1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2006, 2009, 2010, 2011, 2012, 2013, 2014 Free Software Foundation, Inc.
4 This program is free software: you can redistribute it and/or modify
5 it under the terms of the GNU General Public License as published by
6 the Free Software Foundation, either version 3 of the License, or
7 (at your option) any later version.
9 This program is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 GNU General Public License for more details.
14 You should have received a copy of the GNU General Public License
15 along with this program. If not, see <http://www.gnu.org/licenses/>. */
19 - How to calculate significance of symmetric and directional measures?
20 - How to calculate ASE for asymmetric lambda?
21 - ASE of Goodman and Kruskal's tau is not calculated.
22 - ASE of symmetric somers' d is wrong.
23 - Approx. T of uncertainty coefficient is wrong.
31 #include <gsl/gsl_cdf.h>
35 #include "data/case.h"
36 #include "data/casegrouper.h"
37 #include "data/casereader.h"
38 #include "data/data-out.h"
39 #include "data/dataset.h"
40 #include "data/dictionary.h"
41 #include "data/format.h"
42 #include "data/value-labels.h"
43 #include "data/variable.h"
44 #include "language/command.h"
45 #include "language/dictionary/split-file.h"
46 #include "language/lexer/lexer.h"
47 #include "language/lexer/variable-parser.h"
48 #include "libpspp/array.h"
49 #include "libpspp/assertion.h"
50 #include "libpspp/compiler.h"
51 #include "libpspp/hash-functions.h"
52 #include "libpspp/hmap.h"
53 #include "libpspp/hmapx.h"
54 #include "libpspp/message.h"
55 #include "libpspp/misc.h"
56 #include "libpspp/pool.h"
57 #include "libpspp/str.h"
58 #include "output/tab.h"
60 #include "gl/minmax.h"
61 #include "gl/xalloc.h"
65 #define _(msgid) gettext (msgid)
66 #define N_(msgid) msgid
74 missing=miss:!table/include/report;
75 +write[wr_]=none,cells,all;
76 +format=val:!avalue/dvalue,
78 tabl:!tables/notables,
81 +cells[cl_]=count,expected,row,column,total,residual,sresidual,
83 +statistics[st_]=chisq,phi,cc,lambda,uc,none,btau,ctau,risk,gamma,d,
89 /* Number of chi-square statistics. */
92 /* Number of symmetric statistics. */
95 /* Number of directional statistics. */
96 #define N_DIRECTIONAL 13
98 /* A single table entry for general mode. */
101 struct hmap_node node; /* Entry in hash table. */
102 double freq; /* Frequency count. */
103 union value values[1]; /* Values. */
107 table_entry_size (size_t n_values)
109 return (offsetof (struct table_entry, values)
110 + n_values * sizeof (union value));
113 /* Indexes into the 'vars' member of struct pivot_table and
114 struct crosstab member. */
117 ROW_VAR = 0, /* Row variable. */
118 COL_VAR = 1 /* Column variable. */
119 /* Higher indexes cause multiple tables to be output. */
122 /* A crosstabulation of 2 or more variables. */
125 struct crosstabs_proc *proc;
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 struct hmap_node hmap_node; /* In struct crosstabs_proc var_ranges map. */
166 const struct variable *var; /* The variable. */
167 int min; /* Minimum value. */
168 int max; /* Maximum value + 1. */
169 int count; /* max - min. */
172 struct crosstabs_proc
174 const struct dictionary *dict;
175 enum { INTEGER, GENERAL } mode;
176 enum mv_class exclude;
179 struct fmt_spec weight_format;
181 /* Variables specifies on VARIABLES. */
182 const struct variable **variables;
184 struct hmap var_ranges;
187 struct pivot_table *pivots;
191 int n_cells; /* Number of cells requested. */
192 unsigned int cells; /* Bit k is 1 if cell k is requested. */
193 int a_cells[CRS_CL_count]; /* 0...n_cells-1 are the requested cells. */
196 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
198 bool descending; /* True if descending sort order is requested. */
201 const struct var_range *get_var_range (const struct crosstabs_proc *,
202 const struct variable *);
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 var_range *range, *next_range;
219 struct crosstabs_proc proc;
220 struct casegrouper *grouper;
221 struct casereader *input, *group;
222 struct cmd_crosstabs cmd;
223 struct pivot_table *pt;
228 proc.dict = dataset_dict (ds);
229 proc.bad_warn = true;
230 proc.variables = NULL;
231 proc.n_variables = 0;
232 hmap_init (&proc.var_ranges);
235 proc.descending = false;
236 proc.weight_format = wv ? *var_get_print_format (wv) : F_8_0;
238 if (!parse_crosstabs (lexer, ds, &cmd, &proc))
240 result = CMD_FAILURE;
244 proc.mode = proc.n_variables ? INTEGER : GENERAL;
247 proc.descending = cmd.val == CRS_DVALUE;
251 proc.cells = 1u << CRS_CL_COUNT;
252 else if (cmd.a_cells[CRS_CL_ALL])
253 proc.cells = UINT_MAX;
257 for (i = 0; i < CRS_CL_count; i++)
259 proc.cells |= 1u << i;
261 proc.cells = ((1u << CRS_CL_COUNT)
263 | (1u << CRS_CL_COLUMN)
264 | (1u << CRS_CL_TOTAL));
266 proc.cells &= ((1u << CRS_CL_count) - 1);
267 proc.cells &= ~((1u << CRS_CL_NONE) | (1u << CRS_CL_ALL));
269 for (i = 0; i < CRS_CL_count; i++)
270 if (proc.cells & (1u << i))
271 proc.a_cells[proc.n_cells++] = i;
274 if (cmd.a_statistics[CRS_ST_ALL])
275 proc.statistics = UINT_MAX;
276 else if (cmd.sbc_statistics)
281 for (i = 0; i < CRS_ST_count; i++)
282 if (cmd.a_statistics[i])
283 proc.statistics |= 1u << i;
284 if (proc.statistics == 0)
285 proc.statistics |= 1u << CRS_ST_CHISQ;
291 proc.exclude = (cmd.miss == CRS_TABLE ? MV_ANY
292 : cmd.miss == CRS_INCLUDE ? MV_SYSTEM
294 if (proc.mode == GENERAL && proc.exclude == MV_NEVER)
296 msg (SE, _("Missing mode %s not allowed in general mode. "
297 "Assuming %s."), "REPORT", "MISSING=TABLE");
298 proc.exclude = MV_ANY;
302 proc.pivot = cmd.pivot == CRS_PIVOT;
304 input = casereader_create_filter_weight (proc_open (ds), dataset_dict (ds),
306 grouper = casegrouper_create_splits (input, dataset_dict (ds));
307 while (casegrouper_get_next_group (grouper, &group))
311 /* Output SPLIT FILE variables. */
312 c = casereader_peek (group, 0);
315 output_split_file_values (ds, c);
319 /* Initialize hash tables. */
320 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
321 hmap_init (&pt->data);
324 for (; (c = casereader_read (group)) != NULL; case_unref (c))
325 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
327 double weight = dict_get_case_weight (dataset_dict (ds), c,
329 if (should_tabulate_case (pt, c, proc.exclude))
331 if (proc.mode == GENERAL)
332 tabulate_general_case (pt, c, weight);
334 tabulate_integer_case (pt, c, weight);
337 pt->missing += weight;
339 casereader_destroy (group);
344 ok = casegrouper_destroy (grouper);
345 ok = proc_commit (ds) && ok;
347 result = ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
350 free (proc.variables);
351 HMAP_FOR_EACH_SAFE (range, next_range, struct var_range, hmap_node,
354 hmap_delete (&proc.var_ranges, &range->hmap_node);
357 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
360 free (pt->const_vars);
361 /* We must not call value_destroy on const_values because
362 it is a wild pointer; it never pointed to anything owned
365 The rest of the data was allocated and destroyed at a
