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 size_t 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. */
186 /* Integer mode variable info. */
189 struct hmap_node hmap_node; /* In struct crosstabs_proc var_ranges map. */
190 const struct variable *var; /* The variable. */
191 int min; /* Minimum value. */
192 int max; /* Maximum value + 1. */
193 int count; /* max - min. */
196 struct crosstabs_proc
198 const struct dictionary *dict;
199 enum { INTEGER, GENERAL } mode;
200 enum mv_class exclude;
203 struct fmt_spec weight_format;
205 /* Variables specifies on VARIABLES. */
206 const struct variable **variables;
208 struct hmap var_ranges;
211 struct crosstabulation *pivots;
215 size_t n_cells; /* Number of cells requested. */
216 unsigned int cells; /* Bit k is 1 if cell k is requested. */
217 int a_cells[CRS_N_CELLS]; /* 0...n_cells-1 are the requested cells. */
219 /* Rounding of cells. */
220 bool round_case_weights; /* Round case weights? */
221 bool round_cells; /* If !round_case_weights, round cells? */
222 bool round_down; /* Round down? (otherwise to nearest) */
225 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
227 bool descending; /* True if descending sort order is requested. */
230 static bool parse_crosstabs_tables (struct lexer *, struct dataset *,
231 struct crosstabs_proc *);
232 static bool parse_crosstabs_variables (struct lexer *, struct dataset *,
233 struct crosstabs_proc *);
235 static const struct var_range *get_var_range (const struct crosstabs_proc *,
236 const struct variable *);
238 static bool should_tabulate_case (const struct crosstabulation *,
239 const struct ccase *, enum mv_class exclude);
240 static void tabulate_general_case (struct crosstabulation *, const struct ccase *,
242 static void tabulate_integer_case (struct crosstabulation *, const struct ccase *,
244 static void postcalc (struct crosstabs_proc *, struct lexer *);
247 round_weight (const struct crosstabs_proc *proc, double weight)
249 return proc->round_down ? floor (weight) : floor (weight + 0.5);
252 #define FOR_EACH_POPULATED_COLUMN(C, XT) \
253 for (size_t C = next_populated_column (0, XT); \
254 C < (XT)->vars[COL_VAR].n_values; \
255 C = next_populated_column (C + 1, XT))
257 next_populated_column (size_t c, const struct crosstabulation *xt)
259 size_t n_columns = xt->vars[COL_VAR].n_values;
260 for (; c < n_columns; c++)
266 #define FOR_EACH_POPULATED_ROW(R, XT) \
267 for (size_t R = next_populated_row (0, XT); R < (XT)->vars[ROW_VAR].n_values; \
268 R = next_populated_row (R + 1, XT))
270 next_populated_row (size_t r, const struct crosstabulation *xt)
272 size_t n_rows = xt->vars[ROW_VAR].n_values;
273 for (; r < n_rows; r++)
279 /* Parses and executes the CROSSTABS procedure. */
281 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
283 int result = CMD_FAILURE;
285 struct crosstabs_proc proc = {
286 .dict = dataset_dict (ds),
291 .weight_format = *dict_get_weight_format (dataset_dict (ds)),
295 .var_ranges = HMAP_INITIALIZER (proc.var_ranges),
300 .cells = 1u << CRS_CL_COUNT,
301 /* n_cells and a_cells will be filled in later. */
303 .round_case_weights = false,
304 .round_cells = false,
311 bool show_tables = true;
313 lex_match (lexer, T_SLASH);
316 if (lex_match_id (lexer, "VARIABLES"))
318 if (!parse_crosstabs_variables (lexer, ds, &proc))
321 else if (lex_match_id (lexer, "MISSING"))
323 lex_match (lexer, T_EQUALS);
324 exclude_ofs = lex_ofs (lexer);
325 if (lex_match_id (lexer, "TABLE"))
326 proc.exclude = MV_ANY;
327 else if (lex_match_id (lexer, "INCLUDE"))
328 proc.exclude = MV_SYSTEM;
329 else if (lex_match_id (lexer, "REPORT"))
333 lex_error_expecting (lexer, "TABLE", "INCLUDE", "REPORT");
337 else if (lex_match_id (lexer, "COUNT"))
339 lex_match (lexer, T_EQUALS);
341 /* Default is CELL. */
342 proc.round_case_weights = false;
343 proc.round_cells = true;
345 while (lex_token (lexer) != T_SLASH && lex_token (lexer) != T_ENDCMD)
347 if (lex_match_id (lexer, "ASIS"))
349 proc.round_case_weights = false;
350 proc.round_cells = false;
352 else if (lex_match_id (lexer, "CASE"))
354 proc.round_case_weights = true;
355 proc.round_cells = false;
357 else if (lex_match_id (lexer, "CELL"))
359 proc.round_case_weights = false;
360 proc.round_cells = true;
362 else if (lex_match_id (lexer, "ROUND"))
363 proc.round_down = false;
364 else if (lex_match_id (lexer, "TRUNCATE"))
365 proc.round_down = true;
368 lex_error_expecting (lexer, "ASIS", "CASE", "CELL",
369 "ROUND", "TRUNCATE");
372 lex_match (lexer, T_COMMA);
375 else if (lex_match_id (lexer, "FORMAT"))
377 lex_match (lexer, T_EQUALS);
378 while (lex_token (lexer) != T_SLASH && lex_token (lexer) != T_ENDCMD)
380 if (lex_match_id (lexer, "AVALUE"))
381 proc.descending = false;
382 else if (lex_match_id (lexer, "DVALUE"))
383 proc.descending = true;
384 else if (lex_match_id (lexer, "TABLES"))
386 else if (lex_match_id (lexer, "NOTABLES"))
390 lex_error_expecting (lexer, "AVALUE", "DVALUE",
391 "TABLES", "NOTABLES");
394 lex_match (lexer, T_COMMA);
397 else if (lex_match_id (lexer, "BARCHART"))
398 proc.barchart = true;
399 else if (lex_match_id (lexer, "CELLS"))
401 lex_match (lexer, T_EQUALS);
403 if (lex_match_id (lexer, "NONE"))
405 else if (lex_match (lexer, T_ALL))
406 proc.cells = CRS_ALL_CELLS;
410 while (lex_token (lexer) != T_SLASH && lex_token (lexer) != T_ENDCMD)
412 #define C(KEYWORD, STRING, RC) \
413 if (lex_match_id (lexer, #KEYWORD)) \
415 proc.cells |= 1u << CRS_CL_##KEYWORD; \
421 static const char *cells[] =
423 #define C(KEYWORD, STRING, RC) #KEYWORD,
427 lex_error_expecting_array (lexer, cells,
428 sizeof cells / sizeof *cells);
432 proc.cells = ((1u << CRS_CL_COUNT) | (1u << CRS_CL_ROW)
433 | (1u << CRS_CL_COLUMN) | (1u << CRS_CL_TOTAL));
436 else if (lex_match_id (lexer, "STATISTICS"))
438 lex_match (lexer, T_EQUALS);
440 if (lex_match_id (lexer, "NONE"))
442 else if (lex_match (lexer, T_ALL))
443 proc.statistics = CRS_ALL_STATISTICS;
447 while (lex_token (lexer) != T_SLASH && lex_token (lexer) != T_ENDCMD)
450 if (lex_match_id (lexer, #KEYWORD)) \
452 proc.statistics |= CRS_ST_##KEYWORD; \
457 static const char *stats[] =
459 #define S(KEYWORD) #KEYWORD,
463 lex_error_expecting_array (lexer, stats,
464 sizeof stats / sizeof *stats);
467 if (!proc.statistics)
468 proc.statistics = CRS_ST_CHISQ;
471 else if (!parse_crosstabs_tables (lexer, ds, &proc))
474 if (!lex_match (lexer, T_SLASH))
477 if (!lex_end_of_command (lexer))
482 msg (SE, _("At least one crosstabulation must be requested (using "
483 "the TABLES subcommand)."));
490 for (size_t i = 0; i < CRS_N_CELLS; i++)
491 if (proc.cells & (1u << i))
492 proc.a_cells[proc.n_cells++] = i;
493 assert (proc.n_cells < CRS_N_CELLS);
495 /* Missing values. */
496 if (proc.mode == GENERAL && !proc.exclude)
498 lex_ofs_msg (lexer, SW, exclude_ofs, exclude_ofs,
499 _("Missing mode %s not allowed in general mode. "
500 "Assuming %s."), "REPORT", "MISSING=TABLE");
501 proc.exclude = MV_ANY;
504 struct casereader *input = casereader_create_filter_weight (proc_open (ds),
507 struct casegrouper *grouper = casegrouper_create_splits (input, dataset_dict (ds));
508 struct casereader *group;
509 while (casegrouper_get_next_group (grouper, &group))
511 output_split_file_values_peek (ds, group);
513 /* Initialize hash tables. */
514 for (struct crosstabulation *xt = &proc.pivots[0];
515 xt < &proc.pivots[proc.n_pivots]; xt++)
516 hmap_init (&xt->data);
520 for (; (c = casereader_read (group)) != NULL; case_unref (c))
521 for (struct crosstabulation *xt = &proc.pivots[0];
522 xt < &proc.pivots[proc.n_pivots]; xt++)
524 double weight = dict_get_case_weight (dataset_dict (ds), c,
526 if (proc.round_case_weights)
528 weight = round_weight (&proc, weight);
532 if (should_tabulate_case (xt, c, proc.exclude))
534 if (proc.mode == GENERAL)
535 tabulate_general_case (xt, c, weight);
537 tabulate_integer_case (xt, c, weight);
540 xt->missing += weight;
542 casereader_destroy (group);
545 postcalc (&proc, lexer);
547 bool ok = casegrouper_destroy (grouper);
548 ok = proc_commit (ds) && ok;
550 result = ok ? CMD_SUCCESS : CMD_FAILURE;
553 free (proc.variables);
555 struct var_range *range, *next_range;
556 HMAP_FOR_EACH_SAFE (range, next_range, struct var_range, hmap_node,
