1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2006, 2009, 2010, 2011, 2012 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/dataset.h"
41 #include "data/dictionary.h"
42 #include "data/format.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-functions.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/tab.h"
61 #include "gl/minmax.h"
62 #include "gl/xalloc.h"
66 #define _(msgid) gettext (msgid)
67 #define N_(msgid) msgid
75 missing=miss:!table/include/report;
76 +write[wr_]=none,cells,all;
77 +format=val:!avalue/dvalue,
79 tabl:!tables/notables,
82 +cells[cl_]=count,expected,row,column,total,residual,sresidual,
84 +statistics[st_]=chisq,phi,cc,lambda,uc,none,btau,ctau,risk,gamma,d,
90 /* Number of chi-square statistics. */
93 /* Number of symmetric statistics. */
96 /* Number of directional statistics. */
97 #define N_DIRECTIONAL 13
99 /* A single table entry for general mode. */
102 struct hmap_node node; /* Entry in hash table. */
103 double freq; /* Frequency count. */
104 union value values[1]; /* Values. */
108 table_entry_size (size_t n_values)
110 return (offsetof (struct table_entry, values)
111 + n_values * sizeof (union value));
114 /* Indexes into the 'vars' member of struct pivot_table and
115 struct crosstab member. */
118 ROW_VAR = 0, /* Row variable. */
119 COL_VAR = 1 /* Column variable. */
120 /* Higher indexes cause multiple tables to be output. */
123 /* A crosstabulation of 2 or more variables. */
126 struct fmt_spec weight_format; /* Format for weight variable. */
127 double missing; /* Weight of missing cases. */
129 /* Variables (2 or more). */
131 const struct variable **vars;
133 /* Constants (0 or more). */
135 const struct variable **const_vars;
136 union value *const_values;
140 struct table_entry **entries;
143 /* Column values, number of columns. */
147 /* Row values, number of rows. */
151 /* Number of statistically interesting columns/rows
152 (columns/rows with data in them). */
153 int ns_cols, ns_rows;
155 /* Matrix contents. */
156 double *mat; /* Matrix proper. */
157 double *row_tot; /* Row totals. */
158 double *col_tot; /* Column totals. */
159 double total; /* Grand total. */
162 /* Integer mode variable info. */
165 int min; /* Minimum value. */
166 int max; /* Maximum value + 1. */
167 int count; /* max - min. */
170 static inline struct var_range *
171 get_var_range (const struct variable *v)
173 return var_get_aux (v);
176 struct crosstabs_proc
178 const struct dictionary *dict;
179 enum { INTEGER, GENERAL } mode;
180 enum mv_class exclude;
183 struct fmt_spec weight_format;
185 /* Variables specifies on VARIABLES. */
186 const struct variable **variables;
190 struct pivot_table *pivots;
194 int n_cells; /* Number of cells requested. */
195 unsigned int cells; /* Bit k is 1 if cell k is requested. */
196 int a_cells[CRS_CL_count]; /* 0...n_cells-1 are the requested cells. */
199 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
201 bool descending; /* True if descending sort order is requested. */
204 static bool should_tabulate_case (const struct pivot_table *,
205 const struct ccase *, enum mv_class exclude);
206 static void tabulate_general_case (struct pivot_table *, const struct ccase *,
208 static void tabulate_integer_case (struct pivot_table *, const struct ccase *,
210 static void postcalc (struct crosstabs_proc *);
211 static void submit (struct pivot_table *, struct tab_table *);
213 /* Parses and executes the CROSSTABS procedure. */
215 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
217 const struct variable *wv = dict_get_weight (dataset_dict (ds));
218 struct crosstabs_proc proc;
219 struct casegrouper *grouper;
220 struct casereader *input, *group;
221 struct cmd_crosstabs cmd;
222 struct pivot_table *pt;
227 proc.dict = dataset_dict (ds);
228 proc.bad_warn = true;
229 proc.variables = NULL;
230 proc.n_variables = 0;
233 proc.descending = false;
234 proc.weight_format = wv ? *var_get_print_format (wv) : F_8_0;
236 if (!parse_crosstabs (lexer, ds, &cmd, &proc))
238 result = CMD_FAILURE;
242 proc.mode = proc.n_variables ? INTEGER : GENERAL;
245 proc.descending = cmd.val == CRS_DVALUE;
249 proc.cells = 1u << CRS_CL_COUNT;
250 else if (cmd.a_cells[CRS_CL_ALL])
251 proc.cells = UINT_MAX;
255 for (i = 0; i < CRS_CL_count; i++)
257 proc.cells |= 1u << i;
259 proc.cells = ((1u << CRS_CL_COUNT)
261 | (1u << CRS_CL_COLUMN)
262 | (1u << CRS_CL_TOTAL));
264 proc.cells &= ((1u << CRS_CL_count) - 1);
265 proc.cells &= ~((1u << CRS_CL_NONE) | (1u << CRS_CL_ALL));
267 for (i = 0; i < CRS_CL_count; i++)
268 if (proc.cells & (1u << i))
269 proc.a_cells[proc.n_cells++] = i;
272 if (cmd.a_statistics[CRS_ST_ALL])
273 proc.statistics = UINT_MAX;
274 else if (cmd.sbc_statistics)
279 for (i = 0; i < CRS_ST_count; i++)
280 if (cmd.a_statistics[i])
281 proc.statistics |= 1u << i;
282 if (proc.statistics == 0)
283 proc.statistics |= 1u << CRS_ST_CHISQ;
289 proc.exclude = (cmd.miss == CRS_TABLE ? MV_ANY
290 : cmd.miss == CRS_INCLUDE ? MV_SYSTEM
292 if (proc.mode == GENERAL && proc.exclude == MV_NEVER)
294 msg (SE, _("Missing mode REPORT not allowed in general mode. "
295 "Assuming MISSING=TABLE."));
296 proc.exclude = MV_ANY;
300 proc.pivot = cmd.pivot == CRS_PIVOT;
302 input = casereader_create_filter_weight (proc_open (ds), dataset_dict (ds),
304 grouper = casegrouper_create_splits (input, dataset_dict (ds));
305 while (casegrouper_get_next_group (grouper, &group))
309 /* Output SPLIT FILE variables. */
310 c = casereader_peek (group, 0);
313 output_split_file_values (ds, c);
317 /* Initialize hash tables. */
318 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
319 hmap_init (&pt->data);
322 for (; (c = casereader_read (group)) != NULL; case_unref (c))
323 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
325 double weight = dict_get_case_weight (dataset_dict (ds), c,
327 if (should_tabulate_case (pt, c, proc.exclude))
329 if (proc.mode == GENERAL)
330 tabulate_general_case (pt, c, weight);
332 tabulate_integer_case (pt, c, weight);
335 pt->missing += weight;
337 casereader_destroy (group);
342 ok = casegrouper_destroy (grouper);
343 ok = proc_commit (ds) && ok;
345 result = ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
348 free (proc.variables);
349 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
352 free (pt->const_vars);
353 /* We must not call value_destroy on const_values because
354 it is a wild pointer; it never pointed to anything owned
357 The rest of the data was allocated and destroyed at a
358 lower level already. */
365 /* Parses the TABLES subcommand. */
367 crs_custom_tables (struct lexer *lexer, struct dataset *ds,
368 struct cmd_crosstabs *cmd UNUSED, void *proc_)
370 struct crosstabs_proc *proc = proc_;
371 struct const_var_set *var_set;
373 const struct variable ***by = NULL;
375 size_t *by_nvar = NULL;
380 /* Ensure that this is a TABLES subcommand. */
381 if (!lex_match_id (lexer, "TABLES")
382 && (lex_token (lexer) != T_ID ||
383 dict_lookup_var (dataset_dict (ds), lex_tokcstr (lexer)) == NULL)
384 && lex_token (lexer) != T_ALL)
386 lex_match (lexer, T_EQUALS);
388 if (proc->variables != NULL)
389 var_set = const_var_set_create_from_array (proc->variables,
392 var_set = const_var_set_create_from_dict (dataset_dict (ds));
393 assert (var_set != NULL);
397 by = xnrealloc (by, n_by + 1, sizeof *by);
398 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
399 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
400 PV_NO_DUPLICATE | PV_NO_SCRATCH))
402 if (xalloc_oversized (nx, by_nvar[n_by]))
404 msg (SE, _("Too many cross-tabulation variables or dimensions."));
