1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2006, 2009 Free Software Foundation, Inc.
4 This program is free software: you can redistribute it and/or modify
5 it under the terms of the GNU General Public License as published by
6 the Free Software Foundation, either version 3 of the License, or
7 (at your option) any later version.
9 This program is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 GNU General Public License for more details.
14 You should have received a copy of the GNU General Public License
15 along with this program. If not, see <http://www.gnu.org/licenses/>. */
19 - Pearson's R (but not Spearman!) is off a little.
20 - T values for Spearman's R and Pearson's R are wrong.
21 - How to calculate significance of symmetric and directional measures?
22 - Asymmetric ASEs and T values for lambda are wrong.
23 - ASE of Goodman and Kruskal's tau is not calculated.
24 - ASE of symmetric somers' d is wrong.
25 - Approx. T of uncertainty coefficient is wrong.
32 #include <gsl/gsl_cdf.h>
36 #include <data/case.h>
37 #include <data/casegrouper.h>
38 #include <data/casereader.h>
39 #include <data/data-out.h>
40 #include <data/dictionary.h>
41 #include <data/format.h>
42 #include <data/procedure.h>
43 #include <data/value-labels.h>
44 #include <data/variable.h>
45 #include <language/command.h>
46 #include <language/dictionary/split-file.h>
47 #include <language/lexer/lexer.h>
48 #include <language/lexer/variable-parser.h>
49 #include <libpspp/array.h>
50 #include <libpspp/assertion.h>
51 #include <libpspp/compiler.h>
52 #include <libpspp/hash.h>
53 #include <libpspp/hmap.h>
54 #include <libpspp/hmapx.h>
55 #include <libpspp/message.h>
56 #include <libpspp/misc.h>
57 #include <libpspp/pool.h>
58 #include <libpspp/str.h>
59 #include <output/output.h>
60 #include <output/table.h>
67 #define _(msgid) gettext (msgid)
68 #define N_(msgid) msgid
76 missing=miss:!table/include/report;
77 +write[wr_]=none,cells,all;
78 +format=fmt:!labels/nolabels/novallabs,
81 tabl:!tables/notables,
84 +cells[cl_]=count,expected,row,column,total,residual,sresidual,
86 +statistics[st_]=chisq,phi,cc,lambda,uc,none,btau,ctau,risk,gamma,d,
92 /* Number of chi-square statistics. */
95 /* Number of symmetric statistics. */
98 /* Number of directional statistics. */
99 #define N_DIRECTIONAL 13
101 /* A single table entry for general mode. */
104 struct hmap_node node; /* Entry in hash table. */
105 double freq; /* Frequency count. */
106 union value values[1]; /* Values. */
110 table_entry_size (size_t n_values)
112 return (offsetof (struct table_entry, values)
113 + n_values * sizeof (union value));
116 /* Indexes into the 'vars' member of struct pivot_table and
117 struct crosstab member. */
120 ROW_VAR = 0, /* Row variable. */
121 COL_VAR = 1 /* Column variable. */
122 /* Higher indexes cause multiple tables to be output. */
125 /* A crosstabulation of 2 or more variables. */
128 struct fmt_spec weight_format; /* Format for weight variable. */
129 double missing; /* Weight of missing cases. */
131 /* Variables (2 or more). */
133 const struct variable **vars;
135 /* Constants (0 or more). */
137 const struct variable **const_vars;
138 union value *const_values;
142 struct table_entry **entries;
145 /* Column values, number of columns. */
149 /* Row values, number of rows. */
153 /* Number of statistically interesting columns/rows
154 (columns/rows with data in them). */
155 int ns_cols, ns_rows;
157 /* Matrix contents. */
158 double *mat; /* Matrix proper. */
159 double *row_tot; /* Row totals. */
160 double *col_tot; /* Column totals. */
161 double total; /* Grand total. */
164 /* Integer mode variable info. */
167 int min; /* Minimum value. */
168 int max; /* Maximum value + 1. */
169 int count; /* max - min. */
172 static inline struct var_range *
173 get_var_range (const struct variable *v)
175 return var_get_aux (v);
178 struct crosstabs_proc
180 enum { INTEGER, GENERAL } mode;
181 enum mv_class exclude;
184 struct fmt_spec weight_format;
186 /* Variables specifies on VARIABLES. */
187 const struct variable **variables;
191 struct pivot_table *pivots;
195 int n_cells; /* Number of cells requested. */
196 unsigned int cells; /* Bit k is 1 if cell k is requested. */
197 int a_cells[CRS_CL_count]; /* 0...n_cells-1 are the requested cells. */
200 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
203 /* Auxiliary data structure for tab_dim. */
204 struct crosstabs_dim_aux
206 enum mv_class exclude;
210 init_proc (struct crosstabs_proc *proc, struct dataset *ds)
212 const struct variable *wv = dict_get_weight (dataset_dict (ds));
213 proc->bad_warn = true;
214 proc->variables = NULL;
215 proc->n_variables = 0;
218 proc->weight_format = wv ? *var_get_print_format (wv) : F_8_0;
222 free_proc (struct crosstabs_proc *proc)
224 struct pivot_table *pt;
226 free (proc->variables);
227 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
230 free (pt->const_vars);
231 /* We must not call value_destroy on const_values because
232 it is a wild pointer; it never pointed to anything owned
235 The rest of the data was allocated and destroyed at a
236 lower level already. */
241 static int internal_cmd_crosstabs (struct lexer *lexer, struct dataset *ds,
242 struct crosstabs_proc *);
243 static bool should_tabulate_case (const struct pivot_table *,
244 const struct ccase *, enum mv_class exclude);
245 static void tabulate_general_case (struct pivot_table *, const struct ccase *,
247 static void tabulate_integer_case (struct pivot_table *, const struct ccase *,
249 static void postcalc (struct crosstabs_proc *);
250 static void submit (struct crosstabs_proc *, struct pivot_table *,
253 /* Parse and execute CROSSTABS, then clean up. */
255 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
257 struct crosstabs_proc proc;
260 init_proc (&proc, ds);
261 result = internal_cmd_crosstabs (lexer, ds, &proc);
267 /* Parses and executes the CROSSTABS procedure. */
269 internal_cmd_crosstabs (struct lexer *lexer, struct dataset *ds,
270 struct crosstabs_proc *proc)
272 struct casegrouper *grouper;
273 struct casereader *input, *group;
274 struct cmd_crosstabs cmd;
275 struct pivot_table *pt;
279 if (!parse_crosstabs (lexer, ds, &cmd, proc))
282 proc->mode = proc->n_variables ? INTEGER : GENERAL;
286 proc->cells = 1u << CRS_CL_COUNT;
287 else if (cmd.a_cells[CRS_CL_ALL])
288 proc->cells = UINT_MAX;
292 for (i = 0; i < CRS_CL_count; i++)
294 proc->cells |= 1u << i;
295 if (proc->cells == 0)
296 proc->cells = ((1u << CRS_CL_COUNT)
298 | (1u << CRS_CL_COLUMN)
299 | (1u << CRS_CL_TOTAL));
301 proc->cells &= ((1u << CRS_CL_count) - 1);
302 proc->cells &= ~((1u << CRS_CL_NONE) | (1u << CRS_CL_ALL));
304 for (i = 0; i < CRS_CL_count; i++)
305 if (proc->cells & (1u << i))
306 proc->a_cells[proc->n_cells++] = i;
309 if (cmd.a_statistics[CRS_ST_ALL])
310 proc->statistics = UINT_MAX;
311 else if (cmd.sbc_statistics)
315 proc->statistics = 0;
316 for (i = 0; i < CRS_ST_count; i++)
317 if (cmd.a_statistics[i])
318 proc->statistics |= 1u << i;
319 if (proc->statistics == 0)
320 proc->statistics |= 1u << CRS_ST_CHISQ;
323 proc->statistics = 0;
326 proc->exclude = (cmd.miss == CRS_TABLE ? MV_ANY
327 : cmd.miss == CRS_INCLUDE ? MV_SYSTEM
329 if (proc->mode == GENERAL && proc->mode == MV_NEVER)
331 msg (SE, _("Missing mode REPORT not allowed in general mode. "
332 "Assuming MISSING=TABLE."));
337 proc->pivot = cmd.pivot == CRS_PIVOT;
339 input = casereader_create_filter_weight (proc_open (ds), dataset_dict (ds),
341 grouper = casegrouper_create_splits (input, dataset_dict (ds));
342 while (casegrouper_get_next_group (grouper, &group))
346 /* Output SPLIT FILE variables. */
347 c = casereader_peek (group, 0);
350 output_split_file_values (ds, c);
355 for (; (c = casereader_read (group)) != NULL; case_unref (c))
356 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
358 double weight = dict_get_case_weight (dataset_dict (ds), c,
360 if (should_tabulate_case (pt, c, proc->exclude))
362 if (proc->mode == GENERAL)
363 tabulate_general_case (pt, c, weight);
365 tabulate_integer_case (pt, c, weight);
368 pt->missing += weight;
370 casereader_destroy (group);
375 ok = casegrouper_destroy (grouper);
376 ok = proc_commit (ds) && ok;
378 return ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
381 /* Parses the TABLES subcommand. */
383 crs_custom_tables (struct lexer *lexer, struct dataset *ds,