559 hmap_delete (&proc.var_ranges, &range->hmap_node);
562 for (struct crosstabulation *xt = &proc.pivots[0];
563 xt < &proc.pivots[proc.n_pivots]; xt++)
566 free (xt->const_vars);
567 free (xt->const_indexes);
574 /* Parses the TABLES subcommand. */
576 parse_crosstabs_tables (struct lexer *lexer, struct dataset *ds,
577 struct crosstabs_proc *proc)
579 const struct variable ***by = NULL;
580 size_t *by_nvar = NULL;
583 /* Ensure that this is a TABLES subcommand. */
584 if (!lex_match_id (lexer, "TABLES")
585 && (lex_token (lexer) != T_ID ||
586 dict_lookup_var (dataset_dict (ds), lex_tokcstr (lexer)) == NULL)
587 && lex_token (lexer) != T_ALL)
589 lex_error (lexer, _("Syntax error expecting subcommand name or "
593 lex_match (lexer, T_EQUALS);
595 struct const_var_set *var_set
597 ? const_var_set_create_from_array (proc->variables,
599 : const_var_set_create_from_dict (dataset_dict (ds)));
603 int vars_start = lex_ofs (lexer);
606 by = xnrealloc (by, n_by + 1, sizeof *by);
607 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
608 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
609 PV_NO_DUPLICATE | PV_NO_SCRATCH))
611 size_t n = by_nvar[n_by++];
612 if (xalloc_oversized (nx, n))
615 lexer, vars_start, lex_ofs (lexer) - 1,
616 _("Too many cross-tabulation variables or dimensions."));
621 while (lex_match (lexer, T_BY));
624 bool unused UNUSED = lex_force_match (lexer, T_BY);
627 int vars_end = lex_ofs (lexer) - 1;
629 size_t *by_iter = XCALLOC (n_by, size_t);
630 proc->pivots = xnrealloc (proc->pivots,
631 proc->n_pivots + nx, sizeof *proc->pivots);
632 for (size_t i = 0; i < nx; i++)
634 struct crosstabulation *xt = &proc->pivots[proc->n_pivots++];
636 *xt = (struct crosstabulation) {
638 .weight_format = proc->weight_format,
641 .vars = xcalloc (n_by, sizeof *xt->vars),
644 .const_indexes = NULL,
645 .start_ofs = vars_start,
649 for (size_t j = 0; j < n_by; j++)
650 xt->vars[j].var = by[j][by_iter[j]];
652 for (int j = n_by - 1; j >= 0; j--)
654 if (++by_iter[j] < by_nvar[j])
663 /* All return paths lead here. */
664 for (size_t i = 0; i < n_by; i++)
669 const_var_set_destroy (var_set);
674 /* Parses the VARIABLES subcommand. */
676 parse_crosstabs_variables (struct lexer *lexer, struct dataset *ds,
677 struct crosstabs_proc *proc)
681 lex_next_error (lexer, -1, -1, _("%s must be specified before %s."),
682 "VARIABLES", "TABLES");
686 lex_match (lexer, T_EQUALS);
690 size_t orig_nv = proc->n_variables;
692 if (!parse_variables_const (lexer, dataset_dict (ds),
693 &proc->variables, &proc->n_variables,
694 (PV_APPEND | PV_NUMERIC
695 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
698 if (!lex_force_match (lexer, T_LPAREN))
701 if (!lex_force_int (lexer))
703 long min = lex_integer (lexer);
706 lex_match (lexer, T_COMMA);
708 if (!lex_force_int_range (lexer, NULL, min, LONG_MAX))
710 long max = lex_integer (lexer);
713 if (!lex_force_match (lexer, T_RPAREN))
716 for (size_t i = orig_nv; i < proc->n_variables; i++)
718 const struct variable *var = proc->variables[i];
719 struct var_range *vr = xmalloc (sizeof *vr);
720 *vr = (struct var_range) {
724 .count = max - min + 1,
726 hmap_insert (&proc->var_ranges, &vr->hmap_node,
727 hash_pointer (var, 0));
730 if (lex_token (lexer) == T_SLASH)
734 proc->mode = INTEGER;
738 free (proc->variables);
739 proc->variables = NULL;
740 proc->n_variables = 0;
744 /* Data file processing. */
746 static const struct var_range *
747 get_var_range (const struct crosstabs_proc *proc, const struct variable *var)
749 if (!hmap_is_empty (&proc->var_ranges))
751 const struct var_range *range;
753 HMAP_FOR_EACH_IN_BUCKET (range, struct var_range, hmap_node,
754 hash_pointer (var, 0), &proc->var_ranges)
755 if (range->var == var)
763 should_tabulate_case (const struct crosstabulation *xt, const struct ccase *c,
764 enum mv_class exclude)
766 for (size_t j = 0; j < xt->n_vars; j++)
768 const struct variable *var = xt->vars[j].var;
769 const struct var_range *range = get_var_range (xt->proc, var);
771 if (var_is_value_missing (var, case_data (c, var)) & exclude)
776 double num = case_num (c, var);
777 if (num < range->min || num >= range->max + 1.)
785 tabulate_integer_case (struct crosstabulation *xt, const struct ccase *c,
789 for (size_t j = 0; j < xt->n_vars; j++)
791 /* Throw away fractional parts of values. */
792 hash = hash_int (case_num (c, xt->vars[j].var), hash);
796 HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &xt->data)
798 for (size_t j = 0; j < xt->n_vars; j++)
799 if ((int) case_num (c, xt->vars[j].var) != (int) te->values[j].f)
802 /* Found an existing entry. */
809 /* No existing entry. Create a new one. */
810 te = xmalloc (table_entry_size (xt->n_vars));
812 for (size_t j = 0; j < xt->n_vars; j++)
813 te->values[j].f = (int) case_num (c, xt->vars[j].var);
814 hmap_insert (&xt->data, &te->node, hash);
818 tabulate_general_case (struct crosstabulation *xt, const struct ccase *c,
822 for (size_t j = 0; j < xt->n_vars; j++)
824 const struct variable *var = xt->vars[j].var;
825 hash = value_hash (case_data (c, var), var_get_width (var), hash);
829 HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &xt->data)
831 for (size_t j = 0; j < xt->n_vars; j++)
833 const struct variable *var = xt->vars[j].var;
834 if (!value_equal (case_data (c, var), &te->values[j],
835 var_get_width (var)))
839 /* Found an existing entry. */
846 /* No existing entry. Create a new one. */
847 te = xmalloc (table_entry_size (xt->n_vars));
849 for (size_t j = 0; j < xt->n_vars; j++)
851 const struct variable *var = xt->vars[j].var;
852 value_clone (&te->values[j], case_data (c, var), var_get_width (var));
854 hmap_insert (&xt->data, &te->node, hash);
857 /* Post-data reading calculations. */
859 static int compare_table_entry_vars_3way (const struct freq *a,
860 const struct freq *b,
861 const struct crosstabulation *xt,
863 static int compare_table_entry_3way (const void *ap_, const void *bp_,
865 static int compare_table_entry_3way_inv (const void *ap_, const void *bp_,
868 static void enum_var_values (const struct crosstabulation *, int var_idx,
870 static void free_var_values (const struct crosstabulation *, int var_idx);
871 static void output_crosstabulation (struct crosstabs_proc *,
872 struct crosstabulation *,
874 static void make_crosstabulation_subset (struct crosstabulation *xt,
875 size_t row0, size_t row1,
876 struct crosstabulation *subset);
877 static void make_summary_table (struct crosstabs_proc *);
878 static bool find_crosstab (struct crosstabulation *, size_t *row0p,
882 postcalc (struct crosstabs_proc *proc, struct lexer *lexer)
884 /* Round hash table entries, if requested
886 If this causes any of the cell counts to fall to zero, delete those
888 if (proc->round_cells)
889 for (struct crosstabulation *xt = proc->pivots;
890 xt < &proc->pivots[proc->n_pivots]; xt++)
892 struct freq *e, *next;
893 HMAP_FOR_EACH_SAFE (e, next, struct freq, node, &xt->data)
895 e->count = round_weight (proc, e->count);
898 hmap_delete (&xt->data, &e->node);
904 /* Convert hash tables into sorted arrays of entries. */
905 for (struct crosstabulation *xt = proc->pivots;
906 xt < &proc->pivots[proc->n_pivots]; xt++)
908 xt->n_entries = hmap_count (&xt->data);
909 xt->entries = xnmalloc (xt->n_entries, sizeof *xt->entries);
913 HMAP_FOR_EACH (e, struct freq, node, &xt->data)
914 xt->entries[i++] = e;
916 hmap_destroy (&xt->data);
918 sort (xt->entries, xt->n_entries, sizeof *xt->entries,
919 proc->descending ? compare_table_entry_3way_inv : compare_table_entry_3way,
923 make_summary_table (proc);
925 /* Output each pivot table. */
926 for (struct crosstabulation *xt = proc->pivots;
927 xt < &proc->pivots[proc->n_pivots]; xt++)
929 output_crosstabulation (proc, xt, lexer);
932 int n_vars = (xt->n_vars > 2 ? 2 : xt->n_vars);
933 const struct variable **vars = XCALLOC (n_vars, const struct variable*);
934 for (size_t i = 0; i < n_vars; i++)
935 vars[i] = xt->vars[i].var;
936 chart_submit (barchart_create (vars, n_vars, _("Count"),
938 xt->entries, xt->n_entries));
943 /* Free output and prepare for next split file. */
944 for (struct crosstabulation *xt = proc->pivots;
945 xt < &proc->pivots[proc->n_pivots]; xt++)
949 /* Free the members that were allocated in this function(and the values
950 owned by the entries.