410 if (!lex_match (lexer, T_BY))
414 lex_force_match (lexer, T_BY);
422 by_iter = xcalloc (n_by, sizeof *by_iter);
423 proc->pivots = xnrealloc (proc->pivots,
424 proc->n_pivots + nx, sizeof *proc->pivots);
425 for (i = 0; i < nx; i++)
427 struct pivot_table *pt = &proc->pivots[proc->n_pivots++];
430 pt->weight_format = proc->weight_format;
433 pt->vars = xmalloc (n_by * sizeof *pt->vars);
435 pt->const_vars = NULL;
436 pt->const_values = NULL;
438 for (j = 0; j < n_by; j++)
439 pt->vars[j] = by[j][by_iter[j]];
441 for (j = n_by - 1; j >= 0; j--)
443 if (++by_iter[j] < by_nvar[j])
452 /* All return paths lead here. */
453 for (i = 0; i < n_by; i++)
458 const_var_set_destroy (var_set);
463 /* Parses the VARIABLES subcommand. */
465 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
466 struct cmd_crosstabs *cmd UNUSED, void *proc_)
468 struct crosstabs_proc *proc = proc_;
471 msg (SE, _("VARIABLES must be specified before TABLES."));
475 lex_match (lexer, T_EQUALS);
479 size_t orig_nv = proc->n_variables;
484 if (!parse_variables_const (lexer, dataset_dict (ds),
485 &proc->variables, &proc->n_variables,
486 (PV_APPEND | PV_NUMERIC
487 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
490 if (!lex_force_match (lexer, T_LPAREN))
493 if (!lex_force_int (lexer))
495 min = lex_integer (lexer);
498 lex_match (lexer, T_COMMA);
500 if (!lex_force_int (lexer))
502 max = lex_integer (lexer);
505 msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
511 if (!lex_force_match (lexer, T_RPAREN))
514 for (i = orig_nv; i < proc->n_variables; i++)
516 struct var_range *vr = xmalloc (sizeof *vr);
519 vr->count = max - min + 1;
520 var_attach_aux (proc->variables[i], vr, var_dtor_free);
523 if (lex_token (lexer) == T_SLASH)
530 free (proc->variables);
531 proc->variables = NULL;
532 proc->n_variables = 0;
536 /* Data file processing. */
539 should_tabulate_case (const struct pivot_table *pt, const struct ccase *c,
540 enum mv_class exclude)
543 for (j = 0; j < pt->n_vars; j++)
545 const struct variable *var = pt->vars[j];
546 struct var_range *range = get_var_range (var);
548 if (var_is_value_missing (var, case_data (c, var), exclude))
553 double num = case_num (c, var);
554 if (num < range->min || num > range->max)
562 tabulate_integer_case (struct pivot_table *pt, const struct ccase *c,
565 struct table_entry *te;
570 for (j = 0; j < pt->n_vars; j++)
572 /* Throw away fractional parts of values. */
573 hash = hash_int (case_num (c, pt->vars[j]), hash);
576 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
578 for (j = 0; j < pt->n_vars; j++)
579 if ((int) case_num (c, pt->vars[j]) != (int) te->values[j].f)
582 /* Found an existing entry. */
589 /* No existing entry. Create a new one. */
590 te = xmalloc (table_entry_size (pt->n_vars));
592 for (j = 0; j < pt->n_vars; j++)
593 te->values[j].f = (int) case_num (c, pt->vars[j]);
594 hmap_insert (&pt->data, &te->node, hash);
598 tabulate_general_case (struct pivot_table *pt, const struct ccase *c,
601 struct table_entry *te;
606 for (j = 0; j < pt->n_vars; j++)
608 const struct variable *var = pt->vars[j];
609 hash = value_hash (case_data (c, var), var_get_width (var), hash);
612 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
614 for (j = 0; j < pt->n_vars; j++)
616 const struct variable *var = pt->vars[j];
617 if (!value_equal (case_data (c, var), &te->values[j],
618 var_get_width (var)))
622 /* Found an existing entry. */
629 /* No existing entry. Create a new one. */
630 te = xmalloc (table_entry_size (pt->n_vars));
632 for (j = 0; j < pt->n_vars; j++)
634 const struct variable *var = pt->vars[j];
635 value_clone (&te->values[j], case_data (c, var), var_get_width (var));
637 hmap_insert (&pt->data, &te->node, hash);
640 /* Post-data reading calculations. */
642 static int compare_table_entry_vars_3way (const struct table_entry *a,
643 const struct table_entry *b,
644 const struct pivot_table *pt,
646 static int compare_table_entry_3way (const void *ap_, const void *bp_,
648 static int compare_table_entry_3way_inv (const void *ap_, const void *bp_,
651 static void enum_var_values (const struct pivot_table *, int var_idx,
652 union value **valuesp, int *n_values, bool descending);
653 static void output_pivot_table (struct crosstabs_proc *,
654 struct pivot_table *);
655 static void make_pivot_table_subset (struct pivot_table *pt,
656 size_t row0, size_t row1,
657 struct pivot_table *subset);
658 static void make_summary_table (struct crosstabs_proc *);
659 static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
662 postcalc (struct crosstabs_proc *proc)
664 struct pivot_table *pt;
666 /* Convert hash tables into sorted arrays of entries. */
667 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
669 struct table_entry *e;
672 pt->n_entries = hmap_count (&pt->data);
673 pt->entries = xnmalloc (pt->n_entries, sizeof *pt->entries);
675 HMAP_FOR_EACH (e, struct table_entry, node, &pt->data)
676 pt->entries[i++] = e;
677 hmap_destroy (&pt->data);
679 sort (pt->entries, pt->n_entries, sizeof *pt->entries,
680 proc->descending ? compare_table_entry_3way_inv : compare_table_entry_3way,
684 make_summary_table (proc);
686 /* Output each pivot table. */
687 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
689 if (proc->pivot || pt->n_vars == 2)
690 output_pivot_table (proc, pt);
693 size_t row0 = 0, row1 = 0;
694 while (find_crosstab (pt, &row0, &row1))
696 struct pivot_table subset;
697 make_pivot_table_subset (pt, row0, row1, &subset);
698 output_pivot_table (proc, &subset);
703 /* Free output and prepare for next split file. */
704 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
710 /* Free only the members that were allocated in this
711 function. The other pointer members are either both
712 allocated and destroyed at a lower level (in
713 output_pivot_table), or both allocated and destroyed at
714 a higher level (in crs_custom_tables and free_proc,
716 for (i = 0; i < pt->n_entries; i++)
717 free (pt->entries[i]);
723 make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
724 struct pivot_table *subset)
729 assert (pt->n_consts == 0);
730 subset->missing = pt->missing;
732 subset->vars = pt->vars;
733 subset->n_consts = pt->n_vars - 2;
734 subset->const_vars = pt->vars + 2;
735 subset->const_values = &pt->entries[row0]->values[2];
737 subset->entries = &pt->entries[row0];
738 subset->n_entries = row1 - row0;
742 compare_table_entry_var_3way (const struct table_entry *a,
743 const struct table_entry *b,
744 const struct pivot_table *pt,
747 return value_compare_3way (&a->values[idx], &b->values[idx],
748 var_get_width (pt->vars[idx]));
752 compare_table_entry_vars_3way (const struct table_entry *a,
753 const struct table_entry *b,
754 const struct pivot_table *pt,
759 for (i = idx1 - 1; i >= idx0; i--)
761 int cmp = compare_table_entry_var_3way (a, b, pt, i);
768 /* Compare the struct table_entry at *AP to the one at *BP and
769 return a strcmp()-type result. */
771 compare_table_entry_3way (const void *ap_, const void *bp_, const void *pt_)
773 const struct table_entry *const *ap = ap_;
774 const struct table_entry *const *bp = bp_;
775 const struct table_entry *a = *ap;
776 const struct table_entry *b = *bp;
777 const struct pivot_table *pt = pt_;
780 cmp = compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars);
784 cmp = compare_table_entry_var_3way (a, b, pt, ROW_VAR);
788 return compare_table_entry_var_3way (a, b, pt, COL_VAR);
791 /* Inverted version of compare_table_entry_3way */
793 compare_table_entry_3way_inv (const void *ap_, const void *bp_, const void *pt_)
795 return -compare_table_entry_3way (ap_, bp_, pt_);
