1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2006, 2009, 2010, 2011, 2012, 2013, 2014, 2016 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 some symmetric and directional measures?
20 - How to calculate ASE for symmetric Somers ' d?
21 - How to calculate ASE for Goodman and Kruskal's tau?
22 - How to calculate approx. T of symmetric uncertainty coefficient?
30 #include <gsl/gsl_cdf.h>
34 #include "data/case.h"
35 #include "data/casegrouper.h"
36 #include "data/casereader.h"
37 #include "data/data-out.h"
38 #include "data/dataset.h"
39 #include "data/dictionary.h"
40 #include "data/format.h"
41 #include "data/value-labels.h"
42 #include "data/variable.h"
43 #include "language/command.h"
44 #include "language/stats/freq.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/pivot-table.h"
59 #include "output/charts/barchart.h"
61 #include "gl/minmax.h"
62 #include "gl/xalloc-oversized.h"
63 #include "gl/xalloc.h"
67 #define _(msgid) gettext (msgid)
68 #define N_(msgid) msgid
70 /* Kinds of cells in the crosstabulation. */
72 C(COUNT, N_("Count"), PIVOT_RC_COUNT) \
73 C(EXPECTED, N_("Expected"), PIVOT_RC_OTHER) \
74 C(ROW, N_("Row %"), PIVOT_RC_PERCENT) \
75 C(COLUMN, N_("Column %"), PIVOT_RC_PERCENT) \
76 C(TOTAL, N_("Total %"), PIVOT_RC_PERCENT) \
77 C(RESIDUAL, N_("Residual"), PIVOT_RC_RESIDUAL) \
78 C(SRESIDUAL, N_("Std. Residual"), PIVOT_RC_RESIDUAL) \
79 C(ASRESIDUAL, N_("Adjusted Residual"), PIVOT_RC_RESIDUAL)
82 #define C(KEYWORD, STRING, RC) CRS_CL_##KEYWORD,
87 #define C(KEYWORD, STRING, RC) + 1
88 CRS_N_CELLS = CRS_CELLS
91 #define CRS_ALL_CELLS ((1u << CRS_N_CELLS) - 1)
93 /* Kinds of statistics. */
94 #define CRS_STATISTICS \
108 enum crs_statistic_index {
109 #define S(KEYWORD) CRS_ST_##KEYWORD##_INDEX,
113 enum crs_statistic_bit {
114 #define S(KEYWORD) CRS_ST_##KEYWORD = 1u << CRS_ST_##KEYWORD##_INDEX,
119 #define S(KEYWORD) + 1
120 CRS_N_STATISTICS = CRS_STATISTICS
123 #define CRS_ALL_STATISTICS ((1u << CRS_N_STATISTICS) - 1)
125 /* Number of chi-square statistics. */
128 /* Number of symmetric statistics. */
129 #define N_SYMMETRIC 9
131 /* Number of directional statistics. */
132 #define N_DIRECTIONAL 13
134 /* Indexes into the 'vars' member of struct crosstabulation and
135 struct crosstab member. */
138 ROW_VAR = 0, /* Row variable. */
139 COL_VAR = 1 /* Column variable. */
140 /* Higher indexes cause multiple tables to be output. */
145 const struct variable *var;
150 /* A crosstabulation of 2 or more variables. */
151 struct crosstabulation
153 struct crosstabs_proc *proc;
154 struct fmt_spec weight_format; /* Format for weight variable. */
155 double missing; /* Weight of missing cases. */
157 /* Variables (2 or more). */
159 struct xtab_var *vars;
161 /* Constants (0 or more). */
163 struct xtab_var *const_vars;
164 size_t *const_indexes;
168 struct freq **entries;
171 /* Number of statistically interesting columns/rows
172 (columns/rows with data in them). */
173 int ns_cols, ns_rows;
175 /* Matrix contents. */
176 double *mat; /* Matrix proper. */
177 double *row_tot; /* Row totals. */
178 double *col_tot; /* Column totals. */
179 double total; /* Grand total. */
182 /* Integer mode variable info. */
185 struct hmap_node hmap_node; /* In struct crosstabs_proc var_ranges map. */
186 const struct variable *var; /* The variable. */
187 int min; /* Minimum value. */
188 int max; /* Maximum value + 1. */
189 int count; /* max - min. */
192 struct crosstabs_proc
194 const struct dictionary *dict;
195 enum { INTEGER, GENERAL } mode;
196 enum mv_class exclude;
199 struct fmt_spec weight_format;
201 /* Variables specifies on VARIABLES. */
202 const struct variable **variables;
204 struct hmap var_ranges;
207 struct crosstabulation *pivots;
211 int n_cells; /* Number of cells requested. */
212 unsigned int cells; /* Bit k is 1 if cell k is requested. */
213 int a_cells[CRS_N_CELLS]; /* 0...n_cells-1 are the requested cells. */
215 /* Rounding of cells. */
216 bool round_case_weights; /* Round case weights? */
217 bool round_cells; /* If !round_case_weights, round cells? */
218 bool round_down; /* Round down? (otherwise to nearest) */
221 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
223 bool descending; /* True if descending sort order is requested. */
226 static bool parse_crosstabs_tables (struct lexer *, struct dataset *,
227 struct crosstabs_proc *);
228 static bool parse_crosstabs_variables (struct lexer *, struct dataset *,
229 struct crosstabs_proc *);
231 static const struct var_range *get_var_range (const struct crosstabs_proc *,
232 const struct variable *);
234 static bool should_tabulate_case (const struct crosstabulation *,
235 const struct ccase *, enum mv_class exclude);
236 static void tabulate_general_case (struct crosstabulation *, const struct ccase *,
238 static void tabulate_integer_case (struct crosstabulation *, const struct ccase *,
240 static void postcalc (struct crosstabs_proc *);
243 round_weight (const struct crosstabs_proc *proc, double weight)
245 return proc->round_down ? floor (weight) : floor (weight + 0.5);
248 #define FOR_EACH_POPULATED_COLUMN(C, XT) \
249 for (int C = next_populated_column (0, XT); \
250 C < (XT)->vars[COL_VAR].n_values; \
251 C = next_populated_column (C + 1, XT))
253 next_populated_column (int c, const struct crosstabulation *xt)
255 int n_columns = xt->vars[COL_VAR].n_values;
256 for (; c < n_columns; c++)
262 #define FOR_EACH_POPULATED_ROW(R, XT) \
263 for (int R = next_populated_row (0, XT); R < (XT)->vars[ROW_VAR].n_values; \
264 R = next_populated_row (R + 1, XT))
266 next_populated_row (int r, const struct crosstabulation *xt)
268 int n_rows = xt->vars[ROW_VAR].n_values;
269 for (; r < n_rows; r++)
275 /* Parses and executes the CROSSTABS procedure. */
277 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
279 int result = CMD_FAILURE;
281 struct crosstabs_proc proc = {
282 .dict = dataset_dict (ds),
287 .weight_format = *dict_get_weight_format (dataset_dict (ds)),
291 .var_ranges = HMAP_INITIALIZER (proc.var_ranges),
296 .cells = 1u << CRS_CL_COUNT,
297 /* n_cells and a_cells will be filled in later. */
299 .round_case_weights = false,
300 .round_cells = false,
307 bool show_tables = true;
308 lex_match (lexer, T_SLASH);
311 if (lex_match_id (lexer, "VARIABLES"))
313 if (!parse_crosstabs_variables (lexer, ds, &proc))
316 else if (lex_match_id (lexer, "MISSING"))
318 lex_match (lexer, T_EQUALS);
319 if (lex_match_id (lexer, "TABLE"))
320 proc.exclude = MV_ANY;
321 else if (lex_match_id (lexer, "INCLUDE"))
322 proc.exclude = MV_SYSTEM;
323 else if (lex_match_id (lexer, "REPORT"))
327 lex_error (lexer, NULL);
331 else if (lex_match_id (lexer, "COUNT"))
333 lex_match (lexer, T_EQUALS);
335 /* Default is CELL. */
336 proc.round_case_weights = false;
337 proc.round_cells = true;
339 while (lex_token (lexer) != T_SLASH && lex_token (lexer) != T_ENDCMD)
341 if (lex_match_id (lexer, "ASIS"))
343 proc.round_case_weights = false;
344 proc.round_cells = false;
346 else if (lex_match_id (lexer, "CASE"))
348 proc.round_case_weights = true;
349 proc.round_cells = false;
351 else if (lex_match_id (lexer, "CELL"))
353 proc.round_case_weights = false;
354 proc.round_cells = true;
356 else if (lex_match_id (lexer, "ROUND"))
357 proc.round_down = false;
358 else if (lex_match_id (lexer, "TRUNCATE"))
359 proc.round_down = true;
362 lex_error (lexer, NULL);
365 lex_match (lexer, T_COMMA);
368 else if (lex_match_id (lexer, "FORMAT"))
370 lex_match (lexer, T_EQUALS);
371 while (lex_token (lexer) != T_SLASH && lex_token (lexer) != T_ENDCMD)
373 if (lex_match_id (lexer, "AVALUE"))
374 proc.descending = false;
375 else if (lex_match_id (lexer, "DVALUE"))
376 proc.descending = true;
377 else if (lex_match_id (lexer, "TABLES"))
379 else if (lex_match_id (lexer, "NOTABLES"))
383 lex_error (lexer, NULL);
386 lex_match (lexer, T_COMMA);
389 else if (lex_match_id (lexer, "BARCHART"))
390 proc.barchart = true;
391 else if (lex_match_id (lexer, "CELLS"))
393 lex_match (lexer, T_EQUALS);
395 if (lex_match_id (lexer, "NONE"))
397 else if (lex_match (lexer, T_ALL))
398 proc.cells = CRS_ALL_CELLS;
402 while (lex_token (lexer) != T_SLASH && lex_token (lexer) != T_ENDCMD)
404 #define C(KEYWORD, STRING, RC) \
405 if (lex_match_id (lexer, #KEYWORD)) \
407 proc.cells |= 1u << CRS_CL_##KEYWORD; \
412 lex_error (lexer, NULL);
416 proc.cells = ((1u << CRS_CL_COUNT) | (1u << CRS_CL_ROW)
417 | (1u << CRS_CL_COLUMN) | (1u << CRS_CL_TOTAL));
420 else if (lex_match_id (lexer, "STATISTICS"))
422 lex_match (lexer, T_EQUALS);
424 if (lex_match_id (lexer, "NONE"))
426 else if (lex_match (lexer, T_ALL))
427 proc.statistics = CRS_ALL_STATISTICS;
431 while (lex_token (lexer) != T_SLASH && lex_token (lexer) != T_ENDCMD)
434 if (lex_match_id (lexer, #KEYWORD)) \
436 proc.statistics |= CRS_ST_##KEYWORD; \
441 lex_error (lexer, NULL);
444 if (!proc.statistics)
445 proc.statistics = CRS_ST_CHISQ;
448 else if (!parse_crosstabs_tables (lexer, ds, &proc))
451 if (!lex_match (lexer, T_SLASH))
454 if (!lex_end_of_command (lexer))
459 msg (SE, _("At least one crosstabulation must be requested (using "
460 "the TABLES subcommand)."));
467 for (int i = 0; i < CRS_N_CELLS; i++)
468 if (proc.cells & (1u << i))
469 proc.a_cells[proc.n_cells++] = i;
470 assert (proc.n_cells < CRS_N_CELLS);
472 /* Missing values. */
473 if (proc.mode == GENERAL && !proc.exclude)
