1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2006, 2009 Free Software Foundation, Inc.
4 This program is free software: you can redistribute it and/or modify
5 it under the terms of the GNU General Public License as published by
6 the Free Software Foundation, either version 3 of the License, or
7 (at your option) any later version.
9 This program is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 GNU General Public License for more details.
14 You should have received a copy of the GNU General Public License
15 along with this program. If not, see <http://www.gnu.org/licenses/>. */
19 - Pearson's R (but not Spearman!) is off a little.
20 - T values for Spearman's R and Pearson's R are wrong.
21 - How to calculate significance of symmetric and directional measures?
22 - Asymmetric ASEs and T values for lambda are wrong.
23 - ASE of Goodman and Kruskal's tau is not calculated.
24 - ASE of symmetric somers' d is wrong.
25 - Approx. T of uncertainty coefficient is wrong.
32 #include <gsl/gsl_cdf.h>
36 #include <data/case.h>
37 #include <data/casegrouper.h>
38 #include <data/casereader.h>
39 #include <data/data-out.h>
40 #include <data/dictionary.h>
41 #include <data/format.h>
42 #include <data/procedure.h>
43 #include <data/value-labels.h>
44 #include <data/variable.h>
45 #include <language/command.h>
46 #include <language/dictionary/split-file.h>
47 #include <language/lexer/lexer.h>
48 #include <language/lexer/variable-parser.h>
49 #include <libpspp/array.h>
50 #include <libpspp/assertion.h>
51 #include <libpspp/compiler.h>
52 #include <libpspp/hash.h>
53 #include <libpspp/hmap.h>
54 #include <libpspp/hmapx.h>
55 #include <libpspp/message.h>
56 #include <libpspp/misc.h>
57 #include <libpspp/pool.h>
58 #include <libpspp/str.h>
59 #include <output/output.h>
60 #include <output/table.h>
67 #define _(msgid) gettext (msgid)
68 #define N_(msgid) msgid
76 missing=miss:!table/include/report;
77 +write[wr_]=none,cells,all;
78 +format=fmt:!labels/nolabels/novallabs,
81 tabl:!tables/notables,
84 +cells[cl_]=count,expected,row,column,total,residual,sresidual,
86 +statistics[st_]=chisq,phi,cc,lambda,uc,none,btau,ctau,risk,gamma,d,
92 /* Number of chi-square statistics. */
95 /* Number of symmetric statistics. */
98 /* Number of directional statistics. */
99 #define N_DIRECTIONAL 13
101 /* A single table entry for general mode. */
104 struct hmap_node node; /* Entry in hash table. */
105 double freq; /* Frequency count. */
106 union value values[1]; /* Values. */
110 table_entry_size (size_t n_values)
112 return (offsetof (struct table_entry, values)
113 + n_values * sizeof (union value));
116 /* Indexes into the 'vars' member of struct pivot_table and
117 struct crosstab member. */
120 ROW_VAR = 0, /* Row variable. */
121 COL_VAR = 1 /* Column variable. */
122 /* Higher indexes cause multiple tables to be output. */
125 /* A crosstabulation of 2 or more variables. */
128 struct fmt_spec weight_format; /* Format for weight variable. */
129 double missing; /* Weight of missing cases. */
131 /* Variables (2 or more). */
133 const struct variable **vars;
135 /* Constants (0 or more). */
137 const struct variable **const_vars;
138 union value *const_values;
142 struct table_entry **entries;
145 /* Column values, number of columns. */
149 /* Row values, number of rows. */
153 /* Number of statistically interesting columns/rows
154 (columns/rows with data in them). */
155 int ns_cols, ns_rows;
157 /* Matrix contents. */
158 double *mat; /* Matrix proper. */
159 double *row_tot; /* Row totals. */
160 double *col_tot; /* Column totals. */
161 double total; /* Grand total. */
164 /* Integer mode variable info. */
167 int min; /* Minimum value. */
168 int max; /* Maximum value + 1. */
169 int count; /* max - min. */
172 static inline struct var_range *
173 get_var_range (const struct variable *v)
175 return var_get_aux (v);
178 struct crosstabs_proc
180 const struct dictionary *dict;
181 enum { INTEGER, GENERAL } mode;
182 enum mv_class exclude;
185 struct fmt_spec weight_format;
187 /* Variables specifies on VARIABLES. */
188 const struct variable **variables;
192 struct pivot_table *pivots;
196 int n_cells; /* Number of cells requested. */
197 unsigned int cells; /* Bit k is 1 if cell k is requested. */
198 int a_cells[CRS_CL_count]; /* 0...n_cells-1 are the requested cells. */
201 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
204 /* Auxiliary data structure for tab_dim. */
205 struct crosstabs_dim_aux
207 enum mv_class exclude;
211 init_proc (struct crosstabs_proc *proc, struct dataset *ds)
213 const struct variable *wv = dict_get_weight (dataset_dict (ds));
214 proc->dict = dataset_dict (ds);
215 proc->bad_warn = true;
216 proc->variables = NULL;
217 proc->n_variables = 0;
220 proc->weight_format = wv ? *var_get_print_format (wv) : F_8_0;
224 free_proc (struct crosstabs_proc *proc)
226 struct pivot_table *pt;
228 free (proc->variables);
229 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
232 free (pt->const_vars);
233 /* We must not call value_destroy on const_values because
234 it is a wild pointer; it never pointed to anything owned
237 The rest of the data was allocated and destroyed at a
238 lower level already. */
243 static int internal_cmd_crosstabs (struct lexer *lexer, struct dataset *ds,
244 struct crosstabs_proc *);
245 static bool should_tabulate_case (const struct pivot_table *,
246 const struct ccase *, enum mv_class exclude);
247 static void tabulate_general_case (struct pivot_table *, const struct ccase *,
249 static void tabulate_integer_case (struct pivot_table *, const struct ccase *,
251 static void postcalc (struct crosstabs_proc *);
252 static void submit (struct crosstabs_proc *, struct pivot_table *,
255 /* Parse and execute CROSSTABS, then clean up. */
257 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
259 struct crosstabs_proc proc;
262 init_proc (&proc, ds);
263 result = internal_cmd_crosstabs (lexer, ds, &proc);
269 /* Parses and executes the CROSSTABS procedure. */
271 internal_cmd_crosstabs (struct lexer *lexer, struct dataset *ds,
272 struct crosstabs_proc *proc)
274 struct casegrouper *grouper;
275 struct casereader *input, *group;
276 struct cmd_crosstabs cmd;
277 struct pivot_table *pt;
281 if (!parse_crosstabs (lexer, ds, &cmd, proc))
284 proc->mode = proc->n_variables ? INTEGER : GENERAL;
288 proc->cells = 1u << CRS_CL_COUNT;
289 else if (cmd.a_cells[CRS_CL_ALL])
290 proc->cells = UINT_MAX;
294 for (i = 0; i < CRS_CL_count; i++)
296 proc->cells |= 1u << i;
297 if (proc->cells == 0)
298 proc->cells = ((1u << CRS_CL_COUNT)
300 | (1u << CRS_CL_COLUMN)
301 | (1u << CRS_CL_TOTAL));
303 proc->cells &= ((1u << CRS_CL_count) - 1);
304 proc->cells &= ~((1u << CRS_CL_NONE) | (1u << CRS_CL_ALL));
306 for (i = 0; i < CRS_CL_count; i++)
307 if (proc->cells & (1u << i))
308 proc->a_cells[proc->n_cells++] = i;
311 if (cmd.a_statistics[CRS_ST_ALL])
312 proc->statistics = UINT_MAX;
313 else if (cmd.sbc_statistics)
317 proc->statistics = 0;
318 for (i = 0; i < CRS_ST_count; i++)
319 if (cmd.a_statistics[i])
320 proc->statistics |= 1u << i;
321 if (proc->statistics == 0)
322 proc->statistics |= 1u << CRS_ST_CHISQ;
325 proc->statistics = 0;
328 proc->exclude = (cmd.miss == CRS_TABLE ? MV_ANY
329 : cmd.miss == CRS_INCLUDE ? MV_SYSTEM
331 if (proc->mode == GENERAL && proc->mode == MV_NEVER)
333 msg (SE, _("Missing mode REPORT not allowed in general mode. "
334 "Assuming MISSING=TABLE."));
339 proc->pivot = cmd.pivot == CRS_PIVOT;
341 input = casereader_create_filter_weight (proc_open (ds), dataset_dict (ds),
343 grouper = casegrouper_create_splits (input, dataset_dict (ds));
344 while (casegrouper_get_next_group (grouper, &group))
348 /* Output SPLIT FILE variables. */
349 c = casereader_peek (group, 0);
352 output_split_file_values (ds, c);
357 for (; (c = casereader_read (group)) != NULL; case_unref (c))
358 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
360 double weight = dict_get_case_weight (dataset_dict (ds), c,
362 if (should_tabulate_case (pt, c, proc->exclude))
364 if (proc->mode == GENERAL)
365 tabulate_general_case (pt, c, weight);
367 tabulate_integer_case (pt, c, weight);
370 pt->missing += weight;
372 casereader_destroy (group);
377 ok = casegrouper_destroy (grouper);
378 ok = proc_commit (ds) && ok;