799 find_first_difference (const struct pivot_table *pt, size_t row)
802 return pt->n_vars - 1;
805 const struct table_entry *a = pt->entries[row];
806 const struct table_entry *b = pt->entries[row - 1];
809 for (col = pt->n_vars - 1; col >= 0; col--)
810 if (compare_table_entry_var_3way (a, b, pt, col))
816 /* Output a table summarizing the cases processed. */
818 make_summary_table (struct crosstabs_proc *proc)
820 struct tab_table *summary;
821 struct pivot_table *pt;
825 summary = tab_create (7, 3 + proc->n_pivots);
826 tab_title (summary, _("Summary."));
827 tab_headers (summary, 1, 0, 3, 0);
828 tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
829 tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
830 tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
831 tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
832 tab_hline (summary, TAL_1, 1, 6, 1);
833 tab_hline (summary, TAL_1, 1, 6, 2);
834 tab_vline (summary, TAL_1, 3, 1, 1);
835 tab_vline (summary, TAL_1, 5, 1, 1);
836 for (i = 0; i < 3; i++)
838 tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
839 tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
841 tab_offset (summary, 0, 3);
843 ds_init_empty (&name);
844 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
850 tab_hline (summary, TAL_1, 0, 6, 0);
853 for (i = 0; i < pt->n_vars; i++)
856 ds_put_cstr (&name, " * ");
857 ds_put_cstr (&name, var_to_string (pt->vars[i]));
859 tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
862 for (i = 0; i < pt->n_entries; i++)
863 valid += pt->entries[i]->freq;
868 for (i = 0; i < 3; i++)
870 tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i],
871 &proc->weight_format);
872 tab_text_format (summary, i * 2 + 2, 0, TAB_RIGHT, "%.1f%%",
876 tab_next_row (summary);
880 submit (NULL, summary);
885 static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
886 struct pivot_table *);
887 static struct tab_table *create_chisq_table (struct pivot_table *);
888 static struct tab_table *create_sym_table (struct pivot_table *);
889 static struct tab_table *create_risk_table (struct pivot_table *);
890 static struct tab_table *create_direct_table (struct pivot_table *);
891 static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
892 struct tab_table *, int first_difference);
893 static void display_crosstabulation (struct crosstabs_proc *,
894 struct pivot_table *,
896 static void display_chisq (struct pivot_table *, struct tab_table *,
897 bool *showed_fisher);
898 static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
900 static void display_risk (struct pivot_table *, struct tab_table *);
901 static void display_directional (struct crosstabs_proc *, struct pivot_table *,
903 static void table_value_missing (struct crosstabs_proc *proc,
904 struct tab_table *table, int c, int r,
905 unsigned char opt, const union value *v,
906 const struct variable *var);
907 static void delete_missing (struct pivot_table *);
908 static void build_matrix (struct pivot_table *);
910 /* Output pivot table PT in the context of PROC. */
912 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
914 struct tab_table *table = NULL; /* Crosstabulation table. */
915 struct tab_table *chisq = NULL; /* Chi-square table. */
916 bool showed_fisher = false;
917 struct tab_table *sym = NULL; /* Symmetric measures table. */
918 struct tab_table *risk = NULL; /* Risk estimate table. */
919 struct tab_table *direct = NULL; /* Directional measures table. */
922 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols, proc->descending);
929 ds_init_cstr (&vars, var_to_string (pt->vars[0]));
930 for (i = 1; i < pt->n_vars; i++)
931 ds_put_format (&vars, " * %s", var_to_string (pt->vars[i]));
933 /* TRANSLATORS: The %s here describes a crosstabulation. It takes the
934 form "var1 * var2 * var3 * ...". */
935 msg (SW, _("Crosstabulation %s contained no non-missing cases."),
943 table = create_crosstab_table (proc, pt);
944 if (proc->statistics & (1u << CRS_ST_CHISQ))
945 chisq = create_chisq_table (pt);
946 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
947 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
948 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
949 | (1u << CRS_ST_KAPPA)))
950 sym = create_sym_table (pt);
951 if (proc->statistics & (1u << CRS_ST_RISK))
952 risk = create_risk_table (pt);
953 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
954 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
955 direct = create_direct_table (pt);
958 while (find_crosstab (pt, &row0, &row1))
960 struct pivot_table x;
961 int first_difference;
963 make_pivot_table_subset (pt, row0, row1, &x);
965 /* Find all the row variable values. */
966 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows, proc->descending);
968 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
971 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
972 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
973 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
975 /* Allocate table space for the matrix. */
977 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
978 tab_realloc (table, -1,
979 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
980 tab_nr (table) * pt->n_entries / x.n_entries));
984 /* Find the first variable that differs from the last subtable. */
985 first_difference = find_first_difference (pt, row0);
988 display_dimensions (proc, &x, table, first_difference);
989 display_crosstabulation (proc, &x, table);
992 if (proc->exclude == MV_NEVER)
997 display_dimensions (proc, &x, chisq, first_difference);
998 display_chisq (&x, chisq, &showed_fisher);
1002 display_dimensions (proc, &x, sym, first_difference);
1003 display_symmetric (proc, &x, sym);
1007 display_dimensions (proc, &x, risk, first_difference);
1008 display_risk (&x, risk);
1012 display_dimensions (proc, &x, direct, first_difference);
1013 display_directional (proc, &x, direct);
1016 /* Free the parts of x that are not owned by pt. In
1017 particular we must not free x.cols, which is the same as
1018 pt->cols, which is freed at the end of this function. */
1026 submit (NULL, table);
1031 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
1037 submit (pt, direct);
1043 build_matrix (struct pivot_table *x)
1045 const int col_var_width = var_get_width (x->vars[COL_VAR]);
1046 const int row_var_width = var_get_width (x->vars[ROW_VAR]);
1049 struct table_entry **p;
1053 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1055 const struct table_entry *te = *p;
1057 while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
1059 for (; col < x->n_cols; col++)
1065 while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
1072 if (++col >= x->n_cols)
1078 while (mp < &x->mat[x->n_cols * x->n_rows])
1080 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1082 /* Column totals, row totals, ns_rows. */
1084 for (col = 0; col < x->n_cols; col++)
1085 x->col_tot[col] = 0.0;
1086 for (row = 0; row < x->n_rows; row++)
1087 x->row_tot[row] = 0.0;
1089 for (row = 0; row < x->n_rows; row++)
1091 bool row_is_empty = true;
1092 for (col = 0; col < x->n_cols; col++)
1096 row_is_empty = false;
1097 x->col_tot[col] += *mp;
1098 x->row_tot[row] += *mp;
1105 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1109 for (col = 0; col < x->n_cols; col++)
1110 for (row = 0; row < x->n_rows; row++)
1111 if (x->mat[col + row * x->n_cols] != 0.0)
1119 for (col = 0; col < x->n_cols; col++)
1120 x->total += x->col_tot[col];
1123 static struct tab_table *
1124 create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1131 static const struct tuple names[] =
