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/commands/freq.h"
45 #include "language/commands/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);
604 bool overflow = false;
607 by = xnrealloc (by, n_by + 1, sizeof *by);
608 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
609 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
610 PV_NO_DUPLICATE | PV_NO_SCRATCH))
612 size_t n = by_nvar[n_by++];
613 if (xalloc_oversized (nx, n))
617 while (lex_match (lexer, T_BY));
620 lex_ofs_error (lexer, vars_start, lex_ofs (lexer) - 1,
621 _("Too many cross-tabulation variables or dimensions."));
626 bool unused UNUSED = lex_force_match (lexer, T_BY);
629 int vars_end = lex_ofs (lexer) - 1;
631 size_t *by_iter = XCALLOC (n_by, size_t);
632 proc->pivots = xnrealloc (proc->pivots,
633 proc->n_pivots + nx, sizeof *proc->pivots);
634 for (size_t i = 0; i < nx; i++)
636 struct crosstabulation *xt = &proc->pivots[proc->n_pivots++];
638 *xt = (struct crosstabulation) {
640 .weight_format = proc->weight_format,
643 .vars = xcalloc (n_by, sizeof *xt->vars),
646 .const_indexes = NULL,
647 .start_ofs = vars_start,
651 for (size_t j = 0; j < n_by; j++)
652 xt->vars[j].var = by[j][by_iter[j]];
654 for (int j = n_by - 1; j >= 0; j--)
656 if (++by_iter[j] < by_nvar[j])
665 /* All return paths lead here. */
666 for (size_t i = 0; i < n_by; i++)
671 const_var_set_destroy (var_set);
676 /* Parses the VARIABLES subcommand. */
678 parse_crosstabs_variables (struct lexer *lexer, struct dataset *ds,
679 struct crosstabs_proc *proc)
683 lex_next_error (lexer, -1, -1, _("%s must be specified before %s."),
684 "VARIABLES", "TABLES");
688 lex_match (lexer, T_EQUALS);
692 size_t orig_nv = proc->n_variables;
694 if (!parse_variables_const (lexer, dataset_dict (ds),
695 &proc->variables, &proc->n_variables,
696 (PV_APPEND | PV_NUMERIC
697 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
700 if (!lex_force_match (lexer, T_LPAREN))
703 if (!lex_force_int (lexer))
705 long min = lex_integer (lexer);
708 lex_match (lexer, T_COMMA);
710 if (!lex_force_int_range (lexer, NULL, min, LONG_MAX))
712 long max = lex_integer (lexer);
715 if (!lex_force_match (lexer, T_RPAREN))
718 for (size_t i = orig_nv; i < proc->n_variables; i++)
720 const struct variable *var = proc->variables[i];
721 struct var_range *vr = xmalloc (sizeof *vr);
722 *vr = (struct var_range) {
726 .count = max - min + 1,
728 hmap_insert (&proc->var_ranges, &vr->hmap_node,
729 hash_pointer (var, 0));
732 if (lex_token (lexer) == T_SLASH)
736 proc->mode = INTEGER;
740 free (proc->variables);
741 proc->variables = NULL;
742 proc->n_variables = 0;
746 /* Data file processing. */
748 static const struct var_range *
749 get_var_range (const struct crosstabs_proc *proc, const struct variable *var)
751 if (!hmap_is_empty (&proc->var_ranges))
753 const struct var_range *range;
755 HMAP_FOR_EACH_IN_BUCKET (range, struct var_range, hmap_node,
756 hash_pointer (var, 0), &proc->var_ranges)
757 if (range->var == var)
765 should_tabulate_case (const struct crosstabulation *xt, const struct ccase *c,
766 enum mv_class exclude)
768 for (size_t j = 0; j < xt->n_vars; j++)
770 const struct variable *var = xt->vars[j].var;
771 const struct var_range *range = get_var_range (xt->proc, var);
773 if (var_is_value_missing (var, case_data (c, var)) & exclude)
778 double num = case_num (c, var);
779 if (num < range->min || num >= range->max + 1.)
787 tabulate_integer_case (struct crosstabulation *xt, const struct ccase *c,
791 for (size_t j = 0; j < xt->n_vars; j++)
793 /* Throw away fractional parts of values. */
794 hash = hash_int (case_num (c, xt->vars[j].var), hash);
798 HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &xt->data)
800 for (size_t j = 0; j < xt->n_vars; j++)
801 if ((int) case_num (c, xt->vars[j].var) != (int) te->values[j].f)
804 /* Found an existing entry. */
811 /* No existing entry. Create a new one. */
812 te = xmalloc (table_entry_size (xt->n_vars));
814 for (size_t j = 0; j < xt->n_vars; j++)
815 te->values[j].f = (int) case_num (c, xt->vars[j].var);
816 hmap_insert (&xt->data, &te->node, hash);
820 tabulate_general_case (struct crosstabulation *xt, const struct ccase *c,
824 for (size_t j = 0; j < xt->n_vars; j++)
826 const struct variable *var = xt->vars[j].var;
827 hash = value_hash (case_data (c, var), var_get_width (var), hash);
831 HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &xt->data)
833 for (size_t j = 0; j < xt->n_vars; j++)
835 const struct variable *var = xt->vars[j].var;
836 if (!value_equal (case_data (c, var), &te->values[j],
837 var_get_width (var)))
841 /* Found an existing entry. */
848 /* No existing entry. Create a new one. */
849 te = xmalloc (table_entry_size (xt->n_vars));
851 for (size_t j = 0; j < xt->n_vars; j++)
853 const struct variable *var = xt->vars[j].var;
854 value_clone (&te->values[j], case_data (c, var), var_get_width (var));
856 hmap_insert (&xt->data, &te->node, hash);
859 /* Post-data reading calculations. */
861 static int compare_table_entry_vars_3way (const struct freq *a,
862 const struct freq *b,
863 const struct crosstabulation *xt,
865 static int compare_table_entry_3way (const void *ap_, const void *bp_,
867 static int compare_table_entry_3way_inv (const void *ap_, const void *bp_,
870 static void enum_var_values (const struct crosstabulation *, int var_idx,
872 static void free_var_values (const struct crosstabulation *, int var_idx);
873 static void output_crosstabulation (struct crosstabs_proc *,
874 struct crosstabulation *,
876 static void make_crosstabulation_subset (struct crosstabulation *xt,
877 size_t row0, size_t row1,
878 struct crosstabulation *subset);
879 static void make_summary_table (struct crosstabs_proc *);
880 static bool find_crosstab (struct crosstabulation *, size_t *row0p,
884 postcalc (struct crosstabs_proc *proc, struct lexer *lexer)
886 /* Round hash table entries, if requested
888 If this causes any of the cell counts to fall to zero, delete those
890 if (proc->round_cells)
891 for (struct crosstabulation *xt = proc->pivots;
892 xt < &proc->pivots[proc->n_pivots]; xt++)
894 struct freq *e, *next;
895 HMAP_FOR_EACH_SAFE (e, next, struct freq, node, &xt->data)
897 e->count = round_weight (proc, e->count);
900 hmap_delete (&xt->data, &e->node);
906 /* Convert hash tables into sorted arrays of entries. */
907 for (struct crosstabulation *xt = proc->pivots;
908 xt < &proc->pivots[proc->n_pivots]; xt++)
910 xt->n_entries = hmap_count (&xt->data);
911 xt->entries = xnmalloc (xt->n_entries, sizeof *xt->entries);
915 HMAP_FOR_EACH (e, struct freq, node, &xt->data)
916 xt->entries[i++] = e;
918 hmap_destroy (&xt->data);
920 sort (xt->entries, xt->n_entries, sizeof *xt->entries,
921 proc->descending ? compare_table_entry_3way_inv : compare_table_entry_3way,
925 make_summary_table (proc);
927 /* Output each pivot table. */
928 for (struct crosstabulation *xt = proc->pivots;
929 xt < &proc->pivots[proc->n_pivots]; xt++)
931 output_crosstabulation (proc, xt, lexer);
934 int n_vars = (xt->n_vars > 2 ? 2 : xt->n_vars);
935 const struct variable **vars = XCALLOC (n_vars, const struct variable*);
936 for (size_t i = 0; i < n_vars; i++)
937 vars[i] = xt->vars[i].var;
938 chart_submit (barchart_create (vars, n_vars, _("Count"),
940 xt->entries, xt->n_entries));
945 /* Free output and prepare for next split file. */
946 for (struct crosstabulation *xt = proc->pivots;
947 xt < &proc->pivots[proc->n_pivots]; xt++)
951 /* Free the members that were allocated in this function(and the values
952 owned by the entries.