380 return ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
383 /* Parses the TABLES subcommand. */
385 crs_custom_tables (struct lexer *lexer, struct dataset *ds,
386 struct cmd_crosstabs *cmd UNUSED, void *proc_)
388 struct crosstabs_proc *proc = proc_;
389 struct const_var_set *var_set;
391 const struct variable ***by = NULL;
393 size_t *by_nvar = NULL;
398 /* Ensure that this is a TABLES subcommand. */
399 if (!lex_match_id (lexer, "TABLES")
400 && (lex_token (lexer) != T_ID ||
401 dict_lookup_var (dataset_dict (ds), lex_tokid (lexer)) == NULL)
402 && lex_token (lexer) != T_ALL)
404 lex_match (lexer, '=');
406 if (proc->variables != NULL)
407 var_set = const_var_set_create_from_array (proc->variables,
410 var_set = const_var_set_create_from_dict (dataset_dict (ds));
411 assert (var_set != NULL);
415 by = xnrealloc (by, n_by + 1, sizeof *by);
416 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
417 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
418 PV_NO_DUPLICATE | PV_NO_SCRATCH))
420 if (xalloc_oversized (nx, by_nvar[n_by]))
422 msg (SE, _("Too many cross-tabulation variables or dimensions."));
428 if (!lex_match (lexer, T_BY))
432 lex_error (lexer, _("expecting BY"));
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++)
445 struct pivot_table *pt = &proc->pivots[proc->n_pivots++];
448 pt->weight_format = proc->weight_format;
451 pt->vars = xmalloc (n_by * sizeof *pt->vars);
453 pt->const_vars = NULL;
454 pt->const_values = NULL;
455 hmap_init (&pt->data);
459 for (j = 0; j < n_by; j++)
460 pt->vars[j] = by[j][by_iter[j]];
462 for (j = n_by - 1; j >= 0; j--)
464 if (++by_iter[j] < by_nvar[j])
473 /* All return paths lead here. */
474 for (i = 0; i < n_by; i++)
479 const_var_set_destroy (var_set);
484 /* Parses the VARIABLES subcommand. */
486 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
487 struct cmd_crosstabs *cmd UNUSED, void *proc_)
489 struct crosstabs_proc *proc = proc_;
492 msg (SE, _("VARIABLES must be specified before TABLES."));
496 lex_match (lexer, '=');
500 size_t orig_nv = proc->n_variables;
505 if (!parse_variables_const (lexer, dataset_dict (ds),
506 &proc->variables, &proc->n_variables,
507 (PV_APPEND | PV_NUMERIC
508 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
511 if (lex_token (lexer) != '(')
513 lex_error (lexer, "expecting `('");
518 if (!lex_force_int (lexer))
520 min = lex_integer (lexer);
523 lex_match (lexer, ',');
525 if (!lex_force_int (lexer))
527 max = lex_integer (lexer);
530 msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
536 if (lex_token (lexer) != ')')
538 lex_error (lexer, "expecting `)'");
543 for (i = orig_nv; i < proc->n_variables; i++)
545 struct var_range *vr = xmalloc (sizeof *vr);
548 vr->count = max - min + 1;
549 var_attach_aux (proc->variables[i], vr, var_dtor_free);
552 if (lex_token (lexer) == '/')
559 free (proc->variables);
560 proc->variables = NULL;
561 proc->n_variables = 0;
565 /* Data file processing. */
568 should_tabulate_case (const struct pivot_table *pt, const struct ccase *c,
569 enum mv_class exclude)
572 for (j = 0; j < pt->n_vars; j++)
574 const struct variable *var = pt->vars[j];
575 struct var_range *range = get_var_range (var);
577 if (var_is_value_missing (var, case_data (c, var), exclude))
582 double num = case_num (c, var);
583 if (num < range->min || num > range->max)
591 tabulate_integer_case (struct pivot_table *pt, const struct ccase *c,
594 struct table_entry *te;
599 for (j = 0; j < pt->n_vars; j++)
601 /* Throw away fractional parts of values. */
602 hash = hash_int (case_num (c, pt->vars[j]), hash);
605 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
607 for (j = 0; j < pt->n_vars; j++)
608 if ((int) case_num (c, pt->vars[j]) != (int) te->values[j].f)
611 /* Found an existing entry. */
618 /* No existing entry. Create a new one. */
619 te = xmalloc (table_entry_size (pt->n_vars));
621 for (j = 0; j < pt->n_vars; j++)
622 te->values[j].f = (int) case_num (c, pt->vars[j]);
623 hmap_insert (&pt->data, &te->node, hash);
627 tabulate_general_case (struct pivot_table *pt, const struct ccase *c,
630 struct table_entry *te;
635 for (j = 0; j < pt->n_vars; j++)
637 const struct variable *var = pt->vars[j];
638 hash = value_hash (case_data (c, var), var_get_width (var), hash);
641 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
643 for (j = 0; j < pt->n_vars; j++)
645 const struct variable *var = pt->vars[j];
646 if (!value_equal (case_data (c, var), &te->values[j],
647 var_get_width (var)))
651 /* Found an existing entry. */
658 /* No existing entry. Create a new one. */
659 te = xmalloc (table_entry_size (pt->n_vars));
661 for (j = 0; j < pt->n_vars; j++)
663 const struct variable *var = pt->vars[j];
664 int width = var_get_width (var);
665 value_init (&te->values[j], width);
666 value_copy (&te->values[j], case_data (c, var), width);
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 void enum_var_values (const struct pivot_table *, int var_idx,
680 union value **valuesp, int *n_values);
681 static void output_pivot_table (struct crosstabs_proc *,
682 struct pivot_table *);
683 static void make_pivot_table_subset (struct pivot_table *pt,
684 size_t row0, size_t row1,
685 struct pivot_table *subset);
686 static void make_summary_table (struct crosstabs_proc *);
687 static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
690 postcalc (struct crosstabs_proc *proc)
692 struct pivot_table *pt;
694 /* Convert hash tables into sorted arrays of entries. */
695 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
697 struct table_entry *e;
700 pt->n_entries = hmap_count (&pt->data);
701 pt->entries = xnmalloc (pt->n_entries, sizeof *pt->entries);
703 HMAP_FOR_EACH (e, struct table_entry, node, &pt->data)
704 pt->entries[i++] = e;
705 hmap_destroy (&pt->data);
707 sort (pt->entries, pt->n_entries, sizeof *pt->entries,
708 compare_table_entry_3way, pt);
711 make_summary_table (proc);
713 /* Output each pivot table. */
714 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
716 if (proc->pivot || pt->n_vars == 2)
717 output_pivot_table (proc, pt);
720 size_t row0 = 0, row1 = 0;
721 while (find_crosstab (pt, &row0, &row1))
723 struct pivot_table subset;
724 make_pivot_table_subset (pt, row0, row1, &subset);
725 output_pivot_table (proc, &subset);
730 /* Free output and prepare for next split file. */
731 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
737 /* Free only the members that were allocated in this
738 function. The other pointer members are either both
739 allocated and destroyed at a lower level (in
740 output_pivot_table), or both allocated and destroyed at
741 a higher level (in crs_custom_tables and free_proc,
743 for (i = 0; i < pt->n_entries; i++)
744 free (pt->entries[i]);
750 make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
751 struct pivot_table *subset)
756 assert (pt->n_consts == 0);
757 subset->missing = pt->missing;
759 subset->vars = pt->vars;
760 subset->n_consts = pt->n_vars - 2;
761 subset->const_vars = pt->vars + 2;
762 subset->const_values = &pt->entries[row0]->values[2];
764 subset->entries = &pt->entries[row0];
765 subset->n_entries = row1 - row0;
769 compare_table_entry_var_3way (const struct table_entry *a,
770 const struct table_entry *b,
771 const struct pivot_table *pt,
774 return value_compare_3way (&a->values[idx], &b->values[idx],
775 var_get_width (pt->vars[idx]));
779 compare_table_entry_vars_3way (const struct table_entry *a,
780 const struct table_entry *b,
781 const struct pivot_table *pt,
786 for (i = idx1 - 1; i >= idx0; i--)
788 int cmp = compare_table_entry_var_3way (a, b, pt, i);
795 /* Compare the struct table_entry at *AP to the one at *BP and
796 return a strcmp()-type result. */
798 compare_table_entry_3way (const void *ap_, const void *bp_, const void *pt_)
800 const struct table_entry *const *ap = ap_;
801 const struct table_entry *const *bp = bp_;
802 const struct table_entry *a = *ap;
803 const struct table_entry *b = *bp;
804 const struct pivot_table *pt = pt_;
807 cmp = compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars);
811 cmp = compare_table_entry_var_3way (a, b, pt, ROW_VAR);
815 return compare_table_entry_var_3way (a, b, pt, COL_VAR);
819 find_first_difference (const struct pivot_table *pt, size_t row)
822 return pt->n_vars - 1;