384 struct cmd_crosstabs *cmd UNUSED, void *proc_)
386 struct crosstabs_proc *proc = proc_;
387 struct const_var_set *var_set;
389 const struct variable ***by = NULL;
391 size_t *by_nvar = NULL;
396 /* Ensure that this is a TABLES subcommand. */
397 if (!lex_match_id (lexer, "TABLES")
398 && (lex_token (lexer) != T_ID ||
399 dict_lookup_var (dataset_dict (ds), lex_tokid (lexer)) == NULL)
400 && lex_token (lexer) != T_ALL)
402 lex_match (lexer, '=');
404 if (proc->variables != NULL)
405 var_set = const_var_set_create_from_array (proc->variables,
408 var_set = const_var_set_create_from_dict (dataset_dict (ds));
409 assert (var_set != NULL);
413 by = xnrealloc (by, n_by + 1, sizeof *by);
414 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
415 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
416 PV_NO_DUPLICATE | PV_NO_SCRATCH))
418 if (xalloc_oversized (nx, by_nvar[n_by]))
420 msg (SE, _("Too many cross-tabulation variables or dimensions."));
426 if (!lex_match (lexer, T_BY))
430 lex_error (lexer, _("expecting BY"));
438 by_iter = xcalloc (n_by, sizeof *by_iter);
439 proc->pivots = xnrealloc (proc->pivots,
440 proc->n_pivots + nx, sizeof *proc->pivots);
441 for (i = 0; i < nx; i++)
443 struct pivot_table *pt = &proc->pivots[proc->n_pivots++];
446 pt->weight_format = proc->weight_format;
449 pt->vars = xmalloc (n_by * sizeof *pt->vars);
451 pt->const_vars = NULL;
452 pt->const_values = NULL;
453 hmap_init (&pt->data);
457 for (j = 0; j < n_by; j++)
458 pt->vars[j] = by[j][by_iter[j]];
460 for (j = n_by - 1; j >= 0; j--)
462 if (++by_iter[j] < by_nvar[j])
471 /* All return paths lead here. */
472 for (i = 0; i < n_by; i++)
477 const_var_set_destroy (var_set);
482 /* Parses the VARIABLES subcommand. */
484 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
485 struct cmd_crosstabs *cmd UNUSED, void *proc_)
487 struct crosstabs_proc *proc = proc_;
490 msg (SE, _("VARIABLES must be specified before TABLES."));
494 lex_match (lexer, '=');
498 size_t orig_nv = proc->n_variables;
503 if (!parse_variables_const (lexer, dataset_dict (ds),
504 &proc->variables, &proc->n_variables,
505 (PV_APPEND | PV_NUMERIC
506 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
509 if (lex_token (lexer) != '(')
511 lex_error (lexer, "expecting `('");
516 if (!lex_force_int (lexer))
518 min = lex_integer (lexer);
521 lex_match (lexer, ',');
523 if (!lex_force_int (lexer))
525 max = lex_integer (lexer);
528 msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
534 if (lex_token (lexer) != ')')
536 lex_error (lexer, "expecting `)'");
541 for (i = orig_nv; i < proc->n_variables; i++)
543 struct var_range *vr = xmalloc (sizeof *vr);
546 vr->count = max - min + 1;
547 var_attach_aux (proc->variables[i], vr, var_dtor_free);
550 if (lex_token (lexer) == '/')
557 free (proc->variables);
558 proc->variables = NULL;
559 proc->n_variables = 0;
563 /* Data file processing. */
566 should_tabulate_case (const struct pivot_table *pt, const struct ccase *c,
567 enum mv_class exclude)
570 for (j = 0; j < pt->n_vars; j++)
572 const struct variable *var = pt->vars[j];
573 struct var_range *range = get_var_range (var);
575 if (var_is_value_missing (var, case_data (c, var), exclude))
580 double num = case_num (c, var);
581 if (num < range->min || num > range->max)
589 tabulate_integer_case (struct pivot_table *pt, const struct ccase *c,
592 struct table_entry *te;
597 for (j = 0; j < pt->n_vars; j++)
599 /* Throw away fractional parts of values. */
600 hash = hash_int (case_num (c, pt->vars[j]), hash);
603 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
605 for (j = 0; j < pt->n_vars; j++)
606 if ((int) case_num (c, pt->vars[j]) != (int) te->values[j].f)
609 /* Found an existing entry. */
616 /* No existing entry. Create a new one. */
617 te = xmalloc (table_entry_size (pt->n_vars));
619 for (j = 0; j < pt->n_vars; j++)
620 te->values[j].f = (int) case_num (c, pt->vars[j]);
621 hmap_insert (&pt->data, &te->node, hash);
625 tabulate_general_case (struct pivot_table *pt, const struct ccase *c,
628 struct table_entry *te;
633 for (j = 0; j < pt->n_vars; j++)
635 const struct variable *var = pt->vars[j];
636 hash = value_hash (case_data (c, var), var_get_width (var), hash);
639 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
641 for (j = 0; j < pt->n_vars; j++)
643 const struct variable *var = pt->vars[j];
644 if (!value_equal (case_data (c, var), &te->values[j],
645 var_get_width (var)))
649 /* Found an existing entry. */
656 /* No existing entry. Create a new one. */
657 te = xmalloc (table_entry_size (pt->n_vars));
659 for (j = 0; j < pt->n_vars; j++)
661 const struct variable *var = pt->vars[j];
662 int width = var_get_width (var);
663 value_init (&te->values[j], width);
664 value_copy (&te->values[j], case_data (c, var), width);
666 hmap_insert (&pt->data, &te->node, hash);
669 /* Post-data reading calculations. */
671 static int compare_table_entry_vars_3way (const struct table_entry *a,
672 const struct table_entry *b,
673 const struct pivot_table *pt,
675 static int compare_table_entry_3way (const void *ap_, const void *bp_,
677 static void enum_var_values (const struct pivot_table *, int var_idx,
678 union value **valuesp, int *n_values);
679 static void output_pivot_table (struct crosstabs_proc *,
680 struct pivot_table *);
681 static void make_pivot_table_subset (struct pivot_table *pt,
682 size_t row0, size_t row1,
683 struct pivot_table *subset);
684 static void make_summary_table (struct crosstabs_proc *);
685 static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
688 postcalc (struct crosstabs_proc *proc)
690 struct pivot_table *pt;
692 /* Convert hash tables into sorted arrays of entries. */
693 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
695 struct table_entry *e;
698 pt->n_entries = hmap_count (&pt->data);
699 pt->entries = xnmalloc (pt->n_entries, sizeof *pt->entries);
701 HMAP_FOR_EACH (e, struct table_entry, node, &pt->data)
702 pt->entries[i++] = e;
703 hmap_destroy (&pt->data);
705 sort (pt->entries, pt->n_entries, sizeof *pt->entries,
706 compare_table_entry_3way, pt);
709 make_summary_table (proc);
711 /* Output each pivot table. */
712 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
714 if (proc->pivot || pt->n_vars == 2)
715 output_pivot_table (proc, pt);
718 size_t row0 = 0, row1 = 0;
719 while (find_crosstab (pt, &row0, &row1))
721 struct pivot_table subset;
722 make_pivot_table_subset (pt, row0, row1, &subset);
723 output_pivot_table (proc, &subset);
728 /* Free output and prepare for next split file. */
729 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
735 /* Free only the members that were allocated in this
736 function. The other pointer members are either both
737 allocated and destroyed at a lower level (in
738 output_pivot_table), or both allocated and destroyed at
739 a higher level (in crs_custom_tables and free_proc,
741 for (i = 0; i < pt->n_entries; i++)
742 free (pt->entries[i]);
748 make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
749 struct pivot_table *subset)
754 assert (pt->n_consts == 0);
755 subset->missing = pt->missing;
757 subset->vars = pt->vars;
758 subset->n_consts = pt->n_vars - 2;
759 subset->const_vars = pt->vars + 2;
760 subset->const_values = &pt->entries[row0]->values[2];
762 subset->entries = &pt->entries[row0];
763 subset->n_entries = row1 - row0;
767 compare_table_entry_var_3way (const struct table_entry *a,
768 const struct table_entry *b,
769 const struct pivot_table *pt,
772 return value_compare_3way (&a->values[idx], &b->values[idx],
773 var_get_width (pt->vars[idx]));
777 compare_table_entry_vars_3way (const struct table_entry *a,
778 const struct table_entry *b,
779 const struct pivot_table *pt,
784 for (i = idx1 - 1; i >= idx0; i--)
786 int cmp = compare_table_entry_var_3way (a, b, pt, i);
793 /* Compare the struct table_entry at *AP to the one at *BP and
794 return a strcmp()-type result. */
796 compare_table_entry_3way (const void *ap_, const void *bp_, const void *pt_)
798 const struct table_entry *const *ap = ap_;
799 const struct table_entry *const *bp = bp_;
800 const struct table_entry *a = *ap;
801 const struct table_entry *b = *bp;
802 const struct pivot_table *pt = pt_;
805 cmp = compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars);
809 cmp = compare_table_entry_var_3way (a, b, pt, ROW_VAR);