952 The other pointer members are either both allocated and destroyed at a
953 lower level (in output_crosstabulation), or both allocated and
954 destroyed at a higher level (in crs_custom_tables and free_proc,
956 for (size_t i = 0; i < xt->n_vars; i++)
958 int width = var_get_width (xt->vars[i].var);
959 if (value_needs_init (width))
960 for (size_t j = 0; j < xt->n_entries; j++)
961 value_destroy (&xt->entries[j]->values[i], width);
964 for (size_t i = 0; i < xt->n_entries; i++)
965 free (xt->entries[i]);
971 make_crosstabulation_subset (struct crosstabulation *xt, size_t row0,
972 size_t row1, struct crosstabulation *subset)
977 assert (xt->n_consts == 0);
979 subset->vars = xt->vars;
981 subset->n_consts = xt->n_vars - 2;
982 subset->const_vars = xt->vars + 2;
983 subset->const_indexes = xcalloc (subset->n_consts,
984 sizeof *subset->const_indexes);
985 for (size_t i = 0; i < subset->n_consts; i++)
987 const union value *value = &xt->entries[row0]->values[2 + i];
989 for (size_t j = 0; j < xt->vars[2 + i].n_values; j++)
990 if (value_equal (&xt->vars[2 + i].values[j], value,
991 var_get_width (xt->vars[2 + i].var)))
993 subset->const_indexes[i] = j;
1000 subset->entries = &xt->entries[row0];
1001 subset->n_entries = row1 - row0;
1005 compare_table_entry_var_3way (const struct freq *a,
1006 const struct freq *b,
1007 const struct crosstabulation *xt,
1010 return value_compare_3way (&a->values[idx], &b->values[idx],
1011 var_get_width (xt->vars[idx].var));
1015 compare_table_entry_vars_3way (const struct freq *a,
1016 const struct freq *b,
1017 const struct crosstabulation *xt,
1020 for (int i = idx1 - 1; i >= idx0; i--)
1022 int cmp = compare_table_entry_var_3way (a, b, xt, i);
1029 /* Compare the struct freq at *AP to the one at *BP and
1030 return a strcmp()-type result. */
1032 compare_table_entry_3way (const void *ap_, const void *bp_, const void *xt_)
1034 const struct freq *const *ap = ap_;
1035 const struct freq *const *bp = bp_;
1036 const struct freq *a = *ap;
1037 const struct freq *b = *bp;
1038 const struct crosstabulation *xt = xt_;
1040 int cmp = compare_table_entry_vars_3way (a, b, xt, 2, xt->n_vars);
1044 cmp = compare_table_entry_var_3way (a, b, xt, ROW_VAR);
1048 return compare_table_entry_var_3way (a, b, xt, COL_VAR);
1051 /* Inverted version of compare_table_entry_3way */
1053 compare_table_entry_3way_inv (const void *ap_, const void *bp_, const void *xt_)
1055 return -compare_table_entry_3way (ap_, bp_, xt_);
1058 /* Output a table summarizing the cases processed. */
1060 make_summary_table (struct crosstabs_proc *proc)
1062 struct pivot_table *table = pivot_table_create (N_("Summary"));
1063 pivot_table_set_weight_var (table, dict_get_weight (proc->dict));
1065 pivot_dimension_create (table, PIVOT_AXIS_COLUMN, N_("Statistics"),
1066 N_("N"), PIVOT_RC_COUNT,
1067 N_("Percent"), PIVOT_RC_PERCENT);
1069 struct pivot_dimension *cases = pivot_dimension_create (
1070 table, PIVOT_AXIS_COLUMN, N_("Cases"),
1071 N_("Valid"), N_("Missing"), N_("Total"));
1072 cases->root->show_label = true;
1074 struct pivot_dimension *tables = pivot_dimension_create (
1075 table, PIVOT_AXIS_ROW, N_("Crosstabulation"));
1076 for (struct crosstabulation *xt = &proc->pivots[0];
1077 xt < &proc->pivots[proc->n_pivots]; xt++)
1079 struct string name = DS_EMPTY_INITIALIZER;
1080 for (size_t i = 0; i < xt->n_vars; i++)
1083 ds_put_cstr (&name, " × ");
1084 ds_put_cstr (&name, var_to_string (xt->vars[i].var));
1087 int row = pivot_category_create_leaf (
1089 pivot_value_new_user_text_nocopy (ds_steal_cstr (&name)));
1092 for (size_t i = 0; i < xt->n_entries; i++)
1093 valid += xt->entries[i]->count;
1099 for (int i = 0; i < 3; i++)
1101 pivot_table_put3 (table, 0, i, row, pivot_value_new_number (n[i]));
1102 pivot_table_put3 (table, 1, i, row,
1103 pivot_value_new_number (n[i] / n[2] * 100.0));
1107 pivot_table_submit (table);
1112 static struct pivot_table *create_crosstab_table (
1113 struct crosstabs_proc *, struct crosstabulation *,
1114 size_t crs_leaves[CRS_N_CELLS]);
1115 static struct pivot_table *create_chisq_table (struct crosstabulation *);
1116 static struct pivot_table *create_sym_table (struct crosstabulation *);
1117 static struct pivot_table *create_risk_table (
1118 struct crosstabulation *, struct pivot_dimension **risk_statistics);
1119 static struct pivot_table *create_direct_table (struct crosstabulation *);
1120 static void display_crosstabulation (struct crosstabs_proc *,
1121 struct crosstabulation *,
1122 struct pivot_table *,
1123 size_t crs_leaves[CRS_N_CELLS]);
1124 static void display_chisq (struct crosstabulation *, struct pivot_table *);
1125 static void display_symmetric (struct crosstabs_proc *,
1126 struct crosstabulation *, struct pivot_table *);
1127 static void display_risk (struct crosstabulation *, struct pivot_table *,
1128 struct pivot_dimension *risk_statistics);
1129 static void display_directional (struct crosstabs_proc *,
1130 struct crosstabulation *,
1131 struct pivot_table *);
1132 static void delete_missing (struct crosstabulation *);
1133 static void build_matrix (struct crosstabulation *);
1135 /* Output pivot table XT in the context of PROC. */
1137 output_crosstabulation (struct crosstabs_proc *proc, struct crosstabulation *xt,
1138 struct lexer *lexer)
1140 for (size_t i = 0; i < xt->n_vars; i++)
1141 enum_var_values (xt, i, proc->descending);
1143 if (xt->vars[COL_VAR].n_values == 0)
1147 ds_init_cstr (&vars, var_to_string (xt->vars[0].var));
1148 for (size_t i = 1; i < xt->n_vars; i++)
1149 ds_put_format (&vars, " × %s", var_to_string (xt->vars[i].var));
1151 /* TRANSLATORS: The %s here describes a crosstabulation. It takes the
1152 form "var1 * var2 * var3 * ...". */
1153 lex_ofs_msg (lexer, SW, xt->start_ofs, xt->end_ofs,
1154 _("Crosstabulation %s contained no non-missing cases."),
1158 for (size_t i = 0; i < xt->n_vars; i++)
1159 free_var_values (xt, i);
1163 size_t crs_leaves[CRS_N_CELLS];
1164 struct pivot_table *table = (proc->cells
1165 ? create_crosstab_table (proc, xt, crs_leaves)
1167 struct pivot_table *chisq = (proc->statistics & CRS_ST_CHISQ
1168 ? create_chisq_table (xt)
1170 struct pivot_table *sym
1171 = (proc->statistics & (CRS_ST_PHI | CRS_ST_CC | CRS_ST_BTAU | CRS_ST_CTAU
1172 | CRS_ST_GAMMA | CRS_ST_CORR | CRS_ST_KAPPA)
1173 ? create_sym_table (xt)
1175 struct pivot_dimension *risk_statistics = NULL;
1176 struct pivot_table *risk = (proc->statistics & CRS_ST_RISK
1177 ? create_risk_table (xt, &risk_statistics)
1179 struct pivot_table *direct
1180 = (proc->statistics & (CRS_ST_LAMBDA | CRS_ST_UC | CRS_ST_D | CRS_ST_ETA)
1181 ? create_direct_table (xt)
1186 while (find_crosstab (xt, &row0, &row1))
1188 struct crosstabulation x;
1190 make_crosstabulation_subset (xt, row0, row1, &x);
1192 size_t n_rows = x.vars[ROW_VAR].n_values;
1193 size_t n_cols = x.vars[COL_VAR].n_values;
1194 if (size_overflow_p (xtimes (xtimes (n_rows, n_cols), sizeof (double))))
1196 x.row_tot = xmalloc (n_rows * sizeof *x.row_tot);
1197 x.col_tot = xmalloc (n_cols * sizeof *x.col_tot);
1198 x.mat = xmalloc (n_rows * n_cols * sizeof *x.mat);
1202 /* Find the first variable that differs from the last subtable. */
1204 display_crosstabulation (proc, &x, table, crs_leaves);
1206 if (proc->exclude == 0)
1207 delete_missing (&x);
1210 display_chisq (&x, chisq);
1213 display_symmetric (proc, &x, sym);
1215 display_risk (&x, risk, risk_statistics);
1217 display_directional (proc, &x, direct);
1222 free (x.const_indexes);
1226 pivot_table_submit (table);
1229 pivot_table_submit (chisq);
1232 pivot_table_submit (sym);
1236 if (!pivot_table_is_empty (risk))
1237 pivot_table_submit (risk);
1239 pivot_table_unref (risk);
1243 pivot_table_submit (direct);
1245 for (size_t i = 0; i < xt->n_vars; i++)
1246 free_var_values (xt, i);
1250 build_matrix (struct crosstabulation *x)
