
832 return compare_table_entry_var_3way (a, b, pt, COL_VAR);
835 /* Inverted version of compare_table_entry_3way */
837 compare_table_entry_3way_inv (const void *ap_, const void *bp_, const void *pt_)
839 return -compare_table_entry_3way (ap_, bp_, pt_);
843 find_first_difference (const struct pivot_table *pt, size_t row)
846 return pt->n_vars - 1;
849 const struct table_entry *a = pt->entries[row];
850 const struct table_entry *b = pt->entries[row - 1];
853 for (col = pt->n_vars - 1; col >= 0; col--)
854 if (compare_table_entry_var_3way (a, b, pt, col))
860 /* Output a table summarizing the cases processed. */
862 make_summary_table (struct crosstabs_proc *proc)
864 struct tab_table *summary;
865 struct pivot_table *pt;
869 summary = tab_create (7, 3 + proc->n_pivots);
870 tab_set_format (summary, RC_WEIGHT, &proc->weight_format);
871 tab_title (summary, _("Summary."));
872 tab_headers (summary, 1, 0, 3, 0);
873 tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
874 tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
875 tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
876 tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
877 tab_hline (summary, TAL_1, 1, 6, 1);
878 tab_hline (summary, TAL_1, 1, 6, 2);
879 tab_vline (summary, TAL_1, 3, 1, 1);
880 tab_vline (summary, TAL_1, 5, 1, 1);
881 for (i = 0; i < 3; i++)
883 tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
884 tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
886 tab_offset (summary, 0, 3);
888 ds_init_empty (&name);
889 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
895 tab_hline (summary, TAL_1, 0, 6, 0);
898 for (i = 0; i < pt->n_vars; i++)
901 ds_put_cstr (&name, " * ");
902 ds_put_cstr (&name, var_to_string (pt->vars[i]));
904 tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
907 for (i = 0; i < pt->n_entries; i++)
908 valid += pt->entries[i]->freq;
913 for (i = 0; i < 3; i++)
915 tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i], NULL, RC_WEIGHT);
916 tab_text_format (summary, i * 2 + 2, 0, TAB_RIGHT, "%.1f%%",
920 tab_next_row (summary);
924 submit (NULL, summary);
929 static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
930 struct pivot_table *);
931 static struct tab_table *create_chisq_table (struct crosstabs_proc *proc, struct pivot_table *);
932 static struct tab_table *create_sym_table (struct crosstabs_proc *proc, struct pivot_table *);
933 static struct tab_table *create_risk_table (struct crosstabs_proc *proc, struct pivot_table *);
934 static struct tab_table *create_direct_table (struct crosstabs_proc *proc, struct pivot_table *);
935 static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
936 struct tab_table *, int first_difference);
937 static void display_crosstabulation (struct crosstabs_proc *,
938 struct pivot_table *,
940 static void display_chisq (struct pivot_table *, struct tab_table *,
941 bool *showed_fisher);
942 static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
944 static void display_risk (struct pivot_table *, struct tab_table *);
945 static void display_directional (struct crosstabs_proc *, struct pivot_table *,
947 static void table_value_missing (struct crosstabs_proc *proc,
948 struct tab_table *table, int c, int r,
949 unsigned char opt, const union value *v,
950 const struct variable *var);
951 static void delete_missing (struct pivot_table *);
952 static void build_matrix (struct pivot_table *);
954 /* Output pivot table PT in the context of PROC. */
956 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
958 struct tab_table *table = NULL; /* Crosstabulation table. */
959 struct tab_table *chisq = NULL; /* Chi-square table. */
960 bool showed_fisher = false;
961 struct tab_table *sym = NULL; /* Symmetric measures table. */
962 struct tab_table *risk = NULL; /* Risk estimate table. */
963 struct tab_table *direct = NULL; /* Directional measures table. */
966 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols, proc->descending);
973 ds_init_cstr (&vars, var_to_string (pt->vars[0]));
974 for (i = 1; i < pt->n_vars; i++)
975 ds_put_format (&vars, " * %s", var_to_string (pt->vars[i]));
977 /* TRANSLATORS: The %s here describes a crosstabulation. It takes the
978 form "var1 * var2 * var3 * ...". */
979 msg (SW, _("Crosstabulation %s contained no non-missing cases."),
988 table = create_crosstab_table (proc, pt);
989 if (proc->statistics & (1u << CRS_ST_CHISQ))
990 chisq = create_chisq_table (proc, pt);
991 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
992 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
993 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
994 | (1u << CRS_ST_KAPPA)))
995 sym = create_sym_table (proc, pt);
996 if (proc->statistics & (1u << CRS_ST_RISK))
997 risk = create_risk_table (proc, pt);
998 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
999 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
1000 direct = create_direct_table (proc, pt);
1003 while (find_crosstab (pt, &row0, &row1))
1005 struct pivot_table x;
1006 int first_difference;
1008 make_pivot_table_subset (pt, row0, row1, &x);
1010 /* Find all the row variable values. */
1011 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows, proc->descending);
1013 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
1016 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
1017 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
1018 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
1020 /* Allocate table space for the matrix. */
1022 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
1023 tab_realloc (table, -1,
1024 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
1025 tab_nr (table) * pt->n_entries / x.n_entries));
1029 /* Find the first variable that differs from the last subtable. */
1030 first_difference = find_first_difference (pt, row0);
1033 display_dimensions (proc, &x, table, first_difference);
1034 display_crosstabulation (proc, &x, table);
1037 if (proc->exclude == MV_NEVER)
1038 delete_missing (&x);
1042 display_dimensions (proc, &x, chisq, first_difference);
1043 display_chisq (&x, chisq, &showed_fisher);
1047 display_dimensions (proc, &x, sym, first_difference);
1048 display_symmetric (proc, &x, sym);
1052 display_dimensions (proc, &x, risk, first_difference);
1053 display_risk (&x, risk);
1057 display_dimensions (proc, &x, direct, first_difference);
1058 display_directional (proc, &x, direct);