813 return compare_table_entry_var_3way (a, b, pt, COL_VAR);
817 find_first_difference (const struct pivot_table *pt, size_t row)
820 return pt->n_vars - 1;
823 const struct table_entry *a = pt->entries[row];
824 const struct table_entry *b = pt->entries[row - 1];
827 for (col = pt->n_vars - 1; col >= 0; col--)
828 if (compare_table_entry_var_3way (a, b, pt, col))
834 /* Output a table summarizing the cases processed. */
836 make_summary_table (struct crosstabs_proc *proc)
838 struct tab_table *summary;
839 struct pivot_table *pt;
843 summary = tab_create (7, 3 + proc->n_pivots);
844 tab_title (summary, _("Summary."));
845 tab_headers (summary, 1, 0, 3, 0);
846 tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
847 tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
848 tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
849 tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
850 tab_hline (summary, TAL_1, 1, 6, 1);
851 tab_hline (summary, TAL_1, 1, 6, 2);
852 tab_vline (summary, TAL_1, 3, 1, 1);
853 tab_vline (summary, TAL_1, 5, 1, 1);
854 for (i = 0; i < 3; i++)
856 tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
857 tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
859 tab_offset (summary, 0, 3);
861 ds_init_empty (&name);
862 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
868 tab_hline (summary, TAL_1, 0, 6, 0);
871 for (i = 0; i < pt->n_vars; i++)
874 ds_put_cstr (&name, " * ");
875 ds_put_cstr (&name, var_to_string (pt->vars[i]));
877 tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
880 for (i = 0; i < pt->n_entries; i++)
881 valid += pt->entries[i]->freq;
886 for (i = 0; i < 3; i++)
888 tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i],
889 &proc->weight_format);
890 tab_text_format (summary, i * 2 + 2, 0, TAB_RIGHT, "%.1f%%",
894 tab_next_row (summary);
898 submit (proc, NULL, summary);
903 static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
904 struct pivot_table *);
905 static struct tab_table *create_chisq_table (struct pivot_table *);
906 static struct tab_table *create_sym_table (struct pivot_table *);
907 static struct tab_table *create_risk_table (struct pivot_table *);
908 static struct tab_table *create_direct_table (struct pivot_table *);
909 static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
910 struct tab_table *, int first_difference);
911 static void display_crosstabulation (struct crosstabs_proc *,
912 struct pivot_table *,
914 static void display_chisq (struct pivot_table *, struct tab_table *,
915 bool *showed_fisher);
916 static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
918 static void display_risk (struct pivot_table *, struct tab_table *);
919 static void display_directional (struct crosstabs_proc *, struct pivot_table *,
921 static void crosstabs_dim (struct tab_rendering *, void *aux);
922 static void crosstabs_dim_free (void *aux);
923 static void table_value_missing (struct crosstabs_proc *proc,
924 struct tab_table *table, int c, int r,
925 unsigned char opt, const union value *v,
926 const struct variable *var);
927 static void delete_missing (struct pivot_table *);
928 static void build_matrix (struct pivot_table *);
930 /* Output pivot table beginning at PB and continuing until PE,
931 exclusive. For efficiency, *MATP is a pointer to a matrix that can
932 hold *MAXROWS entries. */
934 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
936 struct tab_table *table = NULL; /* Crosstabulation table. */
937 struct tab_table *chisq = NULL; /* Chi-square table. */
938 bool showed_fisher = false;
939 struct tab_table *sym = NULL; /* Symmetric measures table. */
940 struct tab_table *risk = NULL; /* Risk estimate table. */
941 struct tab_table *direct = NULL; /* Directional measures table. */
944 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols);
947 table = create_crosstab_table (proc, pt);
948 if (proc->statistics & (1u << CRS_ST_CHISQ))
949 chisq = create_chisq_table (pt);
950 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
951 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
952 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
953 | (1u << CRS_ST_KAPPA)))
954 sym = create_sym_table (pt);
955 if (proc->statistics & (1u << CRS_ST_RISK))
956 risk = create_risk_table (pt);
957 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
958 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
959 direct = create_direct_table (pt);
962 while (find_crosstab (pt, &row0, &row1))
964 struct pivot_table x;
965 int first_difference;
967 make_pivot_table_subset (pt, row0, row1, &x);
969 /* Find all the row variable values. */
970 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows);
972 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
975 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
976 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
977 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
979 /* Allocate table space for the matrix. */
981 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
982 tab_realloc (table, -1,
983 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
984 tab_nr (table) * pt->n_entries / x.n_entries));
988 /* Find the first variable that differs from the last subtable. */
989 first_difference = find_first_difference (pt, row0);
992 display_dimensions (proc, &x, table, first_difference);
993 display_crosstabulation (proc, &x, table);
996 if (proc->exclude == MV_NEVER)
1001 display_dimensions (proc, &x, chisq, first_difference);
1002 display_chisq (&x, chisq, &showed_fisher);
1006 display_dimensions (proc, &x, sym, first_difference);
1007 display_symmetric (proc, &x, sym);
1011 display_dimensions (proc, &x, risk, first_difference);
1012 display_risk (&x, risk);
1016 display_dimensions (proc, &x, direct, first_difference);
1017 display_directional (proc, &x, direct);
1020 /* Free the parts of x that are not owned by pt. In
1021 particular we must not free x.cols, which is the same as
1022 pt->cols, which is freed at the end of this function. */
1030 submit (proc, NULL, table);
1035 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
1036 submit (proc, pt, chisq);
1039 submit (proc, pt, sym);
1040 submit (proc, pt, risk);
1041 submit (proc, pt, direct);
1047 build_matrix (struct pivot_table *x)
1049 const int col_var_width = var_get_width (x->vars[COL_VAR]);
1050 const int row_var_width = var_get_width (x->vars[ROW_VAR]);
1053 struct table_entry **p;
1057 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1059 const struct table_entry *te = *p;
1061 while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
1063 for (; col < x->n_cols; col++)
1069 while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
1076 if (++col >= x->n_cols)
1082 while (mp < &x->mat[x->n_cols * x->n_rows])
1084 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1086 /* Column totals, row totals, ns_rows. */
1088 for (col = 0; col < x->n_cols; col++)
1089 x->col_tot[col] = 0.0;
1090 for (row = 0; row < x->n_rows; row++)
1091 x->row_tot[row] = 0.0;
1093 for (row = 0; row < x->n_rows; row++)
1095 bool row_is_empty = true;
1096 for (col = 0; col < x->n_cols; col++)
1100 row_is_empty = false;
1101 x->col_tot[col] += *mp;
1102 x->row_tot[row] += *mp;
1109 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1113 for (col = 0; col < x->n_cols; col++)
1114 for (row = 0; row < x->n_rows; row++)
1115 if (x->mat[col + row * x->n_cols] != 0.0)
1123 for (col = 0; col < x->n_cols; col++)
1124 x->total += x->col_tot[col];
1127 static struct tab_table *
1128 create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1135 static const struct tuple names[] =
1137 {CRS_CL_COUNT, N_("count")},
1138 {CRS_CL_ROW, N_("row %")},
1139 {CRS_CL_COLUMN, N_("column %")},
1140 {CRS_CL_TOTAL, N_("total %")},
1141 {CRS_CL_EXPECTED, N_("expected")},
1142 {CRS_CL_RESIDUAL, N_("residual")},
1143 {CRS_CL_SRESIDUAL, N_("std. resid.")},
1144 {CRS_CL_ASRESIDUAL, N_("adj. resid.")},
1146 const int n_names = sizeof names / sizeof *names;
1147 const struct tuple *t;
1149 struct tab_table *table;
1150 struct string title;
1153 table = tab_create (pt->n_consts + 1 + pt->n_cols + 1,
1154 (pt->n_entries / pt->n_cols) * 3 / 2 * proc->n_cells + 10);
1155 tab_headers (table, pt->n_consts + 1, 0, 2, 0);
1157 /* First header line. */
1158 tab_joint_text (table, pt->n_consts + 1, 0,
1159 (pt->n_consts + 1) + (pt->n_cols - 1), 0,