475 msg (SE, _("Missing mode %s not allowed in general mode. "
476 "Assuming %s."), "REPORT", "MISSING=TABLE");
477 proc.exclude = MV_ANY;
480 struct casereader *input = casereader_create_filter_weight (proc_open (ds),
483 struct casegrouper *grouper = casegrouper_create_splits (input, dataset_dict (ds));
484 struct casereader *group;
485 while (casegrouper_get_next_group (grouper, &group))
489 /* Output SPLIT FILE variables. */
490 c = casereader_peek (group, 0);
493 output_split_file_values (ds, c);
497 /* Initialize hash tables. */
498 for (struct crosstabulation *xt = &proc.pivots[0];
499 xt < &proc.pivots[proc.n_pivots]; xt++)
500 hmap_init (&xt->data);
503 for (; (c = casereader_read (group)) != NULL; case_unref (c))
504 for (struct crosstabulation *xt = &proc.pivots[0];
505 xt < &proc.pivots[proc.n_pivots]; xt++)
507 double weight = dict_get_case_weight (dataset_dict (ds), c,
509 if (proc.round_case_weights)
511 weight = round_weight (&proc, weight);
515 if (should_tabulate_case (xt, c, proc.exclude))
517 if (proc.mode == GENERAL)
518 tabulate_general_case (xt, c, weight);
520 tabulate_integer_case (xt, c, weight);
523 xt->missing += weight;
525 casereader_destroy (group);
530 bool ok = casegrouper_destroy (grouper);
531 ok = proc_commit (ds) && ok;
533 result = ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
536 free (proc.variables);
538 struct var_range *range, *next_range;
539 HMAP_FOR_EACH_SAFE (range, next_range, struct var_range, hmap_node,
542 hmap_delete (&proc.var_ranges, &range->hmap_node);
545 for (struct crosstabulation *xt = &proc.pivots[0];
546 xt < &proc.pivots[proc.n_pivots]; xt++)
549 free (xt->const_vars);
550 free (xt->const_indexes);
557 /* Parses the TABLES subcommand. */
559 parse_crosstabs_tables (struct lexer *lexer, struct dataset *ds,
560 struct crosstabs_proc *proc)
562 const struct variable ***by = NULL;
563 size_t *by_nvar = NULL;
566 /* Ensure that this is a TABLES subcommand. */
567 if (!lex_match_id (lexer, "TABLES")
568 && (lex_token (lexer) != T_ID ||
569 dict_lookup_var (dataset_dict (ds), lex_tokcstr (lexer)) == NULL)
570 && lex_token (lexer) != T_ALL)
572 lex_error (lexer, NULL);
575 lex_match (lexer, T_EQUALS);
577 struct const_var_set *var_set
579 ? const_var_set_create_from_array (proc->variables,
581 : const_var_set_create_from_dict (dataset_dict (ds)));
587 by = xnrealloc (by, n_by + 1, sizeof *by);
588 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
589 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
590 PV_NO_DUPLICATE | PV_NO_SCRATCH))
592 if (xalloc_oversized (nx, by_nvar[n_by]))
594 msg (SE, _("Too many cross-tabulation variables or dimensions."));
600 if (!lex_match (lexer, T_BY))
609 int *by_iter = XCALLOC (n_by, int);
610 proc->pivots = xnrealloc (proc->pivots,
611 proc->n_pivots + nx, sizeof *proc->pivots);
612 for (int i = 0; i < nx; i++)
614 struct crosstabulation *xt = &proc->pivots[proc->n_pivots++];
616 *xt = (struct crosstabulation) {
618 .weight_format = proc->weight_format,
621 .vars = xcalloc (n_by, sizeof *xt->vars),
624 .const_indexes = NULL,
627 for (int j = 0; j < n_by; j++)
628 xt->vars[j].var = by[j][by_iter[j]];
630 for (int j = n_by - 1; j >= 0; j--)
632 if (++by_iter[j] < by_nvar[j])
641 /* All return paths lead here. */
642 for (int i = 0; i < n_by; i++)
647 const_var_set_destroy (var_set);
652 /* Parses the VARIABLES subcommand. */
654 parse_crosstabs_variables (struct lexer *lexer, struct dataset *ds,
655 struct crosstabs_proc *proc)
659 msg (SE, _("%s must be specified before %s."), "VARIABLES", "TABLES");
663 lex_match (lexer, T_EQUALS);
667 size_t orig_nv = proc->n_variables;
669 if (!parse_variables_const (lexer, dataset_dict (ds),
670 &proc->variables, &proc->n_variables,
671 (PV_APPEND | PV_NUMERIC
672 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
675 if (!lex_force_match (lexer, T_LPAREN))
678 if (!lex_force_int (lexer))
680 long min = lex_integer (lexer);
683 lex_match (lexer, T_COMMA);
685 if (!lex_force_int_range (lexer, NULL, min, LONG_MAX))
687 long max = lex_integer (lexer);
690 if (!lex_force_match (lexer, T_RPAREN))
693 for (size_t i = orig_nv; i < proc->n_variables; i++)
695 const struct variable *var = proc->variables[i];
696 struct var_range *vr = xmalloc (sizeof *vr);
701 vr->count = max - min + 1;
702 hmap_insert (&proc->var_ranges, &vr->hmap_node,
703 hash_pointer (var, 0));
706 if (lex_token (lexer) == T_SLASH)
710 proc->mode = INTEGER;
714 free (proc->variables);
715 proc->variables = NULL;
716 proc->n_variables = 0;
720 /* Data file processing. */
722 static const struct var_range *
723 get_var_range (const struct crosstabs_proc *proc, const struct variable *var)
725 if (!hmap_is_empty (&proc->var_ranges))
727 const struct var_range *range;
729 HMAP_FOR_EACH_IN_BUCKET (range, struct var_range, hmap_node,
730 hash_pointer (var, 0), &proc->var_ranges)
731 if (range->var == var)
739 should_tabulate_case (const struct crosstabulation *xt, const struct ccase *c,
740 enum mv_class exclude)
743 for (j = 0; j < xt->n_vars; j++)
745 const struct variable *var = xt->vars[j].var;
746 const struct var_range *range = get_var_range (xt->proc, var);
748 if (var_is_value_missing (var, case_data (c, var)) & exclude)
753 double num = case_num (c, var);
754 if (num < range->min || num >= range->max + 1.)
762 tabulate_integer_case (struct crosstabulation *xt, const struct ccase *c,
770 for (j = 0; j < xt->n_vars; j++)
772 /* Throw away fractional parts of values. */
773 hash = hash_int (case_num (c, xt->vars[j].var), hash);
776 HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &xt->data)
778 for (j = 0; j < xt->n_vars; j++)
779 if ((int) case_num (c, xt->vars[j].var) != (int) te->values[j].f)
782 /* Found an existing entry. */
789 /* No existing entry. Create a new one. */
790 te = xmalloc (table_entry_size (xt->n_vars));
792 for (j = 0; j < xt->n_vars; j++)
793 te->values[j].f = (int) case_num (c, xt->vars[j].var);
794 hmap_insert (&xt->data, &te->node, hash);
798 tabulate_general_case (struct crosstabulation *xt, const struct ccase *c,
806 for (j = 0; j < xt->n_vars; j++)
808 const struct variable *var = xt->vars[j].var;
809 hash = value_hash (case_data (c, var), var_get_width (var), hash);
812 HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &xt->data)
814 for (j = 0; j < xt->n_vars; j++)
816 const struct variable *var = xt->vars[j].var;
817 if (!value_equal (case_data (c, var), &te->values[j],
818 var_get_width (var)))
822 /* Found an existing entry. */
829 /* No existing entry. Create a new one. */
830 te = xmalloc (table_entry_size (xt->n_vars));
832 for (j = 0; j < xt->n_vars; j++)
834 const struct variable *var = xt->vars[j].var;
835 value_clone (&te->values[j], case_data (c, var), var_get_width (var));
837 hmap_insert (&xt->data, &te->node, hash);
840 /* Post-data reading calculations. */
842 static int compare_table_entry_vars_3way (const struct freq *a,
843 const struct freq *b,
844 const struct crosstabulation *xt,
846 static int compare_table_entry_3way (const void *ap_, const void *bp_,
848 static int compare_table_entry_3way_inv (const void *ap_, const void *bp_,
851 static void enum_var_values (const struct crosstabulation *, int var_idx,
853 static void free_var_values (const struct crosstabulation *, int var_idx);
854 static void output_crosstabulation (struct crosstabs_proc *,
855 struct crosstabulation *);
856 static void make_crosstabulation_subset (struct crosstabulation *xt,
857 size_t row0, size_t row1,
858 struct crosstabulation *subset);
859 static void make_summary_table (struct crosstabs_proc *);
860 static bool find_crosstab (struct crosstabulation *, size_t *row0p,
864 postcalc (struct crosstabs_proc *proc)
866 /* Round hash table entries, if requested
868 If this causes any of the cell counts to fall to zero, delete those
870 if (proc->round_cells)
871 for (struct crosstabulation *xt = proc->pivots;
872 xt < &proc->pivots[proc->n_pivots]; xt++)
874 struct freq *e, *next;
875 HMAP_FOR_EACH_SAFE (e, next, struct freq, node, &xt->data)
877 e->count = round_weight (proc, e->count);
880 hmap_delete (&xt->data, &e->node);
886 /* Convert hash tables into sorted arrays of entries. */
887 for (struct crosstabulation *xt = proc->pivots;
888 xt < &proc->pivots[proc->n_pivots]; xt++)
892 xt->n_entries = hmap_count (&xt->data);
893 xt->entries = xnmalloc (xt->n_entries, sizeof *xt->entries);
895 HMAP_FOR_EACH (e, struct freq, node, &xt->data)
896 xt->entries[i++] = e;
897 hmap_destroy (&xt->data);
899 sort (xt->entries, xt->n_entries, sizeof *xt->entries,
900 proc->descending ? compare_table_entry_3way_inv : compare_table_entry_3way,
905 make_summary_table (proc);
907 /* Output each pivot table. */
908 for (struct crosstabulation *xt = proc->pivots;
909 xt < &proc->pivots[proc->n_pivots]; xt++)
911 output_crosstabulation (proc, xt);
914 int n_vars = (xt->n_vars > 2 ? 2 : xt->n_vars);
915 const struct variable **vars = XCALLOC (n_vars, const struct variable*);
916 for (size_t i = 0; i < n_vars; i++)
917 vars[i] = xt->vars[i].var;
918 chart_submit (barchart_create (vars, n_vars, _("Count"),
920 xt->entries, xt->n_entries));
925 /* Free output and prepare for next split file. */
926 for (struct crosstabulation *xt = proc->pivots;
927 xt < &proc->pivots[proc->n_pivots]; xt++)
931 /* Free the members that were allocated in this function(and the values
932 owned by the entries.