1133 {CRS_CL_COUNT, N_("count")},
1134 {CRS_CL_ROW, N_("row %")},
1135 {CRS_CL_COLUMN, N_("column %")},
1136 {CRS_CL_TOTAL, N_("total %")},
1137 {CRS_CL_EXPECTED, N_("expected")},
1138 {CRS_CL_RESIDUAL, N_("residual")},
1139 {CRS_CL_SRESIDUAL, N_("std. resid.")},
1140 {CRS_CL_ASRESIDUAL, N_("adj. resid.")},
1142 const int n_names = sizeof names / sizeof *names;
1143 const struct tuple *t;
1145 struct tab_table *table;
1146 struct string title;
1147 struct pivot_table x;
1151 make_pivot_table_subset (pt, 0, 0, &x);
1153 table = tab_create (x.n_consts + 1 + x.n_cols + 1,
1154 (x.n_entries / x.n_cols) * 3 / 2 * proc->n_cells + 10);
1155 tab_headers (table, x.n_consts + 1, 0, 2, 0);
1157 /* First header line. */
1158 tab_joint_text (table, x.n_consts + 1, 0,
1159 (x.n_consts + 1) + (x.n_cols - 1), 0,
1160 TAB_CENTER | TAT_TITLE, var_to_string (x.vars[COL_VAR]));
1162 tab_hline (table, TAL_1, x.n_consts + 1,
1163 x.n_consts + 2 + x.n_cols - 2, 1);
1165 /* Second header line. */
1166 for (i = 2; i < x.n_consts + 2; i++)
1167 tab_joint_text (table, x.n_consts + 2 - i - 1, 0,
1168 x.n_consts + 2 - i - 1, 1,
1169 TAB_RIGHT | TAT_TITLE, var_to_string (x.vars[i]));
1170 tab_text (table, x.n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1171 var_to_string (x.vars[ROW_VAR]));
1172 for (i = 0; i < x.n_cols; i++)
1173 table_value_missing (proc, table, x.n_consts + 2 + i - 1, 1, TAB_RIGHT,
1174 &x.cols[i], x.vars[COL_VAR]);
1175 tab_text (table, x.n_consts + 2 + x.n_cols - 1, 1, TAB_CENTER, _("Total"));
1177 tab_hline (table, TAL_1, 0, x.n_consts + 2 + x.n_cols - 1, 2);
1178 tab_vline (table, TAL_1, x.n_consts + 2 + x.n_cols - 1, 0, 1);
1181 ds_init_empty (&title);
1182 for (i = 0; i < x.n_consts + 2; i++)
1185 ds_put_cstr (&title, " * ");
1186 ds_put_cstr (&title, var_to_string (x.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_to_string (var));
1195 /* Insert the formatted value of VAR without any leading spaces. */
1196 s = data_out (&pt->const_values[i], var_get_encoding (var),
1197 var_get_print_format (var));
1198 ds_put_cstr (&title, s + strspn (s, " "));
1202 ds_put_cstr (&title, " [");
1204 for (t = names; t < &names[n_names]; t++)
1205 if (proc->cells & (1u << t->value))
1208 ds_put_cstr (&title, ", ");
1209 ds_put_cstr (&title, gettext (t->name));
1211 ds_put_cstr (&title, "].");
1213 tab_title (table, "%s", ds_cstr (&title));
1214 ds_destroy (&title);
1216 tab_offset (table, 0, 2);
1220 static struct tab_table *
1221 create_chisq_table (struct pivot_table *pt)
1223 struct tab_table *chisq;
1225 chisq = tab_create (6 + (pt->n_vars - 2),
1226 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10);
1227 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1229 tab_title (chisq, _("Chi-square tests."));
1231 tab_offset (chisq, pt->n_vars - 2, 0);
1232 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1233 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1234 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1235 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1236 _("Asymp. Sig. (2-tailed)"));
1237 tab_text_format (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1238 _("Exact Sig. (%d-tailed)"), 2);
1239 tab_text_format (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1240 _("Exact Sig. (%d-tailed)"), 1);
1241 tab_offset (chisq, 0, 1);
1246 /* Symmetric measures. */
1247 static struct tab_table *
1248 create_sym_table (struct pivot_table *pt)
1250 struct tab_table *sym;
1252 sym = tab_create (6 + (pt->n_vars - 2),
1253 pt->n_entries / pt->n_cols * 7 + 10);
1254 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1255 tab_title (sym, _("Symmetric measures."));
1257 tab_offset (sym, pt->n_vars - 2, 0);
1258 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1259 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1260 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1261 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1262 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1263 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1264 tab_offset (sym, 0, 1);
1269 /* Risk estimate. */
1270 static struct tab_table *
1271 create_risk_table (struct pivot_table *pt)
1273 struct tab_table *risk;
1275 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10);
1276 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1277 tab_title (risk, _("Risk estimate."));
1279 tab_offset (risk, pt->n_vars - 2, 0);
1280 tab_joint_text_format (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE,
1281 _("95%% Confidence Interval"));
1282 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1283 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1284 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1285 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1286 tab_hline (risk, TAL_1, 2, 3, 1);
1287 tab_vline (risk, TAL_1, 2, 0, 1);
1288 tab_offset (risk, 0, 2);
1293 /* Directional measures. */
1294 static struct tab_table *
1295 create_direct_table (struct pivot_table *pt)
1297 struct tab_table *direct;
1299 direct = tab_create (7 + (pt->n_vars - 2),
1300 pt->n_entries / pt->n_cols * 7 + 10);
1301 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1302 tab_title (direct, _("Directional measures."));
1304 tab_offset (direct, pt->n_vars - 2, 0);
1305 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1306 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1307 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1308 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1309 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1310 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1311 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1312 tab_offset (direct, 0, 1);
1318 /* Delete missing rows and columns for statistical analysis when
1321 delete_missing (struct pivot_table *pt)
1325 for (r = 0; r < pt->n_rows; r++)
1326 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1328 for (c = 0; c < pt->n_cols; c++)
1329 pt->mat[c + r * pt->n_cols] = 0.;
1334 for (c = 0; c < pt->n_cols; c++)
1335 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1337 for (r = 0; r < pt->n_rows; r++)
1338 pt->mat[c + r * pt->n_cols] = 0.;
1343 /* Prepare table T for submission, and submit it. */
1345 submit (struct pivot_table *pt, struct tab_table *t)
1352 tab_resize (t, -1, 0);
1353 if (tab_nr (t) == tab_t (t))
1355 table_unref (&t->table);
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);
1374 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1376 size_t row0 = *row1p;
1379 if (row0 >= pt->n_entries)
1382 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1384 struct table_entry *a = pt->entries[row0];
1385 struct table_entry *b = pt->entries[row1];
1386 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1394 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1395 result. WIDTH_ points to an int which is either 0 for a
1396 numeric value or a string width for a string value. */
1398 compare_value_3way (const void *a_, const void *b_, const void *width_)
1400 const union value *a = a_;
1401 const union value *b = b_;
1402 const int *width = width_;
1404 return value_compare_3way (a, b, *width);
1407 /* Inverted version of the above */
1409 compare_value_3way_inv (const void *a_, const void *b_, const void *width_)
1411 return -compare_value_3way (a_, b_, width_);
1415 /* Given an array of ENTRY_CNT table_entry structures starting at
1416 ENTRIES, creates a sorted list of the values that the variable
1417 with index VAR_IDX takes on. The values are returned as a
1418 malloc()'d array stored in *VALUES, with the number of values
1419 stored in *VALUE_CNT.