1160 TAB_CENTER | TAT_TITLE, var_get_name (pt->vars[COL_VAR]));
1162 tab_hline (table, TAL_1, pt->n_consts + 1,
1163 pt->n_consts + 2 + pt->n_cols - 2, 1);
1165 /* Second header line. */
1166 for (i = 2; i < pt->n_consts + 2; i++)
1167 tab_joint_text (table, pt->n_consts + 2 - i - 1, 0,
1168 pt->n_consts + 2 - i - 1, 1,
1169 TAB_RIGHT | TAT_TITLE, var_to_string (pt->vars[i]));
1170 tab_text (table, pt->n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1171 var_get_name (pt->vars[ROW_VAR]));
1172 for (i = 0; i < pt->n_cols; i++)
1173 table_value_missing (proc, table, pt->n_consts + 2 + i - 1, 1, TAB_RIGHT,
1174 &pt->cols[i], pt->vars[COL_VAR]);
1175 tab_text (table, pt->n_consts + 2 + pt->n_cols - 1, 1, TAB_CENTER, _("Total"));
1177 tab_hline (table, TAL_1, 0, pt->n_consts + 2 + pt->n_cols - 1, 2);
1178 tab_vline (table, TAL_1, pt->n_consts + 2 + pt->n_cols - 1, 0, 1);
1181 ds_init_empty (&title);
1182 for (i = 0; i < pt->n_consts + 2; i++)
1185 ds_put_cstr (&title, " * ");
1186 ds_put_cstr (&title, var_get_name (pt->vars[i]));
1188 for (i = 0; i < pt->n_consts; i++)
1190 const struct variable *var = pt->const_vars[i];
1193 ds_put_format (&title, ", %s=", var_get_name (var));
1195 /* Insert the formatted value of the variable, then trim
1196 leading spaces in what was just inserted. */
1197 ofs = ds_length (&title);
1198 data_out (&pt->const_values[i], var_get_print_format (var),
1199 ds_put_uninit (&title, var_get_width (var)));
1200 ds_remove (&title, ofs, ss_cspan (ds_substr (&title, ofs, SIZE_MAX),
1204 ds_put_cstr (&title, " [");
1206 for (t = names; t < &names[n_names]; t++)
1207 if (proc->cells & (1u << t->value))
1210 ds_put_cstr (&title, ", ");
1211 ds_put_cstr (&title, gettext (t->name));
1213 ds_put_cstr (&title, "].");
1215 tab_title (table, "%s", ds_cstr (&title));
1216 ds_destroy (&title);
1218 tab_offset (table, 0, 2);
1222 static struct tab_table *
1223 create_chisq_table (struct pivot_table *pt)
1225 struct tab_table *chisq;
1227 chisq = tab_create (6 + (pt->n_vars - 2),
1228 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10);
1229 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1231 tab_title (chisq, _("Chi-square tests."));
1233 tab_offset (chisq, pt->n_vars - 2, 0);
1234 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1235 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1236 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1237 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1238 _("Asymp. Sig. (2-sided)"));
1239 tab_text (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1240 _("Exact. Sig. (2-sided)"));
1241 tab_text (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1242 _("Exact. Sig. (1-sided)"));
1243 tab_offset (chisq, 0, 1);
1248 /* Symmetric measures. */
1249 static struct tab_table *
1250 create_sym_table (struct pivot_table *pt)
1252 struct tab_table *sym;
1254 sym = tab_create (6 + (pt->n_vars - 2),
1255 pt->n_entries / pt->n_cols * 7 + 10);
1256 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1257 tab_title (sym, _("Symmetric measures."));
1259 tab_offset (sym, pt->n_vars - 2, 0);
1260 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1261 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1262 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1263 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1264 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1265 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1266 tab_offset (sym, 0, 1);
1271 /* Risk estimate. */
1272 static struct tab_table *
1273 create_risk_table (struct pivot_table *pt)
1275 struct tab_table *risk;
1277 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10);
1278 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1279 tab_title (risk, _("Risk estimate."));
1281 tab_offset (risk, pt->n_vars - 2, 0);
1282 tab_joint_text_format (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE,
1283 _("95%% Confidence Interval"));
1284 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1285 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1286 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1287 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1288 tab_hline (risk, TAL_1, 2, 3, 1);
1289 tab_vline (risk, TAL_1, 2, 0, 1);
1290 tab_offset (risk, 0, 2);
1295 /* Directional measures. */
1296 static struct tab_table *
1297 create_direct_table (struct pivot_table *pt)
1299 struct tab_table *direct;
1301 direct = tab_create (7 + (pt->n_vars - 2),
1302 pt->n_entries / pt->n_cols * 7 + 10);
1303 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1304 tab_title (direct, _("Directional measures."));
1306 tab_offset (direct, pt->n_vars - 2, 0);
1307 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1308 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1309 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1310 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1311 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1312 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1313 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1314 tab_offset (direct, 0, 1);
1320 /* Delete missing rows and columns for statistical analysis when
1323 delete_missing (struct pivot_table *pt)
1327 for (r = 0; r < pt->n_rows; r++)
1328 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1330 for (c = 0; c < pt->n_cols; c++)
1331 pt->mat[c + r * pt->n_cols] = 0.;
1336 for (c = 0; c < pt->n_cols; c++)
1337 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1339 for (r = 0; r < pt->n_rows; r++)
1340 pt->mat[c + r * pt->n_cols] = 0.;
1345 /* Prepare table T for submission, and submit it. */
1347 submit (struct crosstabs_proc *proc, struct pivot_table *pt,
1348 struct tab_table *t)
1350 struct crosstabs_dim_aux *aux;
1356 tab_resize (t, -1, 0);
1357 if (tab_nr (t) == tab_t (t))
1362 tab_offset (t, 0, 0);
1364 for (i = 2; i < pt->n_vars; i++)
1365 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1366 var_to_string (pt->vars[i]));
1367 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1368 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1370 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1372 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1374 aux = xmalloc (sizeof *aux);
1375 aux->exclude = proc->exclude;
1376 tab_dim (t, crosstabs_dim, crosstabs_dim_free, aux);
1381 /* Sets the widths of all the columns and heights of all the rows in
1382 table T for driver D. */
1384 crosstabs_dim (struct tab_rendering *r, void *aux_)
1386 const struct tab_table *t = r->table;
1387 struct outp_driver *d = r->driver;
1388 struct crosstabs_dim_aux *aux = aux_;
1391 /* Width of a numerical column. */
1392 int c = outp_string_width (d, "0.000000", OUTP_PROPORTIONAL);
1393 if (aux->exclude == MV_NEVER)
1394 c += outp_string_width (d, "M", OUTP_PROPORTIONAL);
1396 /* Set width for header columns. */
1402 w = d->width - c * (tab_nc (t) - tab_l (t));
1403 for (i = 0; i <= tab_nc (t); i++)
1407 if (w < d->prop_em_width * 8)
1408 w = d->prop_em_width * 8;
1410 if (w > d->prop_em_width * 15)
1411 w = d->prop_em_width * 15;
1413 for (i = 0; i < tab_l (t); i++)
1417 for (i = tab_l (t); i < tab_nc (t); i++)
1420 for (i = 0; i < tab_nr (t); i++)
1421 r->h[i] = tab_natural_height (r, i);
1425 crosstabs_dim_free (void *aux_)
1427 struct crosstabs_dim_aux *aux = aux_;
1432 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1434 size_t row0 = *row1p;
1437 if (row0 >= pt->n_entries)
1440 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1442 struct table_entry *a = pt->entries[row0];
1443 struct table_entry *b = pt->entries[row1];
1444 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1452 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1453 result. WIDTH_ points to an int which is either 0 for a
1454 numeric value or a string width for a string value. */
1456 compare_value_3way (const void *a_, const void *b_, const void *width_)
1458 const union value *a = a_;
1459 const union value *b = b_;
1460 const int *width = width_;
1462 return value_compare_3way (a, b, *width);
1465 /* Given an array of ENTRY_CNT table_entry structures starting at
1466 ENTRIES, creates a sorted list of the values that the variable
1467 with index VAR_IDX takes on. The values are returned as a
1468 malloc()'d array stored in *VALUES, with the number of values
1469 stored in *VALUE_CNT.