934 The other pointer members are either both allocated and destroyed at a
935 lower level (in output_crosstabulation), or both allocated and
936 destroyed at a higher level (in crs_custom_tables and free_proc,
938 for (size_t i = 0; i < xt->n_vars; i++)
940 int width = var_get_width (xt->vars[i].var);
941 if (value_needs_init (width))
945 for (j = 0; j < xt->n_entries; j++)
946 value_destroy (&xt->entries[j]->values[i], width);
950 for (size_t i = 0; i < xt->n_entries; i++)
951 free (xt->entries[i]);
957 make_crosstabulation_subset (struct crosstabulation *xt, size_t row0,
958 size_t row1, struct crosstabulation *subset)
963 assert (xt->n_consts == 0);
965 subset->vars = xt->vars;
967 subset->n_consts = xt->n_vars - 2;
968 subset->const_vars = xt->vars + 2;
969 subset->const_indexes = xcalloc (subset->n_consts,
970 sizeof *subset->const_indexes);
971 for (size_t i = 0; i < subset->n_consts; i++)
973 const union value *value = &xt->entries[row0]->values[2 + i];
975 for (size_t j = 0; j < xt->vars[2 + i].n_values; j++)
976 if (value_equal (&xt->vars[2 + i].values[j], value,
977 var_get_width (xt->vars[2 + i].var)))
979 subset->const_indexes[i] = j;
986 subset->entries = &xt->entries[row0];
987 subset->n_entries = row1 - row0;
991 compare_table_entry_var_3way (const struct freq *a,
992 const struct freq *b,
993 const struct crosstabulation *xt,
996 return value_compare_3way (&a->values[idx], &b->values[idx],
997 var_get_width (xt->vars[idx].var));
1001 compare_table_entry_vars_3way (const struct freq *a,
1002 const struct freq *b,
1003 const struct crosstabulation *xt,
1008 for (i = idx1 - 1; i >= idx0; i--)
1010 int cmp = compare_table_entry_var_3way (a, b, xt, i);
1017 /* Compare the struct freq at *AP to the one at *BP and
1018 return a strcmp()-type result. */
1020 compare_table_entry_3way (const void *ap_, const void *bp_, const void *xt_)
1022 const struct freq *const *ap = ap_;
1023 const struct freq *const *bp = bp_;
1024 const struct freq *a = *ap;
1025 const struct freq *b = *bp;
1026 const struct crosstabulation *xt = xt_;
1029 cmp = compare_table_entry_vars_3way (a, b, xt, 2, xt->n_vars);
1033 cmp = compare_table_entry_var_3way (a, b, xt, ROW_VAR);
1037 return compare_table_entry_var_3way (a, b, xt, COL_VAR);
1040 /* Inverted version of compare_table_entry_3way */
1042 compare_table_entry_3way_inv (const void *ap_, const void *bp_, const void *xt_)
1044 return -compare_table_entry_3way (ap_, bp_, xt_);
1047 /* Output a table summarizing the cases processed. */
1049 make_summary_table (struct crosstabs_proc *proc)
1051 struct pivot_table *table = pivot_table_create (N_("Summary"));
1052 pivot_table_set_weight_var (table, dict_get_weight (proc->dict));
1054 pivot_dimension_create (table, PIVOT_AXIS_COLUMN, N_("Statistics"),
1055 N_("N"), PIVOT_RC_COUNT,
1056 N_("Percent"), PIVOT_RC_PERCENT);
1058 struct pivot_dimension *cases = pivot_dimension_create (
1059 table, PIVOT_AXIS_COLUMN, N_("Cases"),
1060 N_("Valid"), N_("Missing"), N_("Total"));
1061 cases->root->show_label = true;
1063 struct pivot_dimension *tables = pivot_dimension_create (
1064 table, PIVOT_AXIS_ROW, N_("Crosstabulation"));
1065 for (struct crosstabulation *xt = &proc->pivots[0];
1066 xt < &proc->pivots[proc->n_pivots]; xt++)
1068 struct string name = DS_EMPTY_INITIALIZER;
1069 for (size_t i = 0; i < xt->n_vars; i++)
1072 ds_put_cstr (&name, " × ");
1073 ds_put_cstr (&name, var_to_string (xt->vars[i].var));
1076 int row = pivot_category_create_leaf (
1078 pivot_value_new_user_text_nocopy (ds_steal_cstr (&name)));
1081 for (size_t i = 0; i < xt->n_entries; i++)
1082 valid += xt->entries[i]->count;
1088 for (int i = 0; i < 3; i++)
1090 pivot_table_put3 (table, 0, i, row, pivot_value_new_number (n[i]));
1091 pivot_table_put3 (table, 1, i, row,
1092 pivot_value_new_number (n[i] / n[2] * 100.0));
1096 pivot_table_submit (table);
1101 static struct pivot_table *create_crosstab_table (
1102 struct crosstabs_proc *, struct crosstabulation *,
1103 size_t crs_leaves[CRS_N_CELLS]);
1104 static struct pivot_table *create_chisq_table (struct crosstabulation *);
1105 static struct pivot_table *create_sym_table (struct crosstabulation *);
1106 static struct pivot_table *create_risk_table (
1107 struct crosstabulation *, struct pivot_dimension **risk_statistics);
1108 static struct pivot_table *create_direct_table (struct crosstabulation *);
1109 static void display_crosstabulation (struct crosstabs_proc *,
1110 struct crosstabulation *,
1111 struct pivot_table *,
1112 size_t crs_leaves[CRS_N_CELLS]);
1113 static void display_chisq (struct crosstabulation *, struct pivot_table *);
1114 static void display_symmetric (struct crosstabs_proc *,
1115 struct crosstabulation *, struct pivot_table *);
1116 static void display_risk (struct crosstabulation *, struct pivot_table *,
1117 struct pivot_dimension *risk_statistics);
1118 static void display_directional (struct crosstabs_proc *,
1119 struct crosstabulation *,
1120 struct pivot_table *);
1121 static void delete_missing (struct crosstabulation *);
1122 static void build_matrix (struct crosstabulation *);
1124 /* Output pivot table XT in the context of PROC. */
1126 output_crosstabulation (struct crosstabs_proc *proc, struct crosstabulation *xt)
1128 for (size_t i = 0; i < xt->n_vars; i++)
1129 enum_var_values (xt, i, proc->descending);
1131 if (xt->vars[COL_VAR].n_values == 0)
1136 ds_init_cstr (&vars, var_to_string (xt->vars[0].var));
1137 for (i = 1; i < xt->n_vars; i++)
1138 ds_put_format (&vars, " × %s", var_to_string (xt->vars[i].var));
1140 /* TRANSLATORS: The %s here describes a crosstabulation. It takes the
1141 form "var1 * var2 * var3 * ...". */
1142 msg (SW, _("Crosstabulation %s contained no non-missing cases."),
1146 for (size_t i = 0; i < xt->n_vars; i++)
1147 free_var_values (xt, i);
1151 size_t crs_leaves[CRS_N_CELLS];
1152 struct pivot_table *table = (proc->cells
1153 ? create_crosstab_table (proc, xt, crs_leaves)
1155 struct pivot_table *chisq = (proc->statistics & CRS_ST_CHISQ
1156 ? create_chisq_table (xt)
1158 struct pivot_table *sym
1159 = (proc->statistics & (CRS_ST_PHI | CRS_ST_CC | CRS_ST_BTAU | CRS_ST_CTAU
1160 | CRS_ST_GAMMA | CRS_ST_CORR | CRS_ST_KAPPA)
1161 ? create_sym_table (xt)
1163 struct pivot_dimension *risk_statistics = NULL;
1164 struct pivot_table *risk = (proc->statistics & CRS_ST_RISK
1165 ? create_risk_table (xt, &risk_statistics)
1167 struct pivot_table *direct
1168 = (proc->statistics & (CRS_ST_LAMBDA | CRS_ST_UC | CRS_ST_D | CRS_ST_ETA)
1169 ? create_direct_table (xt)
1174 while (find_crosstab (xt, &row0, &row1))
1176 struct crosstabulation x;
1178 make_crosstabulation_subset (xt, row0, row1, &x);
1180 size_t n_rows = x.vars[ROW_VAR].n_values;
1181 size_t n_cols = x.vars[COL_VAR].n_values;
1182 if (size_overflow_p (xtimes (xtimes (n_rows, n_cols), sizeof (double))))
1184 x.row_tot = xmalloc (n_rows * sizeof *x.row_tot);
1185 x.col_tot = xmalloc (n_cols * sizeof *x.col_tot);
1186 x.mat = xmalloc (n_rows * n_cols * sizeof *x.mat);
1190 /* Find the first variable that differs from the last subtable. */
1192 display_crosstabulation (proc, &x, table, crs_leaves);
1194 if (proc->exclude == 0)
1195 delete_missing (&x);
1198 display_chisq (&x, chisq);
1201 display_symmetric (proc, &x, sym);
1203 display_risk (&x, risk, risk_statistics);
1205 display_directional (proc, &x, direct);
1210 free (x.const_indexes);
1214 pivot_table_submit (table);
1217 pivot_table_submit (chisq);
1220 pivot_table_submit (sym);
1224 if (!pivot_table_is_empty (risk))
1225 pivot_table_submit (risk);
1227 pivot_table_unref (risk);
1231 pivot_table_submit (direct);
1233 for (size_t i = 0; i < xt->n_vars; i++)
1234 free_var_values (xt, i);
1238 build_matrix (struct crosstabulation *x)
1240 const int col_var_width = var_get_width (x->vars[COL_VAR].var);
1241 const int row_var_width = var_get_width (x->vars[ROW_VAR].var);
1242 size_t n_rows = x->vars[ROW_VAR].n_values;
1243 size_t n_cols = x->vars[COL_VAR].n_values;
