1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2006, 2009, 2010, 2011, 2012, 2013, 2014, 2016 Free Software Foundation, Inc.
4 This program is free software: you can redistribute it and/or modify
5 it under the terms of the GNU General Public License as published by
6 the Free Software Foundation, either version 3 of the License, or
7 (at your option) any later version.
9 This program is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 GNU General Public License for more details.
14 You should have received a copy of the GNU General Public License
15 along with this program. If not, see <http://www.gnu.org/licenses/>. */
19 - How to calculate significance of some symmetric and directional measures?
20 - How to calculate ASE for symmetric Somers ' d?
21 - How to calculate ASE for Goodman and Kruskal's tau?
22 - How to calculate approx. T of symmetric uncertainty coefficient?
30 #include <gsl/gsl_cdf.h>
34 #include "data/case.h"
35 #include "data/casegrouper.h"
36 #include "data/casereader.h"
37 #include "data/data-out.h"
38 #include "data/dataset.h"
39 #include "data/dictionary.h"
40 #include "data/format.h"
41 #include "data/value-labels.h"
42 #include "data/variable.h"
43 #include "language/command.h"
44 #include "language/stats/freq.h"
45 #include "language/dictionary/split-file.h"
46 #include "language/lexer/lexer.h"
47 #include "language/lexer/variable-parser.h"
48 #include "libpspp/array.h"
49 #include "libpspp/assertion.h"
50 #include "libpspp/compiler.h"
51 #include "libpspp/hash-functions.h"
52 #include "libpspp/hmap.h"
53 #include "libpspp/hmapx.h"
54 #include "libpspp/message.h"
55 #include "libpspp/misc.h"
56 #include "libpspp/pool.h"
57 #include "libpspp/str.h"
58 #include "output/pivot-table.h"
59 #include "output/charts/barchart.h"
61 #include "gl/minmax.h"
62 #include "gl/xalloc-oversized.h"
63 #include "gl/xalloc.h"
67 #define _(msgid) gettext (msgid)
68 #define N_(msgid) msgid
70 /* Kinds of cells in the crosstabulation. */
72 C(COUNT, N_("Count"), PIVOT_RC_COUNT) \
73 C(EXPECTED, N_("Expected"), PIVOT_RC_OTHER) \
74 C(ROW, N_("Row %"), PIVOT_RC_PERCENT) \
75 C(COLUMN, N_("Column %"), PIVOT_RC_PERCENT) \
76 C(TOTAL, N_("Total %"), PIVOT_RC_PERCENT) \
77 C(RESIDUAL, N_("Residual"), PIVOT_RC_RESIDUAL) \
78 C(SRESIDUAL, N_("Std. Residual"), PIVOT_RC_RESIDUAL) \
79 C(ASRESIDUAL, N_("Adjusted Residual"), PIVOT_RC_RESIDUAL)
82 #define C(KEYWORD, STRING, RC) CRS_CL_##KEYWORD,
87 #define C(KEYWORD, STRING, RC) + 1
88 CRS_N_CELLS = CRS_CELLS
91 #define CRS_ALL_CELLS ((1u << CRS_N_CELLS) - 1)
93 /* Kinds of statistics. */
94 #define CRS_STATISTICS \
108 enum crs_statistic_index {
109 #define S(KEYWORD) CRS_ST_##KEYWORD##_INDEX,
113 enum crs_statistic_bit {
114 #define S(KEYWORD) CRS_ST_##KEYWORD = 1u << CRS_ST_##KEYWORD##_INDEX,
119 #define S(KEYWORD) + 1
120 CRS_N_STATISTICS = CRS_STATISTICS
123 #define CRS_ALL_STATISTICS ((1u << CRS_N_STATISTICS) - 1)
125 /* Number of chi-square statistics. */
128 /* Number of symmetric statistics. */
129 #define N_SYMMETRIC 9
131 /* Number of directional statistics. */
132 #define N_DIRECTIONAL 13
134 /* Indexes into the 'vars' member of struct crosstabulation and
135 struct crosstab member. */
138 ROW_VAR = 0, /* Row variable. */
139 COL_VAR = 1 /* Column variable. */
140 /* Higher indexes cause multiple tables to be output. */
145 const struct variable *var;
150 /* A crosstabulation of 2 or more variables. */
151 struct crosstabulation
153 struct crosstabs_proc *proc;
154 struct fmt_spec weight_format; /* Format for weight variable. */
155 double missing; /* Weight of missing cases. */