366 lower level already. */
373 /* Parses the TABLES subcommand. */
375 crs_custom_tables (struct lexer *lexer, struct dataset *ds,
376 struct cmd_crosstabs *cmd UNUSED, void *proc_)
378 struct crosstabs_proc *proc = proc_;
379 struct const_var_set *var_set;
381 const struct variable ***by = NULL;
383 size_t *by_nvar = NULL;
388 /* Ensure that this is a TABLES subcommand. */
389 if (!lex_match_id (lexer, "TABLES")
390 && (lex_token (lexer) != T_ID ||
391 dict_lookup_var (dataset_dict (ds), lex_tokcstr (lexer)) == NULL)
392 && lex_token (lexer) != T_ALL)
394 lex_match (lexer, T_EQUALS);
396 if (proc->variables != NULL)
397 var_set = const_var_set_create_from_array (proc->variables,
400 var_set = const_var_set_create_from_dict (dataset_dict (ds));
401 assert (var_set != NULL);
405 by = xnrealloc (by, n_by + 1, sizeof *by);
406 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
407 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
408 PV_NO_DUPLICATE | PV_NO_SCRATCH))
410 if (xalloc_oversized (nx, by_nvar[n_by]))
412 msg (SE, _("Too many cross-tabulation variables or dimensions."));
418 if (!lex_match (lexer, T_BY))
422 lex_force_match (lexer, T_BY);
430 by_iter = xcalloc (n_by, sizeof *by_iter);
431 proc->pivots = xnrealloc (proc->pivots,
432 proc->n_pivots + nx, sizeof *proc->pivots);
433 for (i = 0; i < nx; i++)
435 struct pivot_table *pt = &proc->pivots[proc->n_pivots++];
439 pt->weight_format = proc->weight_format;
442 pt->vars = xmalloc (n_by * sizeof *pt->vars);
444 pt->const_vars = NULL;
445 pt->const_values = NULL;
447 for (j = 0; j < n_by; j++)
448 pt->vars[j] = by[j][by_iter[j]];
450 for (j = n_by - 1; j >= 0; j--)
452 if (++by_iter[j] < by_nvar[j])
461 /* All return paths lead here. */
462 for (i = 0; i < n_by; i++)
467 const_var_set_destroy (var_set);
472 /* Parses the VARIABLES subcommand. */
474 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
475 struct cmd_crosstabs *cmd UNUSED, void *proc_)
477 struct crosstabs_proc *proc = proc_;
480 msg (SE, _("%s must be specified before %s."), "VARIABLES", "TABLES");
484 lex_match (lexer, T_EQUALS);
488 size_t orig_nv = proc->n_variables;
493 if (!parse_variables_const (lexer, dataset_dict (ds),
494 &proc->variables, &proc->n_variables,
495 (PV_APPEND | PV_NUMERIC
496 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
499 if (!lex_force_match (lexer, T_LPAREN))
502 if (!lex_force_int (lexer))
504 min = lex_integer (lexer);
507 lex_match (lexer, T_COMMA);
509 if (!lex_force_int (lexer))
511 max = lex_integer (lexer);
514 msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
520 if (!lex_force_match (lexer, T_RPAREN))
523 for (i = orig_nv; i < proc->n_variables; i++)
525 const struct variable *var = proc->variables[i];
526 struct var_range *vr = xmalloc (sizeof *vr);
531 vr->count = max - min + 1;
532 hmap_insert (&proc->var_ranges, &vr->hmap_node,
533 hash_pointer (var, 0));
536 if (lex_token (lexer) == T_SLASH)
543 free (proc->variables);
544 proc->variables = NULL;
545 proc->n_variables = 0;
549 /* Data file processing. */
551 const struct var_range *
552 get_var_range (const struct crosstabs_proc *proc, const struct variable *var)
554 if (!hmap_is_empty (&proc->var_ranges))
556 const struct var_range *range;
558 HMAP_FOR_EACH_IN_BUCKET (range, struct var_range, hmap_node,
559 hash_pointer (var, 0), &proc->var_ranges)
560 if (range->var == var)
568 should_tabulate_case (const struct pivot_table *pt, const struct ccase *c,
569 enum mv_class exclude)
572 for (j = 0; j < pt->n_vars; j++)
574 const struct variable *var = pt->vars[j];
575 const struct var_range *range = get_var_range (pt->proc, var);
577 if (var_is_value_missing (var, case_data (c, var), exclude))
582 double num = case_num (c, var);
583 if (num < range->min || num > range->max)
591 tabulate_integer_case (struct pivot_table *pt, const struct ccase *c,
594 struct table_entry *te;
599 for (j = 0; j < pt->n_vars; j++)
601 /* Throw away fractional parts of values. */
602 hash = hash_int (case_num (c, pt->vars[j]), hash);
605 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
607 for (j = 0; j < pt->n_vars; j++)
608 if ((int) case_num (c, pt->vars[j]) != (int) te->values[j].f)
611 /* Found an existing entry. */
618 /* No existing entry. Create a new one. */
619 te = xmalloc (table_entry_size (pt->n_vars));
621 for (j = 0; j < pt->n_vars; j++)
622 te->values[j].f = (int) case_num (c, pt->vars[j]);
623 hmap_insert (&pt->data, &te->node, hash);
627 tabulate_general_case (struct pivot_table *pt, const struct ccase *c,
630 struct table_entry *te;
635 for (j = 0; j < pt->n_vars; j++)
637 const struct variable *var = pt->vars[j];
638 hash = value_hash (case_data (c, var), var_get_width (var), hash);
641 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
643 for (j = 0; j < pt->n_vars; j++)
645 const struct variable *var = pt->vars[j];
646 if (!value_equal (case_data (c, var), &te->values[j],
647 var_get_width (var)))
651 /* Found an existing entry. */
658 /* No existing entry. Create a new one. */
659 te = xmalloc (table_entry_size (pt->n_vars));
661 for (j = 0; j < pt->n_vars; j++)
663 const struct variable *var = pt->vars[j];
664 value_clone (&te->values[j], case_data (c, var), var_get_width (var));
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 int compare_table_entry_3way_inv (const void *ap_, const void *bp_,
680 static void enum_var_values (const struct pivot_table *, int var_idx,
681 union value **valuesp, int *n_values, bool descending);
682 static void output_pivot_table (struct crosstabs_proc *,
683 struct pivot_table *);
684 static void make_pivot_table_subset (struct pivot_table *pt,
685 size_t row0, size_t row1,
686 struct pivot_table *subset);
687 static void make_summary_table (struct crosstabs_proc *);
688 static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
691 postcalc (struct crosstabs_proc *proc)
693 struct pivot_table *pt;
695 /* Convert hash tables into sorted arrays of entries. */
696 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
698 struct table_entry *e;
701 pt->n_entries = hmap_count (&pt->data);
702 pt->entries = xnmalloc (pt->n_entries, sizeof *pt->entries);
704 HMAP_FOR_EACH (e, struct table_entry, node, &pt->data)
705 pt->entries[i++] = e;
706 hmap_destroy (&pt->data);
708 sort (pt->entries, pt->n_entries, sizeof *pt->entries,
709 proc->descending ? compare_table_entry_3way_inv : compare_table_entry_3way,
713 make_summary_table (proc);
715 /* Output each pivot table. */
716 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
718 if (proc->pivot || pt->n_vars == 2)
719 output_pivot_table (proc, pt);
722 size_t row0 = 0, row1 = 0;
723 while (find_crosstab (pt, &row0, &row1))
725 struct pivot_table subset;
726 make_pivot_table_subset (pt, row0, row1, &subset);
727 output_pivot_table (proc, &subset);
732 /* Free output and prepare for next split file. */
733 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
739 /* Free the members that were allocated in this function(and the values
740 owned by the entries.