1250 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1252 const struct freq *te = *p;
1254 while (!value_equal (&x->vars[ROW_VAR].values[row],
1255 &te->values[ROW_VAR], row_var_width))
1257 for (; col < n_cols; col++)
1263 while (!value_equal (&x->vars[COL_VAR].values[col],
1264 &te->values[COL_VAR], col_var_width))
1271 if (++col >= n_cols)
1277 while (mp < &x->mat[n_cols * n_rows])
1279 assert (mp == &x->mat[n_cols * n_rows]);
1281 /* Column totals, row totals, ns_rows. */
1283 for (col = 0; col < n_cols; col++)
1284 x->col_tot[col] = 0.0;
1285 for (row = 0; row < n_rows; row++)
1286 x->row_tot[row] = 0.0;
1288 for (row = 0; row < n_rows; row++)
1290 bool row_is_empty = true;
1291 for (col = 0; col < n_cols; col++)
1295 row_is_empty = false;
1296 x->col_tot[col] += *mp;
1297 x->row_tot[row] += *mp;
1304 assert (mp == &x->mat[n_cols * n_rows]);
1308 for (col = 0; col < n_cols; col++)
1309 for (row = 0; row < n_rows; row++)
1310 if (x->mat[col + row * n_cols] != 0.0)
1318 for (col = 0; col < n_cols; col++)
1319 x->total += x->col_tot[col];
1323 add_var_dimension (struct pivot_table *table, const struct xtab_var *var,
1324 enum pivot_axis_type axis_type, bool total)
1326 struct pivot_dimension *d = pivot_dimension_create__ (
1327 table, axis_type, pivot_value_new_variable (var->var));
1329 struct pivot_footnote *missing_footnote = pivot_table_create_footnote (
1330 table, pivot_value_new_text (N_("Missing value")));
1332 struct pivot_category *group = pivot_category_create_group__ (
1333 d->root, pivot_value_new_variable (var->var));
1334 for (size_t j = 0; j < var->n_values; j++)
1336 struct pivot_value *value = pivot_value_new_var_value (
1337 var->var, &var->values[j]);
1338 if (var_is_value_missing (var->var, &var->values[j]))
1339 pivot_value_add_footnote (value, missing_footnote);
1340 pivot_category_create_leaf (group, value);
1344 pivot_category_create_leaf (d->root, pivot_value_new_text (N_("Total")));
1347 static struct pivot_table *
1348 create_crosstab_table (struct crosstabs_proc *proc, struct crosstabulation *xt,
1349 size_t crs_leaves[CRS_N_CELLS])
1352 struct string title = DS_EMPTY_INITIALIZER;
1353 for (size_t i = 0; i < xt->n_vars; i++)
1356 ds_put_cstr (&title, " × ");
1357 ds_put_cstr (&title, var_to_string (xt->vars[i].var));
1359 for (size_t i = 0; i < xt->n_consts; i++)
1361 const struct variable *var = xt->const_vars[i].var;
1362 const union value *value = &xt->entries[0]->values[2 + i];
1365 ds_put_format (&title, ", %s=", var_to_string (var));
1367 /* Insert the formatted value of VAR without any leading spaces. */
1368 s = data_out (value, var_get_encoding (var), var_get_print_format (var),
1369 settings_get_fmt_settings ());
1370 ds_put_cstr (&title, s + strspn (s, " "));
1373 struct pivot_table *table = pivot_table_create__ (
1374 pivot_value_new_user_text_nocopy (ds_steal_cstr (&title)),
1376 pivot_table_set_weight_format (table, &proc->weight_format);
1378 struct pivot_dimension *statistics = pivot_dimension_create (
1379 table, PIVOT_AXIS_ROW, N_("Statistics"));
1386 static const struct statistic stats[CRS_N_CELLS] =
1388 #define C(KEYWORD, STRING, RC) { STRING, RC },
1392 for (size_t i = 0; i < CRS_N_CELLS; i++)
1393 if (proc->cells & (1u << i) && stats[i].label)
1394 crs_leaves[i] = pivot_category_create_leaf_rc (
1395 statistics->root, pivot_value_new_text (stats[i].label),
1398 for (size_t i = 0; i < xt->n_vars; i++)
1399 add_var_dimension (table, &xt->vars[i],
1400 i == COL_VAR ? PIVOT_AXIS_COLUMN : PIVOT_AXIS_ROW,
1406 static struct pivot_table *
1407 create_chisq_table (struct crosstabulation *xt)
1409 struct pivot_table *chisq = pivot_table_create (N_("Chi-Square Tests"));
1410 pivot_table_set_weight_format (chisq, &xt->weight_format);
1412 pivot_dimension_create (
1413 chisq, PIVOT_AXIS_ROW, N_("Statistics"),
1414 N_("Pearson Chi-Square"),
1415 N_("Likelihood Ratio"),
1416 N_("Fisher's Exact Test"),
1417 N_("Continuity Correction"),
1418 N_("Linear-by-Linear Association"),
1419 N_("N of Valid Cases"), PIVOT_RC_COUNT);
1421 pivot_dimension_create (
1422 chisq, PIVOT_AXIS_COLUMN, N_("Statistics"),
1423 N_("Value"), PIVOT_RC_OTHER,
1424 N_("df"), PIVOT_RC_COUNT,
1425 N_("Asymptotic Sig. (2-tailed)"), PIVOT_RC_SIGNIFICANCE,
1426 N_("Exact Sig. (2-tailed)"), PIVOT_RC_SIGNIFICANCE,
1427 N_("Exact Sig. (1-tailed)"), PIVOT_RC_SIGNIFICANCE);
1429 for (size_t i = 2; i < xt->n_vars; i++)
1430 add_var_dimension (chisq, &xt->vars[i], PIVOT_AXIS_ROW, false);
1435 /* Symmetric measures. */
1436 static struct pivot_table *
1437 create_sym_table (struct crosstabulation *xt)
1439 struct pivot_table *sym = pivot_table_create (N_("Symmetric Measures"));
1440 pivot_table_set_weight_format (sym, &xt->weight_format);
1442 pivot_dimension_create (
1443 sym, PIVOT_AXIS_COLUMN, N_("Values"),
1444 N_("Value"), PIVOT_RC_OTHER,
1445 N_("Asymp. Std. Error"), PIVOT_RC_OTHER,
1446 N_("Approx. T"), PIVOT_RC_OTHER,
1447 N_("Approx. Sig."), PIVOT_RC_SIGNIFICANCE);
1449 struct pivot_dimension *statistics = pivot_dimension_create (
1450 sym, PIVOT_AXIS_ROW, N_("Statistics"));
1451 pivot_category_create_group (
1452 statistics->root, N_("Nominal by Nominal"),
1453 N_("Phi"), N_("Cramer's V"), N_("Contingency Coefficient"));
1454 pivot_category_create_group (
1455 statistics->root, N_("Ordinal by Ordinal"),
1456 N_("Kendall's tau-b"), N_("Kendall's tau-c"),
1457 N_("Gamma"), N_("Spearman Correlation"));
1458 pivot_category_create_group (
1459 statistics->root, N_("Interval by Interval"),
1461 pivot_category_create_group (
1462 statistics->root, N_("Measure of Agreement"),
1464 pivot_category_create_leaves (statistics->root, N_("N of Valid Cases"),
1467 for (size_t i = 2; i < xt->n_vars; i++)
1468 add_var_dimension (sym, &xt->vars[i], PIVOT_AXIS_ROW, false);
1473 /* Risk estimate. */
1474 static struct pivot_table *
1475 create_risk_table (struct crosstabulation *xt,
1476 struct pivot_dimension **risk_statistics)
1478 struct pivot_table *risk = pivot_table_create (N_("Risk Estimate"));
1479 pivot_table_set_weight_format (risk, &xt->weight_format);
1481 struct pivot_dimension *values = pivot_dimension_create (
1482 risk, PIVOT_AXIS_COLUMN, N_("Values"),
1483 N_("Value"), PIVOT_RC_OTHER);
1484 pivot_category_create_group (
1485 /* xgettext:no-c-format */
1486 values->root, N_("95% Confidence Interval"),
1487 N_("Lower"), PIVOT_RC_OTHER,
1488 N_("Upper"), PIVOT_RC_OTHER);
1490 *risk_statistics = pivot_dimension_create (
1491 risk, PIVOT_AXIS_ROW, N_("Statistics"));
1493 for (size_t i = 2; i < xt->n_vars; i++)
1494 add_var_dimension (risk, &xt->vars[i], PIVOT_AXIS_ROW, false);
1500 create_direct_stat (struct pivot_category *parent,
1501 const struct crosstabulation *xt,
1502 const char *name, bool symmetric)
1504 struct pivot_category *group = pivot_category_create_group (
1507 pivot_category_create_leaf (group, pivot_value_new_text (N_("Symmetric")));
1509 char *row_label = xasprintf (_("%s Dependent"),
1510 var_to_string (xt->vars[ROW_VAR].var));
1511 pivot_category_create_leaf (group, pivot_value_new_user_text_nocopy (
1514 char *col_label = xasprintf (_("%s Dependent"),
1515 var_to_string (xt->vars[COL_VAR].var));
1516 pivot_category_create_leaf (group, pivot_value_new_user_text_nocopy (
1520 /* Directional measures. */
1521 static struct pivot_table *
1522 create_direct_table (struct crosstabulation *xt)
1524 struct pivot_table *direct = pivot_table_create (N_("Directional Measures"));
1525 pivot_table_set_weight_format (direct, &xt->weight_format);
1527 pivot_dimension_create (
1528 direct, PIVOT_AXIS_COLUMN, N_("Values"),
1529 N_("Value"), PIVOT_RC_OTHER,
1530 N_("Asymp. Std. Error"), PIVOT_RC_OTHER,
1531 N_("Approx. T"), PIVOT_RC_OTHER,
1532 N_("Approx. Sig."), PIVOT_RC_SIGNIFICANCE);
1534 struct pivot_dimension *statistics = pivot_dimension_create (
1535 direct, PIVOT_AXIS_ROW, N_("Statistics"));
1536 struct pivot_category *nn = pivot_category_create_group (
1537 statistics->root, N_("Nominal by Nominal"));
1538 create_direct_stat (nn, xt, N_("Lambda"), true);
1539 create_direct_stat (nn, xt, N_("Goodman and Kruskal tau"), false);