1061 /* Free the parts of x that are not owned by pt. In
1062 particular we must not free x.cols, which is the same as
1063 pt->cols, which is freed at the end of this function. */
1071 submit (NULL, table);
1076 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
1082 submit (pt, direct);
1088 build_matrix (struct pivot_table *x)
1090 const int col_var_width = var_get_width (x->vars[COL_VAR]);
1091 const int row_var_width = var_get_width (x->vars[ROW_VAR]);
1094 struct table_entry **p;
1098 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1100 const struct table_entry *te = *p;
1102 while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
1104 for (; col < x->n_cols; col++)
1110 while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
1117 if (++col >= x->n_cols)
1123 while (mp < &x->mat[x->n_cols * x->n_rows])
1125 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1127 /* Column totals, row totals, ns_rows. */
1129 for (col = 0; col < x->n_cols; col++)
1130 x->col_tot[col] = 0.0;
1131 for (row = 0; row < x->n_rows; row++)
1132 x->row_tot[row] = 0.0;
1134 for (row = 0; row < x->n_rows; row++)
1136 bool row_is_empty = true;
1137 for (col = 0; col < x->n_cols; col++)
1141 row_is_empty = false;
1142 x->col_tot[col] += *mp;
1143 x->row_tot[row] += *mp;
1150 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1154 for (col = 0; col < x->n_cols; col++)
1155 for (row = 0; row < x->n_rows; row++)
1156 if (x->mat[col + row * x->n_cols] != 0.0)
1164 for (col = 0; col < x->n_cols; col++)
1165 x->total += x->col_tot[col];
1168 static struct tab_table *
1169 create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1176 static const struct tuple names[] =
1178 {CRS_CL_COUNT, N_("count")},
1179 {CRS_CL_ROW, N_("row %")},
1180 {CRS_CL_COLUMN, N_("column %")},
1181 {CRS_CL_TOTAL, N_("total %")},
1182 {CRS_CL_EXPECTED, N_("expected")},
1183 {CRS_CL_RESIDUAL, N_("residual")},
1184 {CRS_CL_SRESIDUAL, N_("std. resid.")},
1185 {CRS_CL_ASRESIDUAL, N_("adj. resid.")},
1187 const int n_names = sizeof names / sizeof *names;
1188 const struct tuple *t;
1190 struct tab_table *table;
1191 struct string title;
1192 struct pivot_table x;
1196 make_pivot_table_subset (pt, 0, 0, &x);
1198 table = tab_create (x.n_consts + 1 + x.n_cols + 1,
1199 (x.n_entries / x.n_cols) * 3 / 2 * proc->n_cells + 10);
1200 tab_headers (table, x.n_consts + 1, 0, 2, 0);
1201 tab_set_format (table, RC_WEIGHT, &proc->weight_format);
1203 /* First header line. */
1204 tab_joint_text (table, x.n_consts + 1, 0,
1205 (x.n_consts + 1) + (x.n_cols - 1), 0,
1206 TAB_CENTER | TAT_TITLE, var_to_string (x.vars[COL_VAR]));
1208 tab_hline (table, TAL_1, x.n_consts + 1,
1209 x.n_consts + 2 + x.n_cols - 2, 1);
1211 /* Second header line. */
1212 for (i = 2; i < x.n_consts + 2; i++)
1213 tab_joint_text (table, x.n_consts + 2 - i - 1, 0,
1214 x.n_consts + 2 - i - 1, 1,
1215 TAB_RIGHT | TAT_TITLE, var_to_string (x.vars[i]));
1216 tab_text (table, x.n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1217 var_to_string (x.vars[ROW_VAR]));
1218 for (i = 0; i < x.n_cols; i++)
1219 table_value_missing (proc, table, x.n_consts + 2 + i - 1, 1, TAB_RIGHT,
1220 &x.cols[i], x.vars[COL_VAR]);
1221 tab_text (table, x.n_consts + 2 + x.n_cols - 1, 1, TAB_CENTER, _("Total"));
1223 tab_hline (table, TAL_1, 0, x.n_consts + 2 + x.n_cols - 1, 2);
1224 tab_vline (table, TAL_1, x.n_consts + 2 + x.n_cols - 1, 0, 1);
1227 ds_init_empty (&title);
1228 for (i = 0; i < x.n_consts + 2; i++)
1231 ds_put_cstr (&title, " * ");
1232 ds_put_cstr (&title, var_to_string (x.vars[i]));
1234 for (i = 0; i < pt->n_consts; i++)
1236 const struct variable *var = pt->const_vars[i];
1239 ds_put_format (&title, ", %s=", var_to_string (var));
1241 /* Insert the formatted value of VAR without any leading spaces. */
1242 s = data_out (&pt->const_values[i], var_get_encoding (var),
1243 var_get_print_format (var));
1244 ds_put_cstr (&title, s + strspn (s, " "));
1248 ds_put_cstr (&title, " [");
1250 for (t = names; t < &names[n_names]; t++)
1251 if (proc->cells & (1u << t->value))
1254 ds_put_cstr (&title, ", ");
1255 ds_put_cstr (&title, gettext (t->name));
1257 ds_put_cstr (&title, "].");
1259 tab_title (table, "%s", ds_cstr (&title));
1260 ds_destroy (&title);
1262 tab_offset (table, 0, 2);
1266 static struct tab_table *
1267 create_chisq_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1269 struct tab_table *chisq;
1271 chisq = tab_create (6 + (pt->n_vars - 2),
1272 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10);
1273 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1274 tab_set_format (chisq, RC_WEIGHT, &proc->weight_format);
1276 tab_title (chisq, _("Chi-square tests."));
1278 tab_offset (chisq, pt->n_vars - 2, 0);
1279 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1280 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1281 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1282 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1283 _("Asymp. Sig. (2-tailed)"));
1284 tab_text_format (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1285 _("Exact Sig. (%d-tailed)"), 2);
1286 tab_text_format (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1287 _("Exact Sig. (%d-tailed)"), 1);
1288 tab_offset (chisq, 0, 1);
1293 /* Symmetric measures. */
1294 static struct tab_table *
1295 create_sym_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1297 struct tab_table *sym;
1299 sym = tab_create (6 + (pt->n_vars - 2),
1300 pt->n_entries / pt->n_cols * 7 + 10);
1302 tab_set_format (sym, RC_WEIGHT, &proc->weight_format);
1304 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1305 tab_title (sym, _("Symmetric measures."));
1307 tab_offset (sym, pt->n_vars - 2, 0);
1308 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1309 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1310 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1311 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1312 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1313 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1314 tab_offset (sym, 0, 1);
1319 /* Risk estimate. */
1320 static struct tab_table *
1321 create_risk_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1323 struct tab_table *risk;
1325 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10);
1326 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1327 tab_title (risk, _("Risk estimate."));