954 The other pointer members are either both allocated and destroyed at a
955 lower level (in output_crosstabulation), or both allocated and
956 destroyed at a higher level (in crs_custom_tables and free_proc,
958 for (size_t i = 0; i < xt->n_vars; i++)
960 int width = var_get_width (xt->vars[i].var);
961 if (value_needs_init (width))
962 for (size_t j = 0; j < xt->n_entries; j++)
963 value_destroy (&xt->entries[j]->values[i], width);
966 for (size_t i = 0; i < xt->n_entries; i++)
967 free (xt->entries[i]);
973 make_crosstabulation_subset (struct crosstabulation *xt, size_t row0,
974 size_t row1, struct crosstabulation *subset)
979 assert (xt->n_consts == 0);
981 subset->vars = xt->vars;
983 subset->n_consts = xt->n_vars - 2;
984 subset->const_vars = xt->vars + 2;
985 subset->const_indexes = xcalloc (subset->n_consts,
986 sizeof *subset->const_indexes);
987 for (size_t i = 0; i < subset->n_consts; i++)
989 const union value *value = &xt->entries[row0]->values[2 + i];
991 for (size_t j = 0; j < xt->vars[2 + i].n_values; j++)
992 if (value_equal (&xt->vars[2 + i].values[j], value,
993 var_get_width (xt->vars[2 + i].var)))
995 subset->const_indexes[i] = j;
1002 subset->entries = &xt->entries[row0];
1003 subset->n_entries = row1 - row0;
1007 compare_table_entry_var_3way (const struct freq *a,
1008 const struct freq *b,
1009 const struct crosstabulation *xt,
1012 return value_compare_3way (&a->values[idx], &b->values[idx],
1013 var_get_width (xt->vars[idx].var));
1017 compare_table_entry_vars_3way (const struct freq *a,
1018 const struct freq *b,
1019 const struct crosstabulation *xt,
1022 for (int i = idx1 - 1; i >= idx0; i--)
1024 int cmp = compare_table_entry_var_3way (a, b, xt, i);
1031 /* Compare the struct freq at *AP to the one at *BP and
1032 return a strcmp()-type result. */
1034 compare_table_entry_3way (const void *ap_, const void *bp_, const void *xt_)
1036 const struct freq *const *ap = ap_;
1037 const struct freq *const *bp = bp_;
1038 const struct freq *a = *ap;
1039 const struct freq *b = *bp;
1040 const struct crosstabulation *xt = xt_;
1042 int cmp = compare_table_entry_vars_3way (a, b, xt, 2, xt->n_vars);
1046 cmp = compare_table_entry_var_3way (a, b, xt, ROW_VAR);
1050 return compare_table_entry_var_3way (a, b, xt, COL_VAR);
1053 /* Inverted version of compare_table_entry_3way */
1055 compare_table_entry_3way_inv (const void *ap_, const void *bp_, const void *xt_)
1057 return -compare_table_entry_3way (ap_, bp_, xt_);
1060 /* Output a table summarizing the cases processed. */
1062 make_summary_table (struct crosstabs_proc *proc)
1064 struct pivot_table *table = pivot_table_create (N_("Summary"));
1065 pivot_table_set_weight_var (table, dict_get_weight (proc->dict));
1067 pivot_dimension_create (table, PIVOT_AXIS_COLUMN, N_("Statistics"),
1068 N_("N"), PIVOT_RC_COUNT,
1069 N_("Percent"), PIVOT_RC_PERCENT);
1071 struct pivot_dimension *cases = pivot_dimension_create (
1072 table, PIVOT_AXIS_COLUMN, N_("Cases"),
1073 N_("Valid"), N_("Missing"), N_("Total"));
1074 cases->root->show_label = true;
1076 struct pivot_dimension *tables = pivot_dimension_create (
1077 table, PIVOT_AXIS_ROW, N_("Crosstabulation"));
1078 for (struct crosstabulation *xt = &proc->pivots[0];
1079 xt < &proc->pivots[proc->n_pivots]; xt++)
1081 struct string name = DS_EMPTY_INITIALIZER;
1082 for (size_t i = 0; i < xt->n_vars; i++)
1085 ds_put_cstr (&name, " × ");
1086 ds_put_cstr (&name, var_to_string (xt->vars[i].var));
1089 int row = pivot_category_create_leaf (
1091 pivot_value_new_user_text_nocopy (ds_steal_cstr (&name)));
1094 for (size_t i = 0; i < xt->n_entries; i++)
1095 valid += xt->entries[i]->count;
1101 for (int i = 0; i < 3; i++)
1103 pivot_table_put3 (table, 0, i, row, pivot_value_new_number (n[i]));
1104 pivot_table_put3 (table, 1, i, row,
1105 pivot_value_new_number (n[i] / n[2] * 100.0));
1109 pivot_table_submit (table);
1114 static struct pivot_table *create_crosstab_table (
1115 struct crosstabs_proc *, struct crosstabulation *,
1116 size_t crs_leaves[CRS_N_CELLS]);
1117 static struct pivot_table *create_chisq_table (struct crosstabulation *);
1118 static struct pivot_table *create_sym_table (struct crosstabulation *);
1119 static struct pivot_table *create_risk_table (
1120 struct crosstabulation *, struct pivot_dimension **risk_statistics);
1121 static struct pivot_table *create_direct_table (struct crosstabulation *);
1122 static void display_crosstabulation (struct crosstabs_proc *,
1123 struct crosstabulation *,
1124 struct pivot_table *,
1125 size_t crs_leaves[CRS_N_CELLS]);
1126 static void display_chisq (struct crosstabulation *, struct pivot_table *);
1127 static void display_symmetric (struct crosstabs_proc *,
1128 struct crosstabulation *, struct pivot_table *);
1129 static void display_risk (struct crosstabulation *, struct pivot_table *,
1130 struct pivot_dimension *risk_statistics);
1131 static void display_directional (struct crosstabs_proc *,
1132 struct crosstabulation *,
1133 struct pivot_table *);
1134 static void delete_missing (struct crosstabulation *);
1135 static void build_matrix (struct crosstabulation *);
1137 /* Output pivot table XT in the context of PROC. */
1139 output_crosstabulation (struct crosstabs_proc *proc, struct crosstabulation *xt,
1140 struct lexer *lexer)
1142 for (size_t i = 0; i < xt->n_vars; i++)
1143 enum_var_values (xt, i, proc->descending);
1145 if (xt->vars[COL_VAR].n_values == 0)
1149 ds_init_cstr (&vars, var_to_string (xt->vars[0].var));
1150 for (size_t i = 1; i < xt->n_vars; i++)
1151 ds_put_format (&vars, " × %s", var_to_string (xt->vars[i].var));
1153 /* TRANSLATORS: The %s here describes a crosstabulation. It takes the
1154 form "var1 * var2 * var3 * ...". */
1155 lex_ofs_msg (lexer, SW, xt->start_ofs, xt->end_ofs,
1156 _("Crosstabulation %s contained no non-missing cases."),
1160 for (size_t i = 0; i < xt->n_vars; i++)
1161 free_var_values (xt, i);
1165 size_t crs_leaves[CRS_N_CELLS];
1166 struct pivot_table *table = (proc->cells
1167 ? create_crosstab_table (proc, xt, crs_leaves)
1169 struct pivot_table *chisq = (proc->statistics & CRS_ST_CHISQ
1170 ? create_chisq_table (xt)
1172 struct pivot_table *sym
1173 = (proc->statistics & (CRS_ST_PHI | CRS_ST_CC | CRS_ST_BTAU | CRS_ST_CTAU
1174 | CRS_ST_GAMMA | CRS_ST_CORR | CRS_ST_KAPPA)
1175 ? create_sym_table (xt)
1177 struct pivot_dimension *risk_statistics = NULL;
1178 struct pivot_table *risk = (proc->statistics & CRS_ST_RISK
1179 ? create_risk_table (xt, &risk_statistics)
1181 struct pivot_table *direct
1182 = (proc->statistics & (CRS_ST_LAMBDA | CRS_ST_UC | CRS_ST_D | CRS_ST_ETA)
1183 ? create_direct_table (xt)
1188 while (find_crosstab (xt, &row0, &row1))
1190 struct crosstabulation x;
1192 make_crosstabulation_subset (xt, row0, row1, &x);
1194 size_t n_rows = x.vars[ROW_VAR].n_values;
1195 size_t n_cols = x.vars[COL_VAR].n_values;
1196 if (size_overflow_p (xtimes (xtimes (n_rows, n_cols), sizeof (double))))
1198 x.row_tot = xmalloc (n_rows * sizeof *x.row_tot);
1199 x.col_tot = xmalloc (n_cols * sizeof *x.col_tot);
1200 x.mat = xmalloc (n_rows * n_cols * sizeof *x.mat);
1204 /* Find the first variable that differs from the last subtable. */
1206 display_crosstabulation (proc, &x, table, crs_leaves);
1208 if (proc->exclude == 0)
1209 delete_missing (&x);
1212 display_chisq (&x, chisq);
