1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2006, 2009 Free Software Foundation, Inc.
4 This program is free software: you can redistribute it and/or modify
5 it under the terms of the GNU General Public License as published by
6 the Free Software Foundation, either version 3 of the License, or
7 (at your option) any later version.
9 This program is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 GNU General Public License for more details.
14 You should have received a copy of the GNU General Public License
15 along with this program. If not, see <http://www.gnu.org/licenses/>. */
19 - Pearson's R (but not Spearman!) is off a little.
20 - T values for Spearman's R and Pearson's R are wrong.
21 - How to calculate significance of symmetric and directional measures?
22 - Asymmetric ASEs and T values for lambda are wrong.
23 - ASE of Goodman and Kruskal's tau is not calculated.
24 - ASE of symmetric somers' d is wrong.
25 - Approx. T of uncertainty coefficient is wrong.
32 #include <gsl/gsl_cdf.h>
36 #include <data/case.h>
37 #include <data/casegrouper.h>
38 #include <data/casereader.h>
39 #include <data/data-out.h>
40 #include <data/dictionary.h>
41 #include <data/format.h>
42 #include <data/procedure.h>
43 #include <data/value-labels.h>
44 #include <data/variable.h>
45 #include <language/command.h>
46 #include <language/dictionary/split-file.h>
47 #include <language/lexer/lexer.h>
48 #include <language/lexer/variable-parser.h>
49 #include <libpspp/array.h>
50 #include <libpspp/assertion.h>
51 #include <libpspp/compiler.h>
52 #include <libpspp/hash.h>
53 #include <libpspp/hmap.h>
54 #include <libpspp/hmapx.h>
55 #include <libpspp/message.h>
56 #include <libpspp/misc.h>
57 #include <libpspp/pool.h>
58 #include <libpspp/str.h>
59 #include <output/output.h>
60 #include <output/table.h>
67 #define _(msgid) gettext (msgid)
68 #define N_(msgid) msgid
76 missing=miss:!table/include/report;
77 +write[wr_]=none,cells,all;
78 +format=fmt:!labels/nolabels/novallabs,
81 tabl:!tables/notables,
84 +cells[cl_]=count,expected,row,column,total,residual,sresidual,
86 +statistics[st_]=chisq,phi,cc,lambda,uc,none,btau,ctau,risk,gamma,d,
92 /* Number of chi-square statistics. */
95 /* Number of symmetric statistics. */
98 /* Number of directional statistics. */
99 #define N_DIRECTIONAL 13
101 /* A single table entry for general mode. */
104 struct hmap_node node; /* Entry in hash table. */
105 double freq; /* Frequency count. */
106 union value values[1]; /* Values. */
110 table_entry_size (size_t n_values)
112 return (offsetof (struct table_entry, values)
113 + n_values * sizeof (union value));
116 /* Indexes into the 'vars' member of struct pivot_table and
117 struct crosstab member. */
120 ROW_VAR = 0, /* Row variable. */
121 COL_VAR = 1 /* Column variable. */
122 /* Higher indexes cause multiple tables to be output. */
125 /* A crosstabulation of 2 or more variables. */
128 struct fmt_spec weight_format; /* Format for weight variable. */
129 double missing; /* Weight of missing cases. */
131 /* Variables (2 or more). */
133 const struct variable **vars;
135 /* Constants (0 or more). */
137 const struct variable **const_vars;
138 union value *const_values;
142 struct table_entry **entries;
145 /* Column values, number of columns. */
149 /* Row values, number of rows. */
153 /* Number of statistically interesting columns/rows
154 (columns/rows with data in them). */
155 int ns_cols, ns_rows;
157 /* Matrix contents. */
158 double *mat; /* Matrix proper. */
159 double *row_tot; /* Row totals. */
160 double *col_tot; /* Column totals. */
161 double total; /* Grand total. */
164 /* Integer mode variable info. */
167 int min; /* Minimum value. */
168 int max; /* Maximum value + 1. */
169 int count; /* max - min. */
172 static inline struct var_range *
173 get_var_range (const struct variable *v)
175 return var_get_aux (v);
178 struct crosstabs_proc
180 enum { INTEGER, GENERAL } mode;
181 enum mv_class exclude;
184 struct fmt_spec weight_format;
186 /* Variables specifies on VARIABLES. */
187 const struct variable **variables;
191 struct pivot_table *pivots;
195 int n_cells; /* Number of cells requested. */
196 unsigned int cells; /* Bit k is 1 if cell k is requested. */
197 int a_cells[CRS_CL_count]; /* 0...n_cells-1 are the requested cells. */
200 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
204 init_proc (struct crosstabs_proc *proc, struct dataset *ds)
206 const struct variable *wv = dict_get_weight (dataset_dict (ds));
207 proc->bad_warn = true;
208 proc->variables = NULL;
209 proc->n_variables = 0;
212 proc->weight_format = wv ? *var_get_print_format (wv) : F_8_0;
216 free_proc (struct crosstabs_proc *proc)
218 struct pivot_table *pt;
220 free (proc->variables);
221 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
224 free (pt->const_vars);
225 /* We must not call value_destroy on const_values because
226 it is a wild pointer; it never pointed to anything owned
229 The rest of the data was allocated and destroyed at a
230 lower level already. */
235 static int internal_cmd_crosstabs (struct lexer *lexer, struct dataset *ds,
236 struct crosstabs_proc *);
237 static bool should_tabulate_case (const struct pivot_table *,
238 const struct ccase *, enum mv_class exclude);
239 static void tabulate_general_case (struct pivot_table *, const struct ccase *,
241 static void tabulate_integer_case (struct pivot_table *, const struct ccase *,
243 static void postcalc (struct crosstabs_proc *);
244 static void submit (struct crosstabs_proc *, struct pivot_table *,
247 /* Parse and execute CROSSTABS, then clean up. */
249 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
251 struct crosstabs_proc proc;
254 init_proc (&proc, ds);
255 result = internal_cmd_crosstabs (lexer, ds, &proc);
261 /* Parses and executes the CROSSTABS procedure. */
263 internal_cmd_crosstabs (struct lexer *lexer, struct dataset *ds,
264 struct crosstabs_proc *proc)
266 struct casegrouper *grouper;
267 struct casereader *input, *group;
268 struct cmd_crosstabs cmd;
269 struct pivot_table *pt;
273 if (!parse_crosstabs (lexer, ds, &cmd, proc))
276 proc->mode = proc->n_variables ? INTEGER : GENERAL;
280 proc->cells = 1u << CRS_CL_COUNT;
281 else if (cmd.a_cells[CRS_CL_ALL])
282 proc->cells = UINT_MAX;
286 for (i = 0; i < CRS_CL_count; i++)
288 proc->cells |= 1u << i;
289 if (proc->cells == 0)
290 proc->cells = ((1u << CRS_CL_COUNT)
292 | (1u << CRS_CL_COLUMN)
293 | (1u << CRS_CL_TOTAL));
295 proc->cells &= ((1u << CRS_CL_count) - 1);
296 proc->cells &= ~((1u << CRS_CL_NONE) | (1u << CRS_CL_ALL));
298 for (i = 0; i < CRS_CL_count; i++)
299 if (proc->cells & (1u << i))
300 proc->a_cells[proc->n_cells++] = i;
303 if (cmd.a_statistics[CRS_ST_ALL])
304 proc->statistics = UINT_MAX;
305 else if (cmd.sbc_statistics)
309 proc->statistics = 0;
310 for (i = 0; i < CRS_ST_count; i++)
311 if (cmd.a_statistics[i])
312 proc->statistics |= 1u << i;
313 if (proc->statistics == 0)
314 proc->statistics |= 1u << CRS_ST_CHISQ;
317 proc->statistics = 0;
320 proc->exclude = (cmd.miss == CRS_TABLE ? MV_ANY
321 : cmd.miss == CRS_INCLUDE ? MV_SYSTEM
323 if (proc->mode == GENERAL && proc->mode == MV_NEVER)
325 msg (SE, _("Missing mode REPORT not allowed in general mode. "
326 "Assuming MISSING=TABLE."));
331 proc->pivot = cmd.pivot == CRS_PIVOT;
333 input = casereader_create_filter_weight (proc_open (ds), dataset_dict (ds),
335 grouper = casegrouper_create_splits (input, dataset_dict (ds));
336 while (casegrouper_get_next_group (grouper, &group))
340 /* Output SPLIT FILE variables. */
341 c = casereader_peek (group, 0);
344 output_split_file_values (ds, c);
349 for (; (c = casereader_read (group)) != NULL; case_unref (c))
350 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
352 double weight = dict_get_case_weight (dataset_dict (ds), c,
354 if (should_tabulate_case (pt, c, proc->exclude))
356 if (proc->mode == GENERAL)
357 tabulate_general_case (pt, c, weight);
359 tabulate_integer_case (pt, c, weight);