742 The other pointer members are either both allocated and destroyed at a
743 lower level (in output_pivot_table), or both allocated and destroyed
744 at a higher level (in crs_custom_tables and free_proc,
746 for (i = 0; i < pt->n_vars; i++)
748 int width = var_get_width (pt->vars[i]);
749 if (value_needs_init (width))
753 for (j = 0; j < pt->n_entries; j++)
754 value_destroy (&pt->entries[j]->values[i], width);
758 for (i = 0; i < pt->n_entries; i++)
759 free (pt->entries[i]);
765 make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
766 struct pivot_table *subset)
771 assert (pt->n_consts == 0);
772 subset->missing = pt->missing;
774 subset->vars = pt->vars;
775 subset->n_consts = pt->n_vars - 2;
776 subset->const_vars = pt->vars + 2;
777 subset->const_values = &pt->entries[row0]->values[2];
779 subset->entries = &pt->entries[row0];
780 subset->n_entries = row1 - row0;
784 compare_table_entry_var_3way (const struct table_entry *a,
785 const struct table_entry *b,
786 const struct pivot_table *pt,
789 return value_compare_3way (&a->values[idx], &b->values[idx],
790 var_get_width (pt->vars[idx]));
794 compare_table_entry_vars_3way (const struct table_entry *a,
795 const struct table_entry *b,
796 const struct pivot_table *pt,
801 for (i = idx1 - 1; i >= idx0; i--)
803 int cmp = compare_table_entry_var_3way (a, b, pt, i);
810 /* Compare the struct table_entry at *AP to the one at *BP and
811 return a strcmp()-type result. */
813 compare_table_entry_3way (const void *ap_, const void *bp_, const void *pt_)
815 const struct table_entry *const *ap = ap_;
816 const struct table_entry *const *bp = bp_;
817 const struct table_entry *a = *ap;
818 const struct table_entry *b = *bp;
819 const struct pivot_table *pt = pt_;
822 cmp = compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars);
826 cmp = compare_table_entry_var_3way (a, b, pt, ROW_VAR);
830 return compare_table_entry_var_3way (a, b, pt, COL_VAR);
833 /* Inverted version of compare_table_entry_3way */
835 compare_table_entry_3way_inv (const void *ap_, const void *bp_, const void *pt_)
837 return -compare_table_entry_3way (ap_, bp_, pt_);
841 find_first_difference (const struct pivot_table *pt, size_t row)
844 return pt->n_vars - 1;
847 const struct table_entry *a = pt->entries[row];
848 const struct table_entry *b = pt->entries[row - 1];
851 for (col = pt->n_vars - 1; col >= 0; col--)
852 if (compare_table_entry_var_3way (a, b, pt, col))
858 /* Output a table summarizing the cases processed. */
860 make_summary_table (struct crosstabs_proc *proc)
862 struct tab_table *summary;
863 struct pivot_table *pt;
867 summary = tab_create (7, 3 + proc->n_pivots);
868 tab_set_format (summary, RC_WEIGHT, &proc->weight_format);
869 tab_title (summary, _("Summary."));
870 tab_headers (summary, 1, 0, 3, 0);
871 tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
872 tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
873 tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
874 tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
875 tab_hline (summary, TAL_1, 1, 6, 1);
876 tab_hline (summary, TAL_1, 1, 6, 2);
877 tab_vline (summary, TAL_1, 3, 1, 1);
878 tab_vline (summary, TAL_1, 5, 1, 1);
879 for (i = 0; i < 3; i++)
881 tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
882 tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
884 tab_offset (summary, 0, 3);
886 ds_init_empty (&name);
887 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
893 tab_hline (summary, TAL_1, 0, 6, 0);
896 for (i = 0; i < pt->n_vars; i++)
899 ds_put_cstr (&name, " * ");
900 ds_put_cstr (&name, var_to_string (pt->vars[i]));
902 tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
905 for (i = 0; i < pt->n_entries; i++)
906 valid += pt->entries[i]->freq;
911 for (i = 0; i < 3; i++)
913 tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i], NULL, RC_WEIGHT);
914 tab_text_format (summary, i * 2 + 2, 0, TAB_RIGHT, "%.1f%%",
918 tab_next_row (summary);
922 submit (NULL, summary);
927 static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
928 struct pivot_table *);
929 static struct tab_table *create_chisq_table (struct crosstabs_proc *proc, struct pivot_table *);
930 static struct tab_table *create_sym_table (struct crosstabs_proc *proc, struct pivot_table *);
931 static struct tab_table *create_risk_table (struct crosstabs_proc *proc, struct pivot_table *);
932 static struct tab_table *create_direct_table (struct crosstabs_proc *proc, struct pivot_table *);
933 static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
934 struct tab_table *, int first_difference);
935 static void display_crosstabulation (struct crosstabs_proc *,
936 struct pivot_table *,
938 static void display_chisq (struct pivot_table *, struct tab_table *,
939 bool *showed_fisher);
940 static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
942 static void display_risk (struct pivot_table *, struct tab_table *);
943 static void display_directional (struct crosstabs_proc *, struct pivot_table *,
945 static void table_value_missing (struct crosstabs_proc *proc,
946 struct tab_table *table, int c, int r,
947 unsigned char opt, const union value *v,
948 const struct variable *var);
949 static void delete_missing (struct pivot_table *);
950 static void build_matrix (struct pivot_table *);
952 /* Output pivot table PT in the context of PROC. */
954 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
956 struct tab_table *table = NULL; /* Crosstabulation table. */
957 struct tab_table *chisq = NULL; /* Chi-square table. */
958 bool showed_fisher = false;
959 struct tab_table *sym = NULL; /* Symmetric measures table. */
960 struct tab_table *risk = NULL; /* Risk estimate table. */
961 struct tab_table *direct = NULL; /* Directional measures table. */
964 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols, proc->descending);
971 ds_init_cstr (&vars, var_to_string (pt->vars[0]));
972 for (i = 1; i < pt->n_vars; i++)
973 ds_put_format (&vars, " * %s", var_to_string (pt->vars[i]));
975 /* TRANSLATORS: The %s here describes a crosstabulation. It takes the
976 form "var1 * var2 * var3 * ...". */
977 msg (SW, _("Crosstabulation %s contained no non-missing cases."),
986 table = create_crosstab_table (proc, pt);
987 if (proc->statistics & (1u << CRS_ST_CHISQ))
988 chisq = create_chisq_table (proc, pt);
989 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
990 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
991 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
992 | (1u << CRS_ST_KAPPA)))
993 sym = create_sym_table (proc, pt);
994 if (proc->statistics & (1u << CRS_ST_RISK))
995 risk = create_risk_table (proc, pt);
996 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
997 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
998 direct = create_direct_table (proc, pt);
1001 while (find_crosstab (pt, &row0, &row1))
1003 struct pivot_table x;
1004 int first_difference;
1006 make_pivot_table_subset (pt, row0, row1, &x);
1008 /* Find all the row variable values. */
1009 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows, proc->descending);
1011 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
1014 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
1015 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
1016 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
1018 /* Allocate table space for the matrix. */
1020 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
1021 tab_realloc (table, -1,
1022 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
1023 tab_nr (table) * pt->n_entries / x.n_entries));
1027 /* Find the first variable that differs from the last subtable. */
1028 first_difference = find_first_difference (pt, row0);
1031 display_dimensions (proc, &x, table, first_difference);
1032 display_crosstabulation (proc, &x, table);
1035 if (proc->exclude == MV_NEVER)
1036 delete_missing (&x);
1040 display_dimensions (proc, &x, chisq, first_difference);
1041 display_chisq (&x, chisq, &showed_fisher);
1045 display_dimensions (proc, &x, sym, first_difference);
1046 display_symmetric (proc, &x, sym);
1050 display_dimensions (proc, &x, risk, first_difference);
1051 display_risk (&x, risk);
1055 display_dimensions (proc, &x, direct, first_difference);
1056 display_directional (proc, &x, direct);
1059 /* Free the parts of x that are not owned by pt. In
1060 particular we must not free x.cols, which is the same as
1061 pt->cols, which is freed at the end of this function. */
1069 submit (NULL, table);
1074 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
1080 submit (pt, direct);
1086 build_matrix (struct pivot_table *x)
1088 const int col_var_width = var_get_width (x->vars[COL_VAR]);
1089 const int row_var_width = var_get_width (x->vars[ROW_VAR]);
1092 struct table_entry **p;
1096 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1098 const struct table_entry *te = *p;
1100 while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
1102 for (; col < x->n_cols; col++)
1108 while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
1115 if (++col >= x->n_cols)