1215 display_symmetric (proc, &x, sym);
1217 display_risk (&x, risk, risk_statistics);
1219 display_directional (proc, &x, direct);
1224 free (x.const_indexes);
1228 pivot_table_submit (table);
1231 pivot_table_submit (chisq);
1234 pivot_table_submit (sym);
1238 if (!pivot_table_is_empty (risk))
1239 pivot_table_submit (risk);
1241 pivot_table_unref (risk);
1245 pivot_table_submit (direct);
1247 for (size_t i = 0; i < xt->n_vars; i++)
1248 free_var_values (xt, i);
1252 build_matrix (struct crosstabulation *x)
1254 const int col_var_width = var_get_width (x->vars[COL_VAR].var);
1255 const int row_var_width = var_get_width (x->vars[ROW_VAR].var);
1256 size_t n_rows = x->vars[ROW_VAR].n_values;
1257 size_t n_cols = x->vars[COL_VAR].n_values;
1259 double *mp = x->mat;
1262 for (struct freq **p = x->entries; p < &x->entries[x->n_entries]; p++)
1264 const struct freq *te = *p;
1266 while (!value_equal (&x->vars[ROW_VAR].values[row],
1267 &te->values[ROW_VAR], row_var_width))
1269 for (; col < n_cols; col++)
1275 while (!value_equal (&x->vars[COL_VAR].values[col],
1276 &te->values[COL_VAR], col_var_width))
1283 if (++col >= n_cols)
1289 while (mp < &x->mat[n_cols * n_rows])
1291 assert (mp == &x->mat[n_cols * n_rows]);
1293 /* Column totals, row totals, ns_rows. */
1295 for (col = 0; col < n_cols; col++)
1296 x->col_tot[col] = 0.0;
1297 for (row = 0; row < n_rows; row++)
1298 x->row_tot[row] = 0.0;
1300 for (row = 0; row < n_rows; row++)
1302 bool row_is_empty = true;
1303 for (col = 0; col < n_cols; col++)
1307 row_is_empty = false;
1308 x->col_tot[col] += *mp;
1309 x->row_tot[row] += *mp;
1316 assert (mp == &x->mat[n_cols * n_rows]);
1320 for (col = 0; col < n_cols; col++)
1321 for (row = 0; row < n_rows; row++)
1322 if (x->mat[col + row * n_cols] != 0.0)
1330 for (col = 0; col < n_cols; col++)
1331 x->total += x->col_tot[col];
1335 add_var_dimension (struct pivot_table *table, const struct xtab_var *var,
1336 enum pivot_axis_type axis_type, bool total)
1338 struct pivot_dimension *d = pivot_dimension_create__ (
1339 table, axis_type, pivot_value_new_variable (var->var));
1341 struct pivot_footnote *missing_footnote = pivot_table_create_footnote (
1342 table, pivot_value_new_text (N_("Missing value")));
1344 struct pivot_category *group = pivot_category_create_group__ (
1345 d->root, pivot_value_new_variable (var->var));
1346 for (size_t j = 0; j < var->n_values; j++)
1348 struct pivot_value *value = pivot_value_new_var_value (
1349 var->var, &var->values[j]);
1350 if (var_is_value_missing (var->var, &var->values[j]))
1351 pivot_value_add_footnote (value, missing_footnote);
1352 pivot_category_create_leaf (group, value);
1356 pivot_category_create_leaf (d->root, pivot_value_new_text (N_("Total")));
1359 static struct pivot_table *
1360 create_crosstab_table (struct crosstabs_proc *proc, struct crosstabulation *xt,
1361 size_t crs_leaves[CRS_N_CELLS])
1364 struct string title = DS_EMPTY_INITIALIZER;
1365 for (size_t i = 0; i < xt->n_vars; i++)
1368 ds_put_cstr (&title, " × ");
1369 ds_put_cstr (&title, var_to_string (xt->vars[i].var));
1371 for (size_t i = 0; i < xt->n_consts; i++)
1373 const struct variable *var = xt->const_vars[i].var;
1374 const union value *value = &xt->entries[0]->values[2 + i];
1377 ds_put_format (&title, ", %s=", var_to_string (var));
1379 /* Insert the formatted value of VAR without any leading spaces. */
1380 s = data_out (value, var_get_encoding (var), var_get_print_format (var),
1381 settings_get_fmt_settings ());
1382 ds_put_cstr (&title, s + strspn (s, " "));
1385 struct pivot_table *table = pivot_table_create__ (
1386 pivot_value_new_user_text_nocopy (ds_steal_cstr (&title)),
1388 pivot_table_set_weight_format (table, proc->weight_format);
1390 struct pivot_dimension *statistics = pivot_dimension_create (
1391 table, PIVOT_AXIS_ROW, N_("Statistics"));
1398 static const struct statistic stats[CRS_N_CELLS] =
1400 #define C(KEYWORD, STRING, RC) { STRING, RC },
1404 for (size_t i = 0; i < CRS_N_CELLS; i++)
1405 if (proc->cells & (1u << i) && stats[i].label)
1406 crs_leaves[i] = pivot_category_create_leaf_rc (
1407 statistics->root, pivot_value_new_text (stats[i].label),
1410 for (size_t i = 0; i < xt->n_vars; i++)
1411 add_var_dimension (table, &xt->vars[i],
1412 i == COL_VAR ? PIVOT_AXIS_COLUMN : PIVOT_AXIS_ROW,
1418 static struct pivot_table *
1419 create_chisq_table (struct crosstabulation *xt)
1421 struct pivot_table *chisq = pivot_table_create (N_("Chi-Square Tests"));
1422 pivot_table_set_weight_format (chisq, xt->weight_format);
1424 pivot_dimension_create (
1425 chisq, PIVOT_AXIS_ROW, N_("Statistics"),
1426 N_("Pearson Chi-Square"),
1427 N_("Likelihood Ratio"),
1428 N_("Fisher's Exact Test"),
1429 N_("Continuity Correction"),
1430 N_("Linear-by-Linear Association"),
1431 N_("N of Valid Cases"), PIVOT_RC_COUNT);
1433 pivot_dimension_create (
1434 chisq, PIVOT_AXIS_COLUMN, N_("Statistics"),
1435 N_("Value"), PIVOT_RC_OTHER,
1436 N_("df"), PIVOT_RC_COUNT,
1437 N_("Asymptotic Sig. (2-tailed)"), PIVOT_RC_SIGNIFICANCE,
1438 N_("Exact Sig. (2-tailed)"), PIVOT_RC_SIGNIFICANCE,
1439 N_("Exact Sig. (1-tailed)"), PIVOT_RC_SIGNIFICANCE);
1441 for (size_t i = 2; i < xt->n_vars; i++)
1442 add_var_dimension (chisq, &xt->vars[i], PIVOT_AXIS_ROW, false);
1447 /* Symmetric measures. */
1448 static struct pivot_table *
1449 create_sym_table (struct crosstabulation *xt)
1451 struct pivot_table *sym = pivot_table_create (N_("Symmetric Measures"));
1452 pivot_table_set_weight_format (sym, xt->weight_format);
1454 pivot_dimension_create (
1455 sym, PIVOT_AXIS_COLUMN, N_("Values"),
1456 N_("Value"), PIVOT_RC_OTHER,
1457 N_("Asymp. Std. Error"), PIVOT_RC_OTHER,
1458 N_("Approx. T"), PIVOT_RC_OTHER,
1459 N_("Approx. Sig."), PIVOT_RC_SIGNIFICANCE);
1461 struct pivot_dimension *statistics = pivot_dimension_create (
1462 sym, PIVOT_AXIS_ROW, N_("Statistics"));
1463 pivot_category_create_group (
1464 statistics->root, N_("Nominal by Nominal"),
1465 N_("Phi"), N_("Cramer's V"), N_("Contingency Coefficient"));
1466 pivot_category_create_group (
1467 statistics->root, N_("Ordinal by Ordinal"),
1468 N_("Kendall's tau-b"), N_("Kendall's tau-c"),
1469 N_("Gamma"), N_("Spearman Correlation"));
1470 pivot_category_create_group (
1471 statistics->root, N_("Interval by Interval"),
1473 pivot_category_create_group (
1474 statistics->root, N_("Measure of Agreement"),
1476 pivot_category_create_leaves (statistics->root, N_("N of Valid Cases"),
1479 for (size_t i = 2; i < xt->n_vars; i++)
1480 add_var_dimension (sym, &xt->vars[i], PIVOT_AXIS_ROW, false);
1485 /* Risk estimate. */
1486 static struct pivot_table *
1487 create_risk_table (struct crosstabulation *xt,
1488 struct pivot_dimension **risk_statistics)
1490 struct pivot_table *risk = pivot_table_create (N_("Risk Estimate"));
1491 pivot_table_set_weight_format (risk, xt->weight_format);
1493 struct pivot_dimension *values = pivot_dimension_create (
1494 risk, PIVOT_AXIS_COLUMN, N_("Values"),
1495 N_("Value"), PIVOT_RC_OTHER);
1496 pivot_category_create_group (
1497 /* xgettext:no-c-format */
1498 values->root, N_("95% Confidence Interval"),
1499 N_("Lower"), PIVOT_RC_OTHER,
1500 N_("Upper"), PIVOT_RC_OTHER);
1502 *risk_statistics = pivot_dimension_create (
1503 risk, PIVOT_AXIS_ROW, N_("Statistics"));
1505 for (size_t i = 2; i < xt->n_vars; i++)