362 pt->missing += weight;
364 casereader_destroy (group);
369 ok = casegrouper_destroy (grouper);
370 ok = proc_commit (ds) && ok;
372 return ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
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_tokid (lexer)) == NULL)
394 && lex_token (lexer) != T_ALL)
396 lex_match (lexer, '=');
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_error (lexer, _("expecting 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++];
440 pt->weight_format = proc->weight_format;
443 pt->vars = xmalloc (n_by * sizeof *pt->vars);
445 pt->const_vars = NULL;
446 pt->const_values = NULL;
447 hmap_init (&pt->data);
451 for (j = 0; j < n_by; j++)
452 pt->vars[j] = by[j][by_iter[j]];
454 for (j = n_by - 1; j >= 0; j--)
456 if (++by_iter[j] < by_nvar[j])
465 /* All return paths lead here. */
466 for (i = 0; i < n_by; i++)
471 const_var_set_destroy (var_set);
476 /* Parses the VARIABLES subcommand. */
478 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
479 struct cmd_crosstabs *cmd UNUSED, void *proc_)
481 struct crosstabs_proc *proc = proc_;
484 msg (SE, _("VARIABLES must be specified before TABLES."));
488 lex_match (lexer, '=');
492 size_t orig_nv = proc->n_variables;
497 if (!parse_variables_const (lexer, dataset_dict (ds),
498 &proc->variables, &proc->n_variables,
499 (PV_APPEND | PV_NUMERIC
500 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
503 if (lex_token (lexer) != '(')
505 lex_error (lexer, "expecting `('");
510 if (!lex_force_int (lexer))
512 min = lex_integer (lexer);
515 lex_match (lexer, ',');
517 if (!lex_force_int (lexer))
519 max = lex_integer (lexer);
522 msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
528 if (lex_token (lexer) != ')')
530 lex_error (lexer, "expecting `)'");
535 for (i = orig_nv; i < proc->n_variables; i++)
537 struct var_range *vr = xmalloc (sizeof *vr);
540 vr->count = max - min + 1;
541 var_attach_aux (proc->variables[i], vr, var_dtor_free);
544 if (lex_token (lexer) == '/')
551 free (proc->variables);
552 proc->variables = NULL;
553 proc->n_variables = 0;
557 /* Data file processing. */
560 should_tabulate_case (const struct pivot_table *pt, const struct ccase *c,
561 enum mv_class exclude)
564 for (j = 0; j < pt->n_vars; j++)
566 const struct variable *var = pt->vars[j];
567 struct var_range *range = get_var_range (var);
569 if (var_is_value_missing (var, case_data (c, var), exclude))
574 double num = case_num (c, var);
575 if (num < range->min || num > range->max)
583 tabulate_integer_case (struct pivot_table *pt, const struct ccase *c,
586 struct table_entry *te;
591 for (j = 0; j < pt->n_vars; j++)
593 /* Throw away fractional parts of values. */
594 hash = hash_int (case_num (c, pt->vars[j]), hash);
597 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
599 for (j = 0; j < pt->n_vars; j++)
600 if ((int) case_num (c, pt->vars[j]) != (int) te->values[j].f)
603 /* Found an existing entry. */
610 /* No existing entry. Create a new one. */
611 te = xmalloc (table_entry_size (pt->n_vars));
613 for (j = 0; j < pt->n_vars; j++)
614 te->values[j].f = (int) case_num (c, pt->vars[j]);
615 hmap_insert (&pt->data, &te->node, hash);
619 tabulate_general_case (struct pivot_table *pt, const struct ccase *c,
622 struct table_entry *te;
627 for (j = 0; j < pt->n_vars; j++)
629 const struct variable *var = pt->vars[j];
630 hash = value_hash (case_data (c, var), var_get_width (var), hash);
633 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
635 for (j = 0; j < pt->n_vars; j++)
637 const struct variable *var = pt->vars[j];
638 if (!value_equal (case_data (c, var), &te->values[j],
639 var_get_width (var)))
643 /* Found an existing entry. */
650 /* No existing entry. Create a new one. */
651 te = xmalloc (table_entry_size (pt->n_vars));
653 for (j = 0; j < pt->n_vars; j++)
655 const struct variable *var = pt->vars[j];
656 int width = var_get_width (var);
657 value_init (&te->values[j], width);
658 value_copy (&te->values[j], case_data (c, var), width);
660 hmap_insert (&pt->data, &te->node, hash);
663 /* Post-data reading calculations. */
665 static int compare_table_entry_vars_3way (const struct table_entry *a,
666 const struct table_entry *b,
667 const struct pivot_table *pt,
669 static int compare_table_entry_3way (const void *ap_, const void *bp_,
671 static void enum_var_values (const struct pivot_table *, int var_idx,
672 union value **valuesp, int *n_values);
673 static void output_pivot_table (struct crosstabs_proc *,
674 struct pivot_table *);
675 static void make_pivot_table_subset (struct pivot_table *pt,
676 size_t row0, size_t row1,
677 struct pivot_table *subset);
678 static void make_summary_table (struct crosstabs_proc *);
679 static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
682 postcalc (struct crosstabs_proc *proc)
684 struct pivot_table *pt;
686 /* Convert hash tables into sorted arrays of entries. */
687 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
689 struct table_entry *e;
692 pt->n_entries = hmap_count (&pt->data);
693 pt->entries = xnmalloc (pt->n_entries, sizeof *pt->entries);
695 HMAP_FOR_EACH (e, struct table_entry, node, &pt->data)
696 pt->entries[i++] = e;
697 hmap_destroy (&pt->data);
699 sort (pt->entries, pt->n_entries, sizeof *pt->entries,
700 compare_table_entry_3way, pt);
703 make_summary_table (proc);
705 /* Output each pivot table. */
706 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
708 if (proc->pivot || pt->n_vars == 2)
709 output_pivot_table (proc, pt);
712 size_t row0 = 0, row1 = 0;
713 while (find_crosstab (pt, &row0, &row1))
715 struct pivot_table subset;
716 make_pivot_table_subset (pt, row0, row1, &subset);
717 output_pivot_table (proc, &subset);
722 /* Free output and prepare for next split file. */
723 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
729 /* Free only the members that were allocated in this
730 function. The other pointer members are either both
731 allocated and destroyed at a lower level (in
732 output_pivot_table), or both allocated and destroyed at
733 a higher level (in crs_custom_tables and free_proc,
735 for (i = 0; i < pt->n_entries; i++)
736 free (pt->entries[i]);
742 make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
743 struct pivot_table *subset)
748 assert (pt->n_consts == 0);
749 subset->missing = pt->missing;
751 subset->vars = pt->vars;
752 subset->n_consts = pt->n_vars - 2;
753 subset->const_vars = pt->vars + 2;
754 subset->const_values = &pt->entries[row0]->values[2];
756 subset->entries = &pt->entries[row0];
757 subset->n_entries = row1 - row0;
761 compare_table_entry_var_3way (const struct table_entry *a,
762 const struct table_entry *b,
763 const struct pivot_table *pt,
766 return value_compare_3way (&a->values[idx], &b->values[idx],
767 var_get_width (pt->vars[idx]));
771 compare_table_entry_vars_3way (const struct table_entry *a,
772 const struct table_entry *b,
773 const struct pivot_table *pt,
778 for (i = idx1 - 1; i >= idx0; i--)
780 int cmp = compare_table_entry_var_3way (a, b, pt, i);
787 /* Compare the struct table_entry at *AP to the one at *BP and
788 return a strcmp()-type result. */
790 compare_table_entry_3way (const void *ap_, const void *bp_, const void *pt_)
792 const struct table_entry *const *ap = ap_;
793 const struct table_entry *const *bp = bp_;
794 const struct table_entry *a = *ap;
795 const struct table_entry *b = *bp;
796 const struct pivot_table *pt = pt_;
799 cmp = compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars);
803 cmp = compare_table_entry_var_3way (a, b, pt, ROW_VAR);
807 return compare_table_entry_var_3way (a, b, pt, COL_VAR);
811 find_first_difference (const struct pivot_table *pt, size_t row)
814 return pt->n_vars - 1;
817 const struct table_entry *a = pt->entries[row];
818 const struct table_entry *b = pt->entries[row - 1];
821 for (col = pt->n_vars - 1; col >= 0; col--)
822 if (compare_table_entry_var_3way (a, b, pt, col))
828 /* Output a table summarizing the cases processed. */