1121 while (mp < &x->mat[x->n_cols * x->n_rows])
1123 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1125 /* Column totals, row totals, ns_rows. */
1127 for (col = 0; col < x->n_cols; col++)
1128 x->col_tot[col] = 0.0;
1129 for (row = 0; row < x->n_rows; row++)
1130 x->row_tot[row] = 0.0;
1132 for (row = 0; row < x->n_rows; row++)
1134 bool row_is_empty = true;
1135 for (col = 0; col < x->n_cols; col++)
1139 row_is_empty = false;
1140 x->col_tot[col] += *mp;
1141 x->row_tot[row] += *mp;
1148 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1152 for (col = 0; col < x->n_cols; col++)
1153 for (row = 0; row < x->n_rows; row++)
1154 if (x->mat[col + row * x->n_cols] != 0.0)
1162 for (col = 0; col < x->n_cols; col++)
1163 x->total += x->col_tot[col];
1166 static struct tab_table *
1167 create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1174 static const struct tuple names[] =
1176 {CRS_CL_COUNT, N_("count")},
1177 {CRS_CL_ROW, N_("row %")},
1178 {CRS_CL_COLUMN, N_("column %")},
1179 {CRS_CL_TOTAL, N_("total %")},
1180 {CRS_CL_EXPECTED, N_("expected")},
1181 {CRS_CL_RESIDUAL, N_("residual")},
1182 {CRS_CL_SRESIDUAL, N_("std. resid.")},
1183 {CRS_CL_ASRESIDUAL, N_("adj. resid.")},
1185 const int n_names = sizeof names / sizeof *names;
1186 const struct tuple *t;
1188 struct tab_table *table;
1189 struct string title;
1190 struct pivot_table x;
1194 make_pivot_table_subset (pt, 0, 0, &x);
1196 table = tab_create (x.n_consts + 1 + x.n_cols + 1,
1197 (x.n_entries / x.n_cols) * 3 / 2 * proc->n_cells + 10);
1198 tab_headers (table, x.n_consts + 1, 0, 2, 0);
1199 tab_set_format (table, RC_WEIGHT, &proc->weight_format);
1201 /* First header line. */
1202 tab_joint_text (table, x.n_consts + 1, 0,
1203 (x.n_consts + 1) + (x.n_cols - 1), 0,
1204 TAB_CENTER | TAT_TITLE, var_to_string (x.vars[COL_VAR]));
1206 tab_hline (table, TAL_1, x.n_consts + 1,
1207 x.n_consts + 2 + x.n_cols - 2, 1);
1209 /* Second header line. */
1210 for (i = 2; i < x.n_consts + 2; i++)
1211 tab_joint_text (table, x.n_consts + 2 - i - 1, 0,
1212 x.n_consts + 2 - i - 1, 1,
1213 TAB_RIGHT | TAT_TITLE, var_to_string (x.vars[i]));
1214 tab_text (table, x.n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1215 var_to_string (x.vars[ROW_VAR]));
1216 for (i = 0; i < x.n_cols; i++)
1217 table_value_missing (proc, table, x.n_consts + 2 + i - 1, 1, TAB_RIGHT,
1218 &x.cols[i], x.vars[COL_VAR]);
1219 tab_text (table, x.n_consts + 2 + x.n_cols - 1, 1, TAB_CENTER, _("Total"));
1221 tab_hline (table, TAL_1, 0, x.n_consts + 2 + x.n_cols - 1, 2);
1222 tab_vline (table, TAL_1, x.n_consts + 2 + x.n_cols - 1, 0, 1);
1225 ds_init_empty (&title);
1226 for (i = 0; i < x.n_consts + 2; i++)
1229 ds_put_cstr (&title, " * ");
1230 ds_put_cstr (&title, var_to_string (x.vars[i]));
1232 for (i = 0; i < pt->n_consts; i++)
1234 const struct variable *var = pt->const_vars[i];
1237 ds_put_format (&title, ", %s=", var_to_string (var));
1239 /* Insert the formatted value of VAR without any leading spaces. */
1240 s = data_out (&pt->const_values[i], var_get_encoding (var),
1241 var_get_print_format (var));
1242 ds_put_cstr (&title, s + strspn (s, " "));
1246 ds_put_cstr (&title, " [");
1248 for (t = names; t < &names[n_names]; t++)
1249 if (proc->cells & (1u << t->value))
1252 ds_put_cstr (&title, ", ");
1253 ds_put_cstr (&title, gettext (t->name));
1255 ds_put_cstr (&title, "].");
1257 tab_title (table, "%s", ds_cstr (&title));
1258 ds_destroy (&title);
1260 tab_offset (table, 0, 2);
1264 static struct tab_table *
1265 create_chisq_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1267 struct tab_table *chisq;
1269 chisq = tab_create (6 + (pt->n_vars - 2),
1270 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10);
1271 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1272 tab_set_format (chisq, RC_WEIGHT, &proc->weight_format);
1274 tab_title (chisq, _("Chi-square tests."));
1276 tab_offset (chisq, pt->n_vars - 2, 0);
1277 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1278 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1279 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1280 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1281 _("Asymp. Sig. (2-tailed)"));
1282 tab_text_format (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1283 _("Exact Sig. (%d-tailed)"), 2);
1284 tab_text_format (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1285 _("Exact Sig. (%d-tailed)"), 1);
1286 tab_offset (chisq, 0, 1);
1291 /* Symmetric measures. */
1292 static struct tab_table *
1293 create_sym_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1295 struct tab_table *sym;
1297 sym = tab_create (6 + (pt->n_vars - 2),
1298 pt->n_entries / pt->n_cols * 7 + 10);
1300 tab_set_format (sym, RC_WEIGHT, &proc->weight_format);
1302 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1303 tab_title (sym, _("Symmetric measures."));
1305 tab_offset (sym, pt->n_vars - 2, 0);
1306 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1307 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1308 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1309 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1310 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1311 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1312 tab_offset (sym, 0, 1);
1317 /* Risk estimate. */
1318 static struct tab_table *
1319 create_risk_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1321 struct tab_table *risk;
1323 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10);
1324 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1325 tab_title (risk, _("Risk estimate."));
1326 tab_set_format (risk, RC_WEIGHT, &proc->weight_format);
1328 tab_offset (risk, pt->n_vars - 2, 0);
1329 tab_joint_text_format (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE,
1330 _("95%% Confidence Interval"));
1331 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1332 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1333 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1334 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1335 tab_hline (risk, TAL_1, 2, 3, 1);
1336 tab_vline (risk, TAL_1, 2, 0, 1);
1337 tab_offset (risk, 0, 2);
1342 /* Directional measures. */
1343 static struct tab_table *
1344 create_direct_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1346 struct tab_table *direct;
1348 direct = tab_create (7 + (pt->n_vars - 2),
1349 pt->n_entries / pt->n_cols * 7 + 10);
1350 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1351 tab_title (direct, _("Directional measures."));
1352 tab_set_format (direct, RC_WEIGHT, &proc->weight_format);
1354 tab_offset (direct, pt->n_vars - 2, 0);
1355 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1356 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1357 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1358 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1359 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1360 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1361 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1362 tab_offset (direct, 0, 1);
1368 /* Delete missing rows and columns for statistical analysis when
1371 delete_missing (struct pivot_table *pt)
1375 for (r = 0; r < pt->n_rows; r++)
1376 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1378 for (c = 0; c < pt->n_cols; c++)
1379 pt->mat[c + r * pt->n_cols] = 0.;
1384 for (c = 0; c < pt->n_cols; c++)
1385 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1387 for (r = 0; r < pt->n_rows; r++)
1388 pt->mat[c + r * pt->n_cols] = 0.;
1393 /* Prepare table T for submission, and submit it. */
1395 submit (struct pivot_table *pt, struct tab_table *t)
1402 tab_resize (t, -1, 0);
1403 if (tab_nr (t) == tab_t (t))
1405 table_unref (&t->table);
1408 tab_offset (t, 0, 0);
1410 for (i = 2; i < pt->n_vars; i++)
1411 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1412 var_to_string (pt->vars[i]));
1413 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1414 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1416 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1418 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1424 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1426 size_t row0 = *row1p;
1429 if (row0 >= pt->n_entries)
1432 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1434 struct table_entry *a = pt->entries[row0];
1435 struct table_entry *b = pt->entries[row1];
1436 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1444 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1445 result. WIDTH_ points to an int which is either 0 for a
1446 numeric value or a string width for a string value. */
1448 compare_value_3way (const void *a_, const void *b_, const void *width_)
1450 const union value *a = a_;
1451 const union value *b = b_;
1452 const int *width = width_;
1454 return value_compare_3way (a, b, *width);
1457 /* Inverted version of the above */
1459 compare_value_3way_inv (const void *a_, const void *b_, const void *width_)
1461 return -compare_value_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.