1422 enum_var_values (const struct pivot_table *pt, int var_idx,
1423 union value **valuesp, int *n_values, bool descending)
1425 const struct variable *var = pt->vars[var_idx];
1426 struct var_range *range = get_var_range (var);
1427 union value *values;
1432 values = *valuesp = xnmalloc (range->count, sizeof *values);
1433 *n_values = range->count;
1434 for (i = 0; i < range->count; i++)
1435 values[i].f = range->min + i;
1439 int width = var_get_width (var);
1440 struct hmapx_node *node;
1441 const union value *iter;
1445 for (i = 0; i < pt->n_entries; i++)
1447 const struct table_entry *te = pt->entries[i];
1448 const union value *value = &te->values[var_idx];
1449 size_t hash = value_hash (value, width, 0);
1451 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1452 if (value_equal (iter, value, width))
1455 hmapx_insert (&set, (union value *) value, hash);
1460 *n_values = hmapx_count (&set);
1461 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1463 HMAPX_FOR_EACH (iter, node, &set)
1464 values[i++] = *iter;
1465 hmapx_destroy (&set);
1467 sort (values, *n_values, sizeof *values,
1468 descending ? compare_value_3way_inv : compare_value_3way,
1473 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1474 from V, displayed with print format spec from variable VAR. When
1475 in REPORT missing-value mode, missing values have an M appended. */
1477 table_value_missing (struct crosstabs_proc *proc,
1478 struct tab_table *table, int c, int r, unsigned char opt,
1479 const union value *v, const struct variable *var)
1481 const char *label = var_lookup_value_label (var, v);
1483 tab_text (table, c, r, TAB_LEFT, label);
1486 const struct fmt_spec *print = var_get_print_format (var);
1487 if (proc->exclude == MV_NEVER && var_is_value_missing (var, v, MV_USER))
1489 char *s = data_out (v, dict_get_encoding (proc->dict), print);
1490 tab_text_format (table, c, r, opt, "%sM", s + strspn (s, " "));
1494 tab_value (table, c, r, opt, v, var, print);
1498 /* Draws a line across TABLE at the current row to indicate the most
1499 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1500 that changed, and puts the values that changed into the table. TB
1501 and PT must be the corresponding table_entry and crosstab,
1504 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1505 struct tab_table *table, int first_difference)
1507 tab_hline (table, TAL_1, pt->n_consts + pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1509 for (; first_difference >= 2; first_difference--)
1510 table_value_missing (proc, table, pt->n_consts + pt->n_vars - first_difference - 1, 0,
1511 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1512 pt->vars[first_difference]);
1515 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1516 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1517 additionally suffixed with a letter `M'. */
1519 format_cell_entry (struct tab_table *table, int c, int r, double value,
1520 char suffix, bool mark_missing, const struct dictionary *dict)
1528 s = data_out (&v, dict_get_encoding (dict), settings_get_format ());
1532 suffixes[suffix_len++] = suffix;
1534 suffixes[suffix_len++] = 'M';
1535 suffixes[suffix_len] = '\0';
1537 tab_text_format (table, c, r, TAB_RIGHT, "%s%s",
1538 s + strspn (s, " "), suffixes);
1543 /* Displays the crosstabulation table. */
1545 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1546 struct tab_table *table)
1552 for (r = 0; r < pt->n_rows; r++)
1553 table_value_missing (proc, table, pt->n_consts + pt->n_vars - 2,
1554 r * proc->n_cells, TAB_RIGHT, &pt->rows[r],
1557 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1558 TAB_LEFT, _("Total"));
1560 /* Put in the actual cells. */
1562 tab_offset (table, pt->n_consts + pt->n_vars - 1, -1);
1563 for (r = 0; r < pt->n_rows; r++)
1565 if (proc->n_cells > 1)
1566 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1567 for (c = 0; c < pt->n_cols; c++)
1569 bool mark_missing = false;
1570 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1571 if (proc->exclude == MV_NEVER
1572 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1573 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1575 mark_missing = true;
1576 for (i = 0; i < proc->n_cells; i++)
1581 switch (proc->a_cells[i])
1587 v = *mp / pt->row_tot[r] * 100.;
1591 v = *mp / pt->col_tot[c] * 100.;
1595 v = *mp / pt->total * 100.;
1598 case CRS_CL_EXPECTED:
1601 case CRS_CL_RESIDUAL:
1602 v = *mp - expected_value;
1604 case CRS_CL_SRESIDUAL:
1605 v = (*mp - expected_value) / sqrt (expected_value);
1607 case CRS_CL_ASRESIDUAL:
1608 v = ((*mp - expected_value)
1609 / sqrt (expected_value
1610 * (1. - pt->row_tot[r] / pt->total)
1611 * (1. - pt->col_tot[c] / pt->total)));
1616 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1622 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1626 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1627 for (r = 0; r < pt->n_rows; r++)
1629 bool mark_missing = false;
1631 if (proc->exclude == MV_NEVER
1632 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1633 mark_missing = true;
1635 for (i = 0; i < proc->n_cells; i++)
1640 switch (proc->a_cells[i])
1650 v = pt->row_tot[r] / pt->total * 100.;
1654 v = pt->row_tot[r] / pt->total * 100.;
1657 case CRS_CL_EXPECTED:
1658 case CRS_CL_RESIDUAL:
1659 case CRS_CL_SRESIDUAL:
1660 case CRS_CL_ASRESIDUAL:
1667 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing, proc->dict);
1668 tab_next_row (table);
1672 /* Column totals, grand total. */
1674 if (proc->n_cells > 1)
1675 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1676 for (c = 0; c <= pt->n_cols; c++)
1678 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1679 bool mark_missing = false;
1682 if (proc->exclude == MV_NEVER && c < pt->n_cols
1683 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1684 mark_missing = true;
1686 for (i = 0; i < proc->n_cells; i++)
1691 switch (proc->a_cells[i])
1697 v = ct / pt->total * 100.;
1705 v = ct / pt->total * 100.;
1708 case CRS_CL_EXPECTED:
1709 case CRS_CL_RESIDUAL:
1710 case CRS_CL_SRESIDUAL:
1711 case CRS_CL_ASRESIDUAL:
1717 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1722 tab_offset (table, -1, tab_row (table) + last_row);
1723 tab_offset (table, 0, -1);
1726 static void calc_r (struct pivot_table *,
1727 double *PT, double *Y, double *, double *, double *);
1728 static void calc_chisq (struct pivot_table *,
1729 double[N_CHISQ], int[N_CHISQ], double *, double *);
1731 /* Display chi-square statistics. */
1733 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1734 bool *showed_fisher)
1736 static const char *chisq_stats[N_CHISQ] =
1738 N_("Pearson Chi-Square"),
1739 N_("Likelihood Ratio"),
1740 N_("Fisher's Exact Test"),
1741 N_("Continuity Correction"),
1742 N_("Linear-by-Linear Association"),
1744 double chisq_v[N_CHISQ];
1745 double fisher1, fisher2;
1750 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1752 tab_offset (chisq, pt->n_consts + pt->n_vars - 2, -1);
1754 for (i = 0; i < N_CHISQ; i++)
1756 if ((i != 2 && chisq_v[i] == SYSMIS)
1757 || (i == 2 && fisher1 == SYSMIS))
1760 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1763 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL);
1764 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], &pt->weight_format);
1765 tab_double (chisq, 3, 0, TAB_RIGHT,
1766 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL);
1770 *showed_fisher = true;
1771 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL);
1772 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL);
1774 tab_next_row (chisq);
1777 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1778 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1779 tab_next_row (chisq);
1781 tab_offset (chisq, 0, -1);
1784 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1785 double[N_SYMMETRIC], double[N_SYMMETRIC],