157 /* Variables (2 or more). */
159 struct xtab_var *vars;
161 /* Constants (0 or more). */
163 struct xtab_var *const_vars;
164 size_t *const_indexes;
168 struct freq **entries;
171 /* Number of statistically interesting columns/rows
172 (columns/rows with data in them). */
173 int ns_cols, ns_rows;
175 /* Matrix contents. */
176 double *mat; /* Matrix proper. */
177 double *row_tot; /* Row totals. */
178 double *col_tot; /* Column totals. */
179 double total; /* Grand total. */
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 int 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 (int 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 (int c, const struct crosstabulation *xt)
259 int n_columns = xt->vars[COL_VAR].n_values;
260 for (; c < n_columns; c++)
266 #define FOR_EACH_POPULATED_ROW(R, XT) \
267 for (int 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 (int r, const struct crosstabulation *xt)
272 int 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 (lexer, NULL);
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 (lexer, NULL);
371 lex_match (lexer, T_COMMA);
374 else if (lex_match_id (lexer, "FORMAT"))
376 lex_match (lexer, T_EQUALS);
377 while (lex_token (lexer) != T_SLASH && lex_token (lexer) != T_ENDCMD)
379 if (lex_match_id (lexer, "AVALUE"))
380 proc.descending = false;
381 else if (lex_match_id (lexer, "DVALUE"))
382 proc.descending = true;
383 else if (lex_match_id (lexer, "TABLES"))
385 else if (lex_match_id (lexer, "NOTABLES"))
389 lex_error (lexer, NULL);
392 lex_match (lexer, T_COMMA);
395 else if (lex_match_id (lexer, "BARCHART"))
396 proc.barchart = true;
397 else if (lex_match_id (lexer, "CELLS"))
399 lex_match (lexer, T_EQUALS);
401 if (lex_match_id (lexer, "NONE"))
403 else if (lex_match (lexer, T_ALL))
404 proc.cells = CRS_ALL_CELLS;
408 while (lex_token (lexer) != T_SLASH && lex_token (lexer) != T_ENDCMD)
410 #define C(KEYWORD, STRING, RC) \
411 if (lex_match_id (lexer, #KEYWORD)) \
413 proc.cells |= 1u << CRS_CL_##KEYWORD; \
418 lex_error (lexer, NULL);
422 proc.cells = ((1u << CRS_CL_COUNT) | (1u << CRS_CL_ROW)
423 | (1u << CRS_CL_COLUMN) | (1u << CRS_CL_TOTAL));
426 else if (lex_match_id (lexer, "STATISTICS"))
428 lex_match (lexer, T_EQUALS);
430 if (lex_match_id (lexer, "NONE"))
432 else if (lex_match (lexer, T_ALL))
433 proc.statistics = CRS_ALL_STATISTICS;
437 while (lex_token (lexer) != T_SLASH && lex_token (lexer) != T_ENDCMD)
440 if (lex_match_id (lexer, #KEYWORD)) \
442 proc.statistics |= CRS_ST_##KEYWORD; \
447 lex_error (lexer, NULL);
450 if (!proc.statistics)
451 proc.statistics = CRS_ST_CHISQ;
454 else if (!parse_crosstabs_tables (lexer, ds, &proc))
457 if (!lex_match (lexer, T_SLASH))
460 if (!lex_end_of_command (lexer))
465 msg (SE, _("At least one crosstabulation must be requested (using "
466 "the TABLES subcommand)."));
473 for (int i = 0; i < CRS_N_CELLS; i++)
474 if (proc.cells & (1u << i))
475 proc.a_cells[proc.n_cells++] = i;
476 assert (proc.n_cells < CRS_N_CELLS);
478 /* Missing values. */
479 if (proc.mode == GENERAL && !proc.exclude)
481 lex_ofs_error (lexer, exclude_ofs, exclude_ofs,
482 _("Missing mode %s not allowed in general mode. "
483 "Assuming %s."), "REPORT", "MISSING=TABLE");
484 proc.exclude = MV_ANY;
487 struct casereader *input = casereader_create_filter_weight (proc_open (ds),
490 struct casegrouper *grouper = casegrouper_create_splits (input, dataset_dict (ds));
491 struct casereader *group;
492 while (casegrouper_get_next_group (grouper, &group))
496 /* Output SPLIT FILE variables. */
497 c = casereader_peek (group, 0);