830 make_summary_table (struct crosstabs_proc *proc)
832 struct tab_table *summary;
833 struct pivot_table *pt;
837 summary = tab_create (7, 3 + proc->n_pivots, 1);
838 tab_title (summary, _("Summary."));
839 tab_headers (summary, 1, 0, 3, 0);
840 tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
841 tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
842 tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
843 tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
844 tab_hline (summary, TAL_1, 1, 6, 1);
845 tab_hline (summary, TAL_1, 1, 6, 2);
846 tab_vline (summary, TAL_1, 3, 1, 1);
847 tab_vline (summary, TAL_1, 5, 1, 1);
848 for (i = 0; i < 3; i++)
850 tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
851 tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
853 tab_offset (summary, 0, 3);
855 ds_init_empty (&name);
856 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
862 tab_hline (summary, TAL_1, 0, 6, 0);
865 for (i = 0; i < pt->n_vars; i++)
868 ds_put_cstr (&name, " * ");
869 ds_put_cstr (&name, var_to_string (pt->vars[i]));
871 tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
874 for (i = 0; i < pt->n_entries; i++)
875 valid += pt->entries[i]->freq;
880 for (i = 0; i < 3; i++)
882 tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i],
883 &proc->weight_format);
884 tab_text_format (summary, i * 2 + 2, 0, TAB_RIGHT, "%.1f%%",
888 tab_next_row (summary);
892 submit (proc, NULL, summary);
897 static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
898 struct pivot_table *);
899 static struct tab_table *create_chisq_table (struct pivot_table *);
900 static struct tab_table *create_sym_table (struct pivot_table *);
901 static struct tab_table *create_risk_table (struct pivot_table *);
902 static struct tab_table *create_direct_table (struct pivot_table *);
903 static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
904 struct tab_table *, int first_difference);
905 static void display_crosstabulation (struct crosstabs_proc *,
906 struct pivot_table *,
908 static void display_chisq (struct pivot_table *, struct tab_table *,
909 bool *showed_fisher);
910 static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
912 static void display_risk (struct pivot_table *, struct tab_table *);
913 static void display_directional (struct crosstabs_proc *, struct pivot_table *,
915 static void crosstabs_dim (struct tab_table *, struct outp_driver *,
917 static void table_value_missing (struct crosstabs_proc *proc,
918 struct tab_table *table, int c, int r,
919 unsigned char opt, const union value *v,
920 const struct variable *var);
921 static void delete_missing (struct pivot_table *);
922 static void build_matrix (struct pivot_table *);
924 /* Output pivot table beginning at PB and continuing until PE,
925 exclusive. For efficiency, *MATP is a pointer to a matrix that can
926 hold *MAXROWS entries. */
928 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
930 struct tab_table *table = NULL; /* Crosstabulation table. */
931 struct tab_table *chisq = NULL; /* Chi-square table. */
932 bool showed_fisher = false;
933 struct tab_table *sym = NULL; /* Symmetric measures table. */
934 struct tab_table *risk = NULL; /* Risk estimate table. */
935 struct tab_table *direct = NULL; /* Directional measures table. */
938 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols);
941 table = create_crosstab_table (proc, pt);
942 if (proc->statistics & (1u << CRS_ST_CHISQ))
943 chisq = create_chisq_table (pt);
944 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
945 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
946 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
947 | (1u << CRS_ST_KAPPA)))
948 sym = create_sym_table (pt);
949 if (proc->statistics & (1u << CRS_ST_RISK))
950 risk = create_risk_table (pt);
951 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
952 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
953 direct = create_direct_table (pt);
956 while (find_crosstab (pt, &row0, &row1))
958 struct pivot_table x;
959 int first_difference;
961 make_pivot_table_subset (pt, row0, row1, &x);
963 /* Find all the row variable values. */
964 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows);
966 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
969 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
970 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
971 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
973 /* Allocate table space for the matrix. */
975 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
976 tab_realloc (table, -1,
977 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
978 tab_nr (table) * pt->n_entries / x.n_entries));
982 /* Find the first variable that differs from the last subtable. */
983 first_difference = find_first_difference (pt, row0);
986 display_dimensions (proc, &x, table, first_difference);
987 display_crosstabulation (proc, &x, table);
990 if (proc->exclude == MV_NEVER)
995 display_dimensions (proc, &x, chisq, first_difference);
996 display_chisq (&x, chisq, &showed_fisher);
1000 display_dimensions (proc, &x, sym, first_difference);
1001 display_symmetric (proc, &x, sym);
1005 display_dimensions (proc, &x, risk, first_difference);
1006 display_risk (&x, risk);
1010 display_dimensions (proc, &x, direct, first_difference);
1011 display_directional (proc, &x, direct);
1014 /* Free the parts of x that are not owned by pt. In
1015 particular we must not free x.cols, which is the same as
1016 pt->cols, which is freed at the end of this function. */
1024 submit (proc, NULL, table);
1029 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
1030 submit (proc, pt, chisq);
1033 submit (proc, pt, sym);
1034 submit (proc, pt, risk);
1035 submit (proc, pt, direct);
1041 build_matrix (struct pivot_table *x)
1043 const int col_var_width = var_get_width (x->vars[COL_VAR]);
1044 const int row_var_width = var_get_width (x->vars[ROW_VAR]);
1047 struct table_entry **p;
1051 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1053 const struct table_entry *te = *p;
1055 while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
1057 for (; col < x->n_cols; col++)
1063 while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
1070 if (++col >= x->n_cols)
1076 while (mp < &x->mat[x->n_cols * x->n_rows])
1078 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1080 /* Column totals, row totals, ns_rows. */
1082 for (col = 0; col < x->n_cols; col++)
1083 x->col_tot[col] = 0.0;
1084 for (row = 0; row < x->n_rows; row++)
1085 x->row_tot[row] = 0.0;
1087 for (row = 0; row < x->n_rows; row++)
1089 bool row_is_empty = true;
1090 for (col = 0; col < x->n_cols; col++)
1094 row_is_empty = false;
1095 x->col_tot[col] += *mp;
1096 x->row_tot[row] += *mp;
1103 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1107 for (col = 0; col < x->n_cols; col++)
1108 for (row = 0; row < x->n_rows; row++)
1109 if (x->mat[col + row * x->n_cols] != 0.0)
1117 for (col = 0; col < x->n_cols; col++)
1118 x->total += x->col_tot[col];
1121 static struct tab_table *
1122 create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1129 static const struct tuple names[] =
1131 {CRS_CL_COUNT, N_("count")},
1132 {CRS_CL_ROW, N_("row %")},
1133 {CRS_CL_COLUMN, N_("column %")},
1134 {CRS_CL_TOTAL, N_("total %")},
1135 {CRS_CL_EXPECTED, N_("expected")},
1136 {CRS_CL_RESIDUAL, N_("residual")},
1137 {CRS_CL_SRESIDUAL, N_("std. resid.")},
1138 {CRS_CL_ASRESIDUAL, N_("adj. resid.")},
1140 const int n_names = sizeof names / sizeof *names;
1141 const struct tuple *t;
1143 struct tab_table *table;
1144 struct string title;
1147 table = tab_create (pt->n_consts + 1 + pt->n_cols + 1,
1148 (pt->n_entries / pt->n_cols) * 3 / 2 * proc->n_cells + 10,
1150 tab_headers (table, pt->n_consts + 1, 0, 2, 0);
1152 /* First header line. */
1153 tab_joint_text (table, pt->n_consts + 1, 0,
1154 (pt->n_consts + 1) + (pt->n_cols - 1), 0,
1155 TAB_CENTER | TAT_TITLE, var_get_name (pt->vars[COL_VAR]));