1786 double[N_SYMMETRIC],
1787 double[3], double[3], double[3]);
1789 /* Display symmetric measures. */
1791 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1792 struct tab_table *sym)
1794 static const char *categories[] =
1796 N_("Nominal by Nominal"),
1797 N_("Ordinal by Ordinal"),
1798 N_("Interval by Interval"),
1799 N_("Measure of Agreement"),
1802 static const char *stats[N_SYMMETRIC] =
1806 N_("Contingency Coefficient"),
1807 N_("Kendall's tau-b"),
1808 N_("Kendall's tau-c"),
1810 N_("Spearman Correlation"),
1815 static const int stats_categories[N_SYMMETRIC] =
1817 0, 0, 0, 1, 1, 1, 1, 2, 3,
1821 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1822 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1825 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1826 somers_d_v, somers_d_ase, somers_d_t))
1829 tab_offset (sym, pt->n_consts + pt->n_vars - 2, -1);
1831 for (i = 0; i < N_SYMMETRIC; i++)
1833 if (sym_v[i] == SYSMIS)
1836 if (stats_categories[i] != last_cat)
1838 last_cat = stats_categories[i];
1839 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1842 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1843 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL);
1844 if (sym_ase[i] != SYSMIS)
1845 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL);
1846 if (sym_t[i] != SYSMIS)
1847 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL);
1848 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL);*/
1852 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1853 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1856 tab_offset (sym, 0, -1);
1859 static int calc_risk (struct pivot_table *,
1860 double[], double[], double[], union value *);
1862 /* Display risk estimate. */
1864 display_risk (struct pivot_table *pt, struct tab_table *risk)
1867 double risk_v[3], lower[3], upper[3];
1871 if (!calc_risk (pt, risk_v, upper, lower, c))
1874 tab_offset (risk, pt->n_consts + pt->n_vars - 2, -1);
1876 for (i = 0; i < 3; i++)
1878 const struct variable *cv = pt->vars[COL_VAR];
1879 const struct variable *rv = pt->vars[ROW_VAR];
1880 int cvw = var_get_width (cv);
1881 int rvw = var_get_width (rv);
1883 if (risk_v[i] == SYSMIS)
1889 if (var_is_numeric (cv))
1890 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1891 var_to_string (cv), c[0].f, c[1].f);
1893 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1895 cvw, value_str (&c[0], cvw),
1896 cvw, value_str (&c[1], cvw));
1900 if (var_is_numeric (rv))
1901 sprintf (buf, _("For cohort %s = %g"),
1902 var_to_string (rv), pt->rows[i - 1].f);
1904 sprintf (buf, _("For cohort %s = %.*s"),
1906 rvw, value_str (&pt->rows[i - 1], rvw));
1910 tab_text (risk, 0, 0, TAB_LEFT, buf);
1911 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL);
1912 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL);
1913 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL);
1914 tab_next_row (risk);
1917 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1918 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1919 tab_next_row (risk);
1921 tab_offset (risk, 0, -1);
1924 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1925 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1926 double[N_DIRECTIONAL]);
1928 /* Display directional measures. */
1930 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
1931 struct tab_table *direct)
1933 static const char *categories[] =
1935 N_("Nominal by Nominal"),
1936 N_("Ordinal by Ordinal"),
1937 N_("Nominal by Interval"),
1940 static const char *stats[] =
1943 N_("Goodman and Kruskal tau"),
1944 N_("Uncertainty Coefficient"),
1949 static const char *types[] =
1956 static const int stats_categories[N_DIRECTIONAL] =
1958 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
1961 static const int stats_stats[N_DIRECTIONAL] =
1963 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
1966 static const int stats_types[N_DIRECTIONAL] =
1968 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
1971 static const int *stats_lookup[] =
1978 static const char **stats_names[] =
1990 double direct_v[N_DIRECTIONAL];
1991 double direct_ase[N_DIRECTIONAL];
1992 double direct_t[N_DIRECTIONAL];
1996 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t))
1999 tab_offset (direct, pt->n_consts + pt->n_vars - 2, -1);
2001 for (i = 0; i < N_DIRECTIONAL; i++)
2003 if (direct_v[i] == SYSMIS)
2009 for (j = 0; j < 3; j++)
2010 if (last[j] != stats_lookup[j][i])
2013 tab_hline (direct, TAL_1, j, 6, 0);
2018 int k = last[j] = stats_lookup[j][i];
2023 string = var_to_string (pt->vars[0]);
2025 string = var_to_string (pt->vars[1]);
2027 tab_text_format (direct, j, 0, TAB_LEFT,
2028 gettext (stats_names[j][k]), string);
2033 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL);
2034 if (direct_ase[i] != SYSMIS)
2035 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL);
2036 if (direct_t[i] != SYSMIS)
2037 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL);
2038 /*tab_double (direct, 6, 0, TAB_RIGHT, normal_sig (direct_v[i]), NULL);*/
2039 tab_next_row (direct);
2042 tab_offset (direct, 0, -1);
2045 /* Statistical calculations. */
2047 /* Returns the value of the gamma (factorial) function for an integer
2050 gamma_int (double pt)
2055 for (i = 2; i < pt; i++)
2060 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2062 static inline double
2063 Pr (int a, int b, int c, int d)
2065 return (gamma_int (a + b + 1.) / gamma_int (a + 1.)
2066 * gamma_int (c + d + 1.) / gamma_int (b + 1.)
2067 * gamma_int (a + c + 1.) / gamma_int (c + 1.)
2068 * gamma_int (b + d + 1.) / gamma_int (d + 1.)
2069 / gamma_int (a + b + c + d + 1.));
2072 /* Swap the contents of A and B. */
2074 swap (int *a, int *b)
2081 /* Calculate significance for Fisher's exact test as specified in
2082 _SPSS Statistical Algorithms_, Appendix 5. */
2084 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2088 if (MIN (c, d) < MIN (a, b))
2089 swap (&a, &c), swap (&b, &d);
2090 if (MIN (b, d) < MIN (a, c))
2091 swap (&a, &b), swap (&c, &d);
2095 swap (&a, &b), swap (&c, &d);
2097 swap (&a, &c), swap (&b, &d);
2101 for (pt = 0; pt <= a; pt++)
2102 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2104 *fisher2 = *fisher1;
2105 for (pt = 1; pt <= b; pt++)
2106 *fisher2 += Pr (a + pt, b - pt, c - pt, d + pt);
2109 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2110 columns with values COLS and N_ROWS rows with values ROWS. Values
2111 in the matrix sum to pt->total. */
2113 calc_chisq (struct pivot_table *pt,
2114 double chisq[N_CHISQ], int df[N_CHISQ],
2115 double *fisher1, double *fisher2)
2119 chisq[0] = chisq[1] = 0.;
2120 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2121 *fisher1 = *fisher2 = SYSMIS;
2123 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2125 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2127 chisq[0] = chisq[1] = SYSMIS;
2131 for (r = 0; r < pt->n_rows; r++)
2132 for (c = 0; c < pt->n_cols; c++)
2134 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2135 const double freq = pt->mat[pt->n_cols * r + c];
2136 const double residual = freq - expected;
2138 chisq[0] += residual * residual / expected;
2140 chisq[1] += freq * log (expected / freq);
2151 /* Calculate Yates and Fisher exact test. */
2152 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2154 double f11, f12, f21, f22;
2160 for (i = j = 0; i < pt->n_cols; i++)
2161 if (pt->col_tot[i] != 0.)
2170 f11 = pt->mat[nz_cols[0]];
2171 f12 = pt->mat[nz_cols[1]];
2172 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2173 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2178 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2181 chisq[3] = (pt->total * pow2 (pt_)
2182 / (f11 + f12) / (f21 + f22)
2183 / (f11 + f21) / (f12 + f22));
2191 if (f11 < 5. || f12 < 5. || f21 < 5. || f22 < 5.)