1328 tab_set_format (risk, RC_WEIGHT, &proc->weight_format);
1330 tab_offset (risk, pt->n_vars - 2, 0);
1331 tab_joint_text_format (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE,
1332 _("95%% Confidence Interval"));
1333 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1334 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1335 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1336 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1337 tab_hline (risk, TAL_1, 2, 3, 1);
1338 tab_vline (risk, TAL_1, 2, 0, 1);
1339 tab_offset (risk, 0, 2);
1344 /* Directional measures. */
1345 static struct tab_table *
1346 create_direct_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1348 struct tab_table *direct;
1350 direct = tab_create (7 + (pt->n_vars - 2),
1351 pt->n_entries / pt->n_cols * 7 + 10);
1352 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1353 tab_title (direct, _("Directional measures."));
1354 tab_set_format (direct, RC_WEIGHT, &proc->weight_format);
1356 tab_offset (direct, pt->n_vars - 2, 0);
1357 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1358 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1359 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1360 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1361 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1362 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1363 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1364 tab_offset (direct, 0, 1);
1370 /* Delete missing rows and columns for statistical analysis when
1373 delete_missing (struct pivot_table *pt)
1377 for (r = 0; r < pt->n_rows; r++)
1378 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1380 for (c = 0; c < pt->n_cols; c++)
1381 pt->mat[c + r * pt->n_cols] = 0.;
1386 for (c = 0; c < pt->n_cols; c++)
1387 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1389 for (r = 0; r < pt->n_rows; r++)
1390 pt->mat[c + r * pt->n_cols] = 0.;
1395 /* Prepare table T for submission, and submit it. */
1397 submit (struct pivot_table *pt, struct tab_table *t)
1404 tab_resize (t, -1, 0);
1405 if (tab_nr (t) == tab_t (t))
1407 table_unref (&t->table);
1410 tab_offset (t, 0, 0);
1412 for (i = 2; i < pt->n_vars; i++)
1413 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1414 var_to_string (pt->vars[i]));
1415 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1416 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1418 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1420 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1426 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1428 size_t row0 = *row1p;
1431 if (row0 >= pt->n_entries)
1434 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1436 struct table_entry *a = pt->entries[row0];
1437 struct table_entry *b = pt->entries[row1];
1438 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1446 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1447 result. WIDTH_ points to an int which is either 0 for a
1448 numeric value or a string width for a string value. */
1450 compare_value_3way (const void *a_, const void *b_, const void *width_)
1452 const union value *a = a_;
1453 const union value *b = b_;
1454 const int *width = width_;
1456 return value_compare_3way (a, b, *width);
1459 /* Inverted version of the above */
1461 compare_value_3way_inv (const void *a_, const void *b_, const void *width_)
1463 return -compare_value_3way (a_, b_, width_);
1467 /* Given an array of ENTRY_CNT table_entry structures starting at
1468 ENTRIES, creates a sorted list of the values that the variable
1469 with index VAR_IDX takes on. The values are returned as a
1470 malloc()'d array stored in *VALUES, with the number of values
1471 stored in *VALUE_CNT.
1473 The caller must eventually free *VALUES, but each pointer in *VALUES points
1474 to existing data not owned by *VALUES itself. */
1476 enum_var_values (const struct pivot_table *pt, int var_idx,
1477 union value **valuesp, int *n_values, bool descending)
1479 const struct variable *var = pt->vars[var_idx];
1480 const struct var_range *range = get_var_range (pt->proc, var);
1481 union value *values;
1486 values = *valuesp = xnmalloc (range->count, sizeof *values);
1487 *n_values = range->count;
1488 for (i = 0; i < range->count; i++)
1489 values[i].f = range->min + i;
1493 int width = var_get_width (var);
1494 struct hmapx_node *node;
1495 const union value *iter;
1499 for (i = 0; i < pt->n_entries; i++)
1501 const struct table_entry *te = pt->entries[i];
1502 const union value *value = &te->values[var_idx];
1503 size_t hash = value_hash (value, width, 0);
1505 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1506 if (value_equal (iter, value, width))
1509 hmapx_insert (&set, (union value *) value, hash);
1514 *n_values = hmapx_count (&set);
1515 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1517 HMAPX_FOR_EACH (iter, node, &set)
1518 values[i++] = *iter;
1519 hmapx_destroy (&set);
1521 sort (values, *n_values, sizeof *values,
1522 descending ? compare_value_3way_inv : compare_value_3way,
1527 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1528 from V, displayed with print format spec from variable VAR. When
1529 in REPORT missing-value mode, missing values have an M appended. */
1531 table_value_missing (struct crosstabs_proc *proc,
1532 struct tab_table *table, int c, int r, unsigned char opt,
1533 const union value *v, const struct variable *var)
1535 const char *label = var_lookup_value_label (var, v);
1537 tab_text (table, c, r, TAB_LEFT, label);
1540 const struct fmt_spec *print = var_get_print_format (var);
1541 if (proc->exclude == MV_NEVER && var_is_value_missing (var, v, MV_USER))
1543 char *s = data_out (v, dict_get_encoding (proc->dict), print);
1544 tab_text_format (table, c, r, opt, "%sM", s + strspn (s, " "));
1548 tab_value (table, c, r, opt, v, var, print);
1552 /* Draws a line across TABLE at the current row to indicate the most
1553 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1554 that changed, and puts the values that changed into the table. TB
1555 and PT must be the corresponding table_entry and crosstab,
1558 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1559 struct tab_table *table, int first_difference)
1561 tab_hline (table, TAL_1, pt->n_consts + pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1563 for (; first_difference >= 2; first_difference--)