1157 tab_hline (table, TAL_1, pt->n_consts + 1,
1158 pt->n_consts + 2 + pt->n_cols - 2, 1);
1160 /* Second header line. */
1161 for (i = 2; i < pt->n_consts + 2; i++)
1162 tab_joint_text (table, pt->n_consts + 2 - i - 1, 0,
1163 pt->n_consts + 2 - i - 1, 1,
1164 TAB_RIGHT | TAT_TITLE, var_to_string (pt->vars[i]));
1165 tab_text (table, pt->n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1166 var_get_name (pt->vars[ROW_VAR]));
1167 for (i = 0; i < pt->n_cols; i++)
1168 table_value_missing (proc, table, pt->n_consts + 2 + i - 1, 1, TAB_RIGHT,
1169 &pt->cols[i], pt->vars[COL_VAR]);
1170 tab_text (table, pt->n_consts + 2 + pt->n_cols - 1, 1, TAB_CENTER, _("Total"));
1172 tab_hline (table, TAL_1, 0, pt->n_consts + 2 + pt->n_cols - 1, 2);
1173 tab_vline (table, TAL_1, pt->n_consts + 2 + pt->n_cols - 1, 0, 1);
1176 ds_init_empty (&title);
1177 for (i = 0; i < pt->n_consts + 2; i++)
1180 ds_put_cstr (&title, " * ");
1181 ds_put_cstr (&title, var_get_name (pt->vars[i]));
1183 for (i = 0; i < pt->n_consts; i++)
1185 const struct variable *var = pt->const_vars[i];
1188 ds_put_format (&title, ", %s=", var_get_name (var));
1190 /* Insert the formatted value of the variable, then trim
1191 leading spaces in what was just inserted. */
1192 ofs = ds_length (&title);
1193 data_out (&pt->const_values[i], var_get_print_format (var),
1194 ds_put_uninit (&title, var_get_width (var)));
1195 ds_remove (&title, ofs, ss_cspan (ds_substr (&title, ofs, SIZE_MAX),
1199 ds_put_cstr (&title, " [");
1201 for (t = names; t < &names[n_names]; t++)
1202 if (proc->cells & (1u << t->value))
1205 ds_put_cstr (&title, ", ");
1206 ds_put_cstr (&title, gettext (t->name));
1208 ds_put_cstr (&title, "].");
1210 tab_title (table, "%s", ds_cstr (&title));
1211 ds_destroy (&title);
1213 tab_offset (table, 0, 2);
1217 static struct tab_table *
1218 create_chisq_table (struct pivot_table *pt)
1220 struct tab_table *chisq;
1222 chisq = tab_create (6 + (pt->n_vars - 2),
1223 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10,
1225 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1227 tab_title (chisq, _("Chi-square tests."));
1229 tab_offset (chisq, pt->n_vars - 2, 0);
1230 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1231 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1232 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1233 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1234 _("Asymp. Sig. (2-sided)"));
1235 tab_text (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1236 _("Exact. Sig. (2-sided)"));
1237 tab_text (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1238 _("Exact. Sig. (1-sided)"));
1239 tab_offset (chisq, 0, 1);
1244 /* Symmetric measures. */
1245 static struct tab_table *
1246 create_sym_table (struct pivot_table *pt)
1248 struct tab_table *sym;
1250 sym = tab_create (6 + (pt->n_vars - 2),
1251 pt->n_entries / pt->n_cols * 7 + 10, 1);
1252 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1253 tab_title (sym, _("Symmetric measures."));
1255 tab_offset (sym, pt->n_vars - 2, 0);
1256 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1257 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1258 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1259 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1260 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1261 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1262 tab_offset (sym, 0, 1);
1267 /* Risk estimate. */
1268 static struct tab_table *
1269 create_risk_table (struct pivot_table *pt)
1271 struct tab_table *risk;
1273 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10,
1275 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1276 tab_title (risk, _("Risk estimate."));
1278 tab_offset (risk, pt->n_vars - 2, 0);
1279 tab_joint_text_format (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE,
1280 _("95%% Confidence Interval"));
1281 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1282 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1283 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1284 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1285 tab_hline (risk, TAL_1, 2, 3, 1);
1286 tab_vline (risk, TAL_1, 2, 0, 1);
1287 tab_offset (risk, 0, 2);
1292 /* Directional measures. */
1293 static struct tab_table *
1294 create_direct_table (struct pivot_table *pt)
1296 struct tab_table *direct;
1298 direct = tab_create (7 + (pt->n_vars - 2),
1299 pt->n_entries / pt->n_cols * 7 + 10, 1);
1300 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1301 tab_title (direct, _("Directional measures."));
1303 tab_offset (direct, pt->n_vars - 2, 0);
1304 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1305 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1306 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1307 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1308 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1309 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1310 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1311 tab_offset (direct, 0, 1);
1317 /* Delete missing rows and columns for statistical analysis when
1320 delete_missing (struct pivot_table *pt)
1324 for (r = 0; r < pt->n_rows; r++)
1325 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1327 for (c = 0; c < pt->n_cols; c++)
1328 pt->mat[c + r * pt->n_cols] = 0.;
1333 for (c = 0; c < pt->n_cols; c++)
1334 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1336 for (r = 0; r < pt->n_rows; r++)
1337 pt->mat[c + r * pt->n_cols] = 0.;
1342 /* Prepare table T for submission, and submit it. */
1344 submit (struct crosstabs_proc *proc, struct pivot_table *pt,
1345 struct tab_table *t)
1352 tab_resize (t, -1, 0);
1353 if (tab_nr (t) == tab_t (t))
1358 tab_offset (t, 0, 0);
1360 for (i = 2; i < pt->n_vars; i++)
1361 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1362 var_to_string (pt->vars[i]));
1363 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1364 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1366 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1368 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1369 tab_dim (t, crosstabs_dim, proc);
1373 /* Sets the widths of all the columns and heights of all the rows in
1374 table T for driver D. */
1376 crosstabs_dim (struct tab_table *t, struct outp_driver *d, void *proc_)
1378 struct crosstabs_proc *proc = proc_;
1381 /* Width of a numerical column. */
1382 int c = outp_string_width (d, "0.000000", OUTP_PROPORTIONAL);
1383 if (proc->exclude == MV_NEVER)
1384 c += outp_string_width (d, "M", OUTP_PROPORTIONAL);
1386 /* Set width for header columns. */
1392 w = d->width - c * (t->nc - t->l);
1393 for (i = 0; i <= t->nc; i++)
1397 if (w < d->prop_em_width * 8)
1398 w = d->prop_em_width * 8;
1400 if (w > d->prop_em_width * 15)
1401 w = d->prop_em_width * 15;
1403 for (i = 0; i < t->l; i++)
1407 for (i = t->l; i < t->nc; i++)
1410 for (i = 0; i < t->nr; i++)
1411 t->h[i] = tab_natural_height (t, d, i);
1415 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1417 size_t row0 = *row1p;
1420 if (row0 >= pt->n_entries)
1423 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1425 struct table_entry *a = pt->entries[row0];
1426 struct table_entry *b = pt->entries[row1];
1427 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1435 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1436 result. WIDTH_ points to an int which is either 0 for a
1437 numeric value or a string width for a string value. */
1439 compare_value_3way (const void *a_, const void *b_, const void *width_)
1441 const union value *a = a_;
1442 const union value *b = b_;
1443 const int *width = width_;
1445 return value_compare_3way (a, b, *width);
1448 /* Given an array of ENTRY_CNT table_entry structures starting at
1449 ENTRIES, creates a sorted list of the values that the variable
1450 with index VAR_IDX takes on. The values are returned as a
1451 malloc()'d array stored in *VALUES, with the number of values
1452 stored in *VALUE_CNT.