2192 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2195 /* Calculate Mantel-Haenszel. */
2196 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2198 double r, ase_0, ase_1;
2199 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2201 chisq[4] = (pt->total - 1.) * r * r;
2206 /* Calculate the value of Pearson's r. r is stored into R, ase_1 into
2207 ASE_1, and ase_0 into ASE_0. The row and column values must be
2208 passed in PT and Y. */
2210 calc_r (struct pivot_table *pt,
2211 double *PT, double *Y, double *r, double *ase_0, double *ase_1)
2213 double SX, SY, S, T;
2215 double sum_XYf, sum_X2Y2f;
2216 double sum_Xr, sum_X2r;
2217 double sum_Yc, sum_Y2c;
2220 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2221 for (j = 0; j < pt->n_cols; j++)
2223 double fij = pt->mat[j + i * pt->n_cols];
2224 double product = PT[i] * Y[j];
2225 double temp = fij * product;
2227 sum_X2Y2f += temp * product;
2230 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2232 sum_Xr += PT[i] * pt->row_tot[i];
2233 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2235 Xbar = sum_Xr / pt->total;
2237 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2239 sum_Yc += Y[i] * pt->col_tot[i];
2240 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2242 Ybar = sum_Yc / pt->total;
2244 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2245 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2246 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2249 *ase_0 = sqrt ((sum_X2Y2f - pow2 (sum_XYf) / pt->total) / (sum_X2r * sum_Y2c));
2254 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2255 for (j = 0; j < pt->n_cols; j++)
2257 double Xresid, Yresid;
2260 Xresid = PT[i] - Xbar;
2261 Yresid = Y[j] - Ybar;
2262 temp = (T * Xresid * Yresid
2264 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2265 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2270 *ase_1 = sqrt (s) / (T * T);
2274 /* Calculate symmetric statistics and their asymptotic standard
2275 errors. Returns 0 if none could be calculated. */
2277 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2278 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2279 double t[N_SYMMETRIC],
2280 double somers_d_v[3], double somers_d_ase[3],
2281 double somers_d_t[3])
2285 q = MIN (pt->ns_rows, pt->ns_cols);
2289 for (i = 0; i < N_SYMMETRIC; i++)
2290 v[i] = ase[i] = t[i] = SYSMIS;
2292 /* Phi, Cramer's V, contingency coefficient. */
2293 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2295 double Xp = 0.; /* Pearson chi-square. */
2298 for (r = 0; r < pt->n_rows; r++)
2299 for (c = 0; c < pt->n_cols; c++)
2301 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2302 const double freq = pt->mat[pt->n_cols * r + c];
2303 const double residual = freq - expected;
2305 Xp += residual * residual / expected;
2308 if (proc->statistics & (1u << CRS_ST_PHI))
2310 v[0] = sqrt (Xp / pt->total);
2311 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2313 if (proc->statistics & (1u << CRS_ST_CC))
2314 v[2] = sqrt (Xp / (Xp + pt->total));
2317 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2318 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2323 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2327 Dr = Dc = pow2 (pt->total);
2328 for (r = 0; r < pt->n_rows; r++)
2329 Dr -= pow2 (pt->row_tot[r]);
2330 for (c = 0; c < pt->n_cols; c++)
2331 Dc -= pow2 (pt->col_tot[c]);
2333 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2334 for (c = 0; c < pt->n_cols; c++)
2338 for (r = 0; r < pt->n_rows; r++)
2339 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2348 for (i = 0; i < pt->n_rows; i++)
2352 for (j = 1; j < pt->n_cols; j++)
2353 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2356 for (j = 1; j < pt->n_cols; j++)
2357 Dij += cum[j + (i - 1) * pt->n_cols];
2361 double fij = pt->mat[j + i * pt->n_cols];
2365 if (++j == pt->n_cols)
2367 assert (j < pt->n_cols);
2369 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2370 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2374 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2375 Dij -= cum[j + (i - 1) * pt->n_cols];
2381 if (proc->statistics & (1u << CRS_ST_BTAU))
2382 v[3] = (P - Q) / sqrt (Dr * Dc);
2383 if (proc->statistics & (1u << CRS_ST_CTAU))
2384 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2385 if (proc->statistics & (1u << CRS_ST_GAMMA))
2386 v[5] = (P - Q) / (P + Q);
2388 /* ASE for tau-b, tau-c, gamma. Calculations could be
2389 eliminated here, at expense of memory. */
2394 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2395 for (i = 0; i < pt->n_rows; i++)
2399 for (j = 1; j < pt->n_cols; j++)
2400 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2403 for (j = 1; j < pt->n_cols; j++)
2404 Dij += cum[j + (i - 1) * pt->n_cols];
2408 double fij = pt->mat[j + i * pt->n_cols];
2410 if (proc->statistics & (1u << CRS_ST_BTAU))
2412 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2413 + v[3] * (pt->row_tot[i] * Dc
2414 + pt->col_tot[j] * Dr));
2415 btau_cum += fij * temp * temp;
2419 const double temp = Cij - Dij;
2420 ctau_cum += fij * temp * temp;
2423 if (proc->statistics & (1u << CRS_ST_GAMMA))
2425 const double temp = Q * Cij - P * Dij;
2426 gamma_cum += fij * temp * temp;
2429 if (proc->statistics & (1u << CRS_ST_D))
2431 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2432 - (P - Q) * (pt->total - pt->row_tot[i]));
2433 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2434 - (Q - P) * (pt->total - pt->col_tot[j]));
2437 if (++j == pt->n_cols)
2439 assert (j < pt->n_cols);
2441 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2442 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2446 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2447 Dij -= cum[j + (i - 1) * pt->n_cols];
2453 btau_var = ((btau_cum
2454 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2456 if (proc->statistics & (1u << CRS_ST_BTAU))
2458 ase[3] = sqrt (btau_var);
2459 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2462 if (proc->statistics & (1u << CRS_ST_CTAU))
2464 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2465 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2466 t[4] = v[4] / ase[4];
2468 if (proc->statistics & (1u << CRS_ST_GAMMA))
2470 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2471 t[5] = v[5] / (2. / (P + Q)
2472 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2474 if (proc->statistics & (1u << CRS_ST_D))
2476 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2477 somers_d_ase[0] = 2. * btau_var / (Dr + Dc) * sqrt (Dr * Dc);
2478 somers_d_t[0] = (somers_d_v[0]
2480 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2481 somers_d_v[1] = (P - Q) / Dc;
2482 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2483 somers_d_t[1] = (somers_d_v[1]
2485 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2486 somers_d_v[2] = (P - Q) / Dr;
2487 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2488 somers_d_t[2] = (somers_d_v[2]
2490 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2496 /* Spearman correlation, Pearson's r. */
2497 if (proc->statistics & (1u << CRS_ST_CORR))
2499 double *R = xmalloc (sizeof *R * pt->n_rows);
2500 double *C = xmalloc (sizeof *C * pt->n_cols);
2503 double y, t, c = 0., s = 0.;
2508 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2509 y = pt->row_tot[i] - c;
2513 if (++i == pt->n_rows)
2515 assert (i < pt->n_rows);
2520 double y, t, c = 0., s = 0.;
2525 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2526 y = pt->col_tot[j] - c;
2530 if (++j == pt->n_cols)
2532 assert (j < pt->n_cols);
2536 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2542 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2546 /* Cohen's kappa. */
2547 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2549 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2552 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2553 i < pt->ns_rows; i++, j++)
2557 while (pt->col_tot[j] == 0.)
2560 prod = pt->row_tot[i] * pt->col_tot[j];
2561 sum = pt->row_tot[i] + pt->col_tot[j];
2563 sum_fii += pt->mat[j + i * pt->n_cols];
2565 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2566 sum_riciri_ci += prod * sum;
2568 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2569 for (j = 0; j < pt->ns_cols; j++)
2571 double sum = pt->row_tot[i] + pt->col_tot[j];
2572 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2575 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2577 ase[8] = sqrt ((pow2 (pt->total) * sum_rici
2578 + sum_rici * sum_rici
2579 - pt->total * sum_riciri_ci)
2580 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2582 t[8] = v[8] / sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2583 / pow2 (pow2 (pt->total) - sum_rici))
2584 + ((2. * (pt->total - sum_fii)
2585 * (2. * sum_fii * sum_rici
2586 - pt->total * sum_fiiri_ci))
2587 / cube (pow2 (pt->total) - sum_rici))
2588 + (pow2 (pt->total - sum_fii)
2589 * (pt->total * sum_fijri_ci2 - 4.
2590 * sum_rici * sum_rici)
2591 / pow4 (pow2 (pt->total) - sum_rici))));
2593 t[8] = v[8] / ase[8];
2600 /* Calculate risk estimate. */
2602 calc_risk (struct pivot_table *pt,
2603 double *value, double *upper, double *lower, union value *c)
2605 double f11, f12, f21, f22;
2611 for (i = 0; i < 3; i++)
2612 value[i] = upper[i] = lower[i] = SYSMIS;
2615 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2622 for (i = j = 0; i < pt->n_cols; i++)
2623 if (pt->col_tot[i] != 0.)