1472 enum_var_values (const struct pivot_table *pt, int var_idx,
1473 union value **valuesp, int *n_values)
1475 const struct variable *var = pt->vars[var_idx];
1476 struct var_range *range = get_var_range (var);
1477 union value *values;
1482 values = *valuesp = xnmalloc (range->count, sizeof *values);
1483 *n_values = range->count;
1484 for (i = 0; i < range->count; i++)
1485 values[i].f = range->min + i;
1489 int width = var_get_width (var);
1490 struct hmapx_node *node;
1491 const union value *iter;
1495 for (i = 0; i < pt->n_entries; i++)
1497 const struct table_entry *te = pt->entries[i];
1498 const union value *value = &te->values[var_idx];
1499 size_t hash = value_hash (value, width, 0);
1501 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1502 if (value_equal (iter, value, width))
1505 hmapx_insert (&set, (union value *) value, hash);
1510 *n_values = hmapx_count (&set);
1511 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1513 HMAPX_FOR_EACH (iter, node, &set)
1514 values[i++] = *iter;
1515 hmapx_destroy (&set);
1517 sort (values, *n_values, sizeof *values, compare_value_3way, &width);
1521 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1522 from V, displayed with print format spec from variable VAR. When
1523 in REPORT missing-value mode, missing values have an M appended. */
1525 table_value_missing (struct crosstabs_proc *proc,
1526 struct tab_table *table, int c, int r, unsigned char opt,
1527 const union value *v, const struct variable *var)
1529 const char *label = var_lookup_value_label (var, v);
1531 tab_text (table, c, r, TAB_LEFT, label);
1534 const struct fmt_spec *print = var_get_print_format (var);
1535 if (proc->exclude == MV_NEVER && var_is_value_missing (var, v, MV_USER))
1537 char *s = xmalloc (print->w + 2);
1538 strcpy (&s[print->w], "M");
1539 tab_text (table, c, r, opt, s + strspn (s, " "));
1543 tab_value (table, c, r, opt, v, print);
1547 /* Draws a line across TABLE at the current row to indicate the most
1548 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1549 that changed, and puts the values that changed into the table. TB
1550 and PT must be the corresponding table_entry and crosstab,
1553 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1554 struct tab_table *table, int first_difference)
1556 tab_hline (table, TAL_1, pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1558 for (; first_difference >= 2; first_difference--)
1559 table_value_missing (proc, table, pt->n_vars - first_difference - 1, 0,
1560 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1561 pt->vars[first_difference]);
1564 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1565 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1566 additionally suffixed with a letter `M'. */
1568 format_cell_entry (struct tab_table *table, int c, int r, double value,
1569 char suffix, bool mark_missing)
1571 const struct fmt_spec f = {FMT_F, 10, 1};
1577 data_out (&v, &f, s);
1584 tab_text (table, c, r, TAB_RIGHT, s + strspn (s, " "));
1587 /* Displays the crosstabulation table. */
1589 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1590 struct tab_table *table)
1596 for (r = 0; r < pt->n_rows; r++)
1597 table_value_missing (proc, table, pt->n_vars - 2, r * proc->n_cells,
1598 TAB_RIGHT, &pt->rows[r], pt->vars[ROW_VAR]);
1600 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1601 TAB_LEFT, _("Total"));
1603 /* Put in the actual cells. */
1605 tab_offset (table, pt->n_vars - 1, -1);
1606 for (r = 0; r < pt->n_rows; r++)
1608 if (proc->n_cells > 1)
1609 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1610 for (c = 0; c < pt->n_cols; c++)
1612 bool mark_missing = false;
1613 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1614 if (proc->exclude == MV_NEVER
1615 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1616 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1618 mark_missing = true;
1619 for (i = 0; i < proc->n_cells; i++)
1624 switch (proc->a_cells[i])
1630 v = *mp / pt->row_tot[r] * 100.;
1634 v = *mp / pt->col_tot[c] * 100.;
1638 v = *mp / pt->total * 100.;
1641 case CRS_CL_EXPECTED:
1644 case CRS_CL_RESIDUAL:
1645 v = *mp - expected_value;
1647 case CRS_CL_SRESIDUAL:
1648 v = (*mp - expected_value) / sqrt (expected_value);
1650 case CRS_CL_ASRESIDUAL:
1651 v = ((*mp - expected_value)
1652 / sqrt (expected_value
1653 * (1. - pt->row_tot[r] / pt->total)
1654 * (1. - pt->col_tot[c] / pt->total)));
1659 format_cell_entry (table, c, i, v, suffix, mark_missing);
1665 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1669 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1670 for (r = 0; r < pt->n_rows; r++)
1672 bool mark_missing = false;
1674 if (proc->exclude == MV_NEVER
1675 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1676 mark_missing = true;
1678 for (i = 0; i < proc->n_cells; i++)
1683 switch (proc->a_cells[i])
1693 v = pt->row_tot[r] / pt->total * 100.;
1697 v = pt->row_tot[r] / pt->total * 100.;
1700 case CRS_CL_EXPECTED:
1701 case CRS_CL_RESIDUAL:
1702 case CRS_CL_SRESIDUAL:
1703 case CRS_CL_ASRESIDUAL:
1710 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing);
1711 tab_next_row (table);
1715 /* Column totals, grand total. */
1717 if (proc->n_cells > 1)
1718 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1719 for (c = 0; c <= pt->n_cols; c++)
1721 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1722 bool mark_missing = false;
1725 if (proc->exclude == MV_NEVER && c < pt->n_cols
1726 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1727 mark_missing = true;
1729 for (i = 0; i < proc->n_cells; i++)
1734 switch (proc->a_cells[i])
1740 v = ct / pt->total * 100.;
1748 v = ct / pt->total * 100.;
1751 case CRS_CL_EXPECTED:
1752 case CRS_CL_RESIDUAL:
1753 case CRS_CL_SRESIDUAL:
1754 case CRS_CL_ASRESIDUAL:
1760 format_cell_entry (table, c, i, v, suffix, mark_missing);
1765 tab_offset (table, -1, tab_row (table) + last_row);
1766 tab_offset (table, 0, -1);
1769 static void calc_r (struct pivot_table *,
1770 double *PT, double *Y, double *, double *, double *);
1771 static void calc_chisq (struct pivot_table *,
1772 double[N_CHISQ], int[N_CHISQ], double *, double *);
1774 /* Display chi-square statistics. */
1776 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1777 bool *showed_fisher)
1779 static const char *chisq_stats[N_CHISQ] =
1781 N_("Pearson Chi-Square"),
1782 N_("Likelihood Ratio"),
1783 N_("Fisher's Exact Test"),
1784 N_("Continuity Correction"),
1785 N_("Linear-by-Linear Association"),
1787 double chisq_v[N_CHISQ];
1788 double fisher1, fisher2;
1793 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1795 tab_offset (chisq, pt->n_vars - 2, -1);
1797 for (i = 0; i < N_CHISQ; i++)
1799 if ((i != 2 && chisq_v[i] == SYSMIS)
1800 || (i == 2 && fisher1 == SYSMIS))
1803 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1806 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL);
1807 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], &pt->weight_format);
1808 tab_double (chisq, 3, 0, TAB_RIGHT,
1809 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL);
1813 *showed_fisher = true;
1814 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL);
1815 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL);
1817 tab_next_row (chisq);
1820 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1821 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1822 tab_next_row (chisq);
1824 tab_offset (chisq, 0, -1);
1827 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1828 double[N_SYMMETRIC], double[N_SYMMETRIC],
1829 double[N_SYMMETRIC],
1830 double[3], double[3], double[3]);
1832 /* Display symmetric measures. */