500 output_split_file_values (ds, c);
504 /* Initialize hash tables. */
505 for (struct crosstabulation *xt = &proc.pivots[0];
506 xt < &proc.pivots[proc.n_pivots]; xt++)
507 hmap_init (&xt->data);
510 for (; (c = casereader_read (group)) != NULL; case_unref (c))
511 for (struct crosstabulation *xt = &proc.pivots[0];
512 xt < &proc.pivots[proc.n_pivots]; xt++)
514 double weight = dict_get_case_weight (dataset_dict (ds), c,
516 if (proc.round_case_weights)
518 weight = round_weight (&proc, weight);
522 if (should_tabulate_case (xt, c, proc.exclude))
524 if (proc.mode == GENERAL)
525 tabulate_general_case (xt, c, weight);
527 tabulate_integer_case (xt, c, weight);
530 xt->missing += weight;
532 casereader_destroy (group);
535 postcalc (&proc, lexer);
537 bool ok = casegrouper_destroy (grouper);
538 ok = proc_commit (ds) && ok;
540 result = ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
543 free (proc.variables);
545 struct var_range *range, *next_range;
546 HMAP_FOR_EACH_SAFE (range, next_range, struct var_range, hmap_node,
549 hmap_delete (&proc.var_ranges, &range->hmap_node);
552 for (struct crosstabulation *xt = &proc.pivots[0];
553 xt < &proc.pivots[proc.n_pivots]; xt++)
556 free (xt->const_vars);
557 free (xt->const_indexes);
564 /* Parses the TABLES subcommand. */
566 parse_crosstabs_tables (struct lexer *lexer, struct dataset *ds,
567 struct crosstabs_proc *proc)
569 const struct variable ***by = NULL;
570 size_t *by_nvar = NULL;
573 /* Ensure that this is a TABLES subcommand. */
574 if (!lex_match_id (lexer, "TABLES")
575 && (lex_token (lexer) != T_ID ||
576 dict_lookup_var (dataset_dict (ds), lex_tokcstr (lexer)) == NULL)
577 && lex_token (lexer) != T_ALL)
579 lex_error (lexer, NULL);
582 lex_match (lexer, T_EQUALS);
584 struct const_var_set *var_set
586 ? const_var_set_create_from_array (proc->variables,
588 : const_var_set_create_from_dict (dataset_dict (ds)));
592 int vars_start = lex_ofs (lexer);
595 by = xnrealloc (by, n_by + 1, sizeof *by);
596 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
597 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
598 PV_NO_DUPLICATE | PV_NO_SCRATCH))
600 if (xalloc_oversized (nx, by_nvar[n_by]))
603 lexer, vars_start, lex_ofs (lexer),
604 _("Too many cross-tabulation variables or dimensions."));
610 if (!lex_match (lexer, T_BY))
618 int vars_end = lex_ofs (lexer) - 1;
620 int *by_iter = XCALLOC (n_by, int);
621 proc->pivots = xnrealloc (proc->pivots,
622 proc->n_pivots + nx, sizeof *proc->pivots);
623 for (int i = 0; i < nx; i++)
625 struct crosstabulation *xt = &proc->pivots[proc->n_pivots++];
627 *xt = (struct crosstabulation) {
629 .weight_format = proc->weight_format,
632 .vars = xcalloc (n_by, sizeof *xt->vars),
635 .const_indexes = NULL,
636 .start_ofs = vars_start,
640 for (int j = 0; j < n_by; j++)
641 xt->vars[j].var = by[j][by_iter[j]];
643 for (int j = n_by - 1; j >= 0; j--)
645 if (++by_iter[j] < by_nvar[j])
654 /* All return paths lead here. */
655 for (int i = 0; i < n_by; i++)
660 const_var_set_destroy (var_set);
665 /* Parses the VARIABLES subcommand. */
667 parse_crosstabs_variables (struct lexer *lexer, struct dataset *ds,
668 struct crosstabs_proc *proc)
672 lex_next_error (lexer, -1, -1, _("%s must be specified before %s."),
673 "VARIABLES", "TABLES");
677 lex_match (lexer, T_EQUALS);
681 size_t orig_nv = proc->n_variables;
683 if (!parse_variables_const (lexer, dataset_dict (ds),
684 &proc->variables, &proc->n_variables,
685 (PV_APPEND | PV_NUMERIC
686 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
689 if (!lex_force_match (lexer, T_LPAREN))