1252 const int col_var_width = var_get_width (x->vars[COL_VAR].var);
1253 const int row_var_width = var_get_width (x->vars[ROW_VAR].var);
1254 size_t n_rows = x->vars[ROW_VAR].n_values;
1255 size_t n_cols = x->vars[COL_VAR].n_values;
1257 double *mp = x->mat;
1260 for (struct freq **p = x->entries; p < &x->entries[x->n_entries]; p++)
1262 const struct freq *te = *p;
1264 while (!value_equal (&x->vars[ROW_VAR].values[row],
1265 &te->values[ROW_VAR], row_var_width))
1267 for (; col < n_cols; col++)
1273 while (!value_equal (&x->vars[COL_VAR].values[col],
1274 &te->values[COL_VAR], col_var_width))
1281 if (++col >= n_cols)
1287 while (mp < &x->mat[n_cols * n_rows])
1289 assert (mp == &x->mat[n_cols * n_rows]);
1291 /* Column totals, row totals, ns_rows. */
1293 for (col = 0; col < n_cols; col++)
1294 x->col_tot[col] = 0.0;
1295 for (row = 0; row < n_rows; row++)
1296 x->row_tot[row] = 0.0;
1298 for (row = 0; row < n_rows; row++)
1300 bool row_is_empty = true;
1301 for (col = 0; col < n_cols; col++)
1305 row_is_empty = false;
1306 x->col_tot[col] += *mp;
1307 x->row_tot[row] += *mp;
1314 assert (mp == &x->mat[n_cols * n_rows]);
1318 for (col = 0; col < n_cols; col++)
1319 for (row = 0; row < n_rows; row++)
1320 if (x->mat[col + row * n_cols] != 0.0)
1328 for (col = 0; col < n_cols; col++)
1329 x->total += x->col_tot[col];
1333 add_var_dimension (struct pivot_table *table, const struct xtab_var *var,
1334 enum pivot_axis_type axis_type, bool total)
1336 struct pivot_dimension *d = pivot_dimension_create__ (
1337 table, axis_type, pivot_value_new_variable (var->var));
1339 struct pivot_footnote *missing_footnote = pivot_table_create_footnote (
1340 table, pivot_value_new_text (N_("Missing value")));
1342 struct pivot_category *group = pivot_category_create_group__ (
1343 d->root, pivot_value_new_variable (var->var));
1344 for (size_t j = 0; j < var->n_values; j++)
1346 struct pivot_value *value = pivot_value_new_var_value (
1347 var->var, &var->values[j]);
1348 if (var_is_value_missing (var->var, &var->values[j]))
1349 pivot_value_add_footnote (value, missing_footnote);
1350 pivot_category_create_leaf (group, value);
1354 pivot_category_create_leaf (d->root, pivot_value_new_text (N_("Total")));
1357 static struct pivot_table *
1358 create_crosstab_table (struct crosstabs_proc *proc, struct crosstabulation *xt,
1359 size_t crs_leaves[CRS_N_CELLS])
1362 struct string title = DS_EMPTY_INITIALIZER;
1363 for (size_t i = 0; i < xt->n_vars; i++)
1366 ds_put_cstr (&title, " × ");
1367 ds_put_cstr (&title, var_to_string (xt->vars[i].var));
1369 for (size_t i = 0; i < xt->n_consts; i++)
1371 const struct variable *var = xt->const_vars[i].var;
1372 const union value *value = &xt->entries[0]->values[2 + i];
1375 ds_put_format (&title, ", %s=", var_to_string (var));
1377 /* Insert the formatted value of VAR without any leading spaces. */
1378 s = data_out (value, var_get_encoding (var), var_get_print_format (var),
1379 settings_get_fmt_settings ());
1380 ds_put_cstr (&title, s + strspn (s, " "));
1383 struct pivot_table *table = pivot_table_create__ (
1384 pivot_value_new_user_text_nocopy (ds_steal_cstr (&title)),
1386 pivot_table_set_weight_format (table, &proc->weight_format);
1388 struct pivot_dimension *statistics = pivot_dimension_create (
1389 table, PIVOT_AXIS_ROW, N_("Statistics"));
1396 static const struct statistic stats[CRS_N_CELLS] =
1398 #define C(KEYWORD, STRING, RC) { STRING, RC },
1402 for (size_t i = 0; i < CRS_N_CELLS; i++)
1403 if (proc->cells & (1u << i) && stats[i].label)
1404 crs_leaves[i] = pivot_category_create_leaf_rc (
1405 statistics->root, pivot_value_new_text (stats[i].label),
1408 for (size_t i = 0; i < xt->n_vars; i++)
1409 add_var_dimension (table, &xt->vars[i],
1410 i == COL_VAR ? PIVOT_AXIS_COLUMN : PIVOT_AXIS_ROW,
1416 static struct pivot_table *
1417 create_chisq_table (struct crosstabulation *xt)
1419 struct pivot_table *chisq = pivot_table_create (N_("Chi-Square Tests"));
1420 pivot_table_set_weight_format (chisq, &xt->weight_format);
1422 pivot_dimension_create (
1423 chisq, PIVOT_AXIS_ROW, N_("Statistics"),
1424 N_("Pearson Chi-Square"),
1425 N_("Likelihood Ratio"),
1426 N_("Fisher's Exact Test"),
1427 N_("Continuity Correction"),
1428 N_("Linear-by-Linear Association"),
1429 N_("N of Valid Cases"), PIVOT_RC_COUNT);
1431 pivot_dimension_create (
1432 chisq, PIVOT_AXIS_COLUMN, N_("Statistics"),
1433 N_("Value"), PIVOT_RC_OTHER,
1434 N_("df"), PIVOT_RC_COUNT,
1435 N_("Asymptotic Sig. (2-tailed)"), PIVOT_RC_SIGNIFICANCE,
1436 N_("Exact Sig. (2-tailed)"), PIVOT_RC_SIGNIFICANCE,
1437 N_("Exact Sig. (1-tailed)"), PIVOT_RC_SIGNIFICANCE);
1439 for (size_t i = 2; i < xt->n_vars; i++)
1440 add_var_dimension (chisq, &xt->vars[i], PIVOT_AXIS_ROW, false);
1445 /* Symmetric measures. */
1446 static struct pivot_table *
1447 create_sym_table (struct crosstabulation *xt)
1449 struct pivot_table *sym = pivot_table_create (N_("Symmetric Measures"));
1450 pivot_table_set_weight_format (sym, &xt->weight_format);
1452 pivot_dimension_create (
1453 sym, PIVOT_AXIS_COLUMN, N_("Values"),
1454 N_("Value"), PIVOT_RC_OTHER,
1455 N_("Asymp. Std. Error"), PIVOT_RC_OTHER,
1456 N_("Approx. T"), PIVOT_RC_OTHER,
1457 N_("Approx. Sig."), PIVOT_RC_SIGNIFICANCE);
1459 struct pivot_dimension *statistics = pivot_dimension_create (
1460 sym, PIVOT_AXIS_ROW, N_("Statistics"));
1461 pivot_category_create_group (
1462 statistics->root, N_("Nominal by Nominal"),
1463 N_("Phi"), N_("Cramer's V"), N_("Contingency Coefficient"));
1464 pivot_category_create_group (
1465 statistics->root, N_("Ordinal by Ordinal"),
1466 N_("Kendall's tau-b"), N_("Kendall's tau-c"),
1467 N_("Gamma"), N_("Spearman Correlation"));
1468 pivot_category_create_group (
1469 statistics->root, N_("Interval by Interval"),
1471 pivot_category_create_group (
1472 statistics->root, N_("Measure of Agreement"),
1474 pivot_category_create_leaves (statistics->root, N_("N of Valid Cases"),
1477 for (size_t i = 2; i < xt->n_vars; i++)
1478 add_var_dimension (sym, &xt->vars[i], PIVOT_AXIS_ROW, false);
1483 /* Risk estimate. */
1484 static struct pivot_table *
1485 create_risk_table (struct crosstabulation *xt,
1486 struct pivot_dimension **risk_statistics)
1488 struct pivot_table *risk = pivot_table_create (N_("Risk Estimate"));
1489 pivot_table_set_weight_format (risk, &xt->weight_format);
1491 struct pivot_dimension *values = pivot_dimension_create (
1492 risk, PIVOT_AXIS_COLUMN, N_("Values"),
1493 N_("Value"), PIVOT_RC_OTHER);
1494 pivot_category_create_group (
1495 /* xgettext:no-c-format */
1496 values->root, N_("95% Confidence Interval"),
1497 N_("Lower"), PIVOT_RC_OTHER,
1498 N_("Upper"), PIVOT_RC_OTHER);
1500 *risk_statistics = pivot_dimension_create (
1501 risk, PIVOT_AXIS_ROW, N_("Statistics"));
1503 for (size_t i = 2; i < xt->n_vars; i++)
1504 add_var_dimension (risk, &xt->vars[i], PIVOT_AXIS_ROW, false);
1510 create_direct_stat (struct pivot_category *parent,
1511 const struct crosstabulation *xt,
1512 const char *name, bool symmetric)
1514 struct pivot_category *group = pivot_category_create_group (
1517 pivot_category_create_leaf (group, pivot_value_new_text (N_("Symmetric")));
1519 char *row_label = xasprintf (_("%s Dependent"),
1520 var_to_string (xt->vars[ROW_VAR].var));
1521 pivot_category_create_leaf (group, pivot_value_new_user_text_nocopy (
1524 char *col_label = xasprintf (_("%s Dependent"),
1525 var_to_string (xt->vars[COL_VAR].var));
1526 pivot_category_create_leaf (group, pivot_value_new_user_text_nocopy (
1530 /* Directional measures. */
1531 static struct pivot_table *
1532 create_direct_table (struct crosstabulation *xt)
1534 struct pivot_table *direct = pivot_table_create (N_("Directional Measures"));
1535 pivot_table_set_weight_format (direct, &xt->weight_format);
1537 pivot_dimension_create (
1538 direct, PIVOT_AXIS_COLUMN, N_("Values"),