1455 enum_var_values (const struct pivot_table *pt, int var_idx,
1456 union value **valuesp, int *n_values)
1458 const struct variable *var = pt->vars[var_idx];
1459 struct var_range *range = get_var_range (var);
1460 union value *values;
1465 values = *valuesp = xnmalloc (range->count, sizeof *values);
1466 *n_values = range->count;
1467 for (i = 0; i < range->count; i++)
1468 values[i].f = range->min + i;
1472 int width = var_get_width (var);
1473 struct hmapx_node *node;
1474 const union value *iter;
1478 for (i = 0; i < pt->n_entries; i++)
1480 const struct table_entry *te = pt->entries[i];
1481 const union value *value = &te->values[var_idx];
1482 size_t hash = value_hash (value, width, 0);
1484 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1485 if (value_equal (iter, value, width))
1488 hmapx_insert (&set, (union value *) value, hash);
1493 *n_values = hmapx_count (&set);
1494 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1496 HMAPX_FOR_EACH (iter, node, &set)
1497 values[i++] = *iter;
1498 hmapx_destroy (&set);
1500 sort (values, *n_values, sizeof *values, compare_value_3way, &width);
1504 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1505 from V, displayed with print format spec from variable VAR. When
1506 in REPORT missing-value mode, missing values have an M appended. */
1508 table_value_missing (struct crosstabs_proc *proc,
1509 struct tab_table *table, int c, int r, unsigned char opt,
1510 const union value *v, const struct variable *var)
1513 const struct fmt_spec *print = var_get_print_format (var);
1515 const char *label = var_lookup_value_label (var, v);
1518 tab_text (table, c, r, TAB_LEFT, label);
1522 s.string = tab_alloc (table, print->w);
1523 data_out (v, print, s.string);
1524 s.length = print->w;
1525 if (proc->exclude == MV_NEVER && var_is_num_missing (var, v->f, MV_USER))
1526 s.string[s.length++] = 'M';
1527 while (s.length && *s.string == ' ')
1532 tab_raw (table, c, r, opt, &s);
1535 /* Draws a line across TABLE at the current row to indicate the most
1536 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1537 that changed, and puts the values that changed into the table. TB
1538 and PT must be the corresponding table_entry and crosstab,
1541 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1542 struct tab_table *table, int first_difference)
1544 tab_hline (table, TAL_1, pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1546 for (; first_difference >= 2; first_difference--)
1547 table_value_missing (proc, table, pt->n_vars - first_difference - 1, 0,
1548 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1549 pt->vars[first_difference]);
1552 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1553 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1554 additionally suffixed with a letter `M'. */
1556 format_cell_entry (struct tab_table *table, int c, int r, double value,
1557 char suffix, bool mark_missing)
1559 const struct fmt_spec f = {FMT_F, 10, 1};
1564 s.string = tab_alloc (table, 16);
1566 data_out (&v, &f, s.string);
1567 while (*s.string == ' ')
1573 s.string[s.length++] = suffix;
1575 s.string[s.length++] = 'M';
1577 tab_raw (table, c, r, TAB_RIGHT, &s);
1580 /* Displays the crosstabulation table. */
1582 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1583 struct tab_table *table)
1589 for (r = 0; r < pt->n_rows; r++)
1590 table_value_missing (proc, table, pt->n_vars - 2, r * proc->n_cells,
1591 TAB_RIGHT, &pt->rows[r], pt->vars[ROW_VAR]);
1593 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1594 TAB_LEFT, _("Total"));
1596 /* Put in the actual cells. */
1598 tab_offset (table, pt->n_vars - 1, -1);
1599 for (r = 0; r < pt->n_rows; r++)
1601 if (proc->n_cells > 1)
1602 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1603 for (c = 0; c < pt->n_cols; c++)
1605 bool mark_missing = false;
1606 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1607 if (proc->exclude == MV_NEVER
1608 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1609 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1611 mark_missing = true;
1612 for (i = 0; i < proc->n_cells; i++)
1617 switch (proc->a_cells[i])
1623 v = *mp / pt->row_tot[r] * 100.;
1627 v = *mp / pt->col_tot[c] * 100.;
1631 v = *mp / pt->total * 100.;
1634 case CRS_CL_EXPECTED:
1637 case CRS_CL_RESIDUAL:
1638 v = *mp - expected_value;
1640 case CRS_CL_SRESIDUAL:
1641 v = (*mp - expected_value) / sqrt (expected_value);
1643 case CRS_CL_ASRESIDUAL:
1644 v = ((*mp - expected_value)
1645 / sqrt (expected_value
1646 * (1. - pt->row_tot[r] / pt->total)
1647 * (1. - pt->col_tot[c] / pt->total)));
1652 format_cell_entry (table, c, i, v, suffix, mark_missing);
1658 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1662 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1663 for (r = 0; r < pt->n_rows; r++)
1665 bool mark_missing = false;
1667 if (proc->exclude == MV_NEVER
1668 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1669 mark_missing = true;
1671 for (i = 0; i < proc->n_cells; i++)
1676 switch (proc->a_cells[i])
1686 v = pt->row_tot[r] / pt->total * 100.;
1690 v = pt->row_tot[r] / pt->total * 100.;
1693 case CRS_CL_EXPECTED:
1694 case CRS_CL_RESIDUAL:
1695 case CRS_CL_SRESIDUAL:
1696 case CRS_CL_ASRESIDUAL:
1703 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing);
1704 tab_next_row (table);
1708 /* Column totals, grand total. */
1710 if (proc->n_cells > 1)
1711 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1712 for (c = 0; c <= pt->n_cols; c++)
1714 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1715 bool mark_missing = false;
1718 if (proc->exclude == MV_NEVER && c < pt->n_cols
1719 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1720 mark_missing = true;
1722 for (i = 0; i < proc->n_cells; i++)
1727 switch (proc->a_cells[i])
1733 v = ct / pt->total * 100.;
1741 v = ct / pt->total * 100.;
1744 case CRS_CL_EXPECTED:
1745 case CRS_CL_RESIDUAL:
1746 case CRS_CL_SRESIDUAL:
1747 case CRS_CL_ASRESIDUAL:
1753 format_cell_entry (table, c, i, v, suffix, mark_missing);
1758 tab_offset (table, -1, tab_row (table) + last_row);
1759 tab_offset (table, 0, -1);
1762 static void calc_r (struct pivot_table *,
1763 double *PT, double *Y, double *, double *, double *);
1764 static void calc_chisq (struct pivot_table *,
1765 double[N_CHISQ], int[N_CHISQ], double *, double *);
1767 /* Display chi-square statistics. */
1769 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1770 bool *showed_fisher)
1772 static const char *chisq_stats[N_CHISQ] =
1774 N_("Pearson Chi-Square"),
1775 N_("Likelihood Ratio"),
1776 N_("Fisher's Exact Test"),
1777 N_("Continuity Correction"),
1778 N_("Linear-by-Linear Association"),
1780 double chisq_v[N_CHISQ];
1781 double fisher1, fisher2;
1786 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1788 tab_offset (chisq, pt->n_vars - 2, -1);
1790 for (i = 0; i < N_CHISQ; i++)
1792 if ((i != 2 && chisq_v[i] == SYSMIS)
1793 || (i == 2 && fisher1 == SYSMIS))
1796 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1799 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL);
1800 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], &pt->weight_format);
1801 tab_double (chisq, 3, 0, TAB_RIGHT,
1802 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL);
1806 *showed_fisher = true;
1807 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL);
1808 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL);
1810 tab_next_row (chisq);
1813 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1814 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1815 tab_next_row (chisq);
1817 tab_offset (chisq, 0, -1);
1820 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1821 double[N_SYMMETRIC], double[N_SYMMETRIC],