692 if (!lex_force_int (lexer))
694 long min = lex_integer (lexer);
697 lex_match (lexer, T_COMMA);
699 if (!lex_force_int_range (lexer, NULL, min, LONG_MAX))
701 long max = lex_integer (lexer);
704 if (!lex_force_match (lexer, T_RPAREN))
707 for (size_t i = orig_nv; i < proc->n_variables; i++)
709 const struct variable *var = proc->variables[i];
710 struct var_range *vr = xmalloc (sizeof *vr);
715 vr->count = max - min + 1;
716 hmap_insert (&proc->var_ranges, &vr->hmap_node,
717 hash_pointer (var, 0));
720 if (lex_token (lexer) == T_SLASH)
724 proc->mode = INTEGER;
728 free (proc->variables);
729 proc->variables = NULL;
730 proc->n_variables = 0;
734 /* Data file processing. */
736 static const struct var_range *
737 get_var_range (const struct crosstabs_proc *proc, const struct variable *var)
739 if (!hmap_is_empty (&proc->var_ranges))
741 const struct var_range *range;
743 HMAP_FOR_EACH_IN_BUCKET (range, struct var_range, hmap_node,
744 hash_pointer (var, 0), &proc->var_ranges)
745 if (range->var == var)
753 should_tabulate_case (const struct crosstabulation *xt, const struct ccase *c,
754 enum mv_class exclude)
757 for (j = 0; j < xt->n_vars; j++)
759 const struct variable *var = xt->vars[j].var;
760 const struct var_range *range = get_var_range (xt->proc, var);
762 if (var_is_value_missing (var, case_data (c, var)) & exclude)
767 double num = case_num (c, var);
768 if (num < range->min || num >= range->max + 1.)
776 tabulate_integer_case (struct crosstabulation *xt, const struct ccase *c,
784 for (j = 0; j < xt->n_vars; j++)
786 /* Throw away fractional parts of values. */
787 hash = hash_int (case_num (c, xt->vars[j].var), hash);
790 HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &xt->data)
792 for (j = 0; j < xt->n_vars; j++)
793 if ((int) case_num (c, xt->vars[j].var) != (int) te->values[j].f)
796 /* Found an existing entry. */
803 /* No existing entry. Create a new one. */
804 te = xmalloc (table_entry_size (xt->n_vars));
806 for (j = 0; j < xt->n_vars; j++)
807 te->values[j].f = (int) case_num (c, xt->vars[j].var);
808 hmap_insert (&xt->data, &te->node, hash);
812 tabulate_general_case (struct crosstabulation *xt, const struct ccase *c,
820 for (j = 0; j < xt->n_vars; j++)
822 const struct variable *var = xt->vars[j].var;
823 hash = value_hash (case_data (c, var), var_get_width (var), hash);
826 HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &xt->data)
828 for (j = 0; j < xt->n_vars; j++)
830 const struct variable *var = xt->vars[j].var;
831 if (!value_equal (case_data (c, var), &te->values[j],
832 var_get_width (var)))
836 /* Found an existing entry. */
843 /* No existing entry. Create a new one. */
844 te = xmalloc (table_entry_size (xt->n_vars));
846 for (j = 0; j < xt->n_vars; j++)
848 const struct variable *var = xt->vars[j].var;
849 value_clone (&te->values[j], case_data (c, var), var_get_width (var));
851 hmap_insert (&xt->data, &te->node, hash);
854 /* Post-data reading calculations. */
856 static int compare_table_entry_vars_3way (const struct freq *a,
857 const struct freq *b,
858 const struct crosstabulation *xt,
860 static int compare_table_entry_3way (const void *ap_, const void *bp_,
862 static int compare_table_entry_3way_inv (const void *ap_, const void *bp_,
865 static void enum_var_values (const struct crosstabulation *, int var_idx,
867 static void free_var_values (const struct crosstabulation *, int var_idx);
868 static void output_crosstabulation (struct crosstabs_proc *,
869 struct crosstabulation *,
871 static void make_crosstabulation_subset (struct crosstabulation *xt,