1506 add_var_dimension (risk, &xt->vars[i], PIVOT_AXIS_ROW, false);
1512 create_direct_stat (struct pivot_category *parent,
1513 const struct crosstabulation *xt,
1514 const char *name, bool symmetric)
1516 struct pivot_category *group = pivot_category_create_group (
1519 pivot_category_create_leaf (group, pivot_value_new_text (N_("Symmetric")));
1521 char *row_label = xasprintf (_("%s Dependent"),
1522 var_to_string (xt->vars[ROW_VAR].var));
1523 pivot_category_create_leaf (group, pivot_value_new_user_text_nocopy (
1526 char *col_label = xasprintf (_("%s Dependent"),
1527 var_to_string (xt->vars[COL_VAR].var));
1528 pivot_category_create_leaf (group, pivot_value_new_user_text_nocopy (
1532 /* Directional measures. */
1533 static struct pivot_table *
1534 create_direct_table (struct crosstabulation *xt)
1536 struct pivot_table *direct = pivot_table_create (N_("Directional Measures"));
1537 pivot_table_set_weight_format (direct, xt->weight_format);
1539 pivot_dimension_create (
1540 direct, PIVOT_AXIS_COLUMN, N_("Values"),
1541 N_("Value"), PIVOT_RC_OTHER,
1542 N_("Asymp. Std. Error"), PIVOT_RC_OTHER,
1543 N_("Approx. T"), PIVOT_RC_OTHER,
1544 N_("Approx. Sig."), PIVOT_RC_SIGNIFICANCE);
1546 struct pivot_dimension *statistics = pivot_dimension_create (
1547 direct, PIVOT_AXIS_ROW, N_("Statistics"));
1548 struct pivot_category *nn = pivot_category_create_group (
1549 statistics->root, N_("Nominal by Nominal"));
1550 create_direct_stat (nn, xt, N_("Lambda"), true);
1551 create_direct_stat (nn, xt, N_("Goodman and Kruskal tau"), false);
1552 create_direct_stat (nn, xt, N_("Uncertainty Coefficient"), true);
1553 struct pivot_category *oo = pivot_category_create_group (
1554 statistics->root, N_("Ordinal by Ordinal"));
1555 create_direct_stat (oo, xt, N_("Somers' d"), true);
1556 struct pivot_category *ni = pivot_category_create_group (
1557 statistics->root, N_("Nominal by Interval"));
1558 create_direct_stat (ni, xt, N_("Eta"), false);
1560 for (size_t i = 2; i < xt->n_vars; i++)
1561 add_var_dimension (direct, &xt->vars[i], PIVOT_AXIS_ROW, false);
1566 /* Delete missing rows and columns for statistical analysis when
1569 delete_missing (struct crosstabulation *xt)
1571 size_t n_rows = xt->vars[ROW_VAR].n_values;
1572 size_t n_cols = xt->vars[COL_VAR].n_values;
1574 for (size_t r = 0; r < n_rows; r++)
1575 if (var_is_num_missing (xt->vars[ROW_VAR].var,
1576 xt->vars[ROW_VAR].values[r].f) == MV_USER)
1578 for (size_t c = 0; c < n_cols; c++)
1579 xt->mat[c + r * n_cols] = 0.;
1584 for (size_t c = 0; c < n_cols; c++)
1585 if (var_is_num_missing (xt->vars[COL_VAR].var,
1586 xt->vars[COL_VAR].values[c].f) == MV_USER)
1588 for (size_t r = 0; r < n_rows; r++)
1589 xt->mat[c + r * n_cols] = 0.;
1595 find_crosstab (struct crosstabulation *xt, size_t *row0p, size_t *row1p)
1597 size_t row0 = *row1p;
1598 if (row0 >= xt->n_entries)
1602 for (row1 = row0 + 1; row1 < xt->n_entries; row1++)
1604 struct freq *a = xt->entries[row0];
1605 struct freq *b = xt->entries[row1];
1606 if (compare_table_entry_vars_3way (a, b, xt, 2, xt->n_vars) != 0)
1614 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1615 result. WIDTH_ points to an int which is either 0 for a
1616 numeric value or a string width for a string value. */
1618 compare_value_3way (const void *a_, const void *b_, const void *width_)
1620 const union value *a = a_;
1621 const union value *b = b_;
1622 const int *width = width_;
1624 return value_compare_3way (a, b, *width);
1627 /* Inverted version of the above */
1629 compare_value_3way_inv (const void *a_, const void *b_, const void *width_)
1631 return -compare_value_3way (a_, b_, width_);
1635 /* Given an array of ENTRY_CNT table_entry structures starting at
1636 ENTRIES, creates a sorted list of the values that the variable
1637 with index VAR_IDX takes on. Stores the array of the values in
1638 XT->values and the number of values in XT->n_values. */
1640 enum_var_values (const struct crosstabulation *xt, int var_idx,
1643 struct xtab_var *xv = &xt->vars[var_idx];
1644 const struct var_range *range = get_var_range (xt->proc, xv->var);
1648 xv->values = xnmalloc (range->count, sizeof *xv->values);
1649 xv->n_values = range->count;
1650 for (size_t i = 0; i < range->count; i++)
1651 xv->values[i].f = range->min + i;
1655 int width = var_get_width (xv->var);
1656 struct hmapx set = HMAPX_INITIALIZER (set);
1658 for (size_t i = 0; i < xt->n_entries; i++)
1660 const struct freq *te = xt->entries[i];
1661 const union value *value = &te->values[var_idx];
1662 size_t hash = value_hash (value, width, 0);
1664 const union value *iter;
1665 struct hmapx_node *node;
1666 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1667 if (value_equal (iter, value, width))
1670 hmapx_insert (&set, (union value *) value, hash);
1675 xv->n_values = hmapx_count (&set);
1676 xv->values = xnmalloc (xv->n_values, sizeof *xv->values);
1678 const union value *iter;
1679 struct hmapx_node *node;
1680 HMAPX_FOR_EACH (iter, node, &set)
1681 xv->values[i++] = *iter;
1682 hmapx_destroy (&set);
1684 sort (xv->values, xv->n_values, sizeof *xv->values,
1685 descending ? compare_value_3way_inv : compare_value_3way,
1691 free_var_values (const struct crosstabulation *xt, int var_idx)
1693 struct xtab_var *xv = &xt->vars[var_idx];
1699 /* Displays the crosstabulation table. */
1701 display_crosstabulation (struct crosstabs_proc *proc,
1702 struct crosstabulation *xt, struct pivot_table *table,
1703 size_t crs_leaves[CRS_N_CELLS])
1705 size_t n_rows = xt->vars[ROW_VAR].n_values;
1706 size_t n_cols = xt->vars[COL_VAR].n_values;
1708 size_t *indexes = xnmalloc (table->n_dimensions, sizeof *indexes);
1709 assert (xt->n_vars == 2);
1710 for (size_t i = 0; i < xt->n_consts; i++)
1711 indexes[i + 3] = xt->const_indexes[i];
1713 /* Put in the actual cells. */
1714 double *mp = xt->mat;
1715 for (size_t r = 0; r < n_rows; r++)
1717 if (!xt->row_tot[r] && proc->mode != INTEGER)
1720 indexes[ROW_VAR + 1] = r;
1721 for (size_t c = 0; c < n_cols; c++)
1723 if (!xt->col_tot[c] && proc->mode != INTEGER)
1726 indexes[COL_VAR + 1] = c;
1728 double expected_value = xt->row_tot[r] * xt->col_tot[c] / xt->total;
1729 double residual = *mp - expected_value;
1730 double sresidual = residual / sqrt (expected_value);
1732 = residual / sqrt (expected_value
1733 * (1. - xt->row_tot[r] / xt->total)
1734 * (1. - xt->col_tot[c] / xt->total));
1735 double entries[CRS_N_CELLS] = {
1736 [CRS_CL_COUNT] = *mp,
1737 [CRS_CL_ROW] = *mp / xt->row_tot[r] * 100.,
1738 [CRS_CL_COLUMN] = *mp / xt->col_tot[c] * 100.,
1739 [CRS_CL_TOTAL] = *mp / xt->total * 100.,
1740 [CRS_CL_EXPECTED] = expected_value,
1741 [CRS_CL_RESIDUAL] = residual,
1742 [CRS_CL_SRESIDUAL] = sresidual,
1743 [CRS_CL_ASRESIDUAL] = asresidual,
1745 for (size_t i = 0; i < proc->n_cells; i++)
1747 int cell = proc->a_cells[i];
1748 indexes[0] = crs_leaves[cell];
1749 pivot_table_put (table, indexes, table->n_dimensions,
1750 pivot_value_new_number (entries[cell]));
1758 for (size_t r = 0; r < n_rows; r++)
1760 if (!xt->row_tot[r] && proc->mode != INTEGER)
1763 double expected_value = xt->row_tot[r] / xt->total;
1764 double entries[CRS_N_CELLS] = {
1765 [CRS_CL_COUNT] = xt->row_tot[r],
1766 [CRS_CL_ROW] = 100.0,
1767 [CRS_CL_COLUMN] = expected_value * 100.,
1768 [CRS_CL_TOTAL] = expected_value * 100.,
1769 [CRS_CL_EXPECTED] = expected_value,