1471 The caller must eventually free *VALUES, but each pointer in *VALUES points
1472 to existing data not owned by *VALUES itself. */
1474 enum_var_values (const struct pivot_table *pt, int var_idx,
1475 union value **valuesp, int *n_values, bool descending)
1477 const struct variable *var = pt->vars[var_idx];
1478 const struct var_range *range = get_var_range (pt->proc, var);
1479 union value *values;
1484 values = *valuesp = xnmalloc (range->count, sizeof *values);
1485 *n_values = range->count;
1486 for (i = 0; i < range->count; i++)
1487 values[i].f = range->min + i;
1491 int width = var_get_width (var);
1492 struct hmapx_node *node;
1493 const union value *iter;
1497 for (i = 0; i < pt->n_entries; i++)
1499 const struct table_entry *te = pt->entries[i];
1500 const union value *value = &te->values[var_idx];
1501 size_t hash = value_hash (value, width, 0);
1503 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1504 if (value_equal (iter, value, width))
1507 hmapx_insert (&set, (union value *) value, hash);
1512 *n_values = hmapx_count (&set);
1513 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1515 HMAPX_FOR_EACH (iter, node, &set)
1516 values[i++] = *iter;
1517 hmapx_destroy (&set);
1519 sort (values, *n_values, sizeof *values,
1520 descending ? compare_value_3way_inv : compare_value_3way,
1525 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1526 from V, displayed with print format spec from variable VAR. When
1527 in REPORT missing-value mode, missing values have an M appended. */
1529 table_value_missing (struct crosstabs_proc *proc,
1530 struct tab_table *table, int c, int r, unsigned char opt,
1531 const union value *v, const struct variable *var)
1533 const char *label = var_lookup_value_label (var, v);
1535 tab_text (table, c, r, TAB_LEFT, label);
1538 const struct fmt_spec *print = var_get_print_format (var);
1539 if (proc->exclude == MV_NEVER && var_is_value_missing (var, v, MV_USER))
1541 char *s = data_out (v, dict_get_encoding (proc->dict), print);
1542 tab_text_format (table, c, r, opt, "%sM", s + strspn (s, " "));
1546 tab_value (table, c, r, opt, v, var, print);
1550 /* Draws a line across TABLE at the current row to indicate the most
1551 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1552 that changed, and puts the values that changed into the table. TB
1553 and PT must be the corresponding table_entry and crosstab,
1556 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1557 struct tab_table *table, int first_difference)
1559 tab_hline (table, TAL_1, pt->n_consts + pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1561 for (; first_difference >= 2; first_difference--)
1562 table_value_missing (proc, table, pt->n_consts + pt->n_vars - first_difference - 1, 0,
1563 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1564 pt->vars[first_difference]);
1567 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1568 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1569 additionally suffixed with a letter `M'. */
1571 format_cell_entry (struct tab_table *table, int c, int r, double value,
1572 char suffix, bool mark_missing, const struct dictionary *dict)
1580 s = data_out (&v, dict_get_encoding (dict), settings_get_format ());
1584 suffixes[suffix_len++] = suffix;
1586 suffixes[suffix_len++] = 'M';
1587 suffixes[suffix_len] = '\0';
1589 tab_text_format (table, c, r, TAB_RIGHT, "%s%s",
1590 s + strspn (s, " "), suffixes);
1595 /* Displays the crosstabulation table. */
1597 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1598 struct tab_table *table)
1604 for (r = 0; r < pt->n_rows; r++)
1605 table_value_missing (proc, table, pt->n_consts + pt->n_vars - 2,
1606 r * proc->n_cells, TAB_RIGHT, &pt->rows[r],
1609 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1610 TAB_LEFT, _("Total"));
1612 /* Put in the actual cells. */
1614 tab_offset (table, pt->n_consts + pt->n_vars - 1, -1);
1615 for (r = 0; r < pt->n_rows; r++)
1617 if (proc->n_cells > 1)
1618 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1619 for (c = 0; c < pt->n_cols; c++)
1621 bool mark_missing = false;
1622 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1623 if (proc->exclude == MV_NEVER
1624 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1625 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1627 mark_missing = true;
1628 for (i = 0; i < proc->n_cells; i++)
1633 switch (proc->a_cells[i])
1639 v = *mp / pt->row_tot[r] * 100.;
1643 v = *mp / pt->col_tot[c] * 100.;
1647 v = *mp / pt->total * 100.;
1650 case CRS_CL_EXPECTED:
1653 case CRS_CL_RESIDUAL:
1654 v = *mp - expected_value;
1656 case CRS_CL_SRESIDUAL:
1657 v = (*mp - expected_value) / sqrt (expected_value);
1659 case CRS_CL_ASRESIDUAL:
1660 v = ((*mp - expected_value)
1661 / sqrt (expected_value
1662 * (1. - pt->row_tot[r] / pt->total)
1663 * (1. - pt->col_tot[c] / pt->total)));
1668 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1674 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1678 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1679 for (r = 0; r < pt->n_rows; r++)
1681 bool mark_missing = false;
1683 if (proc->exclude == MV_NEVER
1684 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1685 mark_missing = true;
1687 for (i = 0; i < proc->n_cells; i++)
1692 switch (proc->a_cells[i])
1702 v = pt->row_tot[r] / pt->total * 100.;
1706 v = pt->row_tot[r] / pt->total * 100.;
1709 case CRS_CL_EXPECTED:
1710 case CRS_CL_RESIDUAL:
1711 case CRS_CL_SRESIDUAL:
1712 case CRS_CL_ASRESIDUAL:
1719 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing, proc->dict);
1720 tab_next_row (table);
1724 /* Column totals, grand total. */
1726 if (proc->n_cells > 1)
1727 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1728 for (c = 0; c <= pt->n_cols; c++)
1730 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1731 bool mark_missing = false;
1734 if (proc->exclude == MV_NEVER && c < pt->n_cols
1735 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1736 mark_missing = true;
1738 for (i = 0; i < proc->n_cells; i++)
1743 switch (proc->a_cells[i])
1749 v = ct / pt->total * 100.;
1757 v = ct / pt->total * 100.;
1760 case CRS_CL_EXPECTED:
1761 case CRS_CL_RESIDUAL:
1762 case CRS_CL_SRESIDUAL:
1763 case CRS_CL_ASRESIDUAL:
1769 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1774 tab_offset (table, -1, tab_row (table) + last_row);
1775 tab_offset (table, 0, -1);
1778 static void calc_r (struct pivot_table *,
1779 double *PT, double *Y, double *, double *, double *);
1780 static void calc_chisq (struct pivot_table *,
1781 double[N_CHISQ], int[N_CHISQ], double *, double *);
1783 /* Display chi-square statistics. */
1785 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1786 bool *showed_fisher)
1788 static const char *chisq_stats[N_CHISQ] =
1790 N_("Pearson Chi-Square"),
1791 N_("Likelihood Ratio"),
1792 N_("Fisher's Exact Test"),
1793 N_("Continuity Correction"),
1794 N_("Linear-by-Linear Association"),
1796 double chisq_v[N_CHISQ];
1797 double fisher1, fisher2;
1802 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1804 tab_offset (chisq, pt->n_consts + pt->n_vars - 2, -1);
1806 for (i = 0; i < N_CHISQ; i++)
1808 if ((i != 2 && chisq_v[i] == SYSMIS)
1809 || (i == 2 && fisher1 == SYSMIS))
1812 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1815 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL, RC_OTHER);
1816 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], NULL, RC_WEIGHT);
1817 tab_double (chisq, 3, 0, TAB_RIGHT,
1818 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL, RC_PVALUE);
1822 *showed_fisher = true;
1823 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL, RC_PVALUE);
1824 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL, RC_PVALUE);
1826 tab_next_row (chisq);
1829 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1830 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, NULL, RC_WEIGHT);