825 const struct table_entry *a = pt->entries[row];
826 const struct table_entry *b = pt->entries[row - 1];
829 for (col = pt->n_vars - 1; col >= 0; col--)
830 if (compare_table_entry_var_3way (a, b, pt, col))
836 /* Output a table summarizing the cases processed. */
838 make_summary_table (struct crosstabs_proc *proc)
840 struct tab_table *summary;
841 struct pivot_table *pt;
845 summary = tab_create (7, 3 + proc->n_pivots);
846 tab_title (summary, _("Summary."));
847 tab_headers (summary, 1, 0, 3, 0);
848 tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
849 tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
850 tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
851 tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
852 tab_hline (summary, TAL_1, 1, 6, 1);
853 tab_hline (summary, TAL_1, 1, 6, 2);
854 tab_vline (summary, TAL_1, 3, 1, 1);
855 tab_vline (summary, TAL_1, 5, 1, 1);
856 for (i = 0; i < 3; i++)
858 tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
859 tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
861 tab_offset (summary, 0, 3);
863 ds_init_empty (&name);
864 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
870 tab_hline (summary, TAL_1, 0, 6, 0);
873 for (i = 0; i < pt->n_vars; i++)
876 ds_put_cstr (&name, " * ");
877 ds_put_cstr (&name, var_to_string (pt->vars[i]));
879 tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
882 for (i = 0; i < pt->n_entries; i++)
883 valid += pt->entries[i]->freq;
888 for (i = 0; i < 3; i++)
890 tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i],
891 &proc->weight_format);
892 tab_text_format (summary, i * 2 + 2, 0, TAB_RIGHT, "%.1f%%",
896 tab_next_row (summary);
900 submit (proc, NULL, summary);
905 static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
906 struct pivot_table *);
907 static struct tab_table *create_chisq_table (struct pivot_table *);
908 static struct tab_table *create_sym_table (struct pivot_table *);
909 static struct tab_table *create_risk_table (struct pivot_table *);
910 static struct tab_table *create_direct_table (struct pivot_table *);
911 static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
912 struct tab_table *, int first_difference);
913 static void display_crosstabulation (struct crosstabs_proc *,
914 struct pivot_table *,
916 static void display_chisq (struct pivot_table *, struct tab_table *,
917 bool *showed_fisher);
918 static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
920 static void display_risk (struct pivot_table *, struct tab_table *);
921 static void display_directional (struct crosstabs_proc *, struct pivot_table *,
923 static void crosstabs_dim (struct tab_rendering *, void *aux);
924 static void crosstabs_dim_free (void *aux);
925 static void table_value_missing (struct crosstabs_proc *proc,
926 struct tab_table *table, int c, int r,
927 unsigned char opt, const union value *v,
928 const struct variable *var);
929 static void delete_missing (struct pivot_table *);
930 static void build_matrix (struct pivot_table *);
932 /* Output pivot table beginning at PB and continuing until PE,
933 exclusive. For efficiency, *MATP is a pointer to a matrix that can
934 hold *MAXROWS entries. */
936 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
938 struct tab_table *table = NULL; /* Crosstabulation table. */
939 struct tab_table *chisq = NULL; /* Chi-square table. */
940 bool showed_fisher = false;
941 struct tab_table *sym = NULL; /* Symmetric measures table. */
942 struct tab_table *risk = NULL; /* Risk estimate table. */
943 struct tab_table *direct = NULL; /* Directional measures table. */
946 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols);
949 table = create_crosstab_table (proc, pt);
950 if (proc->statistics & (1u << CRS_ST_CHISQ))
951 chisq = create_chisq_table (pt);
952 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
953 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
954 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
955 | (1u << CRS_ST_KAPPA)))
956 sym = create_sym_table (pt);
957 if (proc->statistics & (1u << CRS_ST_RISK))
958 risk = create_risk_table (pt);
959 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
960 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
961 direct = create_direct_table (pt);
964 while (find_crosstab (pt, &row0, &row1))
966 struct pivot_table x;
967 int first_difference;
969 make_pivot_table_subset (pt, row0, row1, &x);
971 /* Find all the row variable values. */
972 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows);
974 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
977 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
978 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
979 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
981 /* Allocate table space for the matrix. */
983 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
984 tab_realloc (table, -1,
985 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
986 tab_nr (table) * pt->n_entries / x.n_entries));
990 /* Find the first variable that differs from the last subtable. */
991 first_difference = find_first_difference (pt, row0);
994 display_dimensions (proc, &x, table, first_difference);
995 display_crosstabulation (proc, &x, table);
998 if (proc->exclude == MV_NEVER)
1003 display_dimensions (proc, &x, chisq, first_difference);
1004 display_chisq (&x, chisq, &showed_fisher);
1008 display_dimensions (proc, &x, sym, first_difference);
1009 display_symmetric (proc, &x, sym);
1013 display_dimensions (proc, &x, risk, first_difference);
1014 display_risk (&x, risk);
1018 display_dimensions (proc, &x, direct, first_difference);
1019 display_directional (proc, &x, direct);
1022 /* Free the parts of x that are not owned by pt. In
1023 particular we must not free x.cols, which is the same as
1024 pt->cols, which is freed at the end of this function. */
1032 submit (proc, NULL, table);
1037 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
1038 submit (proc, pt, chisq);
1041 submit (proc, pt, sym);
1042 submit (proc, pt, risk);
1043 submit (proc, pt, direct);
1049 build_matrix (struct pivot_table *x)
1051 const int col_var_width = var_get_width (x->vars[COL_VAR]);
1052 const int row_var_width = var_get_width (x->vars[ROW_VAR]);
1055 struct table_entry **p;
1059 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1061 const struct table_entry *te = *p;
1063 while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
1065 for (; col < x->n_cols; col++)
1071 while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
1078 if (++col >= x->n_cols)
1084 while (mp < &x->mat[x->n_cols * x->n_rows])
1086 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1088 /* Column totals, row totals, ns_rows. */
1090 for (col = 0; col < x->n_cols; col++)
1091 x->col_tot[col] = 0.0;
1092 for (row = 0; row < x->n_rows; row++)
1093 x->row_tot[row] = 0.0;
1095 for (row = 0; row < x->n_rows; row++)
1097 bool row_is_empty = true;
1098 for (col = 0; col < x->n_cols; col++)
1102 row_is_empty = false;
1103 x->col_tot[col] += *mp;
1104 x->row_tot[row] += *mp;
1111 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1115 for (col = 0; col < x->n_cols; col++)
1116 for (row = 0; row < x->n_rows; row++)
1117 if (x->mat[col + row * x->n_cols] != 0.0)
1125 for (col = 0; col < x->n_cols; col++)
1126 x->total += x->col_tot[col];
1129 static struct tab_table *
1130 create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1137 static const struct tuple names[] =
1139 {CRS_CL_COUNT, N_("count")},
1140 {CRS_CL_ROW, N_("row %")},
1141 {CRS_CL_COLUMN, N_("column %")},
1142 {CRS_CL_TOTAL, N_("total %")},
1143 {CRS_CL_EXPECTED, N_("expected")},
1144 {CRS_CL_RESIDUAL, N_("residual")},
1145 {CRS_CL_SRESIDUAL, N_("std. resid.")},
1146 {CRS_CL_ASRESIDUAL, N_("adj. resid.")},
1148 const int n_names = sizeof names / sizeof *names;
1149 const struct tuple *t;
1151 struct tab_table *table;
1152 struct string title;
1155 table = tab_create (pt->n_consts + 1 + pt->n_cols + 1,
1156 (pt->n_entries / pt->n_cols) * 3 / 2 * proc->n_cells + 10);
1157 tab_headers (table, pt->n_consts + 1, 0, 2, 0);
1159 /* First header line. */
1160 tab_joint_text (table, pt->n_consts + 1, 0,
1161 (pt->n_consts + 1) + (pt->n_cols - 1), 0,
1162 TAB_CENTER | TAT_TITLE, var_get_name (pt->vars[COL_VAR]));