1539 N_("Value"), PIVOT_RC_OTHER,
1540 N_("Asymp. Std. Error"), PIVOT_RC_OTHER,
1541 N_("Approx. T"), PIVOT_RC_OTHER,
1542 N_("Approx. Sig."), PIVOT_RC_SIGNIFICANCE);
1544 struct pivot_dimension *statistics = pivot_dimension_create (
1545 direct, PIVOT_AXIS_ROW, N_("Statistics"));
1546 struct pivot_category *nn = pivot_category_create_group (
1547 statistics->root, N_("Nominal by Nominal"));
1548 create_direct_stat (nn, xt, N_("Lambda"), true);
1549 create_direct_stat (nn, xt, N_("Goodman and Kruskal tau"), false);
1550 create_direct_stat (nn, xt, N_("Uncertainty Coefficient"), true);
1551 struct pivot_category *oo = pivot_category_create_group (
1552 statistics->root, N_("Ordinal by Ordinal"));
1553 create_direct_stat (oo, xt, N_("Somers' d"), true);
1554 struct pivot_category *ni = pivot_category_create_group (
1555 statistics->root, N_("Nominal by Interval"));
1556 create_direct_stat (ni, xt, N_("Eta"), false);
1558 for (size_t i = 2; i < xt->n_vars; i++)
1559 add_var_dimension (direct, &xt->vars[i], PIVOT_AXIS_ROW, false);
1564 /* Delete missing rows and columns for statistical analysis when
1567 delete_missing (struct crosstabulation *xt)
1569 size_t n_rows = xt->vars[ROW_VAR].n_values;
1570 size_t n_cols = xt->vars[COL_VAR].n_values;
1572 for (size_t r = 0; r < n_rows; r++)
1573 if (var_is_num_missing (xt->vars[ROW_VAR].var,
1574 xt->vars[ROW_VAR].values[r].f) == MV_USER)
1576 for (size_t c = 0; c < n_cols; c++)
1577 xt->mat[c + r * n_cols] = 0.;
1582 for (size_t c = 0; c < n_cols; c++)
1583 if (var_is_num_missing (xt->vars[COL_VAR].var,
1584 xt->vars[COL_VAR].values[c].f) == MV_USER)
1586 for (size_t r = 0; r < n_rows; r++)
1587 xt->mat[c + r * n_cols] = 0.;
1593 find_crosstab (struct crosstabulation *xt, size_t *row0p, size_t *row1p)
1595 size_t row0 = *row1p;
1596 if (row0 >= xt->n_entries)
1600 for (row1 = row0 + 1; row1 < xt->n_entries; row1++)
1602 struct freq *a = xt->entries[row0];
1603 struct freq *b = xt->entries[row1];
1604 if (compare_table_entry_vars_3way (a, b, xt, 2, xt->n_vars) != 0)
1612 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1613 result. WIDTH_ points to an int which is either 0 for a
1614 numeric value or a string width for a string value. */
1616 compare_value_3way (const void *a_, const void *b_, const void *width_)
1618 const union value *a = a_;
1619 const union value *b = b_;
1620 const int *width = width_;
1622 return value_compare_3way (a, b, *width);
1625 /* Inverted version of the above */
1627 compare_value_3way_inv (const void *a_, const void *b_, const void *width_)
1629 return -compare_value_3way (a_, b_, width_);
1633 /* Given an array of ENTRY_CNT table_entry structures starting at
1634 ENTRIES, creates a sorted list of the values that the variable
1635 with index VAR_IDX takes on. Stores the array of the values in
1636 XT->values and the number of values in XT->n_values. */
1638 enum_var_values (const struct crosstabulation *xt, int var_idx,
1641 struct xtab_var *xv = &xt->vars[var_idx];
1642 const struct var_range *range = get_var_range (xt->proc, xv->var);
1646 xv->values = xnmalloc (range->count, sizeof *xv->values);
1647 xv->n_values = range->count;
1648 for (size_t i = 0; i < range->count; i++)
1649 xv->values[i].f = range->min + i;
1653 int width = var_get_width (xv->var);
1654 struct hmapx set = HMAPX_INITIALIZER (set);
1656 for (size_t i = 0; i < xt->n_entries; i++)
1658 const struct freq *te = xt->entries[i];
1659 const union value *value = &te->values[var_idx];
1660 size_t hash = value_hash (value, width, 0);
1662 const union value *iter;
1663 struct hmapx_node *node;
1664 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1665 if (value_equal (iter, value, width))
1668 hmapx_insert (&set, (union value *) value, hash);
1673 xv->n_values = hmapx_count (&set);
1674 xv->values = xnmalloc (xv->n_values, sizeof *xv->values);
1676 const union value *iter;
1677 struct hmapx_node *node;
1678 HMAPX_FOR_EACH (iter, node, &set)
1679 xv->values[i++] = *iter;
1680 hmapx_destroy (&set);
1682 sort (xv->values, xv->n_values, sizeof *xv->values,
1683 descending ? compare_value_3way_inv : compare_value_3way,
1689 free_var_values (const struct crosstabulation *xt, int var_idx)
1691 struct xtab_var *xv = &xt->vars[var_idx];
1697 /* Displays the crosstabulation table. */
1699 display_crosstabulation (struct crosstabs_proc *proc,
1700 struct crosstabulation *xt, struct pivot_table *table,
1701 size_t crs_leaves[CRS_N_CELLS])
1703 size_t n_rows = xt->vars[ROW_VAR].n_values;
1704 size_t n_cols = xt->vars[COL_VAR].n_values;
1706 size_t *indexes = xnmalloc (table->n_dimensions, sizeof *indexes);
1707 assert (xt->n_vars == 2);
1708 for (size_t i = 0; i < xt->n_consts; i++)
1709 indexes[i + 3] = xt->const_indexes[i];
1711 /* Put in the actual cells. */
1712 double *mp = xt->mat;
1713 for (size_t r = 0; r < n_rows; r++)
1715 if (!xt->row_tot[r] && proc->mode != INTEGER)
1718 indexes[ROW_VAR + 1] = r;
1719 for (size_t c = 0; c < n_cols; c++)
1721 if (!xt->col_tot[c] && proc->mode != INTEGER)
1724 indexes[COL_VAR + 1] = c;
1726 double expected_value = xt->row_tot[r] * xt->col_tot[c] / xt->total;
1727 double residual = *mp - expected_value;
1728 double sresidual = residual / sqrt (expected_value);
1730 = residual / sqrt (expected_value
1731 * (1. - xt->row_tot[r] / xt->total)
1732 * (1. - xt->col_tot[c] / xt->total));
1733 double entries[CRS_N_CELLS] = {
1734 [CRS_CL_COUNT] = *mp,
1735 [CRS_CL_ROW] = *mp / xt->row_tot[r] * 100.,
1736 [CRS_CL_COLUMN] = *mp / xt->col_tot[c] * 100.,
1737 [CRS_CL_TOTAL] = *mp / xt->total * 100.,
1738 [CRS_CL_EXPECTED] = expected_value,
1739 [CRS_CL_RESIDUAL] = residual,
1740 [CRS_CL_SRESIDUAL] = sresidual,
1741 [CRS_CL_ASRESIDUAL] = asresidual,
1743 for (size_t i = 0; i < proc->n_cells; i++)
1745 int cell = proc->a_cells[i];
1746 indexes[0] = crs_leaves[cell];
1747 pivot_table_put (table, indexes, table->n_dimensions,
1748 pivot_value_new_number (entries[cell]));
1756 for (size_t r = 0; r < n_rows; r++)
1758 if (!xt->row_tot[r] && proc->mode != INTEGER)
1761 double expected_value = xt->row_tot[r] / xt->total;
1762 double entries[CRS_N_CELLS] = {
1763 [CRS_CL_COUNT] = xt->row_tot[r],
1764 [CRS_CL_ROW] = 100.0,
1765 [CRS_CL_COLUMN] = expected_value * 100.,
1766 [CRS_CL_TOTAL] = expected_value * 100.,
1767 [CRS_CL_EXPECTED] = expected_value,
1768 [CRS_CL_RESIDUAL] = SYSMIS,
1769 [CRS_CL_SRESIDUAL] = SYSMIS,
1770 [CRS_CL_ASRESIDUAL] = SYSMIS,
1772 for (size_t i = 0; i < proc->n_cells; i++)
1774 int cell = proc->a_cells[i];
1775 double entry = entries[cell];
1776 if (entry != SYSMIS)
1778 indexes[ROW_VAR + 1] = r;
1779 indexes[COL_VAR + 1] = n_cols;
1780 indexes[0] = crs_leaves[cell];
1781 pivot_table_put (table, indexes, table->n_dimensions,
1782 pivot_value_new_number (entry));
1787 for (size_t c = 0; c <= n_cols; c++)
1789 if (c < n_cols && !xt->col_tot[c] && proc->mode != INTEGER)
1792 double ct = c < n_cols ? xt->col_tot[c] : xt->total;
1793 double expected_value = ct / xt->total;
1794 double entries[CRS_N_CELLS] = {
1795 [CRS_CL_COUNT] = ct,
1796 [CRS_CL_ROW] = expected_value * 100.0,
1797 [CRS_CL_COLUMN] = 100.0,
1798 [CRS_CL_TOTAL] = expected_value * 100.,
1799 [CRS_CL_EXPECTED] = expected_value,
1800 [CRS_CL_RESIDUAL] = SYSMIS,
1801 [CRS_CL_SRESIDUAL] = SYSMIS,
1802 [CRS_CL_ASRESIDUAL] = SYSMIS,
1804 for (size_t i = 0; i < proc->n_cells; i++)
1806 size_t cell = proc->a_cells[i];
1807 double entry = entries[cell];
1808 if (entry != SYSMIS)
1810 indexes[ROW_VAR + 1] = n_rows;
1811 indexes[COL_VAR + 1] = c;
1812 indexes[0] = crs_leaves[cell];
1813 pivot_table_put (table, indexes, table->n_dimensions,
1814 pivot_value_new_number (entry));
1822 static void calc_r (struct crosstabulation *,
1823 double *XT, double *Y, double *, double *, double *);
1824 static void calc_chisq (struct crosstabulation *,
1825 double[N_CHISQ], int[N_CHISQ], double *, double *);