1540 create_direct_stat (nn, xt, N_("Uncertainty Coefficient"), true);
1541 struct pivot_category *oo = pivot_category_create_group (
1542 statistics->root, N_("Ordinal by Ordinal"));
1543 create_direct_stat (oo, xt, N_("Somers' d"), true);
1544 struct pivot_category *ni = pivot_category_create_group (
1545 statistics->root, N_("Nominal by Interval"));
1546 create_direct_stat (ni, xt, N_("Eta"), false);
1548 for (size_t i = 2; i < xt->n_vars; i++)
1549 add_var_dimension (direct, &xt->vars[i], PIVOT_AXIS_ROW, false);
1554 /* Delete missing rows and columns for statistical analysis when
1557 delete_missing (struct crosstabulation *xt)
1559 size_t n_rows = xt->vars[ROW_VAR].n_values;
1560 size_t n_cols = xt->vars[COL_VAR].n_values;
1563 for (r = 0; r < n_rows; r++)
1564 if (var_is_num_missing (xt->vars[ROW_VAR].var,
1565 xt->vars[ROW_VAR].values[r].f) == MV_USER)
1567 for (c = 0; c < n_cols; c++)
1568 xt->mat[c + r * n_cols] = 0.;
1573 for (c = 0; c < n_cols; c++)
1574 if (var_is_num_missing (xt->vars[COL_VAR].var,
1575 xt->vars[COL_VAR].values[c].f) == MV_USER)
1577 for (r = 0; r < n_rows; r++)
1578 xt->mat[c + r * n_cols] = 0.;
1584 find_crosstab (struct crosstabulation *xt, size_t *row0p, size_t *row1p)
1586 size_t row0 = *row1p;
1589 if (row0 >= xt->n_entries)
1592 for (row1 = row0 + 1; row1 < xt->n_entries; row1++)
1594 struct freq *a = xt->entries[row0];
1595 struct freq *b = xt->entries[row1];
1596 if (compare_table_entry_vars_3way (a, b, xt, 2, xt->n_vars) != 0)
1604 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1605 result. WIDTH_ points to an int which is either 0 for a
1606 numeric value or a string width for a string value. */
1608 compare_value_3way (const void *a_, const void *b_, const void *width_)
1610 const union value *a = a_;
1611 const union value *b = b_;
1612 const int *width = width_;
1614 return value_compare_3way (a, b, *width);
1617 /* Inverted version of the above */
1619 compare_value_3way_inv (const void *a_, const void *b_, const void *width_)
1621 return -compare_value_3way (a_, b_, width_);
1625 /* Given an array of ENTRY_CNT table_entry structures starting at
1626 ENTRIES, creates a sorted list of the values that the variable
1627 with index VAR_IDX takes on. Stores the array of the values in
1628 XT->values and the number of values in XT->n_values. */
1630 enum_var_values (const struct crosstabulation *xt, int var_idx,
1633 struct xtab_var *xv = &xt->vars[var_idx];
1634 const struct var_range *range = get_var_range (xt->proc, xv->var);
1638 xv->values = xnmalloc (range->count, sizeof *xv->values);
1639 xv->n_values = range->count;
1640 for (size_t i = 0; i < range->count; i++)
1641 xv->values[i].f = range->min + i;
1645 int width = var_get_width (xv->var);
1646 struct hmapx_node *node;
1647 const union value *iter;
1651 for (size_t i = 0; i < xt->n_entries; i++)
1653 const struct freq *te = xt->entries[i];
1654 const union value *value = &te->values[var_idx];
1655 size_t hash = value_hash (value, width, 0);
1657 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1658 if (value_equal (iter, value, width))
1661 hmapx_insert (&set, (union value *) value, hash);
1666 xv->n_values = hmapx_count (&set);
1667 xv->values = xnmalloc (xv->n_values, sizeof *xv->values);
1669 HMAPX_FOR_EACH (iter, node, &set)
1670 xv->values[i++] = *iter;
1671 hmapx_destroy (&set);
1673 sort (xv->values, xv->n_values, sizeof *xv->values,
1674 descending ? compare_value_3way_inv : compare_value_3way,
1680 free_var_values (const struct crosstabulation *xt, int var_idx)
1682 struct xtab_var *xv = &xt->vars[var_idx];
1688 /* Displays the crosstabulation table. */
1690 display_crosstabulation (struct crosstabs_proc *proc,
1691 struct crosstabulation *xt, struct pivot_table *table,
1692 size_t crs_leaves[CRS_N_CELLS])
1694 size_t n_rows = xt->vars[ROW_VAR].n_values;
1695 size_t n_cols = xt->vars[COL_VAR].n_values;
1697 size_t *indexes = xnmalloc (table->n_dimensions, sizeof *indexes);
1698 assert (xt->n_vars == 2);
1699 for (size_t i = 0; i < xt->n_consts; i++)
1700 indexes[i + 3] = xt->const_indexes[i];
1702 /* Put in the actual cells. */
1703 double *mp = xt->mat;
1704 for (size_t r = 0; r < n_rows; r++)
1706 if (!xt->row_tot[r] && proc->mode != INTEGER)
1709 indexes[ROW_VAR + 1] = r;
1710 for (size_t c = 0; c < n_cols; c++)
1712 if (!xt->col_tot[c] && proc->mode != INTEGER)
1715 indexes[COL_VAR + 1] = c;
1717 double expected_value = xt->row_tot[r] * xt->col_tot[c] / xt->total;
1718 double residual = *mp - expected_value;
1719 double sresidual = residual / sqrt (expected_value);
1720 double asresidual = (sresidual
1721 * (1. - xt->row_tot[r] / xt->total)
1722 * (1. - xt->col_tot[c] / xt->total));
1723 double entries[CRS_N_CELLS] = {
1724 [CRS_CL_COUNT] = *mp,
1725 [CRS_CL_ROW] = *mp / xt->row_tot[r] * 100.,
1726 [CRS_CL_COLUMN] = *mp / xt->col_tot[c] * 100.,
1727 [CRS_CL_TOTAL] = *mp / xt->total * 100.,
1728 [CRS_CL_EXPECTED] = expected_value,
1729 [CRS_CL_RESIDUAL] = residual,
1730 [CRS_CL_SRESIDUAL] = sresidual,
1731 [CRS_CL_ASRESIDUAL] = asresidual,
1733 for (size_t i = 0; i < proc->n_cells; i++)
1735 int cell = proc->a_cells[i];
1736 indexes[0] = crs_leaves[cell];
1737 pivot_table_put (table, indexes, table->n_dimensions,
1738 pivot_value_new_number (entries[cell]));
1746 for (size_t r = 0; r < n_rows; r++)
1748 if (!xt->row_tot[r] && proc->mode != INTEGER)
1751 double expected_value = xt->row_tot[r] / xt->total;
1752 double entries[CRS_N_CELLS] = {
1753 [CRS_CL_COUNT] = xt->row_tot[r],
1754 [CRS_CL_ROW] = 100.0,
1755 [CRS_CL_COLUMN] = expected_value * 100.,
1756 [CRS_CL_TOTAL] = expected_value * 100.,
1757 [CRS_CL_EXPECTED] = expected_value,
1758 [CRS_CL_RESIDUAL] = SYSMIS,
1759 [CRS_CL_SRESIDUAL] = SYSMIS,
1760 [CRS_CL_ASRESIDUAL] = SYSMIS,
1762 for (size_t i = 0; i < proc->n_cells; i++)
1764 int cell = proc->a_cells[i];
1765 double entry = entries[cell];
1766 if (entry != SYSMIS)
1768 indexes[ROW_VAR + 1] = r;
1769 indexes[COL_VAR + 1] = n_cols;
1770 indexes[0] = crs_leaves[cell];
1771 pivot_table_put (table, indexes, table->n_dimensions,
1772 pivot_value_new_number (entry));
1777 for (size_t c = 0; c <= n_cols; c++)
1779 if (c < n_cols && !xt->col_tot[c] && proc->mode != INTEGER)
1782 double ct = c < n_cols ? xt->col_tot[c] : xt->total;
1783 double expected_value = ct / xt->total;
1784 double entries[CRS_N_CELLS] = {
1785 [CRS_CL_COUNT] = ct,
1786 [CRS_CL_ROW] = expected_value * 100.0,
1787 [CRS_CL_COLUMN] = 100.0,
1788 [CRS_CL_TOTAL] = expected_value * 100.,
1789 [CRS_CL_EXPECTED] = expected_value,
1790 [CRS_CL_RESIDUAL] = SYSMIS,
1791 [CRS_CL_SRESIDUAL] = SYSMIS,
1792 [CRS_CL_ASRESIDUAL] = SYSMIS,
1794 for (size_t i = 0; i < proc->n_cells; i++)
1796 int cell = proc->a_cells[i];
1797 double entry = entries[cell];
1798 if (entry != SYSMIS)
1800 indexes[ROW_VAR + 1] = n_rows;
1801 indexes[COL_VAR + 1] = c;
1802 indexes[0] = crs_leaves[cell];
1803 pivot_table_put (table, indexes, table->n_dimensions,
1804 pivot_value_new_number (entry));
1812 static void calc_r (struct crosstabulation *,
1813 double *XT, double *Y, double *, double *, double *);
1814 static void calc_chisq (struct crosstabulation *,
1815 double[N_CHISQ], int[N_CHISQ], double *, double *);
1817 /* Display chi-square statistics. */
1819 display_chisq (struct crosstabulation *xt, struct pivot_table *chisq)
1821 double chisq_v[N_CHISQ];
1822 double fisher1, fisher2;
1824 calc_chisq (xt, chisq_v, df, &fisher1, &fisher2);
1826 size_t *indexes = xnmalloc (chisq->n_dimensions, sizeof *indexes);
1827 assert (xt->n_vars == 2);
1828 for (size_t i = 0; i < xt->n_consts; i++)
1829 indexes[i + 2] = xt->const_indexes[i];
1830 for (int i = 0; i < N_CHISQ; i++)
1834 double entries[5] = { SYSMIS, SYSMIS, SYSMIS, SYSMIS, SYSMIS };
1837 entries[3] = fisher2;
1838 entries[4] = fisher1;
1840 else if (chisq_v[i] != SYSMIS)
1842 entries[0] = chisq_v[i];
1844 entries[2] = gsl_cdf_chisq_Q (chisq_v[i], df[i]);
1847 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1848 if (entries[j] != SYSMIS)