1164 tab_hline (table, TAL_1, pt->n_consts + 1,
1165 pt->n_consts + 2 + pt->n_cols - 2, 1);
1167 /* Second header line. */
1168 for (i = 2; i < pt->n_consts + 2; i++)
1169 tab_joint_text (table, pt->n_consts + 2 - i - 1, 0,
1170 pt->n_consts + 2 - i - 1, 1,
1171 TAB_RIGHT | TAT_TITLE, var_to_string (pt->vars[i]));
1172 tab_text (table, pt->n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1173 var_get_name (pt->vars[ROW_VAR]));
1174 for (i = 0; i < pt->n_cols; i++)
1175 table_value_missing (proc, table, pt->n_consts + 2 + i - 1, 1, TAB_RIGHT,
1176 &pt->cols[i], pt->vars[COL_VAR]);
1177 tab_text (table, pt->n_consts + 2 + pt->n_cols - 1, 1, TAB_CENTER, _("Total"));
1179 tab_hline (table, TAL_1, 0, pt->n_consts + 2 + pt->n_cols - 1, 2);
1180 tab_vline (table, TAL_1, pt->n_consts + 2 + pt->n_cols - 1, 0, 1);
1183 ds_init_empty (&title);
1184 for (i = 0; i < pt->n_consts + 2; i++)
1187 ds_put_cstr (&title, " * ");
1188 ds_put_cstr (&title, var_get_name (pt->vars[i]));
1190 for (i = 0; i < pt->n_consts; i++)
1192 const struct variable *var = pt->const_vars[i];
1196 ds_put_format (&title, ", %s=", var_get_name (var));
1198 /* Insert the formatted value of the variable, then trim
1199 leading spaces in what was just inserted. */
1200 ofs = ds_length (&title);
1201 s = data_out (&pt->const_values[i], dict_get_encoding (proc->dict), var_get_print_format (var));
1202 ds_put_cstr (&title, s);
1204 ds_remove (&title, ofs, ss_cspan (ds_substr (&title, ofs, SIZE_MAX),
1208 ds_put_cstr (&title, " [");
1210 for (t = names; t < &names[n_names]; t++)
1211 if (proc->cells & (1u << t->value))
1214 ds_put_cstr (&title, ", ");
1215 ds_put_cstr (&title, gettext (t->name));
1217 ds_put_cstr (&title, "].");
1219 tab_title (table, "%s", ds_cstr (&title));
1220 ds_destroy (&title);
1222 tab_offset (table, 0, 2);
1226 static struct tab_table *
1227 create_chisq_table (struct pivot_table *pt)
1229 struct tab_table *chisq;
1231 chisq = tab_create (6 + (pt->n_vars - 2),
1232 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10);
1233 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1235 tab_title (chisq, _("Chi-square tests."));
1237 tab_offset (chisq, pt->n_vars - 2, 0);
1238 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1239 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1240 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1241 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1242 _("Asymp. Sig. (2-sided)"));
1243 tab_text (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1244 _("Exact Sig. (2-sided)"));
1245 tab_text (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1246 _("Exact Sig. (1-sided)"));
1247 tab_offset (chisq, 0, 1);
1252 /* Symmetric measures. */
1253 static struct tab_table *
1254 create_sym_table (struct pivot_table *pt)
1256 struct tab_table *sym;
1258 sym = tab_create (6 + (pt->n_vars - 2),
1259 pt->n_entries / pt->n_cols * 7 + 10);
1260 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1261 tab_title (sym, _("Symmetric measures."));
1263 tab_offset (sym, pt->n_vars - 2, 0);
1264 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1265 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1266 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1267 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1268 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1269 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1270 tab_offset (sym, 0, 1);
1275 /* Risk estimate. */
1276 static struct tab_table *
1277 create_risk_table (struct pivot_table *pt)
1279 struct tab_table *risk;
1281 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10);
1282 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1283 tab_title (risk, _("Risk estimate."));
1285 tab_offset (risk, pt->n_vars - 2, 0);
1286 tab_joint_text_format (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE,
1287 _("95%% Confidence Interval"));
1288 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1289 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1290 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1291 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1292 tab_hline (risk, TAL_1, 2, 3, 1);
1293 tab_vline (risk, TAL_1, 2, 0, 1);
1294 tab_offset (risk, 0, 2);
1299 /* Directional measures. */
1300 static struct tab_table *
1301 create_direct_table (struct pivot_table *pt)
1303 struct tab_table *direct;
1305 direct = tab_create (7 + (pt->n_vars - 2),
1306 pt->n_entries / pt->n_cols * 7 + 10);
1307 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1308 tab_title (direct, _("Directional measures."));
1310 tab_offset (direct, pt->n_vars - 2, 0);
1311 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1312 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1313 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1314 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1315 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1316 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1317 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1318 tab_offset (direct, 0, 1);
1324 /* Delete missing rows and columns for statistical analysis when
1327 delete_missing (struct pivot_table *pt)
1331 for (r = 0; r < pt->n_rows; r++)
1332 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1334 for (c = 0; c < pt->n_cols; c++)
1335 pt->mat[c + r * pt->n_cols] = 0.;
1340 for (c = 0; c < pt->n_cols; c++)
1341 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1343 for (r = 0; r < pt->n_rows; r++)
1344 pt->mat[c + r * pt->n_cols] = 0.;
1349 /* Prepare table T for submission, and submit it. */
1351 submit (struct crosstabs_proc *proc, struct pivot_table *pt,
1352 struct tab_table *t)
1354 struct crosstabs_dim_aux *aux;
1360 tab_resize (t, -1, 0);
1361 if (tab_nr (t) == tab_t (t))
1366 tab_offset (t, 0, 0);
1368 for (i = 2; i < pt->n_vars; i++)
1369 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1370 var_to_string (pt->vars[i]));
1371 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1372 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1374 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1376 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1378 aux = xmalloc (sizeof *aux);
1379 aux->exclude = proc->exclude;
1380 tab_dim (t, crosstabs_dim, crosstabs_dim_free, aux);
1385 /* Sets the widths of all the columns and heights of all the rows in
1386 table T for driver D. */
1388 crosstabs_dim (struct tab_rendering *r, void *aux_)
1390 const struct tab_table *t = r->table;
1391 struct outp_driver *d = r->driver;
1392 struct crosstabs_dim_aux *aux = aux_;
1395 /* Width of a numerical column. */
1396 int c = outp_string_width (d, "0.000000", OUTP_PROPORTIONAL);
1397 if (aux->exclude == MV_NEVER)
1398 c += outp_string_width (d, "M", OUTP_PROPORTIONAL);
1400 /* Set width for header columns. */
1406 w = d->width - c * (tab_nc (t) - tab_l (t));
1407 for (i = 0; i <= tab_nc (t); i++)
1411 if (w < d->prop_em_width * 8)
1412 w = d->prop_em_width * 8;
1414 if (w > d->prop_em_width * 15)
1415 w = d->prop_em_width * 15;
1417 for (i = 0; i < tab_l (t); i++)
1421 for (i = tab_l (t); i < tab_nc (t); i++)
1424 for (i = 0; i < tab_nr (t); i++)
1425 r->h[i] = tab_natural_height (r, i);
1429 crosstabs_dim_free (void *aux_)
1431 struct crosstabs_dim_aux *aux = aux_;
1436 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1438 size_t row0 = *row1p;
1441 if (row0 >= pt->n_entries)
1444 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1446 struct table_entry *a = pt->entries[row0];
1447 struct table_entry *b = pt->entries[row1];
1448 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1456 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1457 result. WIDTH_ points to an int which is either 0 for a
1458 numeric value or a string width for a string value. */
1460 compare_value_3way (const void *a_, const void *b_, const void *width_)
1462 const union value *a = a_;
1463 const union value *b = b_;
1464 const int *width = width_;
1466 return value_compare_3way (a, b, *width);
1469 /* Given an array of ENTRY_CNT table_entry structures starting at
1470 ENTRIES, creates a sorted list of the values that the variable
1471 with index VAR_IDX takes on. The values are returned as a
1472 malloc()'d array stored in *VALUES, with the number of values
1473 stored in *VALUE_CNT.