1564 table_value_missing (proc, table, pt->n_consts + pt->n_vars - first_difference - 1, 0,
1565 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1566 pt->vars[first_difference]);
1569 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1570 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1571 additionally suffixed with a letter `M'. */
1573 format_cell_entry (struct tab_table *table, int c, int r, double value,
1574 char suffix, bool mark_missing, const struct dictionary *dict)
1582 s = data_out (&v, dict_get_encoding (dict), settings_get_format ());
1586 suffixes[suffix_len++] = suffix;
1588 suffixes[suffix_len++] = 'M';
1589 suffixes[suffix_len] = '\0';
1591 tab_text_format (table, c, r, TAB_RIGHT, "%s%s",
1592 s + strspn (s, " "), suffixes);
1597 /* Displays the crosstabulation table. */
1599 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1600 struct tab_table *table)
1606 for (r = 0; r < pt->n_rows; r++)
1607 table_value_missing (proc, table, pt->n_consts + pt->n_vars - 2,
1608 r * proc->n_cells, TAB_RIGHT, &pt->rows[r],
1611 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1612 TAB_LEFT, _("Total"));
1614 /* Put in the actual cells. */
1616 tab_offset (table, pt->n_consts + pt->n_vars - 1, -1);
1617 for (r = 0; r < pt->n_rows; r++)
1619 if (proc->n_cells > 1)
1620 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1621 for (c = 0; c < pt->n_cols; c++)
1623 bool mark_missing = false;
1624 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1625 if (proc->exclude == MV_NEVER
1626 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1627 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1629 mark_missing = true;
1630 for (i = 0; i < proc->n_cells; i++)
1635 switch (proc->a_cells[i])
1641 v = *mp / pt->row_tot[r] * 100.;
1645 v = *mp / pt->col_tot[c] * 100.;
1649 v = *mp / pt->total * 100.;
1652 case CRS_CL_EXPECTED:
1655 case CRS_CL_RESIDUAL:
1656 v = *mp - expected_value;
1658 case CRS_CL_SRESIDUAL:
1659 v = (*mp - expected_value) / sqrt (expected_value);
1661 case CRS_CL_ASRESIDUAL:
1662 v = ((*mp - expected_value)
1663 / sqrt (expected_value
1664 * (1. - pt->row_tot[r] / pt->total)
1665 * (1. - pt->col_tot[c] / pt->total)));
1670 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1676 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1680 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1681 for (r = 0; r < pt->n_rows; r++)
1683 bool mark_missing = false;
1685 if (proc->exclude == MV_NEVER
1686 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1687 mark_missing = true;
1689 for (i = 0; i < proc->n_cells; i++)
1694 switch (proc->a_cells[i])
1704 v = pt->row_tot[r] / pt->total * 100.;
1708 v = pt->row_tot[r] / pt->total * 100.;
1711 case CRS_CL_EXPECTED:
1712 case CRS_CL_RESIDUAL:
1713 case CRS_CL_SRESIDUAL:
1714 case CRS_CL_ASRESIDUAL:
1721 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing, proc->dict);
1722 tab_next_row (table);
1726 /* Column totals, grand total. */
1728 if (proc->n_cells > 1)
1729 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1730 for (c = 0; c <= pt->n_cols; c++)
1732 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1733 bool mark_missing = false;
1736 if (proc->exclude == MV_NEVER && c < pt->n_cols
1737 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1738 mark_missing = true;
1740 for (i = 0; i < proc->n_cells; i++)
1745 switch (proc->a_cells[i])
1751 v = ct / pt->total * 100.;
1759 v = ct / pt->total * 100.;
1762 case CRS_CL_EXPECTED:
1763 case CRS_CL_RESIDUAL:
1764 case CRS_CL_SRESIDUAL:
1765 case CRS_CL_ASRESIDUAL:
1771 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1776 tab_offset (table, -1, tab_row (table) + last_row);
1777 tab_offset (table, 0, -1);
1780 static void calc_r (struct pivot_table *,
1781 double *PT, double *Y, double *, double *, double *);
1782 static void calc_chisq (struct pivot_table *,
1783 double[N_CHISQ], int[N_CHISQ], double *, double *);
1785 /* Display chi-square statistics. */
1787 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1788 bool *showed_fisher)
1790 static const char *chisq_stats[N_CHISQ] =
1792 N_("Pearson Chi-Square"),
1793 N_("Likelihood Ratio"),
1794 N_("Fisher's Exact Test"),
1795 N_("Continuity Correction"),
1796 N_("Linear-by-Linear Association"),
1798 double chisq_v[N_CHISQ];
1799 double fisher1, fisher2;
1804 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1806 tab_offset (chisq, pt->n_consts + pt->n_vars - 2, -1);
1808 for (i = 0; i < N_CHISQ; i++)
1810 if ((i != 2 && chisq_v[i] == SYSMIS)
1811 || (i == 2 && fisher1 == SYSMIS))
1814 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1817 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL, RC_OTHER);
1818 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], NULL, RC_WEIGHT);
1819 tab_double (chisq, 3, 0, TAB_RIGHT,
1820 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL, RC_PVALUE);
1824 *showed_fisher = true;
1825 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL, RC_PVALUE);
1826 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL, RC_PVALUE);
1828 tab_next_row (chisq);
1831 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1832 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, NULL, RC_WEIGHT);
1833 tab_next_row (chisq);
1835 tab_offset (chisq, 0, -1);
1838 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1839 double[N_SYMMETRIC], double[N_SYMMETRIC],
1840 double[N_SYMMETRIC],
1841 double[3], double[3], double[3]);
1843 /* Display symmetric measures. */
1845 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1846 struct tab_table *sym)
1848 static const char *categories[] =
1850 N_("Nominal by Nominal"),
1851 N_("Ordinal by Ordinal"),
1852 N_("Interval by Interval"),
1853 N_("Measure of Agreement"),
1856 static const char *stats[N_SYMMETRIC] =
1860 N_("Contingency Coefficient"),
1861 N_("Kendall's tau-b"),
1862 N_("Kendall's tau-c"),
1864 N_("Spearman Correlation"),
1869 static const int stats_categories[N_SYMMETRIC] =
1871 0, 0, 0, 1, 1, 1, 1, 2, 3,
1875 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1876 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1879 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1880 somers_d_v, somers_d_ase, somers_d_t))
1883 tab_offset (sym, pt->n_consts + pt->n_vars - 2, -1);
1885 for (i = 0; i < N_SYMMETRIC; i++)
1887 if (sym_v[i] == SYSMIS)
1890 if (stats_categories[i] != last_cat)
1892 last_cat = stats_categories[i];