1851 pivot_table_put (chisq, indexes, chisq->n_dimensions,
1852 pivot_value_new_number (entries[j]));
1858 pivot_table_put (chisq, indexes, chisq->n_dimensions,
1859 pivot_value_new_number (xt->total));
1864 static int calc_symmetric (struct crosstabs_proc *, struct crosstabulation *,
1865 double[N_SYMMETRIC], double[N_SYMMETRIC],
1866 double[N_SYMMETRIC],
1867 double[3], double[3], double[3]);
1869 /* Display symmetric measures. */
1871 display_symmetric (struct crosstabs_proc *proc, struct crosstabulation *xt,
1872 struct pivot_table *sym)
1874 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1875 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1877 if (!calc_symmetric (proc, xt, sym_v, sym_ase, sym_t,
1878 somers_d_v, somers_d_ase, somers_d_t))
1881 size_t *indexes = xnmalloc (sym->n_dimensions, sizeof *indexes);
1882 assert (xt->n_vars == 2);
1883 for (size_t i = 0; i < xt->n_consts; i++)
1884 indexes[i + 2] = xt->const_indexes[i];
1886 for (int i = 0; i < N_SYMMETRIC; i++)
1888 if (sym_v[i] == SYSMIS)
1893 double entries[] = { sym_v[i], sym_ase[i], sym_t[i] };
1894 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1895 if (entries[j] != SYSMIS)
1898 pivot_table_put (sym, indexes, sym->n_dimensions,
1899 pivot_value_new_number (entries[j]));
1903 indexes[1] = N_SYMMETRIC;
1905 struct pivot_value *total = pivot_value_new_number (xt->total);
1906 pivot_value_set_rc (sym, total, PIVOT_RC_COUNT);
1907 pivot_table_put (sym, indexes, sym->n_dimensions, total);
1912 static bool calc_risk (struct crosstabulation *,
1913 double[], double[], double[], union value *,
1916 /* Display risk estimate. */
1918 display_risk (struct crosstabulation *xt, struct pivot_table *risk,
1919 struct pivot_dimension *risk_statistics)
1921 double risk_v[3], lower[3], upper[3], n_valid;
1923 if (!calc_risk (xt, risk_v, upper, lower, c, &n_valid))
1925 assert (risk_statistics);
1927 size_t *indexes = xnmalloc (risk->n_dimensions, sizeof *indexes);
1928 assert (xt->n_vars == 2);
1929 for (size_t i = 0; i < xt->n_consts; i++)
1930 indexes[i + 2] = xt->const_indexes[i];
1932 for (int i = 0; i < 3; i++)
1934 const struct variable *cv = xt->vars[COL_VAR].var;
1935 const struct variable *rv = xt->vars[ROW_VAR].var;
1937 if (risk_v[i] == SYSMIS)
1940 struct string label = DS_EMPTY_INITIALIZER;
1944 ds_put_format (&label, _("Odds Ratio for %s"), var_to_string (rv));
1945 ds_put_cstr (&label, " (");
1946 var_append_value_name (rv, &c[0], &label);
1947 ds_put_cstr (&label, " / ");
1948 var_append_value_name (rv, &c[1], &label);
1949 ds_put_cstr (&label, ")");
1953 ds_put_format (&label, _("For cohort %s = "), var_to_string (cv));
1954 var_append_value_name (cv, &xt->vars[ROW_VAR].values[i - 1], &label);
1958 indexes[1] = pivot_category_create_leaf (
1959 risk_statistics->root,
1960 pivot_value_new_user_text_nocopy (ds_steal_cstr (&label)));
1962 double entries[] = { risk_v[i], lower[i], upper[i] };
1963 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1966 pivot_table_put (risk, indexes, risk->n_dimensions,
1967 pivot_value_new_number (entries[i]));
1970 indexes[1] = pivot_category_create_leaf (
1971 risk_statistics->root,
1972 pivot_value_new_text (N_("N of Valid Cases")));
1974 pivot_table_put (risk, indexes, risk->n_dimensions,
1975 pivot_value_new_number (n_valid));
1979 static int calc_directional (struct crosstabs_proc *, struct crosstabulation *,
1980 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1981 double[N_DIRECTIONAL], double[N_DIRECTIONAL]);
1983 /* Display directional measures. */
1985 display_directional (struct crosstabs_proc *proc,
1986 struct crosstabulation *xt, struct pivot_table *direct)
1988 double direct_v[N_DIRECTIONAL];
1989 double direct_ase[N_DIRECTIONAL];
1990 double direct_t[N_DIRECTIONAL];
1991 double sig[N_DIRECTIONAL];
1992 if (!calc_directional (proc, xt, direct_v, direct_ase, direct_t, sig))
1995 size_t *indexes = xnmalloc (direct->n_dimensions, sizeof *indexes);
1996 assert (xt->n_vars == 2);
1997 for (size_t i = 0; i < xt->n_consts; i++)
1998 indexes[i + 2] = xt->const_indexes[i];
2000 for (int i = 0; i < N_DIRECTIONAL; i++)
2002 if (direct_v[i] == SYSMIS)
2007 double entries[] = {
2008 direct_v[i], direct_ase[i], direct_t[i], sig[i],
2010 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
2011 if (entries[j] != SYSMIS)
2014 pivot_table_put (direct, indexes, direct->n_dimensions,
2015 pivot_value_new_number (entries[j]));
2022 /* Statistical calculations. */
2024 /* Returns the value of the logarithm of gamma (factorial) function for an integer
2027 log_gamma_int (double xt)
2032 for (i = 2; i < xt; i++)
2038 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2040 static inline double
2041 Pr (int a, int b, int c, int d)
2043 return exp (log_gamma_int (a + b + 1.) - log_gamma_int (a + 1.)
2044 + log_gamma_int (c + d + 1.) - log_gamma_int (b + 1.)
2045 + log_gamma_int (a + c + 1.) - log_gamma_int (c + 1.)
2046 + log_gamma_int (b + d + 1.) - log_gamma_int (d + 1.)
2047 - log_gamma_int (a + b + c + d + 1.));
2050 /* Swap the contents of A and B. */
2052 swap (int *a, int *b)
2059 /* Calculate significance for Fisher's exact test as specified in
2060 _SPSS Statistical Algorithms_, Appendix 5. */
2062 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2067 if (MIN (c, d) < MIN (a, b))
2068 swap (&a, &c), swap (&b, &d);
2069 if (MIN (b, d) < MIN (a, c))
2070 swap (&a, &b), swap (&c, &d);
2074 swap (&a, &b), swap (&c, &d);
2076 swap (&a, &c), swap (&b, &d);
2079 pn1 = Pr (a, b, c, d);
2081 for (xt = 1; xt <= a; xt++)
2083 *fisher1 += Pr (a - xt, b + xt, c + xt, d - xt);
2086 *fisher2 = *fisher1;
2088 for (xt = 1; xt <= b; xt++)
2090 double p = Pr (a + xt, b - xt, c - xt, d + xt);
2096 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2097 columns with values COLS and N_ROWS rows with values ROWS. Values
2098 in the matrix sum to xt->total. */
2100 calc_chisq (struct crosstabulation *xt,
2101 double chisq[N_CHISQ], int df[N_CHISQ],
2102 double *fisher1, double *fisher2)
2104 chisq[0] = chisq[1] = 0.;
2105 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2106 *fisher1 = *fisher2 = SYSMIS;
2108 df[0] = df[1] = (xt->ns_cols - 1) * (xt->ns_rows - 1);
2110 if (xt->ns_rows <= 1 || xt->ns_cols <= 1)
2112 chisq[0] = chisq[1] = SYSMIS;
2116 size_t n_cols = xt->vars[COL_VAR].n_values;
2117 FOR_EACH_POPULATED_ROW (r, xt)
2118 FOR_EACH_POPULATED_COLUMN (c, xt)
2120 const double expected = xt->row_tot[r] * xt->col_tot[c] / xt->total;
2121 const double freq = xt->mat[n_cols * r + c];
2122 const double residual = freq - expected;
2124 chisq[0] += residual * residual / expected;
2126 chisq[1] += freq * log (expected / freq);
2137 /* Calculate Yates and Fisher exact test. */
2138 if (xt->ns_cols == 2 && xt->ns_rows == 2)
2140 double f11, f12, f21, f22;
2146 FOR_EACH_POPULATED_COLUMN (c, xt)
2154 f11 = xt->mat[nz_cols[0]];
2155 f12 = xt->mat[nz_cols[1]];
2156 f21 = xt->mat[nz_cols[0] + n_cols];
2157 f22 = xt->mat[nz_cols[1] + n_cols];
2162 const double xt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * xt->total;
2165 chisq[3] = (xt->total * pow2 (xt_)
2166 / (f11 + f12) / (f21 + f22)
2167 / (f11 + f21) / (f12 + f22));
2175 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2178 /* Calculate Mantel-Haenszel. */
2179 if (var_is_numeric (xt->vars[ROW_VAR].var)
2180 && var_is_numeric (xt->vars[COL_VAR].var))
2182 double r, ase_0, ase_1;
2183 calc_r (xt, (double *) xt->vars[ROW_VAR].values,
2184 (double *) xt->vars[COL_VAR].values,
2185 &r, &ase_0, &ase_1);
2187 chisq[4] = (xt->total - 1.) * r * r;
2192 /* Calculate the value of Pearson's r. r is stored into R, its T value into
2193 T, and standard error into ERROR. The row and column values must be
2194 passed in XT and Y. */
2196 calc_r (struct crosstabulation *xt,
2197 double *XT, double *Y, double *r, double *t, double *error)
2199 size_t n_rows = xt->vars[ROW_VAR].n_values;
2200 size_t n_cols = xt->vars[COL_VAR].n_values;
2201 double SX, SY, S, T;
2203 double sum_XYf, sum_X2Y2f;