1827 /* Display chi-square statistics. */
1829 display_chisq (struct crosstabulation *xt, struct pivot_table *chisq)
1831 double chisq_v[N_CHISQ];
1832 double fisher1, fisher2;
1834 calc_chisq (xt, chisq_v, df, &fisher1, &fisher2);
1836 size_t *indexes = xnmalloc (chisq->n_dimensions, sizeof *indexes);
1837 assert (xt->n_vars == 2);
1838 for (size_t i = 0; i < xt->n_consts; i++)
1839 indexes[i + 2] = xt->const_indexes[i];
1840 for (size_t i = 0; i < N_CHISQ; i++)
1844 double entries[5] = { SYSMIS, SYSMIS, SYSMIS, SYSMIS, SYSMIS };
1847 entries[3] = fisher2;
1848 entries[4] = fisher1;
1850 else if (chisq_v[i] != SYSMIS)
1852 entries[0] = chisq_v[i];
1854 entries[2] = gsl_cdf_chisq_Q (chisq_v[i], df[i]);
1857 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1858 if (entries[j] != SYSMIS)
1861 pivot_table_put (chisq, indexes, chisq->n_dimensions,
1862 pivot_value_new_number (entries[j]));
1868 pivot_table_put (chisq, indexes, chisq->n_dimensions,
1869 pivot_value_new_number (xt->total));
1874 static bool calc_symmetric (struct crosstabs_proc *, struct crosstabulation *,
1875 double[N_SYMMETRIC], double[N_SYMMETRIC],
1876 double[N_SYMMETRIC],
1877 double[3], double[3], double[3]);
1879 /* Display symmetric measures. */
1881 display_symmetric (struct crosstabs_proc *proc, struct crosstabulation *xt,
1882 struct pivot_table *sym)
1884 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1885 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1887 if (!calc_symmetric (proc, xt, sym_v, sym_ase, sym_t,
1888 somers_d_v, somers_d_ase, somers_d_t))
1891 size_t *indexes = xnmalloc (sym->n_dimensions, sizeof *indexes);
1892 assert (xt->n_vars == 2);
1893 for (size_t i = 0; i < xt->n_consts; i++)
1894 indexes[i + 2] = xt->const_indexes[i];
1896 for (size_t i = 0; i < N_SYMMETRIC; i++)
1898 if (sym_v[i] == SYSMIS)
1903 double entries[] = { sym_v[i], sym_ase[i], sym_t[i] };
1904 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1905 if (entries[j] != SYSMIS)
1908 pivot_table_put (sym, indexes, sym->n_dimensions,
1909 pivot_value_new_number (entries[j]));
1913 indexes[1] = N_SYMMETRIC;
1915 struct pivot_value *total = pivot_value_new_number (xt->total);
1916 pivot_value_set_rc (sym, total, PIVOT_RC_COUNT);
1917 pivot_table_put (sym, indexes, sym->n_dimensions, total);
1922 static bool calc_risk (struct crosstabulation *,
1923 double[], double[], double[], union value *,
1926 /* Display risk estimate. */
1928 display_risk (struct crosstabulation *xt, struct pivot_table *risk,
1929 struct pivot_dimension *risk_statistics)
1931 double risk_v[3], lower[3], upper[3], n_valid;
1933 if (!calc_risk (xt, risk_v, upper, lower, c, &n_valid))
1935 assert (risk_statistics);
1937 size_t *indexes = xnmalloc (risk->n_dimensions, sizeof *indexes);
1938 assert (xt->n_vars == 2);
1939 for (size_t i = 0; i < xt->n_consts; i++)
1940 indexes[i + 2] = xt->const_indexes[i];
1942 for (size_t i = 0; i < 3; i++)
1944 const struct variable *cv = xt->vars[COL_VAR].var;
1945 const struct variable *rv = xt->vars[ROW_VAR].var;
1947 if (risk_v[i] == SYSMIS)
1950 struct string label = DS_EMPTY_INITIALIZER;
1954 ds_put_format (&label, _("Odds Ratio for %s"), var_to_string (rv));
1955 ds_put_cstr (&label, " (");
1956 var_append_value_name (rv, &c[0], &label);
1957 ds_put_cstr (&label, " / ");
1958 var_append_value_name (rv, &c[1], &label);
1959 ds_put_cstr (&label, ")");
1963 ds_put_format (&label, _("For cohort %s = "), var_to_string (cv));
1964 var_append_value_name (cv, &xt->vars[ROW_VAR].values[i - 1], &label);
1968 indexes[1] = pivot_category_create_leaf (
1969 risk_statistics->root,
1970 pivot_value_new_user_text_nocopy (ds_steal_cstr (&label)));
1972 double entries[] = { risk_v[i], lower[i], upper[i] };
1973 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1976 pivot_table_put (risk, indexes, risk->n_dimensions,
1977 pivot_value_new_number (entries[i]));
1980 indexes[1] = pivot_category_create_leaf (
1981 risk_statistics->root,
1982 pivot_value_new_text (N_("N of Valid Cases")));
1984 pivot_table_put (risk, indexes, risk->n_dimensions,
1985 pivot_value_new_number (n_valid));
1989 static void calc_directional (struct crosstabs_proc *, struct crosstabulation *,
1990 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1991 double[N_DIRECTIONAL], double[N_DIRECTIONAL]);
1993 /* Display directional measures. */
1995 display_directional (struct crosstabs_proc *proc,
1996 struct crosstabulation *xt, struct pivot_table *direct)
1998 double direct_v[N_DIRECTIONAL];
1999 double direct_ase[N_DIRECTIONAL];
2000 double direct_t[N_DIRECTIONAL];
2001 double sig[N_DIRECTIONAL];
2002 calc_directional (proc, xt, direct_v, direct_ase, direct_t, sig);
2004 size_t *indexes = xnmalloc (direct->n_dimensions, sizeof *indexes);
2005 assert (xt->n_vars == 2);
2006 for (size_t i = 0; i < xt->n_consts; i++)
2007 indexes[i + 2] = xt->const_indexes[i];
2009 for (size_t i = 0; i < N_DIRECTIONAL; i++)
2011 if (direct_v[i] == SYSMIS)
2016 double entries[] = {
2017 direct_v[i], direct_ase[i], direct_t[i], sig[i],
2019 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
2020 if (entries[j] != SYSMIS)
2023 pivot_table_put (direct, indexes, direct->n_dimensions,
2024 pivot_value_new_number (entries[j]));
2031 /* Statistical calculations. */
2033 /* Returns the value of the logarithm of gamma (factorial) function for an integer
2036 log_gamma_int (double xt)
2039 for (int i = 2; i < xt; i++)
2044 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2046 static inline double
2047 Pr (int a, int b, int c, int d)
2049 return exp (log_gamma_int (a + b + 1.) - log_gamma_int (a + 1.)
2050 + log_gamma_int (c + d + 1.) - log_gamma_int (b + 1.)
2051 + log_gamma_int (a + c + 1.) - log_gamma_int (c + 1.)
2052 + log_gamma_int (b + d + 1.) - log_gamma_int (d + 1.)
2053 - log_gamma_int (a + b + c + d + 1.));
2056 /* Swap the contents of A and B. */
2058 swap (int *a, int *b)
2065 /* Calculate significance for Fisher's exact test as specified in
2066 _SPSS Statistical Algorithms_, Appendix 5. */
2068 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2070 if (MIN (c, d) < MIN (a, b))
2071 swap (&a, &c), swap (&b, &d);
2072 if (MIN (b, d) < MIN (a, c))
2073 swap (&a, &b), swap (&c, &d);
2077 swap (&a, &b), swap (&c, &d);
2079 swap (&a, &c), swap (&b, &d);
2082 double pn1 = Pr (a, b, c, d);
2084 for (int xt = 1; xt <= a; xt++)
2085 *fisher1 += Pr (a - xt, b + xt, c + xt, d - xt);
2087 *fisher2 = *fisher1;
2088 for (int 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)
2143 FOR_EACH_POPULATED_COLUMN (c, xt)
2151 double f11 = xt->mat[nz_cols[0]];
2152 double f12 = xt->mat[nz_cols[1]];
2153 double f21 = xt->mat[nz_cols[0] + n_cols];
2154 double f22 = xt->mat[nz_cols[1] + n_cols];
2157 const double xt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * xt->total;
2160 chisq[3] = (xt->total * pow2 (xt_)
2161 / (f11 + f12) / (f21 + f22)
2162 / (f11 + f21) / (f12 + f22));
2169 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2172 /* Calculate Mantel-Haenszel. */
2173 if (var_is_numeric (xt->vars[ROW_VAR].var)
2174 && var_is_numeric (xt->vars[COL_VAR].var))
2176 double r, ase_0, ase_1;
2177 calc_r (xt, (double *) xt->vars[ROW_VAR].values,
2178 (double *) xt->vars[COL_VAR].values,
2179 &r, &ase_0, &ase_1);
2181 chisq[4] = (xt->total - 1.) * r * r;
2186 /* Calculate the value of Pearson's r. r is stored into R, its T value into
2187 T, and standard error into ERROR. The row and column values must be
2188 passed in XT and Y. */
2190 calc_r (struct crosstabulation *xt,
2191 double *XT, double *Y, double *r, double *t, double *error)
2193 size_t n_rows = xt->vars[ROW_VAR].n_values;
2194 size_t n_cols = xt->vars[COL_VAR].n_values;
2197 for (size_t i = 0; i < n_rows; i++)
2198 for (size_t j = 0; j < n_cols; j++)
2200 double fij = xt->mat[j + i * n_cols];
2201 double product = XT[i] * Y[j];