1893 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1896 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1897 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL, RC_OTHER);
1898 if (sym_ase[i] != SYSMIS)
1899 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL, RC_OTHER);
1900 if (sym_t[i] != SYSMIS)
1901 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL, RC_OTHER);
1902 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL, RC_PVALUE);*/
1906 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1907 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, NULL, RC_WEIGHT);
1910 tab_offset (sym, 0, -1);
1913 static int calc_risk (struct pivot_table *,
1914 double[], double[], double[], union value *);
1916 /* Display risk estimate. */
1918 display_risk (struct pivot_table *pt, struct tab_table *risk)
1921 double risk_v[3], lower[3], upper[3];
1925 if (!calc_risk (pt, risk_v, upper, lower, c))
1928 tab_offset (risk, pt->n_consts + pt->n_vars - 2, -1);
1930 for (i = 0; i < 3; i++)
1932 const struct variable *cv = pt->vars[COL_VAR];
1933 const struct variable *rv = pt->vars[ROW_VAR];
1934 int cvw = var_get_width (cv);
1935 int rvw = var_get_width (rv);
1937 if (risk_v[i] == SYSMIS)
1943 if (var_is_numeric (cv))
1944 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1945 var_to_string (cv), c[0].f, c[1].f);
1947 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1949 cvw, value_str (&c[0], cvw),
1950 cvw, value_str (&c[1], cvw));
1954 if (var_is_numeric (rv))
1955 sprintf (buf, _("For cohort %s = %.*g"),
1956 var_to_string (rv), DBL_DIG + 1, pt->rows[i - 1].f);
1958 sprintf (buf, _("For cohort %s = %.*s"),
1960 rvw, value_str (&pt->rows[i - 1], rvw));
1964 tab_text (risk, 0, 0, TAB_LEFT, buf);
1965 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL, RC_OTHER);
1966 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL, RC_OTHER);
1967 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL, RC_OTHER);
1968 tab_next_row (risk);
1971 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1972 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, NULL, RC_WEIGHT);
1973 tab_next_row (risk);
1975 tab_offset (risk, 0, -1);
1978 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1979 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1980 double[N_DIRECTIONAL]);
1982 /* Display directional measures. */
1984 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
1985 struct tab_table *direct)
1987 static const char *categories[] =
1989 N_("Nominal by Nominal"),
1990 N_("Ordinal by Ordinal"),
1991 N_("Nominal by Interval"),
1994 static const char *stats[] =
1997 N_("Goodman and Kruskal tau"),
1998 N_("Uncertainty Coefficient"),
2003 static const char *types[] =
2010 static const int stats_categories[N_DIRECTIONAL] =
2012 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
2015 static const int stats_stats[N_DIRECTIONAL] =
2017 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
2020 static const int stats_types[N_DIRECTIONAL] =
2022 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
2025 static const int *stats_lookup[] =
2032 static const char **stats_names[] =
2044 double direct_v[N_DIRECTIONAL];
2045 double direct_ase[N_DIRECTIONAL];
2046 double direct_t[N_DIRECTIONAL];
2050 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t))
2053 tab_offset (direct, pt->n_consts + pt->n_vars - 2, -1);
2055 for (i = 0; i < N_DIRECTIONAL; i++)
2057 if (direct_v[i] == SYSMIS)
2063 for (j = 0; j < 3; j++)
2064 if (last[j] != stats_lookup[j][i])
2067 tab_hline (direct, TAL_1, j, 6, 0);
2072 int k = last[j] = stats_lookup[j][i];
2077 string = var_to_string (pt->vars[0]);
2079 string = var_to_string (pt->vars[1]);
2081 tab_text_format (direct, j, 0, TAB_LEFT,
2082 gettext (stats_names[j][k]), string);
2087 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL, RC_OTHER);
2088 if (direct_ase[i] != SYSMIS)
2089 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL, RC_OTHER);
2090 if (direct_t[i] != SYSMIS)
2091 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL, RC_OTHER);
2092 /*tab_double (direct, 6, 0, TAB_RIGHT, normal_sig (direct_v[i]), NULL, RC_PVALUE);*/
2093 tab_next_row (direct);
2096 tab_offset (direct, 0, -1);
2099 /* Statistical calculations. */
2101 /* Returns the value of the logarithm of gamma (factorial) function for an integer
2104 log_gamma_int (double pt)
2109 for (i = 2; i < pt; i++)
2115 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2117 static inline double
2118 Pr (int a, int b, int c, int d)
2120 return exp (log_gamma_int (a + b + 1.) - log_gamma_int (a + 1.)
2121 + log_gamma_int (c + d + 1.) - log_gamma_int (b + 1.)
2122 + log_gamma_int (a + c + 1.) - log_gamma_int (c + 1.)
2123 + log_gamma_int (b + d + 1.) - log_gamma_int (d + 1.)
2124 - log_gamma_int (a + b + c + d + 1.));
2127 /* Swap the contents of A and B. */
2129 swap (int *a, int *b)
2136 /* Calculate significance for Fisher's exact test as specified in
2137 _SPSS Statistical Algorithms_, Appendix 5. */
2139 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);
2156 pn1 = Pr (a, b, c, d);
2158 for (pt = 1; pt <= a; pt++)
2160 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2163 *fisher2 = *fisher1;
2165 for (pt = 1; pt <= b; pt++)
2167 double p = Pr (a + pt, b - pt, c - pt, d + pt);
2173 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2174 columns with values COLS and N_ROWS rows with values ROWS. Values
2175 in the matrix sum to pt->total. */
2177 calc_chisq (struct pivot_table *pt,
2178 double chisq[N_CHISQ], int df[N_CHISQ],
2179 double *fisher1, double *fisher2)
2183 chisq[0] = chisq[1] = 0.;
2184 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2185 *fisher1 = *fisher2 = SYSMIS;
2187 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2189 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2191 chisq[0] = chisq[1] = SYSMIS;
2195 for (r = 0; r < pt->n_rows; r++)
2196 for (c = 0; c < pt->n_cols; c++)
2198 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2199 const double freq = pt->mat[pt->n_cols * r + c];
2200 const double residual = freq - expected;
2202 chisq[0] += residual * residual / expected;
2204 chisq[1] += freq * log (expected / freq);
2215 /* Calculate Yates and Fisher exact test. */
2216 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2218 double f11, f12, f21, f22;
2224 for (i = j = 0; i < pt->n_cols; i++)
2225 if (pt->col_tot[i] != 0.)