1476 enum_var_values (const struct pivot_table *pt, int var_idx,
1477 union value **valuesp, int *n_values)
1479 const struct variable *var = pt->vars[var_idx];
1480 struct var_range *range = get_var_range (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, compare_value_3way, &width);
1525 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1526 from V, displayed with print format spec from variable VAR. When
1527 in REPORT missing-value mode, missing values have an M appended. */
1529 table_value_missing (struct crosstabs_proc *proc,
1530 struct tab_table *table, int c, int r, unsigned char opt,
1531 const union value *v, const struct variable *var)
1533 const char *label = var_lookup_value_label (var, v);
1535 tab_text (table, c, r, TAB_LEFT, label);
1538 const struct fmt_spec *print = var_get_print_format (var);
1539 if (proc->exclude == MV_NEVER && var_is_value_missing (var, v, MV_USER))
1541 char *s = data_out (v, dict_get_encoding (proc->dict), print);
1542 tab_text_format (table, c, r, opt, "%sM", s + strspn (s, " "));
1546 tab_value (table, c, r, opt, v, proc->dict, print);
1550 /* Draws a line across TABLE at the current row to indicate the most
1551 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1552 that changed, and puts the values that changed into the table. TB
1553 and PT must be the corresponding table_entry and crosstab,
1556 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1557 struct tab_table *table, int first_difference)
1559 tab_hline (table, TAL_1, pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1561 for (; first_difference >= 2; first_difference--)
1562 table_value_missing (proc, table, pt->n_vars - first_difference - 1, 0,
1563 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1564 pt->vars[first_difference]);
1567 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1568 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1569 additionally suffixed with a letter `M'. */
1571 format_cell_entry (struct tab_table *table, int c, int r, double value,
1572 char suffix, bool mark_missing, const struct dictionary *dict)
1574 const struct fmt_spec f = {FMT_F, 10, 1};
1581 s = data_out (&v, dict_get_encoding (dict), &f);
1585 suffixes[suffix_len++] = suffix;
1587 suffixes[suffix_len++] = 'M';
1588 suffixes[suffix_len] = '\0';
1590 tab_text_format (table, c, r, TAB_RIGHT, "%s%s",
1591 s + strspn (s, " "), suffixes);
1594 /* Displays the crosstabulation table. */
1596 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1597 struct tab_table *table)
1603 for (r = 0; r < pt->n_rows; r++)
1604 table_value_missing (proc, table, pt->n_vars - 2, r * proc->n_cells,
1605 TAB_RIGHT, &pt->rows[r], pt->vars[ROW_VAR]);
1607 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1608 TAB_LEFT, _("Total"));
1610 /* Put in the actual cells. */
1612 tab_offset (table, pt->n_vars - 1, -1);
1613 for (r = 0; r < pt->n_rows; r++)
1615 if (proc->n_cells > 1)
1616 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1617 for (c = 0; c < pt->n_cols; c++)
1619 bool mark_missing = false;
1620 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1621 if (proc->exclude == MV_NEVER
1622 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1623 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1625 mark_missing = true;
1626 for (i = 0; i < proc->n_cells; i++)
1631 switch (proc->a_cells[i])
1637 v = *mp / pt->row_tot[r] * 100.;
1641 v = *mp / pt->col_tot[c] * 100.;
1645 v = *mp / pt->total * 100.;
1648 case CRS_CL_EXPECTED:
1651 case CRS_CL_RESIDUAL:
1652 v = *mp - expected_value;
1654 case CRS_CL_SRESIDUAL:
1655 v = (*mp - expected_value) / sqrt (expected_value);
1657 case CRS_CL_ASRESIDUAL:
1658 v = ((*mp - expected_value)
1659 / sqrt (expected_value
1660 * (1. - pt->row_tot[r] / pt->total)
1661 * (1. - pt->col_tot[c] / pt->total)));
1666 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1672 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1676 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1677 for (r = 0; r < pt->n_rows; r++)
1679 bool mark_missing = false;
1681 if (proc->exclude == MV_NEVER
1682 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1683 mark_missing = true;
1685 for (i = 0; i < proc->n_cells; i++)
1690 switch (proc->a_cells[i])
1700 v = pt->row_tot[r] / pt->total * 100.;
1704 v = pt->row_tot[r] / pt->total * 100.;
1707 case CRS_CL_EXPECTED:
1708 case CRS_CL_RESIDUAL:
1709 case CRS_CL_SRESIDUAL:
1710 case CRS_CL_ASRESIDUAL:
1717 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing, proc->dict);
1718 tab_next_row (table);
1722 /* Column totals, grand total. */
1724 if (proc->n_cells > 1)
1725 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1726 for (c = 0; c <= pt->n_cols; c++)
1728 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1729 bool mark_missing = false;
1732 if (proc->exclude == MV_NEVER && c < pt->n_cols
1733 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1734 mark_missing = true;
1736 for (i = 0; i < proc->n_cells; i++)
1741 switch (proc->a_cells[i])
1747 v = ct / pt->total * 100.;
1755 v = ct / pt->total * 100.;
1758 case CRS_CL_EXPECTED:
1759 case CRS_CL_RESIDUAL:
1760 case CRS_CL_SRESIDUAL:
1761 case CRS_CL_ASRESIDUAL:
1767 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1772 tab_offset (table, -1, tab_row (table) + last_row);
1773 tab_offset (table, 0, -1);
1776 static void calc_r (struct pivot_table *,
1777 double *PT, double *Y, double *, double *, double *);
1778 static void calc_chisq (struct pivot_table *,
1779 double[N_CHISQ], int[N_CHISQ], double *, double *);
1781 /* Display chi-square statistics. */
1783 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1784 bool *showed_fisher)
1786 static const char *chisq_stats[N_CHISQ] =
1788 N_("Pearson Chi-Square"),
1789 N_("Likelihood Ratio"),
1790 N_("Fisher's Exact Test"),
1791 N_("Continuity Correction"),
1792 N_("Linear-by-Linear Association"),
1794 double chisq_v[N_CHISQ];
1795 double fisher1, fisher2;
1800 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1802 tab_offset (chisq, pt->n_vars - 2, -1);
1804 for (i = 0; i < N_CHISQ; i++)
1806 if ((i != 2 && chisq_v[i] == SYSMIS)
1807 || (i == 2 && fisher1 == SYSMIS))
1810 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1813 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL);
1814 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], &pt->weight_format);
1815 tab_double (chisq, 3, 0, TAB_RIGHT,
1816 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL);
1820 *showed_fisher = true;
1821 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL);
1822 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL);
1824 tab_next_row (chisq);
1827 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1828 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1829 tab_next_row (chisq);
1831 tab_offset (chisq, 0, -1);
1834 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1835 double[N_SYMMETRIC], double[N_SYMMETRIC],
1836 double[N_SYMMETRIC],
1837 double[3], double[3], double[3]);
1839 /* Display symmetric measures. */
1841 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1842 struct tab_table *sym)
1844 static const char *categories[] =
1846 N_("Nominal by Nominal"),
1847 N_("Ordinal by Ordinal"),
1848 N_("Interval by Interval"),
1849 N_("Measure of Agreement"),
1852 static const char *stats[N_SYMMETRIC] =