2632 f11 = pt->mat[nz_cols[0]];
2633 f12 = pt->mat[nz_cols[1]];
2634 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2635 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2637 c[0] = pt->cols[nz_cols[0]];
2638 c[1] = pt->cols[nz_cols[1]];
2641 value[0] = (f11 * f22) / (f12 * f21);
2642 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2643 lower[0] = value[0] * exp (-1.960 * v);
2644 upper[0] = value[0] * exp (1.960 * v);
2646 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2647 v = sqrt ((f12 / (f11 * (f11 + f12)))
2648 + (f22 / (f21 * (f21 + f22))));
2649 lower[1] = value[1] * exp (-1.960 * v);
2650 upper[1] = value[1] * exp (1.960 * v);
2652 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2653 v = sqrt ((f11 / (f12 * (f11 + f12)))
2654 + (f21 / (f22 * (f21 + f22))));
2655 lower[2] = value[2] * exp (-1.960 * v);
2656 upper[2] = value[2] * exp (1.960 * v);
2661 /* Calculate directional measures. */
2663 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2664 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2665 double t[N_DIRECTIONAL])
2670 for (i = 0; i < N_DIRECTIONAL; i++)
2671 v[i] = ase[i] = t[i] = SYSMIS;
2675 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2677 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2678 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2679 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2680 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2681 double sum_fim, sum_fmj;
2683 int rm_index, cm_index;
2686 /* Find maximum for each row and their sum. */
2687 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2689 double max = pt->mat[i * pt->n_cols];
2692 for (j = 1; j < pt->n_cols; j++)
2693 if (pt->mat[j + i * pt->n_cols] > max)
2695 max = pt->mat[j + i * pt->n_cols];
2699 sum_fim += fim[i] = max;
2700 fim_index[i] = index;
2703 /* Find maximum for each column. */
2704 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2706 double max = pt->mat[j];
2709 for (i = 1; i < pt->n_rows; i++)
2710 if (pt->mat[j + i * pt->n_cols] > max)
2712 max = pt->mat[j + i * pt->n_cols];
2716 sum_fmj += fmj[j] = max;
2717 fmj_index[j] = index;
2720 /* Find maximum row total. */
2721 rm = pt->row_tot[0];
2723 for (i = 1; i < pt->n_rows; i++)
2724 if (pt->row_tot[i] > rm)
2726 rm = pt->row_tot[i];
2730 /* Find maximum column total. */
2731 cm = pt->col_tot[0];
2733 for (j = 1; j < pt->n_cols; j++)
2734 if (pt->col_tot[j] > cm)
2736 cm = pt->col_tot[j];
2740 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2741 v[1] = (sum_fmj - rm) / (pt->total - rm);
2742 v[2] = (sum_fim - cm) / (pt->total - cm);
2744 /* ASE1 for Y given PT. */
2748 for (accum = 0., i = 0; i < pt->n_rows; i++)
2749 for (j = 0; j < pt->n_cols; j++)
2751 const int deltaj = j == cm_index;
2752 accum += (pt->mat[j + i * pt->n_cols]
2753 * pow2 ((j == fim_index[i])
2758 ase[2] = sqrt (accum - pt->total * v[0]) / (pt->total - cm);
2761 /* ASE0 for Y given PT. */
2765 for (accum = 0., i = 0; i < pt->n_rows; i++)
2766 if (cm_index != fim_index[i])
2767 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2768 + pt->mat[i * pt->n_cols + cm_index]);
2769 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2772 /* ASE1 for PT given Y. */
2776 for (accum = 0., i = 0; i < pt->n_rows; i++)
2777 for (j = 0; j < pt->n_cols; j++)
2779 const int deltaj = i == rm_index;
2780 accum += (pt->mat[j + i * pt->n_cols]
2781 * pow2 ((i == fmj_index[j])
2786 ase[1] = sqrt (accum - pt->total * v[0]) / (pt->total - rm);
2789 /* ASE0 for PT given Y. */
2793 for (accum = 0., j = 0; j < pt->n_cols; j++)
2794 if (rm_index != fmj_index[j])
2795 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2796 + pt->mat[j + pt->n_cols * rm_index]);
2797 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2800 /* Symmetric ASE0 and ASE1. */
2805 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2806 for (j = 0; j < pt->n_cols; j++)
2808 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2809 int temp1 = (i == rm_index) + (j == cm_index);
2810 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2811 accum1 += (pt->mat[j + i * pt->n_cols]
2812 * pow2 (temp0 + (v[0] - 1.) * temp1));
2814 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2815 t[0] = v[0] / (sqrt (accum0 - pow2 ((sum_fim + sum_fmj - cm - rm) / pt->total))
2816 / (2. * pt->total - rm - cm));
2825 double sum_fij2_ri, sum_fij2_ci;
2826 double sum_ri2, sum_cj2;
2828 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2829 for (j = 0; j < pt->n_cols; j++)
2831 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2832 sum_fij2_ri += temp / pt->row_tot[i];
2833 sum_fij2_ci += temp / pt->col_tot[j];
2836 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2837 sum_ri2 += pow2 (pt->row_tot[i]);
2839 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2840 sum_cj2 += pow2 (pt->col_tot[j]);
2842 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2843 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2847 if (proc->statistics & (1u << CRS_ST_UC))
2849 double UX, UY, UXY, P;
2850 double ase1_yx, ase1_xy, ase1_sym;
2853 for (UX = 0., i = 0; i < pt->n_rows; i++)
2854 if (pt->row_tot[i] > 0.)
2855 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2857 for (UY = 0., j = 0; j < pt->n_cols; j++)
2858 if (pt->col_tot[j] > 0.)
2859 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2861 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2862 for (j = 0; j < pt->n_cols; j++)
2864 double entry = pt->mat[j + i * pt->n_cols];
2869 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2870 UXY -= entry / pt->total * log (entry / pt->total);
2873 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2874 for (j = 0; j < pt->n_cols; j++)
2876 double entry = pt->mat[j + i * pt->n_cols];
2881 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2882 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2883 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2884 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2885 ase1_sym += entry * pow2 ((UXY
2886 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2887 - (UX + UY) * log (entry / pt->total));
2890 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2891 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2892 t[5] = v[5] / ((2. / (pt->total * (UX + UY)))
2893 * sqrt (P - pow2 (UX + UY - UXY) / pt->total));
2895 v[6] = (UX + UY - UXY) / UX;
2896 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2897 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2899 v[7] = (UX + UY - UXY) / UY;
2900 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2901 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2905 if (proc->statistics & (1u << CRS_ST_D))
2907 double v_dummy[N_SYMMETRIC];
2908 double ase_dummy[N_SYMMETRIC];
2909 double t_dummy[N_SYMMETRIC];
2910 double somers_d_v[3];
2911 double somers_d_ase[3];
2912 double somers_d_t[3];
2914 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2915 somers_d_v, somers_d_ase, somers_d_t))
2918 for (i = 0; i < 3; i++)
2920 v[8 + i] = somers_d_v[i];
2921 ase[8 + i] = somers_d_ase[i];
2922 t[8 + i] = somers_d_t[i];
2928 if (proc->statistics & (1u << CRS_ST_ETA))
2931 double sum_Xr, sum_X2r;
2935 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2937 sum_Xr += pt->rows[i].f * pt->row_tot[i];
2938 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
2940 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2942 for (SXW = 0., j = 0; j < pt->n_cols; j++)
2946 for (cum = 0., i = 0; i < pt->n_rows; i++)
2948 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
2949 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
2952 SXW -= cum * cum / pt->col_tot[j];
2954 v[11] = sqrt (1. - SXW / SX);
2958 double sum_Yc, sum_Y2c;
2962 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2964 sum_Yc += pt->cols[i].f * pt->col_tot[i];
2965 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
2967 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
2969 for (SYW = 0., i = 0; i < pt->n_rows; i++)
2973 for (cum = 0., j = 0; j < pt->n_cols; j++)
2975 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
2976 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
2979 SYW -= cum * cum / pt->row_tot[i];
2981 v[12] = sqrt (1. - SYW / SY);