1770 [CRS_CL_RESIDUAL] = SYSMIS,
1771 [CRS_CL_SRESIDUAL] = SYSMIS,
1772 [CRS_CL_ASRESIDUAL] = SYSMIS,
1774 for (size_t i = 0; i < proc->n_cells; i++)
1776 int cell = proc->a_cells[i];
1777 double entry = entries[cell];
1778 if (entry != SYSMIS)
1780 indexes[ROW_VAR + 1] = r;
1781 indexes[COL_VAR + 1] = n_cols;
1782 indexes[0] = crs_leaves[cell];
1783 pivot_table_put (table, indexes, table->n_dimensions,
1784 pivot_value_new_number (entry));
1789 for (size_t c = 0; c <= n_cols; c++)
1791 if (c < n_cols && !xt->col_tot[c] && proc->mode != INTEGER)
1794 double ct = c < n_cols ? xt->col_tot[c] : xt->total;
1795 double expected_value = ct / xt->total;
1796 double entries[CRS_N_CELLS] = {
1797 [CRS_CL_COUNT] = ct,
1798 [CRS_CL_ROW] = expected_value * 100.0,
1799 [CRS_CL_COLUMN] = 100.0,
1800 [CRS_CL_TOTAL] = expected_value * 100.,
1801 [CRS_CL_EXPECTED] = expected_value,
1802 [CRS_CL_RESIDUAL] = SYSMIS,
1803 [CRS_CL_SRESIDUAL] = SYSMIS,
1804 [CRS_CL_ASRESIDUAL] = SYSMIS,
1806 for (size_t i = 0; i < proc->n_cells; i++)
1808 size_t cell = proc->a_cells[i];
1809 double entry = entries[cell];
1810 if (entry != SYSMIS)
1812 indexes[ROW_VAR + 1] = n_rows;
1813 indexes[COL_VAR + 1] = c;
1814 indexes[0] = crs_leaves[cell];
1815 pivot_table_put (table, indexes, table->n_dimensions,
1816 pivot_value_new_number (entry));
1824 static void calc_r (struct crosstabulation *,
1825 double *XT, double *Y, double *, double *, double *);
1826 static void calc_chisq (struct crosstabulation *,
1827 double[N_CHISQ], int[N_CHISQ], double *, double *);
1829 /* Display chi-square statistics. */
1831 display_chisq (struct crosstabulation *xt, struct pivot_table *chisq)
1833 double chisq_v[N_CHISQ];
1834 double fisher1, fisher2;
1836 calc_chisq (xt, chisq_v, df, &fisher1, &fisher2);
1838 size_t *indexes = xnmalloc (chisq->n_dimensions, sizeof *indexes);
1839 assert (xt->n_vars == 2);
1840 for (size_t i = 0; i < xt->n_consts; i++)
1841 indexes[i + 2] = xt->const_indexes[i];
1842 for (size_t i = 0; i < N_CHISQ; i++)
1846 double entries[5] = { SYSMIS, SYSMIS, SYSMIS, SYSMIS, SYSMIS };
1849 entries[3] = fisher2;
1850 entries[4] = fisher1;
1852 else if (chisq_v[i] != SYSMIS)
1854 entries[0] = chisq_v[i];
1856 entries[2] = gsl_cdf_chisq_Q (chisq_v[i], df[i]);
1859 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1860 if (entries[j] != SYSMIS)
1863 pivot_table_put (chisq, indexes, chisq->n_dimensions,
1864 pivot_value_new_number (entries[j]));
1870 pivot_table_put (chisq, indexes, chisq->n_dimensions,
1871 pivot_value_new_number (xt->total));
1876 static bool calc_symmetric (struct crosstabs_proc *, struct crosstabulation *,
1877 double[N_SYMMETRIC], double[N_SYMMETRIC],
1878 double[N_SYMMETRIC],
1879 double[3], double[3], double[3]);
1881 /* Display symmetric measures. */
1883 display_symmetric (struct crosstabs_proc *proc, struct crosstabulation *xt,
1884 struct pivot_table *sym)
1886 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1887 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1889 if (!calc_symmetric (proc, xt, sym_v, sym_ase, sym_t,
1890 somers_d_v, somers_d_ase, somers_d_t))
1893 size_t *indexes = xnmalloc (sym->n_dimensions, sizeof *indexes);
1894 assert (xt->n_vars == 2);
1895 for (size_t i = 0; i < xt->n_consts; i++)
1896 indexes[i + 2] = xt->const_indexes[i];
1898 for (size_t i = 0; i < N_SYMMETRIC; i++)
1900 if (sym_v[i] == SYSMIS)
1905 double entries[] = { sym_v[i], sym_ase[i], sym_t[i] };
1906 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1907 if (entries[j] != SYSMIS)
1910 pivot_table_put (sym, indexes, sym->n_dimensions,
1911 pivot_value_new_number (entries[j]));
1915 indexes[1] = N_SYMMETRIC;
1917 struct pivot_value *total = pivot_value_new_number (xt->total);
1918 pivot_value_set_rc (sym, total, PIVOT_RC_COUNT);
1919 pivot_table_put (sym, indexes, sym->n_dimensions, total);
1924 static bool calc_risk (struct crosstabulation *,
1925 double[], double[], double[], union value *,
1928 /* Display risk estimate. */
1930 display_risk (struct crosstabulation *xt, struct pivot_table *risk,
1931 struct pivot_dimension *risk_statistics)
1933 double risk_v[3], lower[3], upper[3], n_valid;
1935 if (!calc_risk (xt, risk_v, upper, lower, c, &n_valid))
1937 assert (risk_statistics);
1939 size_t *indexes = xnmalloc (risk->n_dimensions, sizeof *indexes);
1940 assert (xt->n_vars == 2);
1941 for (size_t i = 0; i < xt->n_consts; i++)
1942 indexes[i + 2] = xt->const_indexes[i];
1944 for (size_t i = 0; i < 3; i++)
1946 const struct variable *cv = xt->vars[COL_VAR].var;
1947 const struct variable *rv = xt->vars[ROW_VAR].var;
1949 if (risk_v[i] == SYSMIS)
1952 struct string label = DS_EMPTY_INITIALIZER;
1956 ds_put_format (&label, _("Odds Ratio for %s"), var_to_string (rv));
1957 ds_put_cstr (&label, " (");
1958 var_append_value_name (rv, &c[0], &label);
1959 ds_put_cstr (&label, " / ");
1960 var_append_value_name (rv, &c[1], &label);
1961 ds_put_cstr (&label, ")");
1965 ds_put_format (&label, _("For cohort %s = "), var_to_string (cv));
1966 var_append_value_name (cv, &xt->vars[ROW_VAR].values[i - 1], &label);
1970 indexes[1] = pivot_category_create_leaf (
1971 risk_statistics->root,
1972 pivot_value_new_user_text_nocopy (ds_steal_cstr (&label)));
1974 double entries[] = { risk_v[i], lower[i], upper[i] };
1975 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1978 pivot_table_put (risk, indexes, risk->n_dimensions,
1979 pivot_value_new_number (entries[j]));
1982 indexes[1] = pivot_category_create_leaf (
1983 risk_statistics->root,
1984 pivot_value_new_text (N_("N of Valid Cases")));
1986 pivot_table_put (risk, indexes, risk->n_dimensions,
1987 pivot_value_new_number (n_valid));
1991 static void calc_directional (struct crosstabs_proc *, struct crosstabulation *,
1992 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1993 double[N_DIRECTIONAL], double[N_DIRECTIONAL]);
1995 /* Display directional measures. */
1997 display_directional (struct crosstabs_proc *proc,
1998 struct crosstabulation *xt, struct pivot_table *direct)
2000 double direct_v[N_DIRECTIONAL];
2001 double direct_ase[N_DIRECTIONAL];
2002 double direct_t[N_DIRECTIONAL];
2003 double sig[N_DIRECTIONAL];
2004 calc_directional (proc, xt, direct_v, direct_ase, direct_t, sig);
2006 size_t *indexes = xnmalloc (direct->n_dimensions, sizeof *indexes);
2007 assert (xt->n_vars == 2);
2008 for (size_t i = 0; i < xt->n_consts; i++)
2009 indexes[i + 2] = xt->const_indexes[i];
2011 for (size_t i = 0; i < N_DIRECTIONAL; i++)
2013 if (direct_v[i] == SYSMIS)
2018 double entries[] = {
2019 direct_v[i], direct_ase[i], direct_t[i], sig[i],
2021 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
2022 if (entries[j] != SYSMIS)
2025 pivot_table_put (direct, indexes, direct->n_dimensions,
2026 pivot_value_new_number (entries[j]));
2033 /* Statistical calculations. */
2035 /* Returns the value of the logarithm of gamma (factorial) function for an integer
2038 log_gamma_int (double xt)
2041 for (int i = 2; i < xt; i++)
2046 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2048 static inline double
2049 Pr (int a, int b, int c, int d)
2051 return exp (log_gamma_int (a + b + 1.) - log_gamma_int (a + 1.)
2052 + log_gamma_int (c + d + 1.) - log_gamma_int (b + 1.)
2053 + log_gamma_int (a + c + 1.) - log_gamma_int (c + 1.)
2054 + log_gamma_int (b + d + 1.) - log_gamma_int (d + 1.)