2204 double sum_Xr, sum_X2r;
2205 double sum_Yc, sum_Y2c;
2208 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < n_rows; i++)
2209 for (j = 0; j < n_cols; j++)
2211 double fij = xt->mat[j + i * n_cols];
2212 double product = XT[i] * Y[j];
2213 double temp = fij * product;
2215 sum_X2Y2f += temp * product;
2218 for (sum_Xr = sum_X2r = 0., i = 0; i < n_rows; i++)
2220 sum_Xr += XT[i] * xt->row_tot[i];
2221 sum_X2r += pow2 (XT[i]) * xt->row_tot[i];
2223 Xbar = sum_Xr / xt->total;
2225 for (sum_Yc = sum_Y2c = 0., i = 0; i < n_cols; i++)
2227 sum_Yc += Y[i] * xt->col_tot[i];
2228 sum_Y2c += Y[i] * Y[i] * xt->col_tot[i];
2230 Ybar = sum_Yc / xt->total;
2232 S = sum_XYf - sum_Xr * sum_Yc / xt->total;
2233 SX = sum_X2r - pow2 (sum_Xr) / xt->total;
2234 SY = sum_Y2c - pow2 (sum_Yc) / xt->total;
2237 *t = *r / sqrt (1 - pow2 (*r)) * sqrt (xt->total - 2);
2242 for (s = c = 0., i = 0; i < n_rows; i++)
2243 for (j = 0; j < n_cols; j++)
2245 double Xresid, Yresid;
2248 Xresid = XT[i] - Xbar;
2249 Yresid = Y[j] - Ybar;
2250 temp = (T * Xresid * Yresid
2252 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2253 y = xt->mat[j + i * n_cols] * temp * temp - c;
2258 *error = sqrt (s) / (T * T);
2262 /* Calculate symmetric statistics and their asymptotic standard
2263 errors. Returns 0 if none could be calculated. */
2265 calc_symmetric (struct crosstabs_proc *proc, struct crosstabulation *xt,
2266 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2267 double t[N_SYMMETRIC],
2268 double somers_d_v[3], double somers_d_ase[3],
2269 double somers_d_t[3])
2271 size_t n_rows = xt->vars[ROW_VAR].n_values;
2272 size_t n_cols = xt->vars[COL_VAR].n_values;
2275 q = MIN (xt->ns_rows, xt->ns_cols);
2279 for (i = 0; i < N_SYMMETRIC; i++)
2280 v[i] = ase[i] = t[i] = SYSMIS;
2282 /* Phi, Cramer's V, contingency coefficient. */
2283 if (proc->statistics & (CRS_ST_PHI | CRS_ST_CC))
2285 double Xp = 0.; /* Pearson chi-square. */
2287 FOR_EACH_POPULATED_ROW (r, xt)
2288 FOR_EACH_POPULATED_COLUMN (c, xt)
2290 double expected = xt->row_tot[r] * xt->col_tot[c] / xt->total;
2291 double freq = xt->mat[n_cols * r + c];
2292 double residual = freq - expected;
2294 Xp += residual * residual / expected;
2297 if (proc->statistics & CRS_ST_PHI)
2299 v[0] = sqrt (Xp / xt->total);
2300 v[1] = sqrt (Xp / (xt->total * (q - 1)));
2302 if (proc->statistics & CRS_ST_CC)
2303 v[2] = sqrt (Xp / (Xp + xt->total));
2306 if (proc->statistics & (CRS_ST_BTAU | CRS_ST_CTAU
2307 | CRS_ST_GAMMA | CRS_ST_D))
2312 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2316 Dr = Dc = pow2 (xt->total);
2317 for (r = 0; r < n_rows; r++)
2318 Dr -= pow2 (xt->row_tot[r]);
2319 for (c = 0; c < n_cols; c++)
2320 Dc -= pow2 (xt->col_tot[c]);
2322 cum = xnmalloc (n_cols * n_rows, sizeof *cum);
2323 for (c = 0; c < n_cols; c++)
2327 for (r = 0; r < n_rows; r++)
2328 cum[c + r * n_cols] = ct += xt->mat[c + r * n_cols];
2337 for (i = 0; i < n_rows; i++)
2341 for (j = 1; j < n_cols; j++)
2342 Cij += xt->col_tot[j] - cum[j + i * n_cols];
2345 for (j = 1; j < n_cols; j++)
2346 Dij += cum[j + (i - 1) * n_cols];
2350 double fij = xt->mat[j + i * n_cols];
2356 assert (j < n_cols);
2358 Cij -= xt->col_tot[j] - cum[j + i * n_cols];
2359 Dij += xt->col_tot[j - 1] - cum[j - 1 + i * n_cols];
2363 Cij += cum[j - 1 + (i - 1) * n_cols];
2364 Dij -= cum[j + (i - 1) * n_cols];
2370 if (proc->statistics & CRS_ST_BTAU)
2371 v[3] = (P - Q) / sqrt (Dr * Dc);
2372 if (proc->statistics & CRS_ST_CTAU)
2373 v[4] = (q * (P - Q)) / (pow2 (xt->total) * (q - 1));
2374 if (proc->statistics & CRS_ST_GAMMA)
2375 v[5] = (P - Q) / (P + Q);
2377 /* ASE for tau-b, tau-c, gamma. Calculations could be
2378 eliminated here, at expense of memory. */
2383 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2384 for (i = 0; i < n_rows; i++)
2388 for (j = 1; j < n_cols; j++)
2389 Cij += xt->col_tot[j] - cum[j + i * n_cols];
2392 for (j = 1; j < n_cols; j++)
2393 Dij += cum[j + (i - 1) * n_cols];
2397 double fij = xt->mat[j + i * n_cols];
2399 if (proc->statistics & CRS_ST_BTAU)
2401 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2402 + v[3] * (xt->row_tot[i] * Dc
2403 + xt->col_tot[j] * Dr));
2404 btau_cum += fij * temp * temp;
2408 const double temp = Cij - Dij;
2409 ctau_cum += fij * temp * temp;
2412 if (proc->statistics & CRS_ST_GAMMA)
2414 const double temp = Q * Cij - P * Dij;
2415 gamma_cum += fij * temp * temp;
2418 if (proc->statistics & CRS_ST_D)
2420 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2421 - (P - Q) * (xt->total - xt->row_tot[i]));
2422 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2423 - (Q - P) * (xt->total - xt->col_tot[j]));
2428 assert (j < n_cols);
2430 Cij -= xt->col_tot[j] - cum[j + i * n_cols];
2431 Dij += xt->col_tot[j - 1] - cum[j - 1 + i * n_cols];
2435 Cij += cum[j - 1 + (i - 1) * n_cols];
2436 Dij -= cum[j + (i - 1) * n_cols];
2442 btau_var = ((btau_cum
2443 - (xt->total * pow2 (xt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2445 if (proc->statistics & CRS_ST_BTAU)
2447 ase[3] = sqrt (btau_var);
2448 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / xt->total)
2451 if (proc->statistics & CRS_ST_CTAU)
2453 ase[4] = ((2 * q / ((q - 1) * pow2 (xt->total)))
2454 * sqrt (ctau_cum - (P - Q) * (P - Q) / xt->total));
2455 t[4] = v[4] / ase[4];
2457 if (proc->statistics & CRS_ST_GAMMA)
2459 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2460 t[5] = v[5] / (2. / (P + Q)
2461 * sqrt (ctau_cum - (P - Q) * (P - Q) / xt->total));
2463 if (proc->statistics & CRS_ST_D)
2465 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2466 somers_d_ase[0] = SYSMIS;
2467 somers_d_t[0] = (somers_d_v[0]
2469 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2470 somers_d_v[1] = (P - Q) / Dc;
2471 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2472 somers_d_t[1] = (somers_d_v[1]
2474 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2475 somers_d_v[2] = (P - Q) / Dr;
2476 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2477 somers_d_t[2] = (somers_d_v[2]
2479 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2485 /* Spearman correlation, Pearson's r. */
2486 if (proc->statistics & CRS_ST_CORR)
2488 double *R = xmalloc (sizeof *R * n_rows);
2489 double *C = xmalloc (sizeof *C * n_cols);
2492 double y, t, c = 0., s = 0.;
2497 R[i] = s + (xt->row_tot[i] + 1.) / 2.;
2498 y = xt->row_tot[i] - c;
2504 assert (i < n_rows);
2509 double y, t, c = 0., s = 0.;
2514 C[j] = s + (xt->col_tot[j] + 1.) / 2;
2515 y = xt->col_tot[j] - c;
2521 assert (j < n_cols);
2525 calc_r (xt, R, C, &v[6], &t[6], &ase[6]);
2530 calc_r (xt, (double *) xt->vars[ROW_VAR].values,
2531 (double *) xt->vars[COL_VAR].values,
2532 &v[7], &t[7], &ase[7]);
2535 /* Cohen's kappa. */
2536 if (proc->statistics & CRS_ST_KAPPA && xt->ns_rows == xt->ns_cols)
2538 double ase_under_h0;
2539 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2542 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2543 i < xt->ns_rows; i++, j++)
2547 while (xt->col_tot[j] == 0.)
2550 prod = xt->row_tot[i] * xt->col_tot[j];
2551 sum = xt->row_tot[i] + xt->col_tot[j];
2553 sum_fii += xt->mat[j + i * n_cols];
2555 sum_fiiri_ci += xt->mat[j + i * n_cols] * sum;
2556 sum_riciri_ci += prod * sum;
2558 for (sum_fijri_ci2 = 0., i = 0; i < xt->ns_rows; i++)
2559 for (j = 0; j < xt->ns_cols; j++)
2561 double sum = xt->row_tot[i] + xt->col_tot[j];
2562 sum_fijri_ci2 += xt->mat[j + i * n_cols] * sum * sum;
2565 v[8] = (xt->total * sum_fii - sum_rici) / (pow2 (xt->total) - sum_rici);
2567 ase_under_h0 = sqrt ((pow2 (xt->total) * sum_rici
2568 + sum_rici * sum_rici
2569 - xt->total * sum_riciri_ci)
2570 / (xt->total * (pow2 (xt->total) - sum_rici) * (pow2 (xt->total) - sum_rici)));
2572 ase[8] = sqrt (xt->total * (((sum_fii * (xt->total - sum_fii))
2573 / pow2 (pow2 (xt->total) - sum_rici))
2574 + ((2. * (xt->total - sum_fii)
2575 * (2. * sum_fii * sum_rici
2576 - xt->total * sum_fiiri_ci))
2577 / pow3 (pow2 (xt->total) - sum_rici))
2578 + (pow2 (xt->total - sum_fii)
2579 * (xt->total * sum_fijri_ci2 - 4.