2234 f11 = pt->mat[nz_cols[0]];
2235 f12 = pt->mat[nz_cols[1]];
2236 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2237 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2242 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2245 chisq[3] = (pt->total * pow2 (pt_)
2246 / (f11 + f12) / (f21 + f22)
2247 / (f11 + f21) / (f12 + f22));
2255 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2258 /* Calculate Mantel-Haenszel. */
2259 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2261 double r, ase_0, ase_1;
2262 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2264 chisq[4] = (pt->total - 1.) * r * r;
2269 /* Calculate the value of Pearson's r. r is stored into R, ase_1 into
2270 ASE_1, and ase_0 into ASE_0. The row and column values must be
2271 passed in PT and Y. */
2273 calc_r (struct pivot_table *pt,
2274 double *PT, double *Y, double *r, double *ase_0, double *ase_1)
2276 double SX, SY, S, T;
2278 double sum_XYf, sum_X2Y2f;
2279 double sum_Xr, sum_X2r;
2280 double sum_Yc, sum_Y2c;
2283 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2284 for (j = 0; j < pt->n_cols; j++)
2286 double fij = pt->mat[j + i * pt->n_cols];
2287 double product = PT[i] * Y[j];
2288 double temp = fij * product;
2290 sum_X2Y2f += temp * product;
2293 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2295 sum_Xr += PT[i] * pt->row_tot[i];
2296 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2298 Xbar = sum_Xr / pt->total;
2300 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2302 sum_Yc += Y[i] * pt->col_tot[i];
2303 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2305 Ybar = sum_Yc / pt->total;
2307 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2308 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2309 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2312 *ase_0 = sqrt ((sum_X2Y2f - pow2 (sum_XYf) / pt->total) / (sum_X2r * sum_Y2c));
2317 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2318 for (j = 0; j < pt->n_cols; j++)
2320 double Xresid, Yresid;
2323 Xresid = PT[i] - Xbar;
2324 Yresid = Y[j] - Ybar;
2325 temp = (T * Xresid * Yresid
2327 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2328 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2333 *ase_1 = sqrt (s) / (T * T);
2337 /* Calculate symmetric statistics and their asymptotic standard
2338 errors. Returns 0 if none could be calculated. */
2340 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2341 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2342 double t[N_SYMMETRIC],
2343 double somers_d_v[3], double somers_d_ase[3],
2344 double somers_d_t[3])
2348 q = MIN (pt->ns_rows, pt->ns_cols);
2352 for (i = 0; i < N_SYMMETRIC; i++)
2353 v[i] = ase[i] = t[i] = SYSMIS;
2355 /* Phi, Cramer's V, contingency coefficient. */
2356 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2358 double Xp = 0.; /* Pearson chi-square. */
2361 for (r = 0; r < pt->n_rows; r++)
2362 for (c = 0; c < pt->n_cols; c++)
2364 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2365 const double freq = pt->mat[pt->n_cols * r + c];
2366 const double residual = freq - expected;
2368 Xp += residual * residual / expected;
2371 if (proc->statistics & (1u << CRS_ST_PHI))
2373 v[0] = sqrt (Xp / pt->total);
2374 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2376 if (proc->statistics & (1u << CRS_ST_CC))
2377 v[2] = sqrt (Xp / (Xp + pt->total));
2380 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2381 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2386 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2390 Dr = Dc = pow2 (pt->total);
2391 for (r = 0; r < pt->n_rows; r++)
2392 Dr -= pow2 (pt->row_tot[r]);
2393 for (c = 0; c < pt->n_cols; c++)
2394 Dc -= pow2 (pt->col_tot[c]);
2396 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2397 for (c = 0; c < pt->n_cols; c++)
2401 for (r = 0; r < pt->n_rows; r++)
2402 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2411 for (i = 0; i < pt->n_rows; i++)
2415 for (j = 1; j < pt->n_cols; j++)
2416 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2419 for (j = 1; j < pt->n_cols; j++)
2420 Dij += cum[j + (i - 1) * pt->n_cols];
2424 double fij = pt->mat[j + i * pt->n_cols];
2428 if (++j == pt->n_cols)
2430 assert (j < pt->n_cols);
2432 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2433 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2437 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2438 Dij -= cum[j + (i - 1) * pt->n_cols];
2444 if (proc->statistics & (1u << CRS_ST_BTAU))
2445 v[3] = (P - Q) / sqrt (Dr * Dc);
2446 if (proc->statistics & (1u << CRS_ST_CTAU))
2447 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2448 if (proc->statistics & (1u << CRS_ST_GAMMA))
2449 v[5] = (P - Q) / (P + Q);
2451 /* ASE for tau-b, tau-c, gamma. Calculations could be
2452 eliminated here, at expense of memory. */
2457 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2458 for (i = 0; i < pt->n_rows; i++)
2462 for (j = 1; j < pt->n_cols; j++)
2463 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2466 for (j = 1; j < pt->n_cols; j++)
2467 Dij += cum[j + (i - 1) * pt->n_cols];
2471 double fij = pt->mat[j + i * pt->n_cols];
2473 if (proc->statistics & (1u << CRS_ST_BTAU))
2475 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2476 + v[3] * (pt->row_tot[i] * Dc
2477 + pt->col_tot[j] * Dr));
2478 btau_cum += fij * temp * temp;
2482 const double temp = Cij - Dij;
2483 ctau_cum += fij * temp * temp;
2486 if (proc->statistics & (1u << CRS_ST_GAMMA))
2488 const double temp = Q * Cij - P * Dij;
2489 gamma_cum += fij * temp * temp;
2492 if (proc->statistics & (1u << CRS_ST_D))
2494 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2495 - (P - Q) * (pt->total - pt->row_tot[i]));
2496 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2497 - (Q - P) * (pt->total - pt->col_tot[j]));
2500 if (++j == pt->n_cols)
2502 assert (j < pt->n_cols);