1856 N_("Contingency Coefficient"),
1857 N_("Kendall's tau-b"),
1858 N_("Kendall's tau-c"),
1860 N_("Spearman Correlation"),
1865 static const int stats_categories[N_SYMMETRIC] =
1867 0, 0, 0, 1, 1, 1, 1, 2, 3,
1871 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1872 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1875 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1876 somers_d_v, somers_d_ase, somers_d_t))
1879 tab_offset (sym, pt->n_vars - 2, -1);
1881 for (i = 0; i < N_SYMMETRIC; i++)
1883 if (sym_v[i] == SYSMIS)
1886 if (stats_categories[i] != last_cat)
1888 last_cat = stats_categories[i];
1889 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1892 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1893 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL);
1894 if (sym_ase[i] != SYSMIS)
1895 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL);
1896 if (sym_t[i] != SYSMIS)
1897 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL);
1898 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL);*/
1902 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1903 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1906 tab_offset (sym, 0, -1);
1909 static int calc_risk (struct pivot_table *,
1910 double[], double[], double[], union value *);
1912 /* Display risk estimate. */
1914 display_risk (struct pivot_table *pt, struct tab_table *risk)
1917 double risk_v[3], lower[3], upper[3];
1921 if (!calc_risk (pt, risk_v, upper, lower, c))
1924 tab_offset (risk, pt->n_vars - 2, -1);
1926 for (i = 0; i < 3; i++)
1928 const struct variable *cv = pt->vars[COL_VAR];
1929 const struct variable *rv = pt->vars[ROW_VAR];
1930 int cvw = var_get_width (cv);
1931 int rvw = var_get_width (rv);
1933 if (risk_v[i] == SYSMIS)
1939 if (var_is_numeric (cv))
1940 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1941 var_get_name (cv), c[0].f, c[1].f);
1943 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1945 cvw, value_str (&c[0], cvw),
1946 cvw, value_str (&c[1], cvw));
1950 if (var_is_numeric (rv))
1951 sprintf (buf, _("For cohort %s = %g"),
1952 var_get_name (rv), pt->rows[i - 1].f);
1954 sprintf (buf, _("For cohort %s = %.*s"),
1956 rvw, value_str (&pt->rows[i - 1], rvw));
1960 tab_text (risk, 0, 0, TAB_LEFT, buf);
1961 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL);
1962 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL);
1963 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL);
1964 tab_next_row (risk);
1967 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1968 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1969 tab_next_row (risk);
1971 tab_offset (risk, 0, -1);
1974 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1975 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1976 double[N_DIRECTIONAL]);
1978 /* Display directional measures. */
1980 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
1981 struct tab_table *direct)
1983 static const char *categories[] =
1985 N_("Nominal by Nominal"),
1986 N_("Ordinal by Ordinal"),
1987 N_("Nominal by Interval"),
1990 static const char *stats[] =
1993 N_("Goodman and Kruskal tau"),
1994 N_("Uncertainty Coefficient"),
1999 static const char *types[] =
2006 static const int stats_categories[N_DIRECTIONAL] =
2008 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
2011 static const int stats_stats[N_DIRECTIONAL] =
2013 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
2016 static const int stats_types[N_DIRECTIONAL] =
2018 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
2021 static const int *stats_lookup[] =
2028 static const char **stats_names[] =
2040 double direct_v[N_DIRECTIONAL];
2041 double direct_ase[N_DIRECTIONAL];
2042 double direct_t[N_DIRECTIONAL];
2046 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t))
2049 tab_offset (direct, pt->n_vars - 2, -1);
2051 for (i = 0; i < N_DIRECTIONAL; i++)
2053 if (direct_v[i] == SYSMIS)
2059 for (j = 0; j < 3; j++)
2060 if (last[j] != stats_lookup[j][i])
2063 tab_hline (direct, TAL_1, j, 6, 0);
2068 int k = last[j] = stats_lookup[j][i];
2073 string = var_get_name (pt->vars[0]);
2075 string = var_get_name (pt->vars[1]);
2077 tab_text_format (direct, j, 0, TAB_LEFT,
2078 gettext (stats_names[j][k]), string);
2083 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL);
2084 if (direct_ase[i] != SYSMIS)
2085 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL);
2086 if (direct_t[i] != SYSMIS)
2087 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL);
2088 /*tab_double (direct, 6, 0, TAB_RIGHT, normal_sig (direct_v[i]), NULL);*/
2089 tab_next_row (direct);
2092 tab_offset (direct, 0, -1);
2095 /* Statistical calculations. */
2097 /* Returns the value of the gamma (factorial) function for an integer
2100 gamma_int (double pt)
2105 for (i = 2; i < pt; i++)
2110 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2112 static inline double
2113 Pr (int a, int b, int c, int d)
2115 return (gamma_int (a + b + 1.) / gamma_int (a + 1.)
2116 * gamma_int (c + d + 1.) / gamma_int (b + 1.)
2117 * gamma_int (a + c + 1.) / gamma_int (c + 1.)
2118 * gamma_int (b + d + 1.) / gamma_int (d + 1.)
2119 / gamma_int (a + b + c + d + 1.));
2122 /* Swap the contents of A and B. */
2124 swap (int *a, int *b)
2131 /* Calculate significance for Fisher's exact test as specified in
2132 _SPSS Statistical Algorithms_, Appendix 5. */
2134 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2138 if (MIN (c, d) < MIN (a, b))
2139 swap (&a, &c), swap (&b, &d);
2140 if (MIN (b, d) < MIN (a, c))
2141 swap (&a, &b), swap (&c, &d);
2145 swap (&a, &b), swap (&c, &d);
2147 swap (&a, &c), swap (&b, &d);
2151 for (pt = 0; pt <= a; pt++)
2152 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2154 *fisher2 = *fisher1;
2155 for (pt = 1; pt <= b; pt++)
2156 *fisher2 += Pr (a + pt, b - pt, c - pt, d + pt);
2159 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2160 columns with values COLS and N_ROWS rows with values ROWS. Values
2161 in the matrix sum to pt->total. */
2163 calc_chisq (struct pivot_table *pt,
2164 double chisq[N_CHISQ], int df[N_CHISQ],
2165 double *fisher1, double *fisher2)
2169 chisq[0] = chisq[1] = 0.;
2170 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2171 *fisher1 = *fisher2 = SYSMIS;
2173 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2175 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2177 chisq[0] = chisq[1] = SYSMIS;
2181 for (r = 0; r < pt->n_rows; r++)
2182 for (c = 0; c < pt->n_cols; c++)
2184 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2185 const double freq = pt->mat[pt->n_cols * r + c];
2186 const double residual = freq - expected;
2188 chisq[0] += residual * residual / expected;
2190 chisq[1] += freq * log (expected / freq);
2201 /* Calculate Yates and Fisher exact test. */
2202 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2204 double f11, f12, f21, f22;
2210 for (i = j = 0; i < pt->n_cols; i++)
2211 if (pt->col_tot[i] != 0.)
2220 f11 = pt->mat[nz_cols[0]];
2221 f12 = pt->mat[nz_cols[1]];
2222 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2223 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2228 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2231 chisq[3] = (pt->total * pow2 (pt_)
2232 / (f11 + f12) / (f21 + f22)
2233 / (f11 + f21) / (f12 + f22));
2241 if (f11 < 5. || f12 < 5. || f21 < 5. || f22 < 5.)