2055 - log_gamma_int (a + b + c + d + 1.));
2058 /* Swap the contents of A and B. */
2060 swap (int *a, int *b)
2067 /* Calculate significance for Fisher's exact test as specified in
2068 _SPSS Statistical Algorithms_, Appendix 5. */
2070 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2072 if (MIN (c, d) < MIN (a, b))
2073 swap (&a, &c), swap (&b, &d);
2074 if (MIN (b, d) < MIN (a, c))
2075 swap (&a, &b), swap (&c, &d);
2079 swap (&a, &b), swap (&c, &d);
2081 swap (&a, &c), swap (&b, &d);
2084 double pn1 = Pr (a, b, c, d);
2086 for (int xt = 1; xt <= a; xt++)
2087 *fisher1 += Pr (a - xt, b + xt, c + xt, d - xt);
2089 *fisher2 = *fisher1;
2090 for (int xt = 1; xt <= b; xt++)
2092 double p = Pr (a + xt, b - xt, c - xt, d + xt);
2098 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2099 columns with values COLS and N_ROWS rows with values ROWS. Values
2100 in the matrix sum to xt->total. */
2102 calc_chisq (struct crosstabulation *xt,
2103 double chisq[N_CHISQ], int df[N_CHISQ],
2104 double *fisher1, double *fisher2)
2106 chisq[0] = chisq[1] = 0.;
2107 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2108 *fisher1 = *fisher2 = SYSMIS;
2110 df[0] = df[1] = (xt->ns_cols - 1) * (xt->ns_rows - 1);
2112 if (xt->ns_rows <= 1 || xt->ns_cols <= 1)
2114 chisq[0] = chisq[1] = SYSMIS;
2118 size_t n_cols = xt->vars[COL_VAR].n_values;
2119 FOR_EACH_POPULATED_ROW (r, xt)
2120 FOR_EACH_POPULATED_COLUMN (c, xt)
2122 const double expected = xt->row_tot[r] * xt->col_tot[c] / xt->total;
2123 const double freq = xt->mat[n_cols * r + c];
2124 const double residual = freq - expected;
2126 chisq[0] += residual * residual / expected;
2128 chisq[1] += freq * log (expected / freq);
2139 /* Calculate Yates and Fisher exact test. */
2140 if (xt->ns_cols == 2 && xt->ns_rows == 2)
2145 FOR_EACH_POPULATED_COLUMN (c, xt)
2153 double f11 = xt->mat[nz_cols[0]];
2154 double f12 = xt->mat[nz_cols[1]];
2155 double f21 = xt->mat[nz_cols[0] + n_cols];
2156 double f22 = xt->mat[nz_cols[1] + n_cols];
2159 const double xt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * xt->total;
2162 chisq[3] = (xt->total * pow2 (xt_)
2163 / (f11 + f12) / (f21 + f22)
2164 / (f11 + f21) / (f12 + f22));
2171 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2174 /* Calculate Mantel-Haenszel. */
2175 if (var_is_numeric (xt->vars[ROW_VAR].var)
2176 && var_is_numeric (xt->vars[COL_VAR].var))
2178 double r, ase_0, ase_1;
2179 calc_r (xt, (double *) xt->vars[ROW_VAR].values,
2180 (double *) xt->vars[COL_VAR].values,
2181 &r, &ase_0, &ase_1);
2183 chisq[4] = (xt->total - 1.) * r * r;
2188 /* Calculate the value of Pearson's r. r is stored into R, its T value into
2189 T, and standard error into ERROR. The row and column values must be
2190 passed in XT and Y. */
2192 calc_r (struct crosstabulation *xt,
2193 double *XT, double *Y, double *r, double *t, double *error)
2195 size_t n_rows = xt->vars[ROW_VAR].n_values;
2196 size_t n_cols = xt->vars[COL_VAR].n_values;
2199 for (size_t i = 0; i < n_rows; i++)
2200 for (size_t j = 0; j < n_cols; j++)
2202 double fij = xt->mat[j + i * n_cols];
2203 double product = XT[i] * Y[j];
2204 double temp = fij * product;
2210 for (size_t i = 0; i < n_rows; i++)
2212 sum_Xr += XT[i] * xt->row_tot[i];
2213 sum_X2r += pow2 (XT[i]) * xt->row_tot[i];
2215 double Xbar = sum_Xr / xt->total;
2219 for (size_t i = 0; i < n_cols; i++)
2221 sum_Yc += Y[i] * xt->col_tot[i];
2222 sum_Y2c += Y[i] * Y[i] * xt->col_tot[i];
2224 double Ybar = sum_Yc / xt->total;
2226 double S = sum_XYf - sum_Xr * sum_Yc / xt->total;
2227 double SX = sum_X2r - pow2 (sum_Xr) / xt->total;
2228 double SY = sum_Y2c - pow2 (sum_Yc) / xt->total;
2229 double T = sqrt (SX * SY);
2231 *t = *r / sqrt (1 - pow2 (*r)) * sqrt (xt->total - 2);
2235 for (size_t i = 0; i < n_rows; i++)
2236 for (size_t j = 0; j < n_cols; j++)
2238 double Xresid = XT[i] - Xbar;
2239 double Yresid = Y[j] - Ybar;
2240 double temp = (T * Xresid * Yresid
2242 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2243 double y = xt->mat[j + i * n_cols] * temp * temp - c;
2248 *error = sqrt (s) / (T * T);
2251 /* Calculate symmetric statistics and their asymptotic standard
2252 errors. Returns false if none could be calculated. */
2254 calc_symmetric (struct crosstabs_proc *proc, struct crosstabulation *xt,
2255 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2256 double t[N_SYMMETRIC],
2257 double somers_d_v[3], double somers_d_ase[3],
2258 double somers_d_t[3])
2260 size_t n_rows = xt->vars[ROW_VAR].n_values;
2261 size_t n_cols = xt->vars[COL_VAR].n_values;
2263 size_t q = MIN (xt->ns_rows, xt->ns_cols);
2267 for (size_t i = 0; i < N_SYMMETRIC; i++)
2268 v[i] = ase[i] = t[i] = SYSMIS;
2270 /* Phi, Cramer's V, contingency coefficient. */
2271 if (proc->statistics & (CRS_ST_PHI | CRS_ST_CC))
2273 double Xp = 0.; /* Pearson chi-square. */
2275 FOR_EACH_POPULATED_ROW (r, xt)
2276 FOR_EACH_POPULATED_COLUMN (c, xt)
2278 double expected = xt->row_tot[r] * xt->col_tot[c] / xt->total;
2279 double freq = xt->mat[n_cols * r + c];
2280 double residual = freq - expected;
2282 Xp += residual * residual / expected;
2285 if (proc->statistics & CRS_ST_PHI)
2287 v[0] = sqrt (Xp / xt->total);
2288 v[1] = sqrt (Xp / (xt->total * (q - 1)));
2290 if (proc->statistics & CRS_ST_CC)
2291 v[2] = sqrt (Xp / (Xp + xt->total));
2294 if (proc->statistics & (CRS_ST_BTAU | CRS_ST_CTAU
2295 | CRS_ST_GAMMA | CRS_ST_D))
2297 double Dr = pow2 (xt->total);
2298 for (size_t r = 0; r < n_rows; r++)
2299 Dr -= pow2 (xt->row_tot[r]);
2301 double Dc = pow2 (xt->total);
2302 for (size_t c = 0; c < n_cols; c++)
2303 Dc -= pow2 (xt->col_tot[c]);
2305 double *cum = xnmalloc (n_cols * n_rows, sizeof *cum);
2306 for (size_t c = 0; c < n_cols; c++)
2310 for (size_t r = 0; r < n_rows; r++)
2311 cum[c + r * n_cols] = ct += xt->mat[c + r * n_cols];
2317 for (size_t i = 0; i < n_rows; i++)
2320 for (size_t j = 1; j < n_cols; j++)
2321 Cij += xt->col_tot[j] - cum[j + i * n_cols];
2325 for (size_t j = 1; j < n_cols; j++)
2326 Dij += cum[j + (i - 1) * n_cols];
2328 for (size_t j = 0;;)
2330 double fij = xt->mat[j + i * n_cols];
2337 Cij -= xt->col_tot[j] - cum[j + i * n_cols];
2338 Dij += xt->col_tot[j - 1] - cum[j - 1 + i * n_cols];
2342 Cij += cum[j - 1 + (i - 1) * n_cols];
2343 Dij -= cum[j + (i - 1) * n_cols];
2348 if (proc->statistics & CRS_ST_BTAU)
2349 v[3] = (P - Q) / sqrt (Dr * Dc);
2350 if (proc->statistics & CRS_ST_CTAU)
2351 v[4] = (q * (P - Q)) / (pow2 (xt->total) * (q - 1));
2352 if (proc->statistics & CRS_ST_GAMMA)
2353 v[5] = (P - Q) / (P + Q);
2355 /* ASE for tau-b, tau-c, gamma. Calculations could be
2356 eliminated here, at expense of memory. */
2357 double btau_cum = 0;
2358 double ctau_cum = 0;
2359 double gamma_cum = 0;