1834 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1835 struct tab_table *sym)
1837 static const char *categories[] =
1839 N_("Nominal by Nominal"),
1840 N_("Ordinal by Ordinal"),
1841 N_("Interval by Interval"),
1842 N_("Measure of Agreement"),
1845 static const char *stats[N_SYMMETRIC] =
1849 N_("Contingency Coefficient"),
1850 N_("Kendall's tau-b"),
1851 N_("Kendall's tau-c"),
1853 N_("Spearman Correlation"),
1858 static const int stats_categories[N_SYMMETRIC] =
1860 0, 0, 0, 1, 1, 1, 1, 2, 3,
1864 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1865 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1868 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1869 somers_d_v, somers_d_ase, somers_d_t))
1872 tab_offset (sym, pt->n_vars - 2, -1);
1874 for (i = 0; i < N_SYMMETRIC; i++)
1876 if (sym_v[i] == SYSMIS)
1879 if (stats_categories[i] != last_cat)
1881 last_cat = stats_categories[i];
1882 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1885 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1886 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL);
1887 if (sym_ase[i] != SYSMIS)
1888 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL);
1889 if (sym_t[i] != SYSMIS)
1890 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL);
1891 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL);*/
1895 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1896 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1899 tab_offset (sym, 0, -1);
1902 static int calc_risk (struct pivot_table *,
1903 double[], double[], double[], union value *);
1905 /* Display risk estimate. */
1907 display_risk (struct pivot_table *pt, struct tab_table *risk)
1910 double risk_v[3], lower[3], upper[3];
1914 if (!calc_risk (pt, risk_v, upper, lower, c))
1917 tab_offset (risk, pt->n_vars - 2, -1);
1919 for (i = 0; i < 3; i++)
1921 const struct variable *cv = pt->vars[COL_VAR];
1922 const struct variable *rv = pt->vars[ROW_VAR];
1923 int cvw = var_get_width (cv);
1924 int rvw = var_get_width (rv);
1926 if (risk_v[i] == SYSMIS)
1932 if (var_is_numeric (cv))
1933 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1934 var_get_name (cv), c[0].f, c[1].f);
1936 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1938 cvw, value_str (&c[0], cvw),
1939 cvw, value_str (&c[1], cvw));
1943 if (var_is_numeric (rv))
1944 sprintf (buf, _("For cohort %s = %g"),
1945 var_get_name (rv), pt->rows[i - 1].f);
1947 sprintf (buf, _("For cohort %s = %.*s"),
1949 rvw, value_str (&pt->rows[i - 1], rvw));
1953 tab_text (risk, 0, 0, TAB_LEFT, buf);
1954 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL);
1955 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL);
1956 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL);
1957 tab_next_row (risk);
1960 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1961 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1962 tab_next_row (risk);
1964 tab_offset (risk, 0, -1);
1967 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1968 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1969 double[N_DIRECTIONAL]);
1971 /* Display directional measures. */
1973 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
1974 struct tab_table *direct)
1976 static const char *categories[] =
1978 N_("Nominal by Nominal"),
1979 N_("Ordinal by Ordinal"),
1980 N_("Nominal by Interval"),
1983 static const char *stats[] =
1986 N_("Goodman and Kruskal tau"),
1987 N_("Uncertainty Coefficient"),
1992 static const char *types[] =
1999 static const int stats_categories[N_DIRECTIONAL] =
2001 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
2004 static const int stats_stats[N_DIRECTIONAL] =
2006 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
2009 static const int stats_types[N_DIRECTIONAL] =
2011 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
2014 static const int *stats_lookup[] =
2021 static const char **stats_names[] =
2033 double direct_v[N_DIRECTIONAL];
2034 double direct_ase[N_DIRECTIONAL];
2035 double direct_t[N_DIRECTIONAL];
2039 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t))
2042 tab_offset (direct, pt->n_vars - 2, -1);
2044 for (i = 0; i < N_DIRECTIONAL; i++)
2046 if (direct_v[i] == SYSMIS)
2052 for (j = 0; j < 3; j++)
2053 if (last[j] != stats_lookup[j][i])
2056 tab_hline (direct, TAL_1, j, 6, 0);
2061 int k = last[j] = stats_lookup[j][i];
2066 string = var_get_name (pt->vars[0]);
2068 string = var_get_name (pt->vars[1]);
2070 tab_text_format (direct, j, 0, TAB_LEFT,
2071 gettext (stats_names[j][k]), string);
2076 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL);
2077 if (direct_ase[i] != SYSMIS)
2078 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL);
2079 if (direct_t[i] != SYSMIS)
2080 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL);
2081 /*tab_double (direct, 6, 0, TAB_RIGHT, normal_sig (direct_v[i]), NULL);*/
2082 tab_next_row (direct);
2085 tab_offset (direct, 0, -1);
2088 /* Statistical calculations. */
2090 /* Returns the value of the gamma (factorial) function for an integer
2093 gamma_int (double pt)
2098 for (i = 2; i < pt; i++)
2103 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2105 static inline double
2106 Pr (int a, int b, int c, int d)
2108 return (gamma_int (a + b + 1.) / gamma_int (a + 1.)
2109 * gamma_int (c + d + 1.) / gamma_int (b + 1.)
2110 * gamma_int (a + c + 1.) / gamma_int (c + 1.)
2111 * gamma_int (b + d + 1.) / gamma_int (d + 1.)
2112 / gamma_int (a + b + c + d + 1.));
2115 /* Swap the contents of A and B. */
2117 swap (int *a, int *b)
2124 /* Calculate significance for Fisher's exact test as specified in
2125 _SPSS Statistical Algorithms_, Appendix 5. */
2127 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2131 if (MIN (c, d) < MIN (a, b))
2132 swap (&a, &c), swap (&b, &d);
2133 if (MIN (b, d) < MIN (a, c))
2134 swap (&a, &b), swap (&c, &d);
2138 swap (&a, &b), swap (&c, &d);
2140 swap (&a, &c), swap (&b, &d);
2144 for (pt = 0; pt <= a; pt++)
2145 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2147 *fisher2 = *fisher1;
2148 for (pt = 1; pt <= b; pt++)
2149 *fisher2 += Pr (a + pt, b - pt, c - pt, d + pt);
2152 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2153 columns with values COLS and N_ROWS rows with values ROWS. Values
2154 in the matrix sum to pt->total. */
2156 calc_chisq (struct pivot_table *pt,
2157 double chisq[N_CHISQ], int df[N_CHISQ],
2158 double *fisher1, double *fisher2)
2162 chisq[0] = chisq[1] = 0.;
2163 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2164 *fisher1 = *fisher2 = SYSMIS;
2166 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2168 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2170 chisq[0] = chisq[1] = SYSMIS;
2174 for (r = 0; r < pt->n_rows; r++)
2175 for (c = 0; c < pt->n_cols; c++)
2177 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2178 const double freq = pt->mat[pt->n_cols * r + c];
2179 const double residual = freq - expected;
2181 chisq[0] += residual * residual / expected;
2183 chisq[1] += freq * log (expected / freq);
2194 /* Calculate Yates and Fisher exact test. */
2195 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2197 double f11, f12, f21, f22;
2203 for (i = j = 0; i < pt->n_cols; i++)
2204 if (pt->col_tot[i] != 0.)
2213 f11 = pt->mat[nz_cols[0]];
2214 f12 = pt->mat[nz_cols[1]];
2215 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2216 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2221 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2224 chisq[3] = (pt->total * pow2 (pt_)
2225 / (f11 + f12) / (f21 + f22)
2226 / (f11 + f21) / (f12 + f22));
2234 if (f11 < 5. || f12 < 5. || f21 < 5. || f22 < 5.)