1831 tab_next_row (chisq);
1833 tab_offset (chisq, 0, -1);
1836 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1837 double[N_SYMMETRIC], double[N_SYMMETRIC],
1838 double[N_SYMMETRIC],
1839 double[3], double[3], double[3]);
1841 /* Display symmetric measures. */
1843 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1844 struct tab_table *sym)
1846 static const char *categories[] =
1848 N_("Nominal by Nominal"),
1849 N_("Ordinal by Ordinal"),
1850 N_("Interval by Interval"),
1851 N_("Measure of Agreement"),
1854 static const char *stats[N_SYMMETRIC] =
1858 N_("Contingency Coefficient"),
1859 N_("Kendall's tau-b"),
1860 N_("Kendall's tau-c"),
1862 N_("Spearman Correlation"),
1867 static const int stats_categories[N_SYMMETRIC] =
1869 0, 0, 0, 1, 1, 1, 1, 2, 3,
1873 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1874 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1877 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1878 somers_d_v, somers_d_ase, somers_d_t))
1881 tab_offset (sym, pt->n_consts + pt->n_vars - 2, -1);
1883 for (i = 0; i < N_SYMMETRIC; i++)
1885 if (sym_v[i] == SYSMIS)
1888 if (stats_categories[i] != last_cat)
1890 last_cat = stats_categories[i];
1891 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1894 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1895 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL, RC_OTHER);
1896 if (sym_ase[i] != SYSMIS)
1897 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL, RC_OTHER);
1898 if (sym_t[i] != SYSMIS)
1899 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL, RC_OTHER);
1900 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL, RC_PVALUE);*/
1904 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1905 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, NULL, RC_WEIGHT);
1908 tab_offset (sym, 0, -1);
1911 static int calc_risk (struct pivot_table *,
1912 double[], double[], double[], union value *);
1914 /* Display risk estimate. */
1916 display_risk (struct pivot_table *pt, struct tab_table *risk)
1919 double risk_v[3], lower[3], upper[3];
1923 if (!calc_risk (pt, risk_v, upper, lower, c))
1926 tab_offset (risk, pt->n_consts + pt->n_vars - 2, -1);
1928 for (i = 0; i < 3; i++)
1930 const struct variable *cv = pt->vars[COL_VAR];
1931 const struct variable *rv = pt->vars[ROW_VAR];
1932 int cvw = var_get_width (cv);
1933 int rvw = var_get_width (rv);
1935 if (risk_v[i] == SYSMIS)
1941 if (var_is_numeric (cv))
1942 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1943 var_to_string (cv), c[0].f, c[1].f);
1945 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1947 cvw, value_str (&c[0], cvw),
1948 cvw, value_str (&c[1], cvw));
1952 if (var_is_numeric (rv))
1953 sprintf (buf, _("For cohort %s = %.*g"),
1954 var_to_string (rv), DBL_DIG + 1, pt->rows[i - 1].f);
1956 sprintf (buf, _("For cohort %s = %.*s"),
1958 rvw, value_str (&pt->rows[i - 1], rvw));
1962 tab_text (risk, 0, 0, TAB_LEFT, buf);
1963 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL, RC_OTHER);
1964 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL, RC_OTHER);
1965 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL, RC_OTHER);
1966 tab_next_row (risk);
1969 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1970 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, NULL, RC_WEIGHT);
1971 tab_next_row (risk);
1973 tab_offset (risk, 0, -1);
1976 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1977 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1978 double[N_DIRECTIONAL]);
1980 /* Display directional measures. */
1982 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
1983 struct tab_table *direct)
1985 static const char *categories[] =
1987 N_("Nominal by Nominal"),
1988 N_("Ordinal by Ordinal"),
1989 N_("Nominal by Interval"),
1992 static const char *stats[] =
1995 N_("Goodman and Kruskal tau"),
1996 N_("Uncertainty Coefficient"),
2001 static const char *types[] =
2008 static const int stats_categories[N_DIRECTIONAL] =
2010 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
2013 static const int stats_stats[N_DIRECTIONAL] =
2015 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
2018 static const int stats_types[N_DIRECTIONAL] =
2020 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
2023 static const int *stats_lookup[] =
2030 static const char **stats_names[] =
2042 double direct_v[N_DIRECTIONAL];
2043 double direct_ase[N_DIRECTIONAL];
2044 double direct_t[N_DIRECTIONAL];
2048 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t))
2051 tab_offset (direct, pt->n_consts + pt->n_vars - 2, -1);
2053 for (i = 0; i < N_DIRECTIONAL; i++)
2055 if (direct_v[i] == SYSMIS)
2061 for (j = 0; j < 3; j++)
2062 if (last[j] != stats_lookup[j][i])
2065 tab_hline (direct, TAL_1, j, 6, 0);
2070 int k = last[j] = stats_lookup[j][i];
2075 string = var_to_string (pt->vars[0]);
2077 string = var_to_string (pt->vars[1]);
2079 tab_text_format (direct, j, 0, TAB_LEFT,
2080 gettext (stats_names[j][k]), string);
2085 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL, RC_OTHER);
2086 if (direct_ase[i] != SYSMIS)
2087 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL, RC_OTHER);
2088 if (direct_t[i] != SYSMIS)
2089 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL, RC_OTHER);
2090 /*tab_double (direct, 6, 0, TAB_RIGHT, normal_sig (direct_v[i]), NULL, RC_PVALUE);*/
2091 tab_next_row (direct);
2094 tab_offset (direct, 0, -1);
2097 /* Statistical calculations. */
2099 /* Returns the value of the logarithm of gamma (factorial) function for an integer
2102 log_gamma_int (double pt)
2107 for (i = 2; i < pt; i++)
2113 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2115 static inline double
2116 Pr (int a, int b, int c, int d)
2118 return exp (log_gamma_int (a + b + 1.) - log_gamma_int (a + 1.)
2119 + log_gamma_int (c + d + 1.) - log_gamma_int (b + 1.)
2120 + log_gamma_int (a + c + 1.) - log_gamma_int (c + 1.)
2121 + log_gamma_int (b + d + 1.) - log_gamma_int (d + 1.)
2122 - log_gamma_int (a + b + c + d + 1.));
2125 /* Swap the contents of A and B. */
2127 swap (int *a, int *b)
2134 /* Calculate significance for Fisher's exact test as specified in
2135 _SPSS Statistical Algorithms_, Appendix 5. */
2137 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2142 if (MIN (c, d) < MIN (a, b))
2143 swap (&a, &c), swap (&b, &d);
2144 if (MIN (b, d) < MIN (a, c))
2145 swap (&a, &b), swap (&c, &d);
2149 swap (&a, &b), swap (&c, &d);
2151 swap (&a, &c), swap (&b, &d);
2154 pn1 = Pr (a, b, c, d);
2156 for (pt = 1; pt <= a; pt++)
2158 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2161 *fisher2 = *fisher1;
2163 for (pt = 1; pt <= b; pt++)
2165 double p = Pr (a + pt, b - pt, c - pt, d + pt);
2171 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2172 columns with values COLS and N_ROWS rows with values ROWS. Values
2173 in the matrix sum to pt->total. */
2175 calc_chisq (struct pivot_table *pt,
2176 double chisq[N_CHISQ], int df[N_CHISQ],
2177 double *fisher1, double *fisher2)
2181 chisq[0] = chisq[1] = 0.;
2182 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2183 *fisher1 = *fisher2 = SYSMIS;
2185 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2187 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2189 chisq[0] = chisq[1] = SYSMIS;
2193 for (r = 0; r < pt->n_rows; r++)
2194 for (c = 0; c < pt->n_cols; c++)
2196 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2197 const double freq = pt->mat[pt->n_cols * r + c];
2198 const double residual = freq - expected;
2200 chisq[0] += residual * residual / expected;
2202 chisq[1] += freq * log (expected / freq);
2213 /* Calculate Yates and Fisher exact test. */
2214 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2216 double f11, f12, f21, f22;
2222 for (i = j = 0; i < pt->n_cols; i++)
2223 if (pt->col_tot[i] != 0.)