2360 double d_yx_cum = 0;
2361 double d_xy_cum = 0;
2362 for (size_t i = 0; i < n_rows; i++)
2365 for (size_t j = 1; j < n_cols; j++)
2366 Cij += xt->col_tot[j] - cum[j + i * n_cols];
2370 for (size_t j = 1; j < n_cols; j++)
2371 Dij += cum[j + (i - 1) * n_cols];
2373 for (size_t j = 0;;)
2375 double fij = xt->mat[j + i * n_cols];
2377 if (proc->statistics & CRS_ST_BTAU)
2378 btau_cum += fij * pow2 (2. * sqrt (Dr * Dc) * (Cij - Dij)
2379 + v[3] * (xt->row_tot[i] * Dc
2380 + xt->col_tot[j] * Dr));
2381 ctau_cum += fij * pow2 (Cij - Dij);
2383 if (proc->statistics & CRS_ST_GAMMA)
2384 gamma_cum += fij * pow2 (Q * Cij - P * Dij);
2386 if (proc->statistics & CRS_ST_D)
2388 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2389 - (P - Q) * (xt->total - xt->row_tot[i]));
2390 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2391 - (Q - P) * (xt->total - xt->col_tot[j]));
2397 Cij -= xt->col_tot[j] - cum[j + i * n_cols];
2398 Dij += xt->col_tot[j - 1] - cum[j - 1 + i * n_cols];
2402 Cij += cum[j - 1 + (i - 1) * n_cols];
2403 Dij -= cum[j + (i - 1) * n_cols];
2408 if (proc->statistics & CRS_ST_BTAU)
2410 double btau_var = ((btau_cum
2411 - (xt->total * pow2 (xt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2413 ase[3] = sqrt (btau_var);
2414 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / xt->total)
2417 if (proc->statistics & CRS_ST_CTAU)
2419 ase[4] = ((2 * q / ((q - 1) * pow2 (xt->total)))
2420 * sqrt (ctau_cum - (P - Q) * (P - Q) / xt->total));
2421 t[4] = v[4] / ase[4];
2423 if (proc->statistics & CRS_ST_GAMMA)
2425 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2426 t[5] = v[5] / (2. / (P + Q)
2427 * sqrt (ctau_cum - (P - Q) * (P - Q) / xt->total));
2429 if (proc->statistics & CRS_ST_D)
2431 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2432 somers_d_ase[0] = SYSMIS;
2433 somers_d_t[0] = (somers_d_v[0]
2435 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2436 somers_d_v[1] = (P - Q) / Dc;
2437 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2438 somers_d_t[1] = (somers_d_v[1]
2440 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2441 somers_d_v[2] = (P - Q) / Dr;
2442 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2443 somers_d_t[2] = (somers_d_v[2]
2445 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2451 /* Spearman correlation, Pearson's r. */
2452 if (proc->statistics & CRS_ST_CORR)
2454 double *R = xmalloc (sizeof *R * n_rows);
2457 for (size_t i = 0; i < n_rows; i++)
2459 R[i] = s + (xt->row_tot[i] + 1.) / 2.;
2460 double y = xt->row_tot[i] - c;
2466 double *C = xmalloc (sizeof *C * n_cols);
2468 for (size_t j = 0; j < n_cols; j++)
2470 C[j] = s + (xt->col_tot[j] + 1.) / 2;
2471 double y = xt->col_tot[j] - c;
2477 calc_r (xt, R, C, &v[6], &t[6], &ase[6]);
2482 calc_r (xt, (double *) xt->vars[ROW_VAR].values,
2483 (double *) xt->vars[COL_VAR].values,
2484 &v[7], &t[7], &ase[7]);
2487 /* Cohen's kappa. */
2488 if (proc->statistics & CRS_ST_KAPPA && xt->ns_rows == xt->ns_cols)
2491 double sum_rici = 0;
2492 double sum_fiiri_ci = 0;
2493 double sum_riciri_ci = 0;
2494 for (size_t i = 0, j = 0; i < xt->ns_rows; i++, j++)
2496 while (xt->col_tot[j] == 0.)
2499 double prod = xt->row_tot[i] * xt->col_tot[j];
2500 double sum = xt->row_tot[i] + xt->col_tot[j];
2502 sum_fii += xt->mat[j + i * n_cols];
2504 sum_fiiri_ci += xt->mat[j + i * n_cols] * sum;
2505 sum_riciri_ci += prod * sum;
2508 double sum_fijri_ci2 = 0;
2509 for (size_t i = 0; i < xt->ns_rows; i++)
2510 for (size_t j = 0; j < xt->ns_cols; j++)
2512 double sum = xt->row_tot[i] + xt->col_tot[j];
2513 sum_fijri_ci2 += xt->mat[j + i * n_cols] * sum * sum;
2516 v[8] = (xt->total * sum_fii - sum_rici) / (pow2 (xt->total) - sum_rici);
2518 double ase_under_h0 = sqrt ((pow2 (xt->total) * sum_rici
2519 + sum_rici * sum_rici
2520 - xt->total * sum_riciri_ci)
2521 / (xt->total * (pow2 (xt->total) - sum_rici) * (pow2 (xt->total) - sum_rici)));
2523 ase[8] = sqrt (xt->total * (((sum_fii * (xt->total - sum_fii))
2524 / pow2 (pow2 (xt->total) - sum_rici))
2525 + ((2. * (xt->total - sum_fii)
2526 * (2. * sum_fii * sum_rici
2527 - xt->total * sum_fiiri_ci))
2528 / pow3 (pow2 (xt->total) - sum_rici))
2529 + (pow2 (xt->total - sum_fii)
2530 * (xt->total * sum_fijri_ci2 - 4.
2531 * sum_rici * sum_rici)
2532 / pow4 (pow2 (xt->total) - sum_rici))));
2534 t[8] = v[8] / ase_under_h0;
2540 /* Calculate risk estimate. */
2542 calc_risk (struct crosstabulation *xt,
2543 double *value, double *upper, double *lower, union value *c,
2546 size_t n_cols = xt->vars[COL_VAR].n_values;
2548 for (size_t i = 0; i < 3; i++)
2549 value[i] = upper[i] = lower[i] = SYSMIS;
2551 if (xt->ns_rows != 2 || xt->ns_cols != 2)
2554 /* Find populated columns. */
2557 FOR_EACH_POPULATED_COLUMN (c, xt)
2561 /* Find populated rows. */
2564 FOR_EACH_POPULATED_ROW (r, xt)
2568 double f11 = xt->mat[nz_cols[0] + n_cols * nz_rows[0]];
2569 double f12 = xt->mat[nz_cols[1] + n_cols * nz_rows[0]];
2570 double f21 = xt->mat[nz_cols[0] + n_cols * nz_rows[1]];
2571 double f22 = xt->mat[nz_cols[1] + n_cols * nz_rows[1]];
2572 *n_valid = f11 + f12 + f21 + f22;
2574 c[0] = xt->vars[COL_VAR].values[nz_cols[0]];
2575 c[1] = xt->vars[COL_VAR].values[nz_cols[1]];
2577 value[0] = (f11 * f22) / (f12 * f21);
2578 double v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2579 lower[0] = value[0] * exp (-1.960 * v);
2580 upper[0] = value[0] * exp (1.960 * v);
2582 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2583 v = sqrt ((f12 / (f11 * (f11 + f12)))
2584 + (f22 / (f21 * (f21 + f22))));
2585 lower[1] = value[1] * exp (-1.960 * v);
2586 upper[1] = value[1] * exp (1.960 * v);
2588 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2589 v = sqrt ((f11 / (f12 * (f11 + f12)))
2590 + (f21 / (f22 * (f21 + f22))));
2591 lower[2] = value[2] * exp (-1.960 * v);
2592 upper[2] = value[2] * exp (1.960 * v);
2597 /* Calculate directional measures. */
2599 calc_directional (struct crosstabs_proc *proc, struct crosstabulation *xt,
2600 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2601 double t[N_DIRECTIONAL], double sig[N_DIRECTIONAL])
2603 size_t n_rows = xt->vars[ROW_VAR].n_values;
2604 size_t n_cols = xt->vars[COL_VAR].n_values;
2605 for (size_t i = 0; i < N_DIRECTIONAL; i++)
2606 v[i] = ase[i] = t[i] = sig[i] = SYSMIS;
2609 if (proc->statistics & CRS_ST_LAMBDA)
2611 /* Find maximum for each row and their sum. */
2612 double *fim = xnmalloc (n_rows, sizeof *fim);
2613 size_t *fim_index = xnmalloc (n_rows, sizeof *fim_index);
2614 double sum_fim = 0.0;
2615 for (size_t i = 0; i < n_rows; i++)
2617 double max = xt->mat[i * n_cols];
2620 for (size_t j = 1; j < n_cols; j++)
2621 if (xt->mat[j + i * n_cols] > max)
2623 max = xt->mat[j + i * n_cols];