2202 double temp = fij * product;
2208 for (size_t i = 0; i < n_rows; i++)
2210 sum_Xr += XT[i] * xt->row_tot[i];
2211 sum_X2r += pow2 (XT[i]) * xt->row_tot[i];
2213 double Xbar = sum_Xr / xt->total;
2217 for (size_t i = 0; i < n_cols; i++)
2219 sum_Yc += Y[i] * xt->col_tot[i];
2220 sum_Y2c += Y[i] * Y[i] * xt->col_tot[i];
2222 double Ybar = sum_Yc / xt->total;
2224 double S = sum_XYf - sum_Xr * sum_Yc / xt->total;
2225 double SX = sum_X2r - pow2 (sum_Xr) / xt->total;
2226 double SY = sum_Y2c - pow2 (sum_Yc) / xt->total;
2227 double T = sqrt (SX * SY);
2229 *t = *r / sqrt (1 - pow2 (*r)) * sqrt (xt->total - 2);
2233 for (size_t i = 0; i < n_rows; i++)
2234 for (size_t j = 0; j < n_cols; j++)
2236 double Xresid = XT[i] - Xbar;
2237 double Yresid = Y[j] - Ybar;
2238 double temp = (T * Xresid * Yresid
2240 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2241 double y = xt->mat[j + i * n_cols] * temp * temp - c;
2246 *error = sqrt (s) / (T * T);
2249 /* Calculate symmetric statistics and their asymptotic standard
2250 errors. Returns false if none could be calculated. */
2252 calc_symmetric (struct crosstabs_proc *proc, struct crosstabulation *xt,
2253 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2254 double t[N_SYMMETRIC],
2255 double somers_d_v[3], double somers_d_ase[3],
2256 double somers_d_t[3])
2258 size_t n_rows = xt->vars[ROW_VAR].n_values;
2259 size_t n_cols = xt->vars[COL_VAR].n_values;
2261 size_t q = MIN (xt->ns_rows, xt->ns_cols);
2265 for (size_t i = 0; i < N_SYMMETRIC; i++)
2266 v[i] = ase[i] = t[i] = SYSMIS;
2268 /* Phi, Cramer's V, contingency coefficient. */
2269 if (proc->statistics & (CRS_ST_PHI | CRS_ST_CC))
2271 double Xp = 0.; /* Pearson chi-square. */
2273 FOR_EACH_POPULATED_ROW (r, xt)
2274 FOR_EACH_POPULATED_COLUMN (c, xt)
2276 double expected = xt->row_tot[r] * xt->col_tot[c] / xt->total;
2277 double freq = xt->mat[n_cols * r + c];
2278 double residual = freq - expected;
2280 Xp += residual * residual / expected;
2283 if (proc->statistics & CRS_ST_PHI)
2285 v[0] = sqrt (Xp / xt->total);
2286 v[1] = sqrt (Xp / (xt->total * (q - 1)));
2288 if (proc->statistics & CRS_ST_CC)
2289 v[2] = sqrt (Xp / (Xp + xt->total));
2292 if (proc->statistics & (CRS_ST_BTAU | CRS_ST_CTAU
2293 | CRS_ST_GAMMA | CRS_ST_D))
2295 double Dr = pow2 (xt->total);
2296 for (size_t r = 0; r < n_rows; r++)
2297 Dr -= pow2 (xt->row_tot[r]);
2299 double Dc = pow2 (xt->total);
2300 for (size_t c = 0; c < n_cols; c++)
2301 Dc -= pow2 (xt->col_tot[c]);
2303 double *cum = xnmalloc (n_cols * n_rows, sizeof *cum);
2304 for (size_t c = 0; c < n_cols; c++)
2308 for (size_t r = 0; r < n_rows; r++)
2309 cum[c + r * n_cols] = ct += xt->mat[c + r * n_cols];
2315 for (size_t i = 0; i < n_rows; i++)
2318 for (size_t j = 1; j < n_cols; j++)
2319 Cij += xt->col_tot[j] - cum[j + i * n_cols];
2323 for (size_t j = 1; j < n_cols; j++)
2324 Dij += cum[j + (i - 1) * n_cols];
2326 for (size_t j = 0;;)
2328 double fij = xt->mat[j + i * n_cols];
2335 Cij -= xt->col_tot[j] - cum[j + i * n_cols];
2336 Dij += xt->col_tot[j - 1] - cum[j - 1 + i * n_cols];
2340 Cij += cum[j - 1 + (i - 1) * n_cols];
2341 Dij -= cum[j + (i - 1) * n_cols];
2346 if (proc->statistics & CRS_ST_BTAU)
2347 v[3] = (P - Q) / sqrt (Dr * Dc);
2348 if (proc->statistics & CRS_ST_CTAU)
2349 v[4] = (q * (P - Q)) / (pow2 (xt->total) * (q - 1));
2350 if (proc->statistics & CRS_ST_GAMMA)
2351 v[5] = (P - Q) / (P + Q);
2353 /* ASE for tau-b, tau-c, gamma. Calculations could be
2354 eliminated here, at expense of memory. */
2355 double btau_cum = 0;
2356 double ctau_cum = 0;
2357 double gamma_cum = 0;
2358 double d_yx_cum = 0;
2359 double d_xy_cum = 0;
2360 for (size_t i = 0; i < n_rows; i++)
2363 for (size_t j = 1; j < n_cols; j++)
2364 Cij += xt->col_tot[j] - cum[j + i * n_cols];
2368 for (size_t j = 1; j < n_cols; j++)
2369 Dij += cum[j + (i - 1) * n_cols];
2371 for (size_t j = 0;;)
2373 double fij = xt->mat[j + i * n_cols];
2375 if (proc->statistics & CRS_ST_BTAU)
2376 btau_cum += fij * pow2 (2. * sqrt (Dr * Dc) * (Cij - Dij)
2377 + v[3] * (xt->row_tot[i] * Dc
2378 + xt->col_tot[j] * Dr));
2379 ctau_cum += fij * pow2 (Cij - Dij);
2381 if (proc->statistics & CRS_ST_GAMMA)
2382 gamma_cum += fij * pow2 (Q * Cij - P * Dij);
2384 if (proc->statistics & CRS_ST_D)
2386 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2387 - (P - Q) * (xt->total - xt->row_tot[i]));
2388 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2389 - (Q - P) * (xt->total - xt->col_tot[j]));
2395 Cij -= xt->col_tot[j] - cum[j + i * n_cols];
2396 Dij += xt->col_tot[j - 1] - cum[j - 1 + i * n_cols];
2400 Cij += cum[j - 1 + (i - 1) * n_cols];
2401 Dij -= cum[j + (i - 1) * n_cols];
2406 if (proc->statistics & CRS_ST_BTAU)
2408 double btau_var = ((btau_cum
2409 - (xt->total * pow2 (xt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2411 ase[3] = sqrt (btau_var);
2412 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / xt->total)
2415 if (proc->statistics & CRS_ST_CTAU)
2417 ase[4] = ((2 * q / ((q - 1) * pow2 (xt->total)))
2418 * sqrt (ctau_cum - (P - Q) * (P - Q) / xt->total));
2419 t[4] = v[4] / ase[4];
2421 if (proc->statistics & CRS_ST_GAMMA)
2423 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2424 t[5] = v[5] / (2. / (P + Q)
2425 * sqrt (ctau_cum - (P - Q) * (P - Q) / xt->total));
2427 if (proc->statistics & CRS_ST_D)
2429 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2430 somers_d_ase[0] = SYSMIS;
2431 somers_d_t[0] = (somers_d_v[0]
2433 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2434 somers_d_v[1] = (P - Q) / Dc;
2435 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2436 somers_d_t[1] = (somers_d_v[1]
2438 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2439 somers_d_v[2] = (P - Q) / Dr;
2440 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2441 somers_d_t[2] = (somers_d_v[2]
2443 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2449 /* Spearman correlation, Pearson's r. */
2450 if (proc->statistics & CRS_ST_CORR)
2452 double *R = xmalloc (sizeof *R * n_rows);
2455 for (size_t i = 0; i < n_rows; i++)
2457 R[i] = s + (xt->row_tot[i] + 1.) / 2.;
2458 double y = xt->row_tot[i] - c;
2464 double *C = xmalloc (sizeof *C * n_cols);
2466 for (size_t j = 0; j < n_cols; j++)
2468 C[j] = s + (xt->col_tot[j] + 1.) / 2;
2469 double y = xt->col_tot[j] - c;
2475 calc_r (xt, R, C, &v[6], &t[6], &ase[6]);
2480 calc_r (xt, (double *) xt->vars[ROW_VAR].values,
2481 (double *) xt->vars[COL_VAR].values,
2482 &v[7], &t[7], &ase[7]);
2485 /* Cohen's kappa. */
2486 if (proc->statistics & CRS_ST_KAPPA && xt->ns_rows == xt->ns_cols)
2489 double sum_rici = 0;
2490 double sum_fiiri_ci = 0;
2491 double sum_riciri_ci = 0;
2492 for (size_t i = 0, j = 0; i < xt->ns_rows; i++, j++)
2494 while (xt->col_tot[j] == 0.)
2497 double prod = xt->row_tot[i] * xt->col_tot[j];
2498 double sum = xt->row_tot[i] + xt->col_tot[j];
2500 sum_fii += xt->mat[j + i * n_cols];
2502 sum_fiiri_ci += xt->mat[j + i * n_cols] * sum;
2503 sum_riciri_ci += prod * sum;
2506 double sum_fijri_ci2 = 0;
2507 for (size_t i = 0; i < xt->ns_rows; i++)
2508 for (size_t j = 0; j < xt->ns_cols; j++)
2510 double sum = xt->row_tot[i] + xt->col_tot[j];
2511 sum_fijri_ci2 += xt->mat[j + i * n_cols] * sum * sum;
2514 v[8] = (xt->total * sum_fii - sum_rici) / (pow2 (xt->total) - sum_rici);
2516 double ase_under_h0 = sqrt ((pow2 (xt->total) * sum_rici
2517 + sum_rici * sum_rici
2518 - xt->total * sum_riciri_ci)
2519 / (xt->total * (pow2 (xt->total) - sum_rici) * (pow2 (xt->total) - sum_rici)));
2521 ase[8] = sqrt (xt->total * (((sum_fii * (xt->total - sum_fii))
2522 / pow2 (pow2 (xt->total) - sum_rici))
2523 + ((2. * (xt->total - sum_fii)
2524 * (2. * sum_fii * sum_rici
2525 - xt->total * sum_fiiri_ci))
2526 / pow3 (pow2 (xt->total) - sum_rici))
2527 + (pow2 (xt->total - sum_fii)
2528 * (xt->total * sum_fijri_ci2 - 4.