1822 double[N_SYMMETRIC],
1823 double[3], double[3], double[3]);
1825 /* Display symmetric measures. */
1827 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1828 struct tab_table *sym)
1830 static const char *categories[] =
1832 N_("Nominal by Nominal"),
1833 N_("Ordinal by Ordinal"),
1834 N_("Interval by Interval"),
1835 N_("Measure of Agreement"),
1838 static const char *stats[N_SYMMETRIC] =
1842 N_("Contingency Coefficient"),
1843 N_("Kendall's tau-b"),
1844 N_("Kendall's tau-c"),
1846 N_("Spearman Correlation"),
1851 static const int stats_categories[N_SYMMETRIC] =
1853 0, 0, 0, 1, 1, 1, 1, 2, 3,
1857 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1858 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1861 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1862 somers_d_v, somers_d_ase, somers_d_t))
1865 tab_offset (sym, pt->n_vars - 2, -1);
1867 for (i = 0; i < N_SYMMETRIC; i++)
1869 if (sym_v[i] == SYSMIS)
1872 if (stats_categories[i] != last_cat)
1874 last_cat = stats_categories[i];
1875 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1878 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1879 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL);
1880 if (sym_ase[i] != SYSMIS)
1881 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL);
1882 if (sym_t[i] != SYSMIS)
1883 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL);
1884 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL);*/
1888 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1889 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1892 tab_offset (sym, 0, -1);
1895 static int calc_risk (struct pivot_table *,
1896 double[], double[], double[], union value *);
1898 /* Display risk estimate. */
1900 display_risk (struct pivot_table *pt, struct tab_table *risk)
1903 double risk_v[3], lower[3], upper[3];
1907 if (!calc_risk (pt, risk_v, upper, lower, c))
1910 tab_offset (risk, pt->n_vars - 2, -1);
1912 for (i = 0; i < 3; i++)
1914 const struct variable *cv = pt->vars[COL_VAR];
1915 const struct variable *rv = pt->vars[ROW_VAR];
1916 int cvw = var_get_width (cv);
1917 int rvw = var_get_width (rv);
1919 if (risk_v[i] == SYSMIS)
1925 if (var_is_numeric (cv))
1926 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1927 var_get_name (cv), c[0].f, c[1].f);
1929 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1931 cvw, value_str (&c[0], cvw),
1932 cvw, value_str (&c[1], cvw));
1936 if (var_is_numeric (rv))
1937 sprintf (buf, _("For cohort %s = %g"),
1938 var_get_name (rv), pt->rows[i - 1].f);
1940 sprintf (buf, _("For cohort %s = %.*s"),
1942 rvw, value_str (&pt->rows[i - 1], rvw));
1946 tab_text (risk, 0, 0, TAB_LEFT, buf);
1947 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL);
1948 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL);
1949 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL);
1950 tab_next_row (risk);
1953 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1954 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1955 tab_next_row (risk);
1957 tab_offset (risk, 0, -1);
1960 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1961 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1962 double[N_DIRECTIONAL]);
1964 /* Display directional measures. */
1966 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
1967 struct tab_table *direct)
1969 static const char *categories[] =
1971 N_("Nominal by Nominal"),
1972 N_("Ordinal by Ordinal"),
1973 N_("Nominal by Interval"),
1976 static const char *stats[] =
1979 N_("Goodman and Kruskal tau"),
1980 N_("Uncertainty Coefficient"),
1985 static const char *types[] =
1992 static const int stats_categories[N_DIRECTIONAL] =
1994 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
1997 static const int stats_stats[N_DIRECTIONAL] =
1999 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
2002 static const int stats_types[N_DIRECTIONAL] =
2004 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
2007 static const int *stats_lookup[] =
2014 static const char **stats_names[] =
2026 double direct_v[N_DIRECTIONAL];
2027 double direct_ase[N_DIRECTIONAL];
2028 double direct_t[N_DIRECTIONAL];
2032 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t))
2035 tab_offset (direct, pt->n_vars - 2, -1);
2037 for (i = 0; i < N_DIRECTIONAL; i++)
2039 if (direct_v[i] == SYSMIS)
2045 for (j = 0; j < 3; j++)
2046 if (last[j] != stats_lookup[j][i])
2049 tab_hline (direct, TAL_1, j, 6, 0);
2054 int k = last[j] = stats_lookup[j][i];
2059 string = var_get_name (pt->vars[0]);
2061 string = var_get_name (pt->vars[1]);
2063 tab_text_format (direct, j, 0, TAB_LEFT,
2064 gettext (stats_names[j][k]), string);
2069 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL);
2070 if (direct_ase[i] != SYSMIS)
2071 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL);
2072 if (direct_t[i] != SYSMIS)
2073 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL);
2074 /*tab_double (direct, 6, 0, TAB_RIGHT, normal_sig (direct_v[i]), NULL);*/
2075 tab_next_row (direct);
2078 tab_offset (direct, 0, -1);
2081 /* Statistical calculations. */
2083 /* Returns the value of the gamma (factorial) function for an integer
2086 gamma_int (double pt)
2091 for (i = 2; i < pt; i++)
2096 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2098 static inline double
2099 Pr (int a, int b, int c, int d)
2101 return (gamma_int (a + b + 1.) / gamma_int (a + 1.)
2102 * gamma_int (c + d + 1.) / gamma_int (b + 1.)
2103 * gamma_int (a + c + 1.) / gamma_int (c + 1.)
2104 * gamma_int (b + d + 1.) / gamma_int (d + 1.)
2105 / gamma_int (a + b + c + d + 1.));
2108 /* Swap the contents of A and B. */
2110 swap (int *a, int *b)
2117 /* Calculate significance for Fisher's exact test as specified in
2118 _SPSS Statistical Algorithms_, Appendix 5. */
2120 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2124 if (MIN (c, d) < MIN (a, b))
2125 swap (&a, &c), swap (&b, &d);
2126 if (MIN (b, d) < MIN (a, c))
2127 swap (&a, &b), swap (&c, &d);
2131 swap (&a, &b), swap (&c, &d);
2133 swap (&a, &c), swap (&b, &d);
2137 for (pt = 0; pt <= a; pt++)
2138 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2140 *fisher2 = *fisher1;
2141 for (pt = 1; pt <= b; pt++)
2142 *fisher2 += Pr (a + pt, b - pt, c - pt, d + pt);
2145 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2146 columns with values COLS and N_ROWS rows with values ROWS. Values
2147 in the matrix sum to pt->total. */
2149 calc_chisq (struct pivot_table *pt,
2150 double chisq[N_CHISQ], int df[N_CHISQ],
2151 double *fisher1, double *fisher2)
2155 chisq[0] = chisq[1] = 0.;
2156 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2157 *fisher1 = *fisher2 = SYSMIS;
2159 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2161 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2163 chisq[0] = chisq[1] = SYSMIS;
2167 for (r = 0; r < pt->n_rows; r++)
2168 for (c = 0; c < pt->n_cols; c++)
2170 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2171 const double freq = pt->mat[pt->n_cols * r + c];
2172 const double residual = freq - expected;
2174 chisq[0] += residual * residual / expected;
2176 chisq[1] += freq * log (expected / freq);
2187 /* Calculate Yates and Fisher exact test. */
2188 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2190 double f11, f12, f21, f22;
2196 for (i = j = 0; i < pt->n_cols; i++)
2197 if (pt->col_tot[i] != 0.)
2206 f11 = pt->mat[nz_cols[0]];
2207 f12 = pt->mat[nz_cols[1]];
2208 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2209 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2214 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2217 chisq[3] = (pt->total * pow2 (pt_)
2218 / (f11 + f12) / (f21 + f22)
2219 / (f11 + f21) / (f12 + f22));
2227 if (f11 < 5. || f12 < 5. || f21 < 5. || f22 < 5.)