872 size_t row0, size_t row1,
873 struct crosstabulation *subset);
874 static void make_summary_table (struct crosstabs_proc *);
875 static bool find_crosstab (struct crosstabulation *, size_t *row0p,
879 postcalc (struct crosstabs_proc *proc, struct lexer *lexer)
881 /* Round hash table entries, if requested
883 If this causes any of the cell counts to fall to zero, delete those
885 if (proc->round_cells)
886 for (struct crosstabulation *xt = proc->pivots;
887 xt < &proc->pivots[proc->n_pivots]; xt++)
889 struct freq *e, *next;
890 HMAP_FOR_EACH_SAFE (e, next, struct freq, node, &xt->data)
892 e->count = round_weight (proc, e->count);
895 hmap_delete (&xt->data, &e->node);
901 /* Convert hash tables into sorted arrays of entries. */
902 for (struct crosstabulation *xt = proc->pivots;
903 xt < &proc->pivots[proc->n_pivots]; xt++)
907 xt->n_entries = hmap_count (&xt->data);
908 xt->entries = xnmalloc (xt->n_entries, sizeof *xt->entries);
910 HMAP_FOR_EACH (e, struct freq, node, &xt->data)
911 xt->entries[i++] = e;
912 hmap_destroy (&xt->data);
914 sort (xt->entries, xt->n_entries, sizeof *xt->entries,
915 proc->descending ? compare_table_entry_3way_inv : compare_table_entry_3way,
920 make_summary_table (proc);
922 /* Output each pivot table. */
923 for (struct crosstabulation *xt = proc->pivots;
924 xt < &proc->pivots[proc->n_pivots]; xt++)
926 output_crosstabulation (proc, xt, lexer);
929 int n_vars = (xt->n_vars > 2 ? 2 : xt->n_vars);
930 const struct variable **vars = XCALLOC (n_vars, const struct variable*);
931 for (size_t i = 0; i < n_vars; i++)
932 vars[i] = xt->vars[i].var;
933 chart_submit (barchart_create (vars, n_vars, _("Count"),
935 xt->entries, xt->n_entries));
940 /* Free output and prepare for next split file. */
941 for (struct crosstabulation *xt = proc->pivots;
942 xt < &proc->pivots[proc->n_pivots]; xt++)
946 /* Free the members that were allocated in this function(and the values
947 owned by the entries.
949 The other pointer members are either both allocated and destroyed at a
950 lower level (in output_crosstabulation), or both allocated and
951 destroyed at a higher level (in crs_custom_tables and free_proc,
953 for (size_t i = 0; i < xt->n_vars; i++)
955 int width = var_get_width (xt->vars[i].var);
956 if (value_needs_init (width))
960 for (j = 0; j < xt->n_entries; j++)
961 value_destroy (&xt->entries[j]->values[i], width);
965 for (size_t i = 0; i < xt->n_entries; i++)
966 free (xt->entries[i]);
972 make_crosstabulation_subset (struct crosstabulation *xt, size_t row0,
973 size_t row1, struct crosstabulation *subset)
978 assert (xt->n_consts == 0);
980 subset->vars = xt->vars;
982 subset->n_consts = xt->n_vars - 2;
983 subset->const_vars = xt->vars + 2;
984 subset->const_indexes = xcalloc (subset->n_consts,
985 sizeof *subset->const_indexes);
986 for (size_t i = 0; i < subset->n_consts; i++)
988 const union value *value = &xt->entries[row0]->values[2 + i];
990 for (size_t j = 0; j < xt->vars[2 + i].n_values; j++)
991 if (value_equal (&xt->vars[2 + i].values[j], value,
992 var_get_width (xt->vars[2 + i].var)))
994 subset->const_indexes[i] = j;
1001 subset->entries = &xt->entries[row0];
1002 subset->n_entries = row1 - row0;
1006 compare_table_entry_var_3way (const struct freq *a,
1007 const struct freq *b,
1008 const struct crosstabulation *xt,
1011 return value_compare_3way (&a->values[idx], &b->values[idx],
1012 var_get_width (xt->vars[idx].var));
1016 compare_table_entry_vars_3way (const struct freq *a,
1017 const struct freq *b,
1018 const struct crosstabulation *xt,
1023 for (i = idx1 - 1; i >= idx0; i--)