2580 * sum_rici * sum_rici)
2581 / pow4 (pow2 (xt->total) - sum_rici))));
2583 t[8] = v[8] / ase_under_h0;
2589 /* Calculate risk estimate. */
2591 calc_risk (struct crosstabulation *xt,
2592 double *value, double *upper, double *lower, union value *c,
2595 size_t n_cols = xt->vars[COL_VAR].n_values;
2596 double f11, f12, f21, f22;
2599 for (int i = 0; i < 3; i++)
2600 value[i] = upper[i] = lower[i] = SYSMIS;
2602 if (xt->ns_rows != 2 || xt->ns_cols != 2)
2606 /* Find populated columns. */
2609 FOR_EACH_POPULATED_COLUMN (c, xt)
2613 /* Find populated rows. */
2616 FOR_EACH_POPULATED_ROW (r, xt)
2620 f11 = xt->mat[nz_cols[0] + n_cols * nz_rows[0]];
2621 f12 = xt->mat[nz_cols[1] + n_cols * nz_rows[0]];
2622 f21 = xt->mat[nz_cols[0] + n_cols * nz_rows[1]];
2623 f22 = xt->mat[nz_cols[1] + n_cols * nz_rows[1]];
2624 *n_valid = f11 + f12 + f21 + f22;
2626 c[0] = xt->vars[COL_VAR].values[nz_cols[0]];
2627 c[1] = xt->vars[COL_VAR].values[nz_cols[1]];
2630 value[0] = (f11 * f22) / (f12 * f21);
2631 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2632 lower[0] = value[0] * exp (-1.960 * v);
2633 upper[0] = value[0] * exp (1.960 * v);
2635 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2636 v = sqrt ((f12 / (f11 * (f11 + f12)))
2637 + (f22 / (f21 * (f21 + f22))));
2638 lower[1] = value[1] * exp (-1.960 * v);
2639 upper[1] = value[1] * exp (1.960 * v);
2641 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2642 v = sqrt ((f11 / (f12 * (f11 + f12)))
2643 + (f21 / (f22 * (f21 + f22))));
2644 lower[2] = value[2] * exp (-1.960 * v);
2645 upper[2] = value[2] * exp (1.960 * v);
2650 /* Calculate directional measures. */
2652 calc_directional (struct crosstabs_proc *proc, struct crosstabulation *xt,
2653 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2654 double t[N_DIRECTIONAL], double sig[N_DIRECTIONAL])
2656 size_t n_rows = xt->vars[ROW_VAR].n_values;
2657 size_t n_cols = xt->vars[COL_VAR].n_values;
2658 for (int i = 0; i < N_DIRECTIONAL; i++)
2659 v[i] = ase[i] = t[i] = sig[i] = SYSMIS;
2662 if (proc->statistics & CRS_ST_LAMBDA)
2664 /* Find maximum for each row and their sum. */
2665 double *fim = xnmalloc (n_rows, sizeof *fim);
2666 int *fim_index = xnmalloc (n_rows, sizeof *fim_index);
2667 double sum_fim = 0.0;
2668 for (int i = 0; i < n_rows; i++)
2670 double max = xt->mat[i * n_cols];
2673 for (int j = 1; j < n_cols; j++)
2674 if (xt->mat[j + i * n_cols] > max)
2676 max = xt->mat[j + i * n_cols];
2682 fim_index[i] = index;
2685 /* Find maximum for each column. */
2686 double *fmj = xnmalloc (n_cols, sizeof *fmj);
2687 int *fmj_index = xnmalloc (n_cols, sizeof *fmj_index);
2688 double sum_fmj = 0.0;
2689 for (int j = 0; j < n_cols; j++)
2691 double max = xt->mat[j];
2694 for (int i = 1; i < n_rows; i++)
2695 if (xt->mat[j + i * n_cols] > max)
2697 max = xt->mat[j + i * n_cols];
2703 fmj_index[j] = index;
2706 /* Find maximum row total. */
2707 double rm = xt->row_tot[0];
2709 for (int i = 1; i < n_rows; i++)
2710 if (xt->row_tot[i] > rm)
2712 rm = xt->row_tot[i];
2716 /* Find maximum column total. */
2717 double cm = xt->col_tot[0];
2719 for (int j = 1; j < n_cols; j++)
2720 if (xt->col_tot[j] > cm)
2722 cm = xt->col_tot[j];
2726 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * xt->total - rm - cm);
2727 v[1] = (sum_fmj - rm) / (xt->total - rm);
2728 v[2] = (sum_fim - cm) / (xt->total - cm);
2730 /* ASE1 for Y given XT. */
2733 for (int i = 0; i < n_rows; i++)
2734 if (cm_index == fim_index[i])
2736 ase[2] = sqrt ((xt->total - sum_fim) * (sum_fim + cm - 2. * accum)
2737 / pow3 (xt->total - cm));
2740 /* ASE0 for Y given XT. */
2743 for (int i = 0; i < n_rows; i++)
2744 if (cm_index != fim_index[i])
2745 accum += (xt->mat[i * n_cols + fim_index[i]]
2746 + xt->mat[i * n_cols + cm_index]);
2747 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / xt->total) / (xt->total - cm));
2750 /* ASE1 for XT given Y. */
2753 for (int j = 0; j < n_cols; j++)
2754 if (rm_index == fmj_index[j])
2756 ase[1] = sqrt ((xt->total - sum_fmj) * (sum_fmj + rm - 2. * accum)
2757 / pow3 (xt->total - rm));
2760 /* ASE0 for XT given Y. */
2763 for (int j = 0; j < n_cols; j++)
2764 if (rm_index != fmj_index[j])
2765 accum += (xt->mat[j + n_cols * fmj_index[j]]
2766 + xt->mat[j + n_cols * rm_index]);
2767 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / xt->total) / (xt->total - rm));
2770 /* Symmetric ASE0 and ASE1. */
2772 double accum0 = 0.0;
2773 double accum1 = 0.0;
2774 for (int i = 0; i < n_rows; i++)
2775 for (int j = 0; j < n_cols; j++)
2777 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2778 int temp1 = (i == rm_index) + (j == cm_index);
2779 accum0 += xt->mat[j + i * n_cols] * pow2 (temp0 - temp1);
2780 accum1 += (xt->mat[j + i * n_cols]
2781 * pow2 (temp0 + (v[0] - 1.) * temp1));
2783 ase[0] = sqrt (accum1 - 4. * xt->total * v[0] * v[0]) / (2. * xt->total - rm - cm);
2784 t[0] = v[0] / (sqrt (accum0 - pow2 (sum_fim + sum_fmj - cm - rm) / xt->total)
2785 / (2. * xt->total - rm - cm));
2788 for (int i = 0; i < 3; i++)
2789 sig[i] = 2 * gsl_cdf_ugaussian_Q (t[i]);
2798 double sum_fij2_ri = 0.0;
2799 double sum_fij2_ci = 0.0;
2800 FOR_EACH_POPULATED_ROW (i, xt)
2801 FOR_EACH_POPULATED_COLUMN (j, xt)
2803 double temp = pow2 (xt->mat[j + i * n_cols]);
2804 sum_fij2_ri += temp / xt->row_tot[i];
2805 sum_fij2_ci += temp / xt->col_tot[j];
2808 double sum_ri2 = 0.0;
2809 for (int i = 0; i < n_rows; i++)
2810 sum_ri2 += pow2 (xt->row_tot[i]);
2812 double sum_cj2 = 0.0;
2813 for (int j = 0; j < n_cols; j++)
2814 sum_cj2 += pow2 (xt->col_tot[j]);
2816 v[3] = (xt->total * sum_fij2_ci - sum_ri2) / (pow2 (xt->total) - sum_ri2);
2817 v[4] = (xt->total * sum_fij2_ri - sum_cj2) / (pow2 (xt->total) - sum_cj2);
2821 if (proc->statistics & CRS_ST_UC)
2824 FOR_EACH_POPULATED_ROW (i, xt)
2825 UX -= xt->row_tot[i] / xt->total * log (xt->row_tot[i] / xt->total);
2828 FOR_EACH_POPULATED_COLUMN (j, xt)
2829 UY -= xt->col_tot[j] / xt->total * log (xt->col_tot[j] / xt->total);
2833 for (int i = 0; i < n_rows; i++)
2834 for (int j = 0; j < n_cols; j++)
2836 double entry = xt->mat[j + i * n_cols];
2841 P += entry * pow2 (log (xt->col_tot[j] * xt->row_tot[i] / (xt->total * entry)));
2842 UXY -= entry / xt->total * log (entry / xt->total);
2845 double ase1_yx = 0.0;
2846 double ase1_xy = 0.0;
2847 double ase1_sym = 0.0;
2848 for (int i = 0; i < n_rows; i++)
2849 for (int j = 0; j < n_cols; j++)
2851 double entry = xt->mat[j + i * n_cols];
2856 ase1_yx += entry * pow2 (UY * log (entry / xt->row_tot[i])
2857 + (UX - UXY) * log (xt->col_tot[j] / xt->total));
2858 ase1_xy += entry * pow2 (UX * log (entry / xt->col_tot[j])
2859 + (UY - UXY) * log (xt->row_tot[i] / xt->total));
2860 ase1_sym += entry * pow2 ((UXY
2861 * log (xt->row_tot[i] * xt->col_tot[j] / pow2 (xt->total)))
2862 - (UX + UY) * log (entry / xt->total));
2865 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2866 ase[5] = (2. / (xt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2869 v[6] = (UX + UY - UXY) / UX;
2870 ase[6] = sqrt (ase1_xy) / (xt->total * UX * UX);
2871 t[6] = v[6] / (sqrt (P - xt->total * pow2 (UX + UY - UXY)) / (xt->total * UX));
2873 v[7] = (UX + UY - UXY) / UY;
2874 ase[7] = sqrt (ase1_yx) / (xt->total * UY * UY);
2875 t[7] = v[7] / (sqrt (P - xt->total * pow2 (UX + UY - UXY)) / (xt->total * UY));
2879 if (proc->statistics & CRS_ST_D)
2881 double v_dummy[N_SYMMETRIC];
2882 double ase_dummy[N_SYMMETRIC];
2883 double t_dummy[N_SYMMETRIC];
2884 double somers_d_v[3];
2885 double somers_d_ase[3];
2886 double somers_d_t[3];
2888 if (calc_symmetric (proc, xt, v_dummy, ase_dummy, t_dummy,
2889 somers_d_v, somers_d_ase, somers_d_t))
2891 for (int i = 0; i < 3; i++)
2893 v[8 + i] = somers_d_v[i];
2894 ase[8 + i] = somers_d_ase[i];
2895 t[8 + i] = somers_d_t[i];
2896 sig[8 + i] = 2 * gsl_cdf_ugaussian_Q (fabs (somers_d_t[i]));
2902 if (proc->statistics & CRS_ST_ETA)
2905 double sum_Xr = 0.0;
2906 double sum_X2r = 0.0;
2907 for (int i = 0; i < n_rows; i++)
2909 sum_Xr += xt->vars[ROW_VAR].values[i].f * xt->row_tot[i];
2910 sum_X2r += pow2 (xt->vars[ROW_VAR].values[i].f) * xt->row_tot[i];
2912 double SX = sum_X2r - pow2 (sum_Xr) / xt->total;
2915 FOR_EACH_POPULATED_COLUMN (j, xt)
2919 for (int i = 0; i < n_rows; i++)
2921 SXW += (pow2 (xt->vars[ROW_VAR].values[i].f)
2922 * xt->mat[j + i * n_cols]);
2923 cum += (xt->vars[ROW_VAR].values[i].f
2924 * xt->mat[j + i * n_cols]);
2927 SXW -= cum * cum / xt->col_tot[j];
2929 v[11] = sqrt (1. - SXW / SX);
2932 double sum_Yc = 0.0;
2933 double sum_Y2c = 0.0;
2934 for (int i = 0; i < n_cols; i++)
2936 sum_Yc += xt->vars[COL_VAR].values[i].f * xt->col_tot[i];
2937 sum_Y2c += pow2 (xt->vars[COL_VAR].values[i].f) * xt->col_tot[i];
2939 double SY = sum_Y2c - pow2 (sum_Yc) / xt->total;
2942 FOR_EACH_POPULATED_ROW (i, xt)
2945 for (int j = 0; j < n_cols; j++)
2947 SYW += (pow2 (xt->vars[COL_VAR].values[j].f)
2948 * xt->mat[j + i * n_cols]);
2949 cum += (xt->vars[COL_VAR].values[j].f
2950 * xt->mat[j + i * n_cols]);
2953 SYW -= cum * cum / xt->row_tot[i];
2955 v[12] = sqrt (1. - SYW / SY);