2235 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2238 /* Calculate Mantel-Haenszel. */
2239 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2241 double r, ase_0, ase_1;
2242 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2244 chisq[4] = (pt->total - 1.) * r * r;
2249 /* Calculate the value of Pearson's r. r is stored into R, ase_1 into
2250 ASE_1, and ase_0 into ASE_0. The row and column values must be
2251 passed in PT and Y. */
2253 calc_r (struct pivot_table *pt,
2254 double *PT, double *Y, double *r, double *ase_0, double *ase_1)
2256 double SX, SY, S, T;
2258 double sum_XYf, sum_X2Y2f;
2259 double sum_Xr, sum_X2r;
2260 double sum_Yc, sum_Y2c;
2263 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2264 for (j = 0; j < pt->n_cols; j++)
2266 double fij = pt->mat[j + i * pt->n_cols];
2267 double product = PT[i] * Y[j];
2268 double temp = fij * product;
2270 sum_X2Y2f += temp * product;
2273 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2275 sum_Xr += PT[i] * pt->row_tot[i];
2276 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2278 Xbar = sum_Xr / pt->total;
2280 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2282 sum_Yc += Y[i] * pt->col_tot[i];
2283 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2285 Ybar = sum_Yc / pt->total;
2287 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2288 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2289 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2292 *ase_0 = sqrt ((sum_X2Y2f - pow2 (sum_XYf) / pt->total) / (sum_X2r * sum_Y2c));
2297 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2298 for (j = 0; j < pt->n_cols; j++)
2300 double Xresid, Yresid;
2303 Xresid = PT[i] - Xbar;
2304 Yresid = Y[j] - Ybar;
2305 temp = (T * Xresid * Yresid
2307 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2308 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2313 *ase_1 = sqrt (s) / (T * T);
2317 /* Calculate symmetric statistics and their asymptotic standard
2318 errors. Returns 0 if none could be calculated. */
2320 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2321 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2322 double t[N_SYMMETRIC],
2323 double somers_d_v[3], double somers_d_ase[3],
2324 double somers_d_t[3])
2328 q = MIN (pt->ns_rows, pt->ns_cols);
2332 for (i = 0; i < N_SYMMETRIC; i++)
2333 v[i] = ase[i] = t[i] = SYSMIS;
2335 /* Phi, Cramer's V, contingency coefficient. */
2336 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2338 double Xp = 0.; /* Pearson chi-square. */
2341 for (r = 0; r < pt->n_rows; r++)
2342 for (c = 0; c < pt->n_cols; c++)
2344 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2345 const double freq = pt->mat[pt->n_cols * r + c];
2346 const double residual = freq - expected;
2348 Xp += residual * residual / expected;
2351 if (proc->statistics & (1u << CRS_ST_PHI))
2353 v[0] = sqrt (Xp / pt->total);
2354 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2356 if (proc->statistics & (1u << CRS_ST_CC))
2357 v[2] = sqrt (Xp / (Xp + pt->total));
2360 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2361 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2366 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2370 Dr = Dc = pow2 (pt->total);
2371 for (r = 0; r < pt->n_rows; r++)
2372 Dr -= pow2 (pt->row_tot[r]);
2373 for (c = 0; c < pt->n_cols; c++)
2374 Dc -= pow2 (pt->col_tot[c]);
2376 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2377 for (c = 0; c < pt->n_cols; c++)
2381 for (r = 0; r < pt->n_rows; r++)
2382 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2391 for (i = 0; i < pt->n_rows; i++)
2395 for (j = 1; j < pt->n_cols; j++)
2396 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2399 for (j = 1; j < pt->n_cols; j++)
2400 Dij += cum[j + (i - 1) * pt->n_cols];
2404 double fij = pt->mat[j + i * pt->n_cols];
2408 if (++j == pt->n_cols)
2410 assert (j < pt->n_cols);
2412 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2413 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2417 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2418 Dij -= cum[j + (i - 1) * pt->n_cols];
2424 if (proc->statistics & (1u << CRS_ST_BTAU))
2425 v[3] = (P - Q) / sqrt (Dr * Dc);
2426 if (proc->statistics & (1u << CRS_ST_CTAU))
2427 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2428 if (proc->statistics & (1u << CRS_ST_GAMMA))
2429 v[5] = (P - Q) / (P + Q);
2431 /* ASE for tau-b, tau-c, gamma. Calculations could be
2432 eliminated here, at expense of memory. */
2437 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2438 for (i = 0; i < pt->n_rows; i++)
2442 for (j = 1; j < pt->n_cols; j++)
2443 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2446 for (j = 1; j < pt->n_cols; j++)
2447 Dij += cum[j + (i - 1) * pt->n_cols];
2451 double fij = pt->mat[j + i * pt->n_cols];
2453 if (proc->statistics & (1u << CRS_ST_BTAU))
2455 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2456 + v[3] * (pt->row_tot[i] * Dc
2457 + pt->col_tot[j] * Dr));
2458 btau_cum += fij * temp * temp;
2462 const double temp = Cij - Dij;
2463 ctau_cum += fij * temp * temp;
2466 if (proc->statistics & (1u << CRS_ST_GAMMA))
2468 const double temp = Q * Cij - P * Dij;
2469 gamma_cum += fij * temp * temp;
2472 if (proc->statistics & (1u << CRS_ST_D))
2474 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2475 - (P - Q) * (pt->total - pt->row_tot[i]));
2476 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2477 - (Q - P) * (pt->total - pt->col_tot[j]));
2480 if (++j == pt->n_cols)
2482 assert (j < pt->n_cols);
2484 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2485 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2489 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2490 Dij -= cum[j + (i - 1) * pt->n_cols];
2496 btau_var = ((btau_cum
2497 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2499 if (proc->statistics & (1u << CRS_ST_BTAU))
2501 ase[3] = sqrt (btau_var);
2502 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2505 if (proc->statistics & (1u << CRS_ST_CTAU))
2507 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2508 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2509 t[4] = v[4] / ase[4];
2511 if (proc->statistics & (1u << CRS_ST_GAMMA))
2513 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2514 t[5] = v[5] / (2. / (P + Q)
2515 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2517 if (proc->statistics & (1u << CRS_ST_D))
2519 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2520 somers_d_ase[0] = 2. * btau_var / (Dr + Dc) * sqrt (Dr * Dc);
2521 somers_d_t[0] = (somers_d_v[0]
2523 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2524 somers_d_v[1] = (P - Q) / Dc;
2525 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2526 somers_d_t[1] = (somers_d_v[1]
2528 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2529 somers_d_v[2] = (P - Q) / Dr;
2530 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2531 somers_d_t[2] = (somers_d_v[2]
2533 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2539 /* Spearman correlation, Pearson's r. */
2540 if (proc->statistics & (1u << CRS_ST_CORR))
2542 double *R = xmalloc (sizeof *R * pt->n_rows);
2543 double *C = xmalloc (sizeof *C * pt->n_cols);
2546 double y, t, c = 0., s = 0.;
2551 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2552 y = pt->row_tot[i] - c;
2556 if (++i == pt->n_rows)
2558 assert (i < pt->n_rows);
2563 double y, t, c = 0., s = 0.;
2568 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2569 y = pt->col_tot[j] - c;
2573 if (++j == pt->n_cols)
2575 assert (j < pt->n_cols);
2579 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2585 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2589 /* Cohen's kappa. */
2590 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2592 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2595 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2596 i < pt->ns_rows; i++, j++)
2600 while (pt->col_tot[j] == 0.)
2603 prod = pt->row_tot[i] * pt->col_tot[j];
2604 sum = pt->row_tot[i] + pt->col_tot[j];
2606 sum_fii += pt->mat[j + i * pt->n_cols];
2608 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2609 sum_riciri_ci += prod * sum;
2611 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2612 for (j = 0; j < pt->ns_cols; j++)
2614 double sum = pt->row_tot[i] + pt->col_tot[j];
2615 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2618 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2620 ase[8] = sqrt ((pow2 (pt->total) * sum_rici
2621 + sum_rici * sum_rici
2622 - pt->total * sum_riciri_ci)
2623 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2625 t[8] = v[8] / sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2626 / pow2 (pow2 (pt->total) - sum_rici))
2627 + ((2. * (pt->total - sum_fii)
2628 * (2. * sum_fii * sum_rici
2629 - pt->total * sum_fiiri_ci))
2630 / cube (pow2 (pt->total) - sum_rici))
2631 + (pow2 (pt->total - sum_fii)
2632 * (pt->total * sum_fijri_ci2 - 4.