2529 * sum_rici * sum_rici)
2530 / pow4 (pow2 (xt->total) - sum_rici))));
2532 t[8] = v[8] / ase_under_h0;
2538 /* Calculate risk estimate. */
2540 calc_risk (struct crosstabulation *xt,
2541 double *value, double *upper, double *lower, union value *c,
2544 size_t n_cols = xt->vars[COL_VAR].n_values;
2546 for (size_t i = 0; i < 3; i++)
2547 value[i] = upper[i] = lower[i] = SYSMIS;
2549 if (xt->ns_rows != 2 || xt->ns_cols != 2)
2552 /* Find populated columns. */
2555 FOR_EACH_POPULATED_COLUMN (c, xt)
2559 /* Find populated rows. */
2562 FOR_EACH_POPULATED_ROW (r, xt)
2566 double f11 = xt->mat[nz_cols[0] + n_cols * nz_rows[0]];
2567 double f12 = xt->mat[nz_cols[1] + n_cols * nz_rows[0]];
2568 double f21 = xt->mat[nz_cols[0] + n_cols * nz_rows[1]];
2569 double f22 = xt->mat[nz_cols[1] + n_cols * nz_rows[1]];
2570 *n_valid = f11 + f12 + f21 + f22;
2572 c[0] = xt->vars[COL_VAR].values[nz_cols[0]];
2573 c[1] = xt->vars[COL_VAR].values[nz_cols[1]];
2575 value[0] = (f11 * f22) / (f12 * f21);
2576 double v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2577 lower[0] = value[0] * exp (-1.960 * v);
2578 upper[0] = value[0] * exp (1.960 * v);
2580 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2581 v = sqrt ((f12 / (f11 * (f11 + f12)))
2582 + (f22 / (f21 * (f21 + f22))));
2583 lower[1] = value[1] * exp (-1.960 * v);
2584 upper[1] = value[1] * exp (1.960 * v);
2586 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2587 v = sqrt ((f11 / (f12 * (f11 + f12)))
2588 + (f21 / (f22 * (f21 + f22))));
2589 lower[2] = value[2] * exp (-1.960 * v);
2590 upper[2] = value[2] * exp (1.960 * v);
2595 /* Calculate directional measures. */
2597 calc_directional (struct crosstabs_proc *proc, struct crosstabulation *xt,
2598 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2599 double t[N_DIRECTIONAL], double sig[N_DIRECTIONAL])
2601 size_t n_rows = xt->vars[ROW_VAR].n_values;
2602 size_t n_cols = xt->vars[COL_VAR].n_values;
2603 for (size_t i = 0; i < N_DIRECTIONAL; i++)
2604 v[i] = ase[i] = t[i] = sig[i] = SYSMIS;
2607 if (proc->statistics & CRS_ST_LAMBDA)
2609 /* Find maximum for each row and their sum. */
2610 double *fim = xnmalloc (n_rows, sizeof *fim);
2611 size_t *fim_index = xnmalloc (n_rows, sizeof *fim_index);
2612 double sum_fim = 0.0;
2613 for (size_t i = 0; i < n_rows; i++)
2615 double max = xt->mat[i * n_cols];
2618 for (size_t j = 1; j < n_cols; j++)
2619 if (xt->mat[j + i * n_cols] > max)
2621 max = xt->mat[j + i * n_cols];
2627 fim_index[i] = index;
2630 /* Find maximum for each column. */
2631 double *fmj = xnmalloc (n_cols, sizeof *fmj);
2632 size_t *fmj_index = xnmalloc (n_cols, sizeof *fmj_index);
2633 double sum_fmj = 0.0;
2634 for (size_t j = 0; j < n_cols; j++)
2636 double max = xt->mat[j];
2639 for (size_t i = 1; i < n_rows; i++)
2640 if (xt->mat[j + i * n_cols] > max)
2642 max = xt->mat[j + i * n_cols];
2648 fmj_index[j] = index;
2651 /* Find maximum row total. */
2652 double rm = xt->row_tot[0];
2653 size_t rm_index = 0;
2654 for (size_t i = 1; i < n_rows; i++)
2655 if (xt->row_tot[i] > rm)
2657 rm = xt->row_tot[i];
2661 /* Find maximum column total. */
2662 double cm = xt->col_tot[0];
2663 size_t cm_index = 0;
2664 for (size_t j = 1; j < n_cols; j++)
2665 if (xt->col_tot[j] > cm)
2667 cm = xt->col_tot[j];
2671 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * xt->total - rm - cm);
2672 v[1] = (sum_fmj - rm) / (xt->total - rm);
2673 v[2] = (sum_fim - cm) / (xt->total - cm);
2675 /* ASE1 for Y given XT. */
2678 for (size_t i = 0; i < n_rows; i++)
2679 if (cm_index == fim_index[i])
2681 ase[2] = sqrt ((xt->total - sum_fim) * (sum_fim + cm - 2. * accum)
2682 / pow3 (xt->total - cm));
2685 /* ASE0 for Y given XT. */
2688 for (size_t i = 0; i < n_rows; i++)
2689 if (cm_index != fim_index[i])
2690 accum += (xt->mat[i * n_cols + fim_index[i]]
2691 + xt->mat[i * n_cols + cm_index]);
2692 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / xt->total) / (xt->total - cm));
2695 /* ASE1 for XT given Y. */
2698 for (size_t j = 0; j < n_cols; j++)
2699 if (rm_index == fmj_index[j])
2701 ase[1] = sqrt ((xt->total - sum_fmj) * (sum_fmj + rm - 2. * accum)
2702 / pow3 (xt->total - rm));
2705 /* ASE0 for XT given Y. */
2708 for (size_t j = 0; j < n_cols; j++)
2709 if (rm_index != fmj_index[j])
2710 accum += (xt->mat[j + n_cols * fmj_index[j]]
2711 + xt->mat[j + n_cols * rm_index]);
2712 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / xt->total) / (xt->total - rm));
2715 /* Symmetric ASE0 and ASE1. */
2717 double accum0 = 0.0;
2718 double accum1 = 0.0;
2719 for (size_t i = 0; i < n_rows; i++)
2720 for (size_t j = 0; j < n_cols; j++)
2722 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2723 int temp1 = (i == rm_index) + (j == cm_index);
2724 accum0 += xt->mat[j + i * n_cols] * pow2 (temp0 - temp1);
2725 accum1 += (xt->mat[j + i * n_cols]
2726 * pow2 (temp0 + (v[0] - 1.) * temp1));
2728 ase[0] = sqrt (accum1 - 4. * xt->total * v[0] * v[0]) / (2. * xt->total - rm - cm);
2729 t[0] = v[0] / (sqrt (accum0 - pow2 (sum_fim + sum_fmj - cm - rm) / xt->total)
2730 / (2. * xt->total - rm - cm));
2733 for (size_t i = 0; i < 3; i++)
2734 sig[i] = 2 * gsl_cdf_ugaussian_Q (t[i]);
2742 double sum_fij2_ri = 0.0;
2743 double sum_fij2_ci = 0.0;
2744 FOR_EACH_POPULATED_ROW (i, xt)
2745 FOR_EACH_POPULATED_COLUMN (j, xt)
2747 double temp = pow2 (xt->mat[j + i * n_cols]);
2748 sum_fij2_ri += temp / xt->row_tot[i];
2749 sum_fij2_ci += temp / xt->col_tot[j];
2752 double sum_ri2 = 0.0;
2753 for (size_t i = 0; i < n_rows; i++)
2754 sum_ri2 += pow2 (xt->row_tot[i]);
2756 double sum_cj2 = 0.0;
2757 for (size_t j = 0; j < n_cols; j++)
2758 sum_cj2 += pow2 (xt->col_tot[j]);
2760 v[3] = (xt->total * sum_fij2_ci - sum_ri2) / (pow2 (xt->total) - sum_ri2);
2761 v[4] = (xt->total * sum_fij2_ri - sum_cj2) / (pow2 (xt->total) - sum_cj2);
2764 if (proc->statistics & CRS_ST_UC)
2767 FOR_EACH_POPULATED_ROW (i, xt)
2768 UX -= xt->row_tot[i] / xt->total * log (xt->row_tot[i] / xt->total);
2771 FOR_EACH_POPULATED_COLUMN (j, xt)
2772 UY -= xt->col_tot[j] / xt->total * log (xt->col_tot[j] / xt->total);
2776 for (size_t i = 0; i < n_rows; i++)
2777 for (size_t j = 0; j < n_cols; j++)
2779 double entry = xt->mat[j + i * n_cols];
2784 P += entry * pow2 (log (xt->col_tot[j] * xt->row_tot[i] / (xt->total * entry)));
2785 UXY -= entry / xt->total * log (entry / xt->total);
2788 double ase1_yx = 0.0;
2789 double ase1_xy = 0.0;
2790 double ase1_sym = 0.0;
2791 for (size_t i = 0; i < n_rows; i++)
2792 for (size_t j = 0; j < n_cols; j++)
2794 double entry = xt->mat[j + i * n_cols];
2799 ase1_yx += entry * pow2 (UY * log (entry / xt->row_tot[i])
2800 + (UX - UXY) * log (xt->col_tot[j] / xt->total));
2801 ase1_xy += entry * pow2 (UX * log (entry / xt->col_tot[j])
2802 + (UY - UXY) * log (xt->row_tot[i] / xt->total));
2803 ase1_sym += entry * pow2 ((UXY
2804 * log (xt->row_tot[i] * xt->col_tot[j] / pow2 (xt->total)))
2805 - (UX + UY) * log (entry / xt->total));
2808 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2809 ase[5] = (2. / (xt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2812 v[6] = (UX + UY - UXY) / UX;
2813 ase[6] = sqrt (ase1_xy) / (xt->total * UX * UX);
2814 t[6] = v[6] / (sqrt (P - xt->total * pow2 (UX + UY - UXY)) / (xt->total * UX));
2816 v[7] = (UX + UY - UXY) / UY;
2817 ase[7] = sqrt (ase1_yx) / (xt->total * UY * UY);
2818 t[7] = v[7] / (sqrt (P - xt->total * pow2 (UX + UY - UXY)) / (xt->total * UY));
2822 if (proc->statistics & CRS_ST_D)
2824 double v_dummy[N_SYMMETRIC];
2825 double ase_dummy[N_SYMMETRIC];
2826 double t_dummy[N_SYMMETRIC];
2827 double somers_d_v[3];
2828 double somers_d_ase[3];
2829 double somers_d_t[3];
2831 if (calc_symmetric (proc, xt, v_dummy, ase_dummy, t_dummy,
2832 somers_d_v, somers_d_ase, somers_d_t))
2834 for (size_t i = 0; i < 3; i++)
2836 v[8 + i] = somers_d_v[i];
2837 ase[8 + i] = somers_d_ase[i];
2838 t[8 + i] = somers_d_t[i];
2839 sig[8 + i] = 2 * gsl_cdf_ugaussian_Q (fabs (somers_d_t[i]));
2845 if (proc->statistics & CRS_ST_ETA)
2848 double sum_Xr = 0.0;
2849 double sum_X2r = 0.0;
2850 for (size_t i = 0; i < n_rows; i++)
2852 sum_Xr += xt->vars[ROW_VAR].values[i].f * xt->row_tot[i];
2853 sum_X2r += pow2 (xt->vars[ROW_VAR].values[i].f) * xt->row_tot[i];
2855 double SX = sum_X2r - pow2 (sum_Xr) / xt->total;
2858 FOR_EACH_POPULATED_COLUMN (j, xt)
2862 for (size_t i = 0; i < n_rows; i++)
2864 SXW += (pow2 (xt->vars[ROW_VAR].values[i].f)
2865 * xt->mat[j + i * n_cols]);
2866 cum += (xt->vars[ROW_VAR].values[i].f
2867 * xt->mat[j + i * n_cols]);
2870 SXW -= cum * cum / xt->col_tot[j];
2872 v[11] = sqrt (1. - SXW / SX);
2875 double sum_Yc = 0.0;
2876 double sum_Y2c = 0.0;
2877 for (size_t i = 0; i < n_cols; i++)
2879 sum_Yc += xt->vars[COL_VAR].values[i].f * xt->col_tot[i];
2880 sum_Y2c += pow2 (xt->vars[COL_VAR].values[i].f) * xt->col_tot[i];
2882 double SY = sum_Y2c - pow2 (sum_Yc) / xt->total;
2885 FOR_EACH_POPULATED_ROW (i, xt)
2888 for (size_t j = 0; j < n_cols; j++)
2890 SYW += (pow2 (xt->vars[COL_VAR].values[j].f)
2891 * xt->mat[j + i * n_cols]);
2892 cum += (xt->vars[COL_VAR].values[j].f
2893 * xt->mat[j + i * n_cols]);
2896 SYW -= cum * cum / xt->row_tot[i];
2898 v[12] = sqrt (1. - SYW / SY);