2629 fim_index[i] = index;
2632 /* Find maximum for each column. */
2633 double *fmj = xnmalloc (n_cols, sizeof *fmj);
2634 size_t *fmj_index = xnmalloc (n_cols, sizeof *fmj_index);
2635 double sum_fmj = 0.0;
2636 for (size_t j = 0; j < n_cols; j++)
2638 double max = xt->mat[j];
2641 for (size_t i = 1; i < n_rows; i++)
2642 if (xt->mat[j + i * n_cols] > max)
2644 max = xt->mat[j + i * n_cols];
2650 fmj_index[j] = index;
2653 /* Find maximum row total. */
2654 double rm = xt->row_tot[0];
2655 size_t rm_index = 0;
2656 for (size_t i = 1; i < n_rows; i++)
2657 if (xt->row_tot[i] > rm)
2659 rm = xt->row_tot[i];
2663 /* Find maximum column total. */
2664 double cm = xt->col_tot[0];
2665 size_t cm_index = 0;
2666 for (size_t j = 1; j < n_cols; j++)
2667 if (xt->col_tot[j] > cm)
2669 cm = xt->col_tot[j];
2673 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * xt->total - rm - cm);
2674 v[1] = (sum_fmj - rm) / (xt->total - rm);
2675 v[2] = (sum_fim - cm) / (xt->total - cm);
2677 /* ASE1 for Y given XT. */
2680 for (size_t i = 0; i < n_rows; i++)
2681 if (cm_index == fim_index[i])
2683 ase[2] = sqrt ((xt->total - sum_fim) * (sum_fim + cm - 2. * accum)
2684 / pow3 (xt->total - cm));
2687 /* ASE0 for Y given XT. */
2690 for (size_t i = 0; i < n_rows; i++)
2691 if (cm_index != fim_index[i])
2692 accum += (xt->mat[i * n_cols + fim_index[i]]
2693 + xt->mat[i * n_cols + cm_index]);
2694 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / xt->total) / (xt->total - cm));
2697 /* ASE1 for XT given Y. */
2700 for (size_t j = 0; j < n_cols; j++)
2701 if (rm_index == fmj_index[j])
2703 ase[1] = sqrt ((xt->total - sum_fmj) * (sum_fmj + rm - 2. * accum)
2704 / pow3 (xt->total - rm));
2707 /* ASE0 for XT given Y. */
2710 for (size_t j = 0; j < n_cols; j++)
2711 if (rm_index != fmj_index[j])
2712 accum += (xt->mat[j + n_cols * fmj_index[j]]
2713 + xt->mat[j + n_cols * rm_index]);
2714 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / xt->total) / (xt->total - rm));
2717 /* Symmetric ASE0 and ASE1. */
2719 double accum0 = 0.0;
2720 double accum1 = 0.0;
2721 for (size_t i = 0; i < n_rows; i++)
2722 for (size_t j = 0; j < n_cols; j++)
2724 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2725 int temp1 = (i == rm_index) + (j == cm_index);
2726 accum0 += xt->mat[j + i * n_cols] * pow2 (temp0 - temp1);
2727 accum1 += (xt->mat[j + i * n_cols]
2728 * pow2 (temp0 + (v[0] - 1.) * temp1));
2730 ase[0] = sqrt (accum1 - 4. * xt->total * v[0] * v[0]) / (2. * xt->total - rm - cm);
2731 t[0] = v[0] / (sqrt (accum0 - pow2 (sum_fim + sum_fmj - cm - rm) / xt->total)
2732 / (2. * xt->total - rm - cm));
2735 for (size_t i = 0; i < 3; i++)
2736 sig[i] = 2 * gsl_cdf_ugaussian_Q (t[i]);
2744 double sum_fij2_ri = 0.0;
2745 double sum_fij2_ci = 0.0;
2746 FOR_EACH_POPULATED_ROW (i, xt)
2747 FOR_EACH_POPULATED_COLUMN (j, xt)
2749 double temp = pow2 (xt->mat[j + i * n_cols]);
2750 sum_fij2_ri += temp / xt->row_tot[i];
2751 sum_fij2_ci += temp / xt->col_tot[j];
2754 double sum_ri2 = 0.0;
2755 for (size_t i = 0; i < n_rows; i++)
2756 sum_ri2 += pow2 (xt->row_tot[i]);
2758 double sum_cj2 = 0.0;
2759 for (size_t j = 0; j < n_cols; j++)
2760 sum_cj2 += pow2 (xt->col_tot[j]);
2762 v[3] = (xt->total * sum_fij2_ci - sum_ri2) / (pow2 (xt->total) - sum_ri2);
2763 v[4] = (xt->total * sum_fij2_ri - sum_cj2) / (pow2 (xt->total) - sum_cj2);
2766 if (proc->statistics & CRS_ST_UC)
2769 FOR_EACH_POPULATED_ROW (i, xt)
2770 UX -= xt->row_tot[i] / xt->total * log (xt->row_tot[i] / xt->total);
2773 FOR_EACH_POPULATED_COLUMN (j, xt)
2774 UY -= xt->col_tot[j] / xt->total * log (xt->col_tot[j] / xt->total);
2778 for (size_t i = 0; i < n_rows; i++)
2779 for (size_t j = 0; j < n_cols; j++)
2781 double entry = xt->mat[j + i * n_cols];
2786 P += entry * pow2 (log (xt->col_tot[j] * xt->row_tot[i] / (xt->total * entry)));
2787 UXY -= entry / xt->total * log (entry / xt->total);
2790 double ase1_yx = 0.0;
2791 double ase1_xy = 0.0;
2792 double ase1_sym = 0.0;
2793 for (size_t i = 0; i < n_rows; i++)
2794 for (size_t j = 0; j < n_cols; j++)
2796 double entry = xt->mat[j + i * n_cols];
2801 ase1_yx += entry * pow2 (UY * log (entry / xt->row_tot[i])
2802 + (UX - UXY) * log (xt->col_tot[j] / xt->total));
2803 ase1_xy += entry * pow2 (UX * log (entry / xt->col_tot[j])
2804 + (UY - UXY) * log (xt->row_tot[i] / xt->total));
2805 ase1_sym += entry * pow2 ((UXY
2806 * log (xt->row_tot[i] * xt->col_tot[j] / pow2 (xt->total)))
2807 - (UX + UY) * log (entry / xt->total));
2810 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2811 ase[5] = (2. / (xt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2814 v[6] = (UX + UY - UXY) / UX;
2815 ase[6] = sqrt (ase1_xy) / (xt->total * UX * UX);
2816 t[6] = v[6] / (sqrt (P - xt->total * pow2 (UX + UY - UXY)) / (xt->total * UX));
2818 v[7] = (UX + UY - UXY) / UY;
2819 ase[7] = sqrt (ase1_yx) / (xt->total * UY * UY);
2820 t[7] = v[7] / (sqrt (P - xt->total * pow2 (UX + UY - UXY)) / (xt->total * UY));
2824 if (proc->statistics & CRS_ST_D)
2826 double v_dummy[N_SYMMETRIC];
2827 double ase_dummy[N_SYMMETRIC];
2828 double t_dummy[N_SYMMETRIC];
2829 double somers_d_v[3];
2830 double somers_d_ase[3];
2831 double somers_d_t[3];
2833 if (calc_symmetric (proc, xt, v_dummy, ase_dummy, t_dummy,
2834 somers_d_v, somers_d_ase, somers_d_t))
2836 for (size_t i = 0; i < 3; i++)
2838 v[8 + i] = somers_d_v[i];
2839 ase[8 + i] = somers_d_ase[i];
2840 t[8 + i] = somers_d_t[i];
2841 sig[8 + i] = 2 * gsl_cdf_ugaussian_Q (fabs (somers_d_t[i]));
2847 if (proc->statistics & CRS_ST_ETA)
2850 double sum_Xr = 0.0;
2851 double sum_X2r = 0.0;
2852 for (size_t i = 0; i < n_rows; i++)
2854 sum_Xr += xt->vars[ROW_VAR].values[i].f * xt->row_tot[i];
2855 sum_X2r += pow2 (xt->vars[ROW_VAR].values[i].f) * xt->row_tot[i];
2857 double SX = sum_X2r - pow2 (sum_Xr) / xt->total;
2860 FOR_EACH_POPULATED_COLUMN (j, xt)
2864 for (size_t i = 0; i < n_rows; i++)
2866 SXW += (pow2 (xt->vars[ROW_VAR].values[i].f)
2867 * xt->mat[j + i * n_cols]);
2868 cum += (xt->vars[ROW_VAR].values[i].f
2869 * xt->mat[j + i * n_cols]);
2872 SXW -= cum * cum / xt->col_tot[j];
2874 v[11] = sqrt (1. - SXW / SX);
2877 double sum_Yc = 0.0;
2878 double sum_Y2c = 0.0;
2879 for (size_t i = 0; i < n_cols; i++)
2881 sum_Yc += xt->vars[COL_VAR].values[i].f * xt->col_tot[i];
2882 sum_Y2c += pow2 (xt->vars[COL_VAR].values[i].f) * xt->col_tot[i];
2884 double SY = sum_Y2c - pow2 (sum_Yc) / xt->total;
2887 FOR_EACH_POPULATED_ROW (i, xt)
2890 for (size_t j = 0; j < n_cols; j++)
2892 SYW += (pow2 (xt->vars[COL_VAR].values[j].f)
2893 * xt->mat[j + i * n_cols]);
2894 cum += (xt->vars[COL_VAR].values[j].f
2895 * xt->mat[j + i * n_cols]);
2898 SYW -= cum * cum / xt->row_tot[i];
2900 v[12] = sqrt (1. - SYW / SY);