1025 int cmp = compare_table_entry_var_3way (a, b, xt, i);
1032 /* Compare the struct freq at *AP to the one at *BP and
1033 return a strcmp()-type result. */
1035 compare_table_entry_3way (const void *ap_, const void *bp_, const void *xt_)
1037 const struct freq *const *ap = ap_;
1038 const struct freq *const *bp = bp_;
1039 const struct freq *a = *ap;
1040 const struct freq *b = *bp;
1041 const struct crosstabulation *xt = xt_;
1044 cmp = compare_table_entry_vars_3way (a, b, xt, 2, xt->n_vars);
1048 cmp = compare_table_entry_var_3way (a, b, xt, ROW_VAR);
1052 return compare_table_entry_var_3way (a, b, xt, COL_VAR);
1055 /* Inverted version of compare_table_entry_3way */
1057 compare_table_entry_3way_inv (const void *ap_, const void *bp_, const void *xt_)
1059 return -compare_table_entry_3way (ap_, bp_, xt_);
1062 /* Output a table summarizing the cases processed. */
1064 make_summary_table (struct crosstabs_proc *proc)
1066 struct pivot_table *table = pivot_table_create (N_("Summary"));
1067 pivot_table_set_weight_var (table, dict_get_weight (proc->dict));
1069 pivot_dimension_create (table, PIVOT_AXIS_COLUMN, N_("Statistics"),
1070 N_("N"), PIVOT_RC_COUNT,
1071 N_("Percent"), PIVOT_RC_PERCENT);
1073 struct pivot_dimension *cases = pivot_dimension_create (
1074 table, PIVOT_AXIS_COLUMN, N_("Cases"),
1075 N_("Valid"), N_("Missing"), N_("Total"));
1076 cases->root->show_label = true;
1078 struct pivot_dimension *tables = pivot_dimension_create (
1079 table, PIVOT_AXIS_ROW, N_("Crosstabulation"));
1080 for (struct crosstabulation *xt = &proc->pivots[0];
1081 xt < &proc->pivots[proc->n_pivots]; xt++)
1083 struct string name = DS_EMPTY_INITIALIZER;
1084 for (size_t i = 0; i < xt->n_vars; i++)
1087 ds_put_cstr (&name, " × ");
1088 ds_put_cstr (&name, var_to_string (xt->vars[i].var));
1091 int row = pivot_category_create_leaf (
1093 pivot_value_new_user_text_nocopy (ds_steal_cstr (&name)));
1096 for (size_t i = 0; i < xt->n_entries; i++)
1097 valid += xt->entries[i]->count;
1103 for (int i = 0; i < 3; i++)
1105 pivot_table_put3 (table, 0, i, row, pivot_value_new_number (n[i]));
1106 pivot_table_put3 (table, 1, i, row,
1107 pivot_value_new_number (n[i] / n[2] * 100.0));
1111 pivot_table_submit (table);
1116 static struct pivot_table *create_crosstab_table (
1117 struct crosstabs_proc *, struct crosstabulation *,
1118 size_t crs_leaves[CRS_N_CELLS]);
1119 static struct pivot_table *create_chisq_table (struct crosstabulation *);
1120 static struct pivot_table *create_sym_table (struct crosstabulation *);
1121 static struct pivot_table *create_risk_table (
1122 struct crosstabulation *, struct pivot_dimension **risk_statistics);
1123 static struct pivot_table *create_direct_table (struct crosstabulation *);
1124 static void display_crosstabulation (struct crosstabs_proc *,
1125 struct crosstabulation *,
1126 struct pivot_table *,
1127 size_t crs_leaves[CRS_N_CELLS]);
1128 static void display_chisq (struct crosstabulation *, struct pivot_table *);
1129 static void display_symmetric (struct crosstabs_proc *,
1130 struct crosstabulation *, struct pivot_table *);
1131 static void display_risk (struct crosstabulation *, struct pivot_table *,
1132 struct pivot_dimension *risk_statistics);
1133 static void display_directional (struct crosstabs_proc *,
1134 struct crosstabulation *,
1135 struct pivot_table *);
1136 static void delete_missing (struct crosstabulation *);
1137 static void build_matrix (struct crosstabulation *);
1139 /* Output pivot table XT in the context of PROC. */
1141 output_crosstabulation (struct crosstabs_proc *proc, struct crosstabulation *xt,