2232 f11 = pt->mat[nz_cols[0]];
2233 f12 = pt->mat[nz_cols[1]];
2234 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2235 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2240 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2243 chisq[3] = (pt->total * pow2 (pt_)
2244 / (f11 + f12) / (f21 + f22)
2245 / (f11 + f21) / (f12 + f22));
2253 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2256 /* Calculate Mantel-Haenszel. */
2257 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2259 double r, ase_0, ase_1;
2260 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2262 chisq[4] = (pt->total - 1.) * r * r;
2267 /* Calculate the value of Pearson's r. r is stored into R, its T value into
2268 T, and standard error into ERROR. The row and column values must be
2269 passed in PT and Y. */
2271 calc_r (struct pivot_table *pt,
2272 double *PT, double *Y, double *r, double *t, double *error)
2274 double SX, SY, S, T;
2276 double sum_XYf, sum_X2Y2f;
2277 double sum_Xr, sum_X2r;
2278 double sum_Yc, sum_Y2c;
2281 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2282 for (j = 0; j < pt->n_cols; j++)
2284 double fij = pt->mat[j + i * pt->n_cols];
2285 double product = PT[i] * Y[j];
2286 double temp = fij * product;
2288 sum_X2Y2f += temp * product;
2291 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2293 sum_Xr += PT[i] * pt->row_tot[i];
2294 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2296 Xbar = sum_Xr / pt->total;
2298 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2300 sum_Yc += Y[i] * pt->col_tot[i];
2301 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2303 Ybar = sum_Yc / pt->total;
2305 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2306 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2307 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2310 *t = *r / sqrt (1 - pow2 (*r)) * sqrt (pt->total - 2);
2315 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2316 for (j = 0; j < pt->n_cols; j++)
2318 double Xresid, Yresid;
2321 Xresid = PT[i] - Xbar;
2322 Yresid = Y[j] - Ybar;
2323 temp = (T * Xresid * Yresid
2325 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2326 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2331 *error = sqrt (s) / (T * T);
2335 /* Calculate symmetric statistics and their asymptotic standard
2336 errors. Returns 0 if none could be calculated. */
2338 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2339 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2340 double t[N_SYMMETRIC],
2341 double somers_d_v[3], double somers_d_ase[3],
2342 double somers_d_t[3])
2346 q = MIN (pt->ns_rows, pt->ns_cols);
2350 for (i = 0; i < N_SYMMETRIC; i++)
2351 v[i] = ase[i] = t[i] = SYSMIS;
2353 /* Phi, Cramer's V, contingency coefficient. */
2354 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2356 double Xp = 0.; /* Pearson chi-square. */
2359 for (r = 0; r < pt->n_rows; r++)
2360 for (c = 0; c < pt->n_cols; c++)
2362 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2363 const double freq = pt->mat[pt->n_cols * r + c];
2364 const double residual = freq - expected;
2366 Xp += residual * residual / expected;
2369 if (proc->statistics & (1u << CRS_ST_PHI))
2371 v[0] = sqrt (Xp / pt->total);
2372 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2374 if (proc->statistics & (1u << CRS_ST_CC))
2375 v[2] = sqrt (Xp / (Xp + pt->total));
2378 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2379 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2384 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2388 Dr = Dc = pow2 (pt->total);
2389 for (r = 0; r < pt->n_rows; r++)
2390 Dr -= pow2 (pt->row_tot[r]);
2391 for (c = 0; c < pt->n_cols; c++)
2392 Dc -= pow2 (pt->col_tot[c]);
2394 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2395 for (c = 0; c < pt->n_cols; c++)
2399 for (r = 0; r < pt->n_rows; r++)
2400 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2409 for (i = 0; i < pt->n_rows; i++)
2413 for (j = 1; j < pt->n_cols; j++)
2414 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2417 for (j = 1; j < pt->n_cols; j++)
2418 Dij += cum[j + (i - 1) * pt->n_cols];
2422 double fij = pt->mat[j + i * pt->n_cols];
2426 if (++j == pt->n_cols)
2428 assert (j < pt->n_cols);
2430 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2431 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2435 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2436 Dij -= cum[j + (i - 1) * pt->n_cols];
2442 if (proc->statistics & (1u << CRS_ST_BTAU))
2443 v[3] = (P - Q) / sqrt (Dr * Dc);
2444 if (proc->statistics & (1u << CRS_ST_CTAU))
2445 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2446 if (proc->statistics & (1u << CRS_ST_GAMMA))
2447 v[5] = (P - Q) / (P + Q);
2449 /* ASE for tau-b, tau-c, gamma. Calculations could be
2450 eliminated here, at expense of memory. */
2455 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2456 for (i = 0; i < pt->n_rows; i++)
2460 for (j = 1; j < pt->n_cols; j++)
2461 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2464 for (j = 1; j < pt->n_cols; j++)
2465 Dij += cum[j + (i - 1) * pt->n_cols];
2469 double fij = pt->mat[j + i * pt->n_cols];
2471 if (proc->statistics & (1u << CRS_ST_BTAU))
2473 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2474 + v[3] * (pt->row_tot[i] * Dc
2475 + pt->col_tot[j] * Dr));
2476 btau_cum += fij * temp * temp;
2480 const double temp = Cij - Dij;
2481 ctau_cum += fij * temp * temp;
2484 if (proc->statistics & (1u << CRS_ST_GAMMA))
2486 const double temp = Q * Cij - P * Dij;
2487 gamma_cum += fij * temp * temp;
2490 if (proc->statistics & (1u << CRS_ST_D))
2492 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2493 - (P - Q) * (pt->total - pt->row_tot[i]));
2494 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2495 - (Q - P) * (pt->total - pt->col_tot[j]));
2498 if (++j == pt->n_cols)
2500 assert (j < pt->n_cols);
2502 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2503 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2507 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2508 Dij -= cum[j + (i - 1) * pt->n_cols];
2514 btau_var = ((btau_cum
2515 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2517 if (proc->statistics & (1u << CRS_ST_BTAU))
2519 ase[3] = sqrt (btau_var);
2520 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2523 if (proc->statistics & (1u << CRS_ST_CTAU))
2525 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2526 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2527 t[4] = v[4] / ase[4];
2529 if (proc->statistics & (1u << CRS_ST_GAMMA))
2531 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2532 t[5] = v[5] / (2. / (P + Q)
2533 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2535 if (proc->statistics & (1u << CRS_ST_D))
2537 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2538 somers_d_ase[0] = 2. * btau_var / (Dr + Dc) * sqrt (Dr * Dc);
2539 somers_d_t[0] = (somers_d_v[0]
2541 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2542 somers_d_v[1] = (P - Q) / Dc;
2543 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2544 somers_d_t[1] = (somers_d_v[1]
2546 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2547 somers_d_v[2] = (P - Q) / Dr;
2548 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2549 somers_d_t[2] = (somers_d_v[2]
2551 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2557 /* Spearman correlation, Pearson's r. */
2558 if (proc->statistics & (1u << CRS_ST_CORR))
2560 double *R = xmalloc (sizeof *R * pt->n_rows);
2561 double *C = xmalloc (sizeof *C * pt->n_cols);
2564 double y, t, c = 0., s = 0.;
2569 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2570 y = pt->row_tot[i] - c;
2574 if (++i == pt->n_rows)
2576 assert (i < pt->n_rows);
2581 double y, t, c = 0., s = 0.;
2586 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2587 y = pt->col_tot[j] - c;
2591 if (++j == pt->n_cols)
2593 assert (j < pt->n_cols);
2597 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2602 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2605 /* Cohen's kappa. */
2606 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2608 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2611 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2612 i < pt->ns_rows; i++, j++)
2616 while (pt->col_tot[j] == 0.)
2619 prod = pt->row_tot[i] * pt->col_tot[j];
2620 sum = pt->row_tot[i] + pt->col_tot[j];
2622 sum_fii += pt->mat[j + i * pt->n_cols];
2624 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2625 sum_riciri_ci += prod * sum;
2627 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2628 for (j = 0; j < pt->ns_cols; j++)
2630 double sum = pt->row_tot[i] + pt->col_tot[j];
2631 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2634 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2636 ase[8] = sqrt ((pow2 (pt->total) * sum_rici
2637 + sum_rici * sum_rici
2638 - pt->total * sum_riciri_ci)
2639 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2641 t[8] = v[8] / sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2642 / pow2 (pow2 (pt->total) - sum_rici))
2643 + ((2. * (pt->total - sum_fii)
2644 * (2. * sum_fii * sum_rici
2645 - pt->total * sum_fiiri_ci))
2646 / cube (pow2 (pt->total) - sum_rici))
2647 + (pow2 (pt->total - sum_fii)
2648 * (pt->total * sum_fijri_ci2 - 4.