2228 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2231 /* Calculate Mantel-Haenszel. */
2232 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2234 double r, ase_0, ase_1;
2235 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2237 chisq[4] = (pt->total - 1.) * r * r;
2242 /* Calculate the value of Pearson's r. r is stored into R, ase_1 into
2243 ASE_1, and ase_0 into ASE_0. The row and column values must be
2244 passed in PT and Y. */
2246 calc_r (struct pivot_table *pt,
2247 double *PT, double *Y, double *r, double *ase_0, double *ase_1)
2249 double SX, SY, S, T;
2251 double sum_XYf, sum_X2Y2f;
2252 double sum_Xr, sum_X2r;
2253 double sum_Yc, sum_Y2c;
2256 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2257 for (j = 0; j < pt->n_cols; j++)
2259 double fij = pt->mat[j + i * pt->n_cols];
2260 double product = PT[i] * Y[j];
2261 double temp = fij * product;
2263 sum_X2Y2f += temp * product;
2266 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2268 sum_Xr += PT[i] * pt->row_tot[i];
2269 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2271 Xbar = sum_Xr / pt->total;
2273 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2275 sum_Yc += Y[i] * pt->col_tot[i];
2276 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2278 Ybar = sum_Yc / pt->total;
2280 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2281 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2282 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2285 *ase_0 = sqrt ((sum_X2Y2f - pow2 (sum_XYf) / pt->total) / (sum_X2r * sum_Y2c));
2290 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2291 for (j = 0; j < pt->n_cols; j++)
2293 double Xresid, Yresid;
2296 Xresid = PT[i] - Xbar;
2297 Yresid = Y[j] - Ybar;
2298 temp = (T * Xresid * Yresid
2300 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2301 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2306 *ase_1 = sqrt (s) / (T * T);
2310 /* Calculate symmetric statistics and their asymptotic standard
2311 errors. Returns 0 if none could be calculated. */
2313 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2314 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2315 double t[N_SYMMETRIC],
2316 double somers_d_v[3], double somers_d_ase[3],
2317 double somers_d_t[3])
2321 q = MIN (pt->ns_rows, pt->ns_cols);
2325 for (i = 0; i < N_SYMMETRIC; i++)
2326 v[i] = ase[i] = t[i] = SYSMIS;
2328 /* Phi, Cramer's V, contingency coefficient. */
2329 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2331 double Xp = 0.; /* Pearson chi-square. */
2334 for (r = 0; r < pt->n_rows; r++)
2335 for (c = 0; c < pt->n_cols; c++)
2337 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2338 const double freq = pt->mat[pt->n_cols * r + c];
2339 const double residual = freq - expected;
2341 Xp += residual * residual / expected;
2344 if (proc->statistics & (1u << CRS_ST_PHI))
2346 v[0] = sqrt (Xp / pt->total);
2347 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2349 if (proc->statistics & (1u << CRS_ST_CC))
2350 v[2] = sqrt (Xp / (Xp + pt->total));
2353 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2354 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2359 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2363 Dr = Dc = pow2 (pt->total);
2364 for (r = 0; r < pt->n_rows; r++)
2365 Dr -= pow2 (pt->row_tot[r]);
2366 for (c = 0; c < pt->n_cols; c++)
2367 Dc -= pow2 (pt->col_tot[c]);
2369 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2370 for (c = 0; c < pt->n_cols; c++)
2374 for (r = 0; r < pt->n_rows; r++)
2375 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2384 for (i = 0; i < pt->n_rows; i++)
2388 for (j = 1; j < pt->n_cols; j++)
2389 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2392 for (j = 1; j < pt->n_cols; j++)
2393 Dij += cum[j + (i - 1) * pt->n_cols];
2397 double fij = pt->mat[j + i * pt->n_cols];
2401 if (++j == pt->n_cols)
2403 assert (j < pt->n_cols);
2405 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2406 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2410 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2411 Dij -= cum[j + (i - 1) * pt->n_cols];
2417 if (proc->statistics & (1u << CRS_ST_BTAU))
2418 v[3] = (P - Q) / sqrt (Dr * Dc);
2419 if (proc->statistics & (1u << CRS_ST_CTAU))
2420 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2421 if (proc->statistics & (1u << CRS_ST_GAMMA))
2422 v[5] = (P - Q) / (P + Q);
2424 /* ASE for tau-b, tau-c, gamma. Calculations could be
2425 eliminated here, at expense of memory. */
2430 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2431 for (i = 0; i < pt->n_rows; i++)
2435 for (j = 1; j < pt->n_cols; j++)
2436 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2439 for (j = 1; j < pt->n_cols; j++)
2440 Dij += cum[j + (i - 1) * pt->n_cols];
2444 double fij = pt->mat[j + i * pt->n_cols];
2446 if (proc->statistics & (1u << CRS_ST_BTAU))
2448 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2449 + v[3] * (pt->row_tot[i] * Dc
2450 + pt->col_tot[j] * Dr));
2451 btau_cum += fij * temp * temp;
2455 const double temp = Cij - Dij;
2456 ctau_cum += fij * temp * temp;
2459 if (proc->statistics & (1u << CRS_ST_GAMMA))
2461 const double temp = Q * Cij - P * Dij;
2462 gamma_cum += fij * temp * temp;
2465 if (proc->statistics & (1u << CRS_ST_D))
2467 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2468 - (P - Q) * (pt->total - pt->row_tot[i]));
2469 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2470 - (Q - P) * (pt->total - pt->col_tot[j]));
2473 if (++j == pt->n_cols)
2475 assert (j < pt->n_cols);
2477 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2478 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2482 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2483 Dij -= cum[j + (i - 1) * pt->n_cols];
2489 btau_var = ((btau_cum
2490 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2492 if (proc->statistics & (1u << CRS_ST_BTAU))
2494 ase[3] = sqrt (btau_var);
2495 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2498 if (proc->statistics & (1u << CRS_ST_CTAU))
2500 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2501 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2502 t[4] = v[4] / ase[4];
2504 if (proc->statistics & (1u << CRS_ST_GAMMA))
2506 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2507 t[5] = v[5] / (2. / (P + Q)
2508 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2510 if (proc->statistics & (1u << CRS_ST_D))
2512 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2513 somers_d_ase[0] = 2. * btau_var / (Dr + Dc) * sqrt (Dr * Dc);
2514 somers_d_t[0] = (somers_d_v[0]
2516 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2517 somers_d_v[1] = (P - Q) / Dc;
2518 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2519 somers_d_t[1] = (somers_d_v[1]
2521 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2522 somers_d_v[2] = (P - Q) / Dr;
2523 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2524 somers_d_t[2] = (somers_d_v[2]
2526 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2532 /* Spearman correlation, Pearson's r. */
2533 if (proc->statistics & (1u << CRS_ST_CORR))
2535 double *R = xmalloc (sizeof *R * pt->n_rows);
2536 double *C = xmalloc (sizeof *C * pt->n_cols);
2539 double y, t, c = 0., s = 0.;
2544 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2545 y = pt->row_tot[i] - c;
2549 if (++i == pt->n_rows)
2551 assert (i < pt->n_rows);
2556 double y, t, c = 0., s = 0.;
2561 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2562 y = pt->col_tot[j] - c;
2566 if (++j == pt->n_cols)
2568 assert (j < pt->n_cols);
2572 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2578 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2582 /* Cohen's kappa. */
2583 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2585 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2588 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2589 i < pt->ns_rows; i++, j++)
2593 while (pt->col_tot[j] == 0.)
2596 prod = pt->row_tot[i] * pt->col_tot[j];
2597 sum = pt->row_tot[i] + pt->col_tot[j];
2599 sum_fii += pt->mat[j + i * pt->n_cols];
2601 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2602 sum_riciri_ci += prod * sum;
2604 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2605 for (j = 0; j < pt->ns_cols; j++)
2607 double sum = pt->row_tot[i] + pt->col_tot[j];
2608 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2611 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2613 ase[8] = sqrt ((pow2 (pt->total) * sum_rici
2614 + sum_rici * sum_rici
2615 - pt->total * sum_riciri_ci)
2616 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2618 t[8] = v[8] / sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2619 / pow2 (pow2 (pt->total) - sum_rici))
2620 + ((2. * (pt->total - sum_fii)
2621 * (2. * sum_fii * sum_rici
2622 - pt->total * sum_fiiri_ci))
2623 / cube (pow2 (pt->total) - sum_rici))
2624 + (pow2 (pt->total - sum_fii)
2625 * (pt->total * sum_fijri_ci2 - 4.
2626 * sum_rici * sum_rici)
2627 / pow4 (pow2 (pt->total) - sum_rici))));
2629 t[8] = v[8] / ase[8];
2636 /* Calculate risk estimate. */
2638 calc_risk (struct pivot_table *pt,
2639 double *value, double *upper, double *lower, union value *c)
2641 double f11, f12, f21, f22;
2647 for (i = 0; i < 3; i++)
2648 value[i] = upper[i] = lower[i] = SYSMIS;
2651 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2658 for (i = j = 0; i < pt->n_cols; i++)
2659 if (pt->col_tot[i] != 0.)