2242 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2245 /* Calculate Mantel-Haenszel. */
2246 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2248 double r, ase_0, ase_1;
2249 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2251 chisq[4] = (pt->total - 1.) * r * r;
2256 /* Calculate the value of Pearson's r. r is stored into R, ase_1 into
2257 ASE_1, and ase_0 into ASE_0. The row and column values must be
2258 passed in PT and Y. */
2260 calc_r (struct pivot_table *pt,
2261 double *PT, double *Y, double *r, double *ase_0, double *ase_1)
2263 double SX, SY, S, T;
2265 double sum_XYf, sum_X2Y2f;
2266 double sum_Xr, sum_X2r;
2267 double sum_Yc, sum_Y2c;
2270 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2271 for (j = 0; j < pt->n_cols; j++)
2273 double fij = pt->mat[j + i * pt->n_cols];
2274 double product = PT[i] * Y[j];
2275 double temp = fij * product;
2277 sum_X2Y2f += temp * product;
2280 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2282 sum_Xr += PT[i] * pt->row_tot[i];
2283 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2285 Xbar = sum_Xr / pt->total;
2287 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2289 sum_Yc += Y[i] * pt->col_tot[i];
2290 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2292 Ybar = sum_Yc / pt->total;
2294 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2295 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2296 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2299 *ase_0 = sqrt ((sum_X2Y2f - pow2 (sum_XYf) / pt->total) / (sum_X2r * sum_Y2c));
2304 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2305 for (j = 0; j < pt->n_cols; j++)
2307 double Xresid, Yresid;
2310 Xresid = PT[i] - Xbar;
2311 Yresid = Y[j] - Ybar;
2312 temp = (T * Xresid * Yresid
2314 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2315 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2320 *ase_1 = sqrt (s) / (T * T);
2324 /* Calculate symmetric statistics and their asymptotic standard
2325 errors. Returns 0 if none could be calculated. */
2327 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2328 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2329 double t[N_SYMMETRIC],
2330 double somers_d_v[3], double somers_d_ase[3],
2331 double somers_d_t[3])
2335 q = MIN (pt->ns_rows, pt->ns_cols);
2339 for (i = 0; i < N_SYMMETRIC; i++)
2340 v[i] = ase[i] = t[i] = SYSMIS;
2342 /* Phi, Cramer's V, contingency coefficient. */
2343 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2345 double Xp = 0.; /* Pearson chi-square. */
2348 for (r = 0; r < pt->n_rows; r++)
2349 for (c = 0; c < pt->n_cols; c++)
2351 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2352 const double freq = pt->mat[pt->n_cols * r + c];
2353 const double residual = freq - expected;
2355 Xp += residual * residual / expected;
2358 if (proc->statistics & (1u << CRS_ST_PHI))
2360 v[0] = sqrt (Xp / pt->total);
2361 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2363 if (proc->statistics & (1u << CRS_ST_CC))
2364 v[2] = sqrt (Xp / (Xp + pt->total));
2367 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2368 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2373 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2377 Dr = Dc = pow2 (pt->total);
2378 for (r = 0; r < pt->n_rows; r++)
2379 Dr -= pow2 (pt->row_tot[r]);
2380 for (c = 0; c < pt->n_cols; c++)
2381 Dc -= pow2 (pt->col_tot[c]);
2383 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2384 for (c = 0; c < pt->n_cols; c++)
2388 for (r = 0; r < pt->n_rows; r++)
2389 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2398 for (i = 0; i < pt->n_rows; i++)
2402 for (j = 1; j < pt->n_cols; j++)
2403 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2406 for (j = 1; j < pt->n_cols; j++)
2407 Dij += cum[j + (i - 1) * pt->n_cols];
2411 double fij = pt->mat[j + i * pt->n_cols];
2415 if (++j == pt->n_cols)
2417 assert (j < pt->n_cols);
2419 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2420 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2424 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2425 Dij -= cum[j + (i - 1) * pt->n_cols];
2431 if (proc->statistics & (1u << CRS_ST_BTAU))
2432 v[3] = (P - Q) / sqrt (Dr * Dc);
2433 if (proc->statistics & (1u << CRS_ST_CTAU))
2434 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2435 if (proc->statistics & (1u << CRS_ST_GAMMA))
2436 v[5] = (P - Q) / (P + Q);
2438 /* ASE for tau-b, tau-c, gamma. Calculations could be
2439 eliminated here, at expense of memory. */
2444 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2445 for (i = 0; i < pt->n_rows; i++)
2449 for (j = 1; j < pt->n_cols; j++)
2450 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2453 for (j = 1; j < pt->n_cols; j++)
2454 Dij += cum[j + (i - 1) * pt->n_cols];
2458 double fij = pt->mat[j + i * pt->n_cols];
2460 if (proc->statistics & (1u << CRS_ST_BTAU))
2462 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2463 + v[3] * (pt->row_tot[i] * Dc
2464 + pt->col_tot[j] * Dr));
2465 btau_cum += fij * temp * temp;
2469 const double temp = Cij - Dij;
2470 ctau_cum += fij * temp * temp;
2473 if (proc->statistics & (1u << CRS_ST_GAMMA))
2475 const double temp = Q * Cij - P * Dij;
2476 gamma_cum += fij * temp * temp;
2479 if (proc->statistics & (1u << CRS_ST_D))
2481 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2482 - (P - Q) * (pt->total - pt->row_tot[i]));
2483 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2484 - (Q - P) * (pt->total - pt->col_tot[j]));
2487 if (++j == pt->n_cols)
2489 assert (j < pt->n_cols);
2491 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2492 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2496 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2497 Dij -= cum[j + (i - 1) * pt->n_cols];
2503 btau_var = ((btau_cum
2504 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2506 if (proc->statistics & (1u << CRS_ST_BTAU))
2508 ase[3] = sqrt (btau_var);
2509 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2512 if (proc->statistics & (1u << CRS_ST_CTAU))
2514 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2515 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2516 t[4] = v[4] / ase[4];
2518 if (proc->statistics & (1u << CRS_ST_GAMMA))
2520 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2521 t[5] = v[5] / (2. / (P + Q)
2522 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2524 if (proc->statistics & (1u << CRS_ST_D))
2526 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2527 somers_d_ase[0] = 2. * btau_var / (Dr + Dc) * sqrt (Dr * Dc);
2528 somers_d_t[0] = (somers_d_v[0]
2530 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2531 somers_d_v[1] = (P - Q) / Dc;
2532 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2533 somers_d_t[1] = (somers_d_v[1]
2535 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2536 somers_d_v[2] = (P - Q) / Dr;
2537 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2538 somers_d_t[2] = (somers_d_v[2]
2540 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2546 /* Spearman correlation, Pearson's r. */
2547 if (proc->statistics & (1u << CRS_ST_CORR))
2549 double *R = xmalloc (sizeof *R * pt->n_rows);
2550 double *C = xmalloc (sizeof *C * pt->n_cols);
2553 double y, t, c = 0., s = 0.;
2558 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2559 y = pt->row_tot[i] - c;
2563 if (++i == pt->n_rows)
2565 assert (i < pt->n_rows);
2570 double y, t, c = 0., s = 0.;
2575 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2576 y = pt->col_tot[j] - c;
2580 if (++j == pt->n_cols)
2582 assert (j < pt->n_cols);
2586 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2592 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2596 /* Cohen's kappa. */
2597 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2599 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2602 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2603 i < pt->ns_rows; i++, j++)
2607 while (pt->col_tot[j] == 0.)
2610 prod = pt->row_tot[i] * pt->col_tot[j];
2611 sum = pt->row_tot[i] + pt->col_tot[j];
2613 sum_fii += pt->mat[j + i * pt->n_cols];
2615 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2616 sum_riciri_ci += prod * sum;
2618 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2619 for (j = 0; j < pt->ns_cols; j++)
2621 double sum = pt->row_tot[i] + pt->col_tot[j];
2622 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2625 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2627 ase[8] = sqrt ((pow2 (pt->total) * sum_rici
2628 + sum_rici * sum_rici
2629 - pt->total * sum_riciri_ci)
2630 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2632 t[8] = v[8] / sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2633 / pow2 (pow2 (pt->total) - sum_rici))
2634 + ((2. * (pt->total - sum_fii)
2635 * (2. * sum_fii * sum_rici
2636 - pt->total * sum_fiiri_ci))
2637 / cube (pow2 (pt->total) - sum_rici))
2638 + (pow2 (pt->total - sum_fii)
2639 * (pt->total * sum_fijri_ci2 - 4.
2640 * sum_rici * sum_rici)
2641 / pow4 (pow2 (pt->total) - sum_rici))));
2643 t[8] = v[8] / ase[8];
2650 /* Calculate risk estimate. */
2652 calc_risk (struct pivot_table *pt,
2653 double *value, double *upper, double *lower, union value *c)
2655 double f11, f12, f21, f22;
2661 for (i = 0; i < 3; i++)
2662 value[i] = upper[i] = lower[i] = SYSMIS;
2665 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2672 for (i = j = 0; i < pt->n_cols; i++)
2673 if (pt->col_tot[i] != 0.)