2504 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2505 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2509 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2510 Dij -= cum[j + (i - 1) * pt->n_cols];
2516 btau_var = ((btau_cum
2517 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2519 if (proc->statistics & (1u << CRS_ST_BTAU))
2521 ase[3] = sqrt (btau_var);
2522 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2525 if (proc->statistics & (1u << CRS_ST_CTAU))
2527 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2528 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2529 t[4] = v[4] / ase[4];
2531 if (proc->statistics & (1u << CRS_ST_GAMMA))
2533 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2534 t[5] = v[5] / (2. / (P + Q)
2535 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2537 if (proc->statistics & (1u << CRS_ST_D))
2539 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2540 somers_d_ase[0] = 2. * btau_var / (Dr + Dc) * sqrt (Dr * Dc);
2541 somers_d_t[0] = (somers_d_v[0]
2543 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2544 somers_d_v[1] = (P - Q) / Dc;
2545 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2546 somers_d_t[1] = (somers_d_v[1]
2548 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2549 somers_d_v[2] = (P - Q) / Dr;
2550 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2551 somers_d_t[2] = (somers_d_v[2]
2553 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2559 /* Spearman correlation, Pearson's r. */
2560 if (proc->statistics & (1u << CRS_ST_CORR))
2562 double *R = xmalloc (sizeof *R * pt->n_rows);
2563 double *C = xmalloc (sizeof *C * pt->n_cols);
2566 double y, t, c = 0., s = 0.;
2571 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2572 y = pt->row_tot[i] - c;
2576 if (++i == pt->n_rows)
2578 assert (i < pt->n_rows);
2583 double y, t, c = 0., s = 0.;
2588 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2589 y = pt->col_tot[j] - c;
2593 if (++j == pt->n_cols)
2595 assert (j < pt->n_cols);
2599 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2605 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2609 /* Cohen's kappa. */
2610 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2612 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2615 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2616 i < pt->ns_rows; i++, j++)
2620 while (pt->col_tot[j] == 0.)
2623 prod = pt->row_tot[i] * pt->col_tot[j];
2624 sum = pt->row_tot[i] + pt->col_tot[j];
2626 sum_fii += pt->mat[j + i * pt->n_cols];
2628 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2629 sum_riciri_ci += prod * sum;
2631 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2632 for (j = 0; j < pt->ns_cols; j++)
2634 double sum = pt->row_tot[i] + pt->col_tot[j];
2635 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2638 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2640 ase[8] = sqrt ((pow2 (pt->total) * sum_rici
2641 + sum_rici * sum_rici
2642 - pt->total * sum_riciri_ci)
2643 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2645 t[8] = v[8] / sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2646 / pow2 (pow2 (pt->total) - sum_rici))
2647 + ((2. * (pt->total - sum_fii)
2648 * (2. * sum_fii * sum_rici
2649 - pt->total * sum_fiiri_ci))
2650 / cube (pow2 (pt->total) - sum_rici))
2651 + (pow2 (pt->total - sum_fii)
2652 * (pt->total * sum_fijri_ci2 - 4.
2653 * sum_rici * sum_rici)
2654 / pow4 (pow2 (pt->total) - sum_rici))));
2656 t[8] = v[8] / ase[8];
2663 /* Calculate risk estimate. */
2665 calc_risk (struct pivot_table *pt,
2666 double *value, double *upper, double *lower, union value *c)
2668 double f11, f12, f21, f22;
2674 for (i = 0; i < 3; i++)
2675 value[i] = upper[i] = lower[i] = SYSMIS;
2678 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2685 for (i = j = 0; i < pt->n_cols; i++)
2686 if (pt->col_tot[i] != 0.)
2695 f11 = pt->mat[nz_cols[0]];
2696 f12 = pt->mat[nz_cols[1]];
2697 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2698 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2700 c[0] = pt->cols[nz_cols[0]];
2701 c[1] = pt->cols[nz_cols[1]];
2704 value[0] = (f11 * f22) / (f12 * f21);
2705 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2706 lower[0] = value[0] * exp (-1.960 * v);
2707 upper[0] = value[0] * exp (1.960 * v);
2709 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2710 v = sqrt ((f12 / (f11 * (f11 + f12)))
2711 + (f22 / (f21 * (f21 + f22))));
2712 lower[1] = value[1] * exp (-1.960 * v);
2713 upper[1] = value[1] * exp (1.960 * v);
2715 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2716 v = sqrt ((f11 / (f12 * (f11 + f12)))
2717 + (f21 / (f22 * (f21 + f22))));
2718 lower[2] = value[2] * exp (-1.960 * v);
2719 upper[2] = value[2] * exp (1.960 * v);
2724 /* Calculate directional measures. */
2726 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2727 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2728 double t[N_DIRECTIONAL])
2733 for (i = 0; i < N_DIRECTIONAL; i++)
2734 v[i] = ase[i] = t[i] = SYSMIS;
2738 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2740 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2741 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2742 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2743 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2744 double sum_fim, sum_fmj;
2746 int rm_index, cm_index;
2749 /* Find maximum for each row and their sum. */
2750 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2752 double max = pt->mat[i * pt->n_cols];
2755 for (j = 1; j < pt->n_cols; j++)
2756 if (pt->mat[j + i * pt->n_cols] > max)
2758 max = pt->mat[j + i * pt->n_cols];
2762 sum_fim += fim[i] = max;
2763 fim_index[i] = index;
2766 /* Find maximum for each column. */
2767 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2769 double max = pt->mat[j];
2772 for (i = 1; i < pt->n_rows; i++)
2773 if (pt->mat[j + i * pt->n_cols] > max)
2775 max = pt->mat[j + i * pt->n_cols];
2779 sum_fmj += fmj[j] = max;
2780 fmj_index[j] = index;
2783 /* Find maximum row total. */
2784 rm = pt->row_tot[0];