2633 * sum_rici * sum_rici)
2634 / pow4 (pow2 (pt->total) - sum_rici))));
2636 t[8] = v[8] / ase[8];
2643 /* Calculate risk estimate. */
2645 calc_risk (struct pivot_table *pt,
2646 double *value, double *upper, double *lower, union value *c)
2648 double f11, f12, f21, f22;
2654 for (i = 0; i < 3; i++)
2655 value[i] = upper[i] = lower[i] = SYSMIS;
2658 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2665 for (i = j = 0; i < pt->n_cols; i++)
2666 if (pt->col_tot[i] != 0.)
2675 f11 = pt->mat[nz_cols[0]];
2676 f12 = pt->mat[nz_cols[1]];
2677 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2678 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2680 c[0] = pt->cols[nz_cols[0]];
2681 c[1] = pt->cols[nz_cols[1]];
2684 value[0] = (f11 * f22) / (f12 * f21);
2685 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2686 lower[0] = value[0] * exp (-1.960 * v);
2687 upper[0] = value[0] * exp (1.960 * v);
2689 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2690 v = sqrt ((f12 / (f11 * (f11 + f12)))
2691 + (f22 / (f21 * (f21 + f22))));
2692 lower[1] = value[1] * exp (-1.960 * v);
2693 upper[1] = value[1] * exp (1.960 * v);
2695 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2696 v = sqrt ((f11 / (f12 * (f11 + f12)))
2697 + (f21 / (f22 * (f21 + f22))));
2698 lower[2] = value[2] * exp (-1.960 * v);
2699 upper[2] = value[2] * exp (1.960 * v);
2704 /* Calculate directional measures. */
2706 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2707 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2708 double t[N_DIRECTIONAL])
2713 for (i = 0; i < N_DIRECTIONAL; i++)
2714 v[i] = ase[i] = t[i] = SYSMIS;
2718 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2720 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2721 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2722 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2723 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2724 double sum_fim, sum_fmj;
2726 int rm_index, cm_index;
2729 /* Find maximum for each row and their sum. */
2730 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2732 double max = pt->mat[i * pt->n_cols];
2735 for (j = 1; j < pt->n_cols; j++)
2736 if (pt->mat[j + i * pt->n_cols] > max)
2738 max = pt->mat[j + i * pt->n_cols];
2742 sum_fim += fim[i] = max;
2743 fim_index[i] = index;
2746 /* Find maximum for each column. */
2747 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2749 double max = pt->mat[j];
2752 for (i = 1; i < pt->n_rows; i++)
2753 if (pt->mat[j + i * pt->n_cols] > max)
2755 max = pt->mat[j + i * pt->n_cols];
2759 sum_fmj += fmj[j] = max;
2760 fmj_index[j] = index;
2763 /* Find maximum row total. */
2764 rm = pt->row_tot[0];
2766 for (i = 1; i < pt->n_rows; i++)
2767 if (pt->row_tot[i] > rm)
2769 rm = pt->row_tot[i];
2773 /* Find maximum column total. */
2774 cm = pt->col_tot[0];
2776 for (j = 1; j < pt->n_cols; j++)
2777 if (pt->col_tot[j] > cm)
2779 cm = pt->col_tot[j];
2783 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2784 v[1] = (sum_fmj - rm) / (pt->total - rm);
2785 v[2] = (sum_fim - cm) / (pt->total - cm);
2787 /* ASE1 for Y given PT. */
2791 for (accum = 0., i = 0; i < pt->n_rows; i++)
2792 for (j = 0; j < pt->n_cols; j++)
2794 const int deltaj = j == cm_index;
2795 accum += (pt->mat[j + i * pt->n_cols]
2796 * pow2 ((j == fim_index[i])
2801 ase[2] = sqrt (accum - pt->total * v[0]) / (pt->total - cm);
2804 /* ASE0 for Y given PT. */
2808 for (accum = 0., i = 0; i < pt->n_rows; i++)
2809 if (cm_index != fim_index[i])
2810 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2811 + pt->mat[i * pt->n_cols + cm_index]);
2812 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2815 /* ASE1 for PT given Y. */
2819 for (accum = 0., i = 0; i < pt->n_rows; i++)
2820 for (j = 0; j < pt->n_cols; j++)
2822 const int deltaj = i == rm_index;
2823 accum += (pt->mat[j + i * pt->n_cols]
2824 * pow2 ((i == fmj_index[j])
2829 ase[1] = sqrt (accum - pt->total * v[0]) / (pt->total - rm);
2832 /* ASE0 for PT given Y. */
2836 for (accum = 0., j = 0; j < pt->n_cols; j++)
2837 if (rm_index != fmj_index[j])
2838 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2839 + pt->mat[j + pt->n_cols * rm_index]);
2840 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2843 /* Symmetric ASE0 and ASE1. */
2848 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2849 for (j = 0; j < pt->n_cols; j++)
2851 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2852 int temp1 = (i == rm_index) + (j == cm_index);
2853 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2854 accum1 += (pt->mat[j + i * pt->n_cols]
2855 * pow2 (temp0 + (v[0] - 1.) * temp1));
2857 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2858 t[0] = v[0] / (sqrt (accum0 - pow2 ((sum_fim + sum_fmj - cm - rm) / pt->total))
2859 / (2. * pt->total - rm - cm));
2868 double sum_fij2_ri, sum_fij2_ci;
2869 double sum_ri2, sum_cj2;
2871 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2872 for (j = 0; j < pt->n_cols; j++)
2874 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2875 sum_fij2_ri += temp / pt->row_tot[i];
2876 sum_fij2_ci += temp / pt->col_tot[j];
2879 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2880 sum_ri2 += pow2 (pt->row_tot[i]);
2882 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2883 sum_cj2 += pow2 (pt->col_tot[j]);
2885 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2886 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2890 if (proc->statistics & (1u << CRS_ST_UC))
2892 double UX, UY, UXY, P;
2893 double ase1_yx, ase1_xy, ase1_sym;
2896 for (UX = 0., i = 0; i < pt->n_rows; i++)
2897 if (pt->row_tot[i] > 0.)
2898 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2900 for (UY = 0., j = 0; j < pt->n_cols; j++)
2901 if (pt->col_tot[j] > 0.)
2902 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2904 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2905 for (j = 0; j < pt->n_cols; j++)
2907 double entry = pt->mat[j + i * pt->n_cols];
2912 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2913 UXY -= entry / pt->total * log (entry / pt->total);
2916 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2917 for (j = 0; j < pt->n_cols; j++)
2919 double entry = pt->mat[j + i * pt->n_cols];
2924 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2925 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2926 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2927 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2928 ase1_sym += entry * pow2 ((UXY
2929 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2930 - (UX + UY) * log (entry / pt->total));
2933 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2934 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2935 t[5] = v[5] / ((2. / (pt->total * (UX + UY)))
2936 * sqrt (P - pow2 (UX + UY - UXY) / pt->total));
2938 v[6] = (UX + UY - UXY) / UX;
2939 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2940 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2942 v[7] = (UX + UY - UXY) / UY;
2943 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2944 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2948 if (proc->statistics & (1u << CRS_ST_D))
2950 double v_dummy[N_SYMMETRIC];
2951 double ase_dummy[N_SYMMETRIC];
2952 double t_dummy[N_SYMMETRIC];
2953 double somers_d_v[3];
2954 double somers_d_ase[3];
2955 double somers_d_t[3];
2957 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2958 somers_d_v, somers_d_ase, somers_d_t))
2961 for (i = 0; i < 3; i++)
2963 v[8 + i] = somers_d_v[i];
2964 ase[8 + i] = somers_d_ase[i];
2965 t[8 + i] = somers_d_t[i];
2971 if (proc->statistics & (1u << CRS_ST_ETA))
2974 double sum_Xr, sum_X2r;
2978 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2980 sum_Xr += pt->rows[i].f * pt->row_tot[i];
2981 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
2983 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2985 for (SXW = 0., j = 0; j < pt->n_cols; j++)
2989 for (cum = 0., i = 0; i < pt->n_rows; i++)
2991 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
2992 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
2995 SXW -= cum * cum / pt->col_tot[j];
2997 v[11] = sqrt (1. - SXW / SX);
3001 double sum_Yc, sum_Y2c;
3005 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
3007 sum_Yc += pt->cols[i].f * pt->col_tot[i];
3008 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
3010 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
3012 for (SYW = 0., i = 0; i < pt->n_rows; i++)
3016 for (cum = 0., j = 0; j < pt->n_cols; j++)
3018 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
3019 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
3022 SYW -= cum * cum / pt->row_tot[i];
3024 v[12] = sqrt (1. - SYW / SY);