2649 * sum_rici * sum_rici)
2650 / pow4 (pow2 (pt->total) - sum_rici))));
2652 t[8] = v[8] / ase[8];
2659 /* Calculate risk estimate. */
2661 calc_risk (struct pivot_table *pt,
2662 double *value, double *upper, double *lower, union value *c)
2664 double f11, f12, f21, f22;
2670 for (i = 0; i < 3; i++)
2671 value[i] = upper[i] = lower[i] = SYSMIS;
2674 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2681 for (i = j = 0; i < pt->n_cols; i++)
2682 if (pt->col_tot[i] != 0.)
2691 f11 = pt->mat[nz_cols[0]];
2692 f12 = pt->mat[nz_cols[1]];
2693 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2694 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2696 c[0] = pt->cols[nz_cols[0]];
2697 c[1] = pt->cols[nz_cols[1]];
2700 value[0] = (f11 * f22) / (f12 * f21);
2701 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2702 lower[0] = value[0] * exp (-1.960 * v);
2703 upper[0] = value[0] * exp (1.960 * v);
2705 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2706 v = sqrt ((f12 / (f11 * (f11 + f12)))
2707 + (f22 / (f21 * (f21 + f22))));
2708 lower[1] = value[1] * exp (-1.960 * v);
2709 upper[1] = value[1] * exp (1.960 * v);
2711 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2712 v = sqrt ((f11 / (f12 * (f11 + f12)))
2713 + (f21 / (f22 * (f21 + f22))));
2714 lower[2] = value[2] * exp (-1.960 * v);
2715 upper[2] = value[2] * exp (1.960 * v);
2720 /* Calculate directional measures. */
2722 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2723 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2724 double t[N_DIRECTIONAL])
2729 for (i = 0; i < N_DIRECTIONAL; i++)
2730 v[i] = ase[i] = t[i] = SYSMIS;
2734 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2736 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2737 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2738 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2739 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2740 double sum_fim, sum_fmj;
2742 int rm_index, cm_index;
2745 /* Find maximum for each row and their sum. */
2746 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2748 double max = pt->mat[i * pt->n_cols];
2751 for (j = 1; j < pt->n_cols; j++)
2752 if (pt->mat[j + i * pt->n_cols] > max)
2754 max = pt->mat[j + i * pt->n_cols];
2758 sum_fim += fim[i] = max;
2759 fim_index[i] = index;
2762 /* Find maximum for each column. */
2763 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2765 double max = pt->mat[j];
2768 for (i = 1; i < pt->n_rows; i++)
2769 if (pt->mat[j + i * pt->n_cols] > max)
2771 max = pt->mat[j + i * pt->n_cols];
2775 sum_fmj += fmj[j] = max;
2776 fmj_index[j] = index;
2779 /* Find maximum row total. */
2780 rm = pt->row_tot[0];
2782 for (i = 1; i < pt->n_rows; i++)
2783 if (pt->row_tot[i] > rm)
2785 rm = pt->row_tot[i];
2789 /* Find maximum column total. */
2790 cm = pt->col_tot[0];
2792 for (j = 1; j < pt->n_cols; j++)
2793 if (pt->col_tot[j] > cm)
2795 cm = pt->col_tot[j];
2799 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2800 v[1] = (sum_fmj - rm) / (pt->total - rm);
2801 v[2] = (sum_fim - cm) / (pt->total - cm);
2803 /* XXX We don't have a working formula for ASE1. */
2806 /* ASE0 for Y given PT. */
2810 for (accum = 0., i = 0; i < pt->n_rows; i++)
2811 if (cm_index != fim_index[i])
2812 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2813 + pt->mat[i * pt->n_cols + cm_index]);
2814 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2817 /* XXX We don't have a working formula for ASE1. */
2820 /* ASE0 for PT given Y. */
2824 for (accum = 0., j = 0; j < pt->n_cols; j++)
2825 if (rm_index != fmj_index[j])
2826 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2827 + pt->mat[j + pt->n_cols * rm_index]);
2828 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2831 /* Symmetric ASE0 and ASE1. */
2836 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2837 for (j = 0; j < pt->n_cols; j++)
2839 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2840 int temp1 = (i == rm_index) + (j == cm_index);
2841 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2842 accum1 += (pt->mat[j + i * pt->n_cols]
2843 * pow2 (temp0 + (v[0] - 1.) * temp1));
2845 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2846 t[0] = v[0] / (sqrt (accum0 - pow2 (sum_fim + sum_fmj - cm - rm) / pt->total)
2847 / (2. * pt->total - rm - cm));
2856 double sum_fij2_ri, sum_fij2_ci;
2857 double sum_ri2, sum_cj2;
2859 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2860 for (j = 0; j < pt->n_cols; j++)
2862 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2863 sum_fij2_ri += temp / pt->row_tot[i];
2864 sum_fij2_ci += temp / pt->col_tot[j];
2867 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2868 sum_ri2 += pow2 (pt->row_tot[i]);
2870 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2871 sum_cj2 += pow2 (pt->col_tot[j]);
2873 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2874 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2878 if (proc->statistics & (1u << CRS_ST_UC))
2880 double UX, UY, UXY, P;
2881 double ase1_yx, ase1_xy, ase1_sym;
2884 for (UX = 0., i = 0; i < pt->n_rows; i++)
2885 if (pt->row_tot[i] > 0.)
2886 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2888 for (UY = 0., j = 0; j < pt->n_cols; j++)
2889 if (pt->col_tot[j] > 0.)
2890 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2892 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2893 for (j = 0; j < pt->n_cols; j++)
2895 double entry = pt->mat[j + i * pt->n_cols];
2900 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2901 UXY -= entry / pt->total * log (entry / pt->total);
2904 for (ase1_yx = ase1_xy = ase1_sym = 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 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2913 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2914 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2915 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2916 ase1_sym += entry * pow2 ((UXY
2917 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2918 - (UX + UY) * log (entry / pt->total));
2921 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2922 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2923 t[5] = v[5] / ((2. / (pt->total * (UX + UY)))
2924 * sqrt (P - pow2 (UX + UY - UXY) / pt->total));
2926 v[6] = (UX + UY - UXY) / UX;
2927 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2928 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2930 v[7] = (UX + UY - UXY) / UY;
2931 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2932 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2936 if (proc->statistics & (1u << CRS_ST_D))
2938 double v_dummy[N_SYMMETRIC];
2939 double ase_dummy[N_SYMMETRIC];
2940 double t_dummy[N_SYMMETRIC];
2941 double somers_d_v[3];
2942 double somers_d_ase[3];
2943 double somers_d_t[3];
2945 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2946 somers_d_v, somers_d_ase, somers_d_t))
2949 for (i = 0; i < 3; i++)
2951 v[8 + i] = somers_d_v[i];
2952 ase[8 + i] = somers_d_ase[i];
2953 t[8 + i] = somers_d_t[i];
2959 if (proc->statistics & (1u << CRS_ST_ETA))
2962 double sum_Xr, sum_X2r;
2966 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2968 sum_Xr += pt->rows[i].f * pt->row_tot[i];
2969 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
2971 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2973 for (SXW = 0., j = 0; j < pt->n_cols; j++)
2977 for (cum = 0., i = 0; i < pt->n_rows; i++)
2979 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
2980 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
2983 SXW -= cum * cum / pt->col_tot[j];
2985 v[11] = sqrt (1. - SXW / SX);
2989 double sum_Yc, sum_Y2c;
2993 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2995 sum_Yc += pt->cols[i].f * pt->col_tot[i];
2996 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
2998 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
3000 for (SYW = 0., i = 0; i < pt->n_rows; i++)
3004 for (cum = 0., j = 0; j < pt->n_cols; j++)
3006 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
3007 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
3010 SYW -= cum * cum / pt->row_tot[i];
3012 v[12] = sqrt (1. - SYW / SY);