2786 for (i = 1; i < pt->n_rows; i++)
2787 if (pt->row_tot[i] > rm)
2789 rm = pt->row_tot[i];
2793 /* Find maximum column total. */
2794 cm = pt->col_tot[0];
2796 for (j = 1; j < pt->n_cols; j++)
2797 if (pt->col_tot[j] > cm)
2799 cm = pt->col_tot[j];
2803 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2804 v[1] = (sum_fmj - rm) / (pt->total - rm);
2805 v[2] = (sum_fim - cm) / (pt->total - cm);
2807 /* ASE1 for Y given PT. */
2811 for (accum = 0., i = 0; i < pt->n_rows; i++)
2812 for (j = 0; j < pt->n_cols; j++)
2814 const int deltaj = j == cm_index;
2815 accum += (pt->mat[j + i * pt->n_cols]
2816 * pow2 ((j == fim_index[i])
2821 ase[2] = sqrt (accum - pt->total * v[0]) / (pt->total - cm);
2824 /* ASE0 for Y given PT. */
2828 for (accum = 0., i = 0; i < pt->n_rows; i++)
2829 if (cm_index != fim_index[i])
2830 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2831 + pt->mat[i * pt->n_cols + cm_index]);
2832 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2835 /* ASE1 for PT given Y. */
2839 for (accum = 0., i = 0; i < pt->n_rows; i++)
2840 for (j = 0; j < pt->n_cols; j++)
2842 const int deltaj = i == rm_index;
2843 accum += (pt->mat[j + i * pt->n_cols]
2844 * pow2 ((i == fmj_index[j])
2849 ase[1] = sqrt (accum - pt->total * v[0]) / (pt->total - rm);
2852 /* ASE0 for PT given Y. */
2856 for (accum = 0., j = 0; j < pt->n_cols; j++)
2857 if (rm_index != fmj_index[j])
2858 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2859 + pt->mat[j + pt->n_cols * rm_index]);
2860 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2863 /* Symmetric ASE0 and ASE1. */
2868 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2869 for (j = 0; j < pt->n_cols; j++)
2871 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2872 int temp1 = (i == rm_index) + (j == cm_index);
2873 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2874 accum1 += (pt->mat[j + i * pt->n_cols]
2875 * pow2 (temp0 + (v[0] - 1.) * temp1));
2877 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2878 t[0] = v[0] / (sqrt (accum0 - pow2 ((sum_fim + sum_fmj - cm - rm) / pt->total))
2879 / (2. * pt->total - rm - cm));
2888 double sum_fij2_ri, sum_fij2_ci;
2889 double sum_ri2, sum_cj2;
2891 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2892 for (j = 0; j < pt->n_cols; j++)
2894 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2895 sum_fij2_ri += temp / pt->row_tot[i];
2896 sum_fij2_ci += temp / pt->col_tot[j];
2899 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2900 sum_ri2 += pow2 (pt->row_tot[i]);
2902 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2903 sum_cj2 += pow2 (pt->col_tot[j]);
2905 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2906 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2910 if (proc->statistics & (1u << CRS_ST_UC))
2912 double UX, UY, UXY, P;
2913 double ase1_yx, ase1_xy, ase1_sym;
2916 for (UX = 0., i = 0; i < pt->n_rows; i++)
2917 if (pt->row_tot[i] > 0.)
2918 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2920 for (UY = 0., j = 0; j < pt->n_cols; j++)
2921 if (pt->col_tot[j] > 0.)
2922 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2924 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2925 for (j = 0; j < pt->n_cols; j++)
2927 double entry = pt->mat[j + i * pt->n_cols];
2932 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2933 UXY -= entry / pt->total * log (entry / pt->total);
2936 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2937 for (j = 0; j < pt->n_cols; j++)
2939 double entry = pt->mat[j + i * pt->n_cols];
2944 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2945 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2946 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2947 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2948 ase1_sym += entry * pow2 ((UXY
2949 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2950 - (UX + UY) * log (entry / pt->total));
2953 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2954 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2955 t[5] = v[5] / ((2. / (pt->total * (UX + UY)))
2956 * sqrt (P - pow2 (UX + UY - UXY) / pt->total));
2958 v[6] = (UX + UY - UXY) / UX;
2959 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2960 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2962 v[7] = (UX + UY - UXY) / UY;
2963 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2964 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2968 if (proc->statistics & (1u << CRS_ST_D))
2970 double v_dummy[N_SYMMETRIC];
2971 double ase_dummy[N_SYMMETRIC];
2972 double t_dummy[N_SYMMETRIC];
2973 double somers_d_v[3];
2974 double somers_d_ase[3];
2975 double somers_d_t[3];
2977 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2978 somers_d_v, somers_d_ase, somers_d_t))
2981 for (i = 0; i < 3; i++)
2983 v[8 + i] = somers_d_v[i];
2984 ase[8 + i] = somers_d_ase[i];
2985 t[8 + i] = somers_d_t[i];
2991 if (proc->statistics & (1u << CRS_ST_ETA))
2994 double sum_Xr, sum_X2r;
2998 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
3000 sum_Xr += pt->rows[i].f * pt->row_tot[i];
3001 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
3003 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
3005 for (SXW = 0., j = 0; j < pt->n_cols; j++)
3009 for (cum = 0., i = 0; i < pt->n_rows; i++)
3011 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
3012 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
3015 SXW -= cum * cum / pt->col_tot[j];
3017 v[11] = sqrt (1. - SXW / SX);
3021 double sum_Yc, sum_Y2c;
3025 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
3027 sum_Yc += pt->cols[i].f * pt->col_tot[i];
3028 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
3030 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
3032 for (SYW = 0., i = 0; i < pt->n_rows; i++)
3036 for (cum = 0., j = 0; j < pt->n_cols; j++)
3038 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
3039 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
3042 SYW -= cum * cum / pt->row_tot[i];
3044 v[12] = sqrt (1. - SYW / SY);