2682 f11 = pt->mat[nz_cols[0]];
2683 f12 = pt->mat[nz_cols[1]];
2684 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2685 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2687 c[0] = pt->cols[nz_cols[0]];
2688 c[1] = pt->cols[nz_cols[1]];
2691 value[0] = (f11 * f22) / (f12 * f21);
2692 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2693 lower[0] = value[0] * exp (-1.960 * v);
2694 upper[0] = value[0] * exp (1.960 * v);
2696 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2697 v = sqrt ((f12 / (f11 * (f11 + f12)))
2698 + (f22 / (f21 * (f21 + f22))));
2699 lower[1] = value[1] * exp (-1.960 * v);
2700 upper[1] = value[1] * exp (1.960 * v);
2702 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2703 v = sqrt ((f11 / (f12 * (f11 + f12)))
2704 + (f21 / (f22 * (f21 + f22))));
2705 lower[2] = value[2] * exp (-1.960 * v);
2706 upper[2] = value[2] * exp (1.960 * v);
2711 /* Calculate directional measures. */
2713 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2714 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2715 double t[N_DIRECTIONAL])
2720 for (i = 0; i < N_DIRECTIONAL; i++)
2721 v[i] = ase[i] = t[i] = SYSMIS;
2725 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2727 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2728 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2729 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2730 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2731 double sum_fim, sum_fmj;
2733 int rm_index, cm_index;
2736 /* Find maximum for each row and their sum. */
2737 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2739 double max = pt->mat[i * pt->n_cols];
2742 for (j = 1; j < pt->n_cols; j++)
2743 if (pt->mat[j + i * pt->n_cols] > max)
2745 max = pt->mat[j + i * pt->n_cols];
2749 sum_fim += fim[i] = max;
2750 fim_index[i] = index;
2753 /* Find maximum for each column. */
2754 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2756 double max = pt->mat[j];
2759 for (i = 1; i < pt->n_rows; i++)
2760 if (pt->mat[j + i * pt->n_cols] > max)
2762 max = pt->mat[j + i * pt->n_cols];
2766 sum_fmj += fmj[j] = max;
2767 fmj_index[j] = index;
2770 /* Find maximum row total. */
2771 rm = pt->row_tot[0];
2773 for (i = 1; i < pt->n_rows; i++)
2774 if (pt->row_tot[i] > rm)
2776 rm = pt->row_tot[i];
2780 /* Find maximum column total. */
2781 cm = pt->col_tot[0];
2783 for (j = 1; j < pt->n_cols; j++)
2784 if (pt->col_tot[j] > cm)
2786 cm = pt->col_tot[j];
2790 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2791 v[1] = (sum_fmj - rm) / (pt->total - rm);
2792 v[2] = (sum_fim - cm) / (pt->total - cm);
2794 /* ASE1 for Y given PT. */
2798 for (accum = 0., i = 0; i < pt->n_rows; i++)
2799 for (j = 0; j < pt->n_cols; j++)
2801 const int deltaj = j == cm_index;
2802 accum += (pt->mat[j + i * pt->n_cols]
2803 * pow2 ((j == fim_index[i])
2808 ase[2] = sqrt (accum - pt->total * v[0]) / (pt->total - cm);
2811 /* ASE0 for Y given PT. */
2815 for (accum = 0., i = 0; i < pt->n_rows; i++)
2816 if (cm_index != fim_index[i])
2817 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2818 + pt->mat[i * pt->n_cols + cm_index]);
2819 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2822 /* ASE1 for PT given Y. */
2826 for (accum = 0., i = 0; i < pt->n_rows; i++)
2827 for (j = 0; j < pt->n_cols; j++)
2829 const int deltaj = i == rm_index;
2830 accum += (pt->mat[j + i * pt->n_cols]
2831 * pow2 ((i == fmj_index[j])
2836 ase[1] = sqrt (accum - pt->total * v[0]) / (pt->total - rm);
2839 /* ASE0 for PT given Y. */
2843 for (accum = 0., j = 0; j < pt->n_cols; j++)
2844 if (rm_index != fmj_index[j])
2845 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2846 + pt->mat[j + pt->n_cols * rm_index]);
2847 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2850 /* Symmetric ASE0 and ASE1. */
2855 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2856 for (j = 0; j < pt->n_cols; j++)
2858 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2859 int temp1 = (i == rm_index) + (j == cm_index);
2860 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2861 accum1 += (pt->mat[j + i * pt->n_cols]
2862 * pow2 (temp0 + (v[0] - 1.) * temp1));
2864 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2865 t[0] = v[0] / (sqrt (accum0 - pow2 ((sum_fim + sum_fmj - cm - rm) / pt->total))
2866 / (2. * pt->total - rm - cm));
2875 double sum_fij2_ri, sum_fij2_ci;
2876 double sum_ri2, sum_cj2;
2878 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2879 for (j = 0; j < pt->n_cols; j++)
2881 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2882 sum_fij2_ri += temp / pt->row_tot[i];
2883 sum_fij2_ci += temp / pt->col_tot[j];
2886 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2887 sum_ri2 += pow2 (pt->row_tot[i]);
2889 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2890 sum_cj2 += pow2 (pt->col_tot[j]);
2892 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2893 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2897 if (proc->statistics & (1u << CRS_ST_UC))
2899 double UX, UY, UXY, P;
2900 double ase1_yx, ase1_xy, ase1_sym;
2903 for (UX = 0., i = 0; i < pt->n_rows; i++)
2904 if (pt->row_tot[i] > 0.)
2905 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2907 for (UY = 0., j = 0; j < pt->n_cols; j++)
2908 if (pt->col_tot[j] > 0.)
2909 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2911 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2912 for (j = 0; j < pt->n_cols; j++)
2914 double entry = pt->mat[j + i * pt->n_cols];
2919 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2920 UXY -= entry / pt->total * log (entry / pt->total);
2923 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2924 for (j = 0; j < pt->n_cols; j++)
2926 double entry = pt->mat[j + i * pt->n_cols];
2931 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2932 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2933 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2934 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2935 ase1_sym += entry * pow2 ((UXY
2936 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2937 - (UX + UY) * log (entry / pt->total));
2940 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2941 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2942 t[5] = v[5] / ((2. / (pt->total * (UX + UY)))
2943 * sqrt (P - pow2 (UX + UY - UXY) / pt->total));
2945 v[6] = (UX + UY - UXY) / UX;
2946 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2947 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2949 v[7] = (UX + UY - UXY) / UY;
2950 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2951 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2955 if (proc->statistics & (1u << CRS_ST_D))
2957 double v_dummy[N_SYMMETRIC];
2958 double ase_dummy[N_SYMMETRIC];
2959 double t_dummy[N_SYMMETRIC];
2960 double somers_d_v[3];
2961 double somers_d_ase[3];
2962 double somers_d_t[3];
2964 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2965 somers_d_v, somers_d_ase, somers_d_t))
2968 for (i = 0; i < 3; i++)
2970 v[8 + i] = somers_d_v[i];
2971 ase[8 + i] = somers_d_ase[i];
2972 t[8 + i] = somers_d_t[i];
2978 if (proc->statistics & (1u << CRS_ST_ETA))
2981 double sum_Xr, sum_X2r;
2985 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2987 sum_Xr += pt->rows[i].f * pt->row_tot[i];
2988 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
2990 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2992 for (SXW = 0., j = 0; j < pt->n_cols; j++)
2996 for (cum = 0., i = 0; i < pt->n_rows; i++)
2998 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
2999 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
3002 SXW -= cum * cum / pt->col_tot[j];
3004 v[11] = sqrt (1. - SXW / SX);
3008 double sum_Yc, sum_Y2c;
3012 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
3014 sum_Yc += pt->cols[i].f * pt->col_tot[i];
3015 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
3017 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
3019 for (SYW = 0., i = 0; i < pt->n_rows; i++)
3023 for (cum = 0., j = 0; j < pt->n_cols; j++)
3025 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
3026 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
3029 SYW -= cum * cum / pt->row_tot[i];
3031 v[12] = sqrt (1. - SYW / SY);