2668 f11 = pt->mat[nz_cols[0]];
2669 f12 = pt->mat[nz_cols[1]];
2670 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2671 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2673 c[0] = pt->cols[nz_cols[0]];
2674 c[1] = pt->cols[nz_cols[1]];
2677 value[0] = (f11 * f22) / (f12 * f21);
2678 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2679 lower[0] = value[0] * exp (-1.960 * v);
2680 upper[0] = value[0] * exp (1.960 * v);
2682 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2683 v = sqrt ((f12 / (f11 * (f11 + f12)))
2684 + (f22 / (f21 * (f21 + f22))));
2685 lower[1] = value[1] * exp (-1.960 * v);
2686 upper[1] = value[1] * exp (1.960 * v);
2688 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2689 v = sqrt ((f11 / (f12 * (f11 + f12)))
2690 + (f21 / (f22 * (f21 + f22))));
2691 lower[2] = value[2] * exp (-1.960 * v);
2692 upper[2] = value[2] * exp (1.960 * v);
2697 /* Calculate directional measures. */
2699 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2700 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2701 double t[N_DIRECTIONAL])
2706 for (i = 0; i < N_DIRECTIONAL; i++)
2707 v[i] = ase[i] = t[i] = SYSMIS;
2711 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2713 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2714 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2715 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2716 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2717 double sum_fim, sum_fmj;
2719 int rm_index, cm_index;
2722 /* Find maximum for each row and their sum. */
2723 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2725 double max = pt->mat[i * pt->n_cols];
2728 for (j = 1; j < pt->n_cols; j++)
2729 if (pt->mat[j + i * pt->n_cols] > max)
2731 max = pt->mat[j + i * pt->n_cols];
2735 sum_fim += fim[i] = max;
2736 fim_index[i] = index;
2739 /* Find maximum for each column. */
2740 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2742 double max = pt->mat[j];
2745 for (i = 1; i < pt->n_rows; i++)
2746 if (pt->mat[j + i * pt->n_cols] > max)
2748 max = pt->mat[j + i * pt->n_cols];
2752 sum_fmj += fmj[j] = max;
2753 fmj_index[j] = index;
2756 /* Find maximum row total. */
2757 rm = pt->row_tot[0];
2759 for (i = 1; i < pt->n_rows; i++)
2760 if (pt->row_tot[i] > rm)
2762 rm = pt->row_tot[i];
2766 /* Find maximum column total. */
2767 cm = pt->col_tot[0];
2769 for (j = 1; j < pt->n_cols; j++)
2770 if (pt->col_tot[j] > cm)
2772 cm = pt->col_tot[j];
2776 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2777 v[1] = (sum_fmj - rm) / (pt->total - rm);
2778 v[2] = (sum_fim - cm) / (pt->total - cm);
2780 /* ASE1 for Y given PT. */
2784 for (accum = 0., i = 0; i < pt->n_rows; i++)
2785 for (j = 0; j < pt->n_cols; j++)
2787 const int deltaj = j == cm_index;
2788 accum += (pt->mat[j + i * pt->n_cols]
2789 * pow2 ((j == fim_index[i])
2794 ase[2] = sqrt (accum - pt->total * v[0]) / (pt->total - cm);
2797 /* ASE0 for Y given PT. */
2801 for (accum = 0., i = 0; i < pt->n_rows; i++)
2802 if (cm_index != fim_index[i])
2803 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2804 + pt->mat[i * pt->n_cols + cm_index]);
2805 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2808 /* ASE1 for PT given Y. */
2812 for (accum = 0., i = 0; i < pt->n_rows; i++)
2813 for (j = 0; j < pt->n_cols; j++)
2815 const int deltaj = i == rm_index;
2816 accum += (pt->mat[j + i * pt->n_cols]
2817 * pow2 ((i == fmj_index[j])
2822 ase[1] = sqrt (accum - pt->total * v[0]) / (pt->total - rm);
2825 /* ASE0 for PT given Y. */
2829 for (accum = 0., j = 0; j < pt->n_cols; j++)
2830 if (rm_index != fmj_index[j])
2831 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2832 + pt->mat[j + pt->n_cols * rm_index]);
2833 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2836 /* Symmetric ASE0 and ASE1. */
2841 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2842 for (j = 0; j < pt->n_cols; j++)
2844 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2845 int temp1 = (i == rm_index) + (j == cm_index);
2846 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2847 accum1 += (pt->mat[j + i * pt->n_cols]
2848 * pow2 (temp0 + (v[0] - 1.) * temp1));
2850 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2851 t[0] = v[0] / (sqrt (accum0 - pow2 ((sum_fim + sum_fmj - cm - rm) / pt->total))
2852 / (2. * pt->total - rm - cm));
2861 double sum_fij2_ri, sum_fij2_ci;
2862 double sum_ri2, sum_cj2;
2864 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2865 for (j = 0; j < pt->n_cols; j++)
2867 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2868 sum_fij2_ri += temp / pt->row_tot[i];
2869 sum_fij2_ci += temp / pt->col_tot[j];
2872 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2873 sum_ri2 += pow2 (pt->row_tot[i]);
2875 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2876 sum_cj2 += pow2 (pt->col_tot[j]);
2878 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2879 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2883 if (proc->statistics & (1u << CRS_ST_UC))
2885 double UX, UY, UXY, P;
2886 double ase1_yx, ase1_xy, ase1_sym;
2889 for (UX = 0., i = 0; i < pt->n_rows; i++)
2890 if (pt->row_tot[i] > 0.)
2891 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2893 for (UY = 0., j = 0; j < pt->n_cols; j++)
2894 if (pt->col_tot[j] > 0.)
2895 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2897 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2898 for (j = 0; j < pt->n_cols; j++)
2900 double entry = pt->mat[j + i * pt->n_cols];
2905 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2906 UXY -= entry / pt->total * log (entry / pt->total);
2909 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2910 for (j = 0; j < pt->n_cols; j++)
2912 double entry = pt->mat[j + i * pt->n_cols];
2917 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2918 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2919 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2920 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2921 ase1_sym += entry * pow2 ((UXY
2922 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2923 - (UX + UY) * log (entry / pt->total));
2926 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2927 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2928 t[5] = v[5] / ((2. / (pt->total * (UX + UY)))
2929 * sqrt (P - pow2 (UX + UY - UXY) / pt->total));
2931 v[6] = (UX + UY - UXY) / UX;
2932 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2933 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2935 v[7] = (UX + UY - UXY) / UY;
2936 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2937 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2941 if (proc->statistics & (1u << CRS_ST_D))
2943 double v_dummy[N_SYMMETRIC];
2944 double ase_dummy[N_SYMMETRIC];
2945 double t_dummy[N_SYMMETRIC];
2946 double somers_d_v[3];
2947 double somers_d_ase[3];
2948 double somers_d_t[3];
2950 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2951 somers_d_v, somers_d_ase, somers_d_t))
2954 for (i = 0; i < 3; i++)
2956 v[8 + i] = somers_d_v[i];
2957 ase[8 + i] = somers_d_ase[i];
2958 t[8 + i] = somers_d_t[i];
2964 if (proc->statistics & (1u << CRS_ST_ETA))
2967 double sum_Xr, sum_X2r;
2971 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2973 sum_Xr += pt->rows[i].f * pt->row_tot[i];
2974 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
2976 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2978 for (SXW = 0., j = 0; j < pt->n_cols; j++)
2982 for (cum = 0., i = 0; i < pt->n_rows; i++)
2984 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
2985 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
2988 SXW -= cum * cum / pt->col_tot[j];
2990 v[11] = sqrt (1. - SXW / SX);
2994 double sum_Yc, sum_Y2c;
2998 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
3000 sum_Yc += pt->cols[i].f * pt->col_tot[i];
3001 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
3003 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
3005 for (SYW = 0., i = 0; i < pt->n_rows; i++)
3009 for (cum = 0., j = 0; j < pt->n_cols; j++)
3011 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
3012 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
3015 SYW -= cum * cum / pt->row_tot[i];
3017 v[12] = sqrt (1. - SYW / SY);