1142 struct lexer *lexer)
1144 for (size_t i = 0; i < xt->n_vars; i++)
1145 enum_var_values (xt, i, proc->descending);
1147 if (xt->vars[COL_VAR].n_values == 0)
1152 ds_init_cstr (&vars, var_to_string (xt->vars[0].var));
1153 for (i = 1; i < xt->n_vars; i++)
1154 ds_put_format (&vars, " × %s", var_to_string (xt->vars[i].var));
1156 /* TRANSLATORS: The %s here describes a crosstabulation. It takes the
1157 form "var1 * var2 * var3 * ...". */
1158 lex_ofs_msg (lexer, SW, xt->start_ofs, xt->end_ofs,
1159 _("Crosstabulation %s contained no non-missing cases."),
1163 for (size_t i = 0; i < xt->n_vars; i++)
1164 free_var_values (xt, i);
1168 size_t crs_leaves[CRS_N_CELLS];
1169 struct pivot_table *table = (proc->cells
1170 ? create_crosstab_table (proc, xt, crs_leaves)
1172 struct pivot_table *chisq = (proc->statistics & CRS_ST_CHISQ
1173 ? create_chisq_table (xt)
1175 struct pivot_table *sym
1176 = (proc->statistics & (CRS_ST_PHI | CRS_ST_CC | CRS_ST_BTAU | CRS_ST_CTAU
1177 | CRS_ST_GAMMA | CRS_ST_CORR | CRS_ST_KAPPA)
1178 ? create_sym_table (xt)
1180 struct pivot_dimension *risk_statistics = NULL;
1181 struct pivot_table *risk = (proc->statistics & CRS_ST_RISK
1182 ? create_risk_table (xt, &risk_statistics)
1184 struct pivot_table *direct
1185 = (proc->statistics & (CRS_ST_LAMBDA | CRS_ST_UC | CRS_ST_D | CRS_ST_ETA)
1186 ? create_direct_table (xt)
1191 while (find_crosstab (xt, &row0, &row1))
1193 struct crosstabulation x;
1195 make_crosstabulation_subset (xt, row0, row1, &x);
1197 size_t n_rows = x.vars[ROW_VAR].n_values;
1198 size_t n_cols = x.vars[COL_VAR].n_values;
1199 if (size_overflow_p (xtimes (xtimes (n_rows, n_cols), sizeof (double))))
1201 x.row_tot = xmalloc (n_rows * sizeof *x.row_tot);
1202 x.col_tot = xmalloc (n_cols * sizeof *x.col_tot);
1203 x.mat = xmalloc (n_rows * n_cols * sizeof *x.mat);
1207 /* Find the first variable that differs from the last subtable. */
1209 display_crosstabulation (proc, &x, table, crs_leaves);
1211 if (proc->exclude == 0)
1212 delete_missing (&x);
1215 display_chisq (&x, chisq);
1218 display_symmetric (proc, &x, sym);
1220 display_risk (&x, risk, risk_statistics);
1222 display_directional (proc, &x, direct);
1227 free (x.const_indexes);
1231 pivot_table_submit (table);
1234 pivot_table_submit (chisq);
1237 pivot_table_submit (sym);
1241 if (!pivot_table_is_empty (risk))
1242 pivot_table_submit (risk);
1244 pivot_table_unref (risk);
1248 pivot_table_submit (direct);
1250 for (size_t i = 0; i < xt->n_vars; i++)
1251 free_var_values (xt, i);
1255 build_matrix (struct crosstabulation *x)
1257 const int col_var_width = var_get_width (x->vars[COL_VAR].var);
1258 const int row_var_width = var_get_width (x->vars[ROW_VAR].var);
1259 size_t n_rows = x->vars[ROW_VAR].n_values;
1260 size_t n_cols = x->vars[COL_VAR].n_values;
1267 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1269 const struct freq *te = *p;
1271 while (!value_equal (&x->vars[ROW_VAR].values[row],
1272 &te->values[ROW_VAR], row_var_width))
1274 for (; col < n_cols; col++)
1280 while (!value_equal (&x->vars[COL_VAR].values[col],
1281 &te->values[COL_VAR], col_var_width))
1288 if (++col >= n_cols)
1294 while (mp < &x->mat[n_cols * n_rows])
1296 assert (mp == &x->mat[n_cols * n_rows]);
1298 /* Column totals, row totals, ns_rows. */
1300 for (col = 0; col < n_cols; col++)
1301 x->col_tot[col] = 0.0;
1302 for (row = 0; row < n_rows; row++)
1303 x->row_tot[row] = 0.0;
1305 for (row = 0; row < n_rows; row++)
1307 bool row_is_empty = true;
1308 for (col = 0; col < n_cols; col++)
1312 row_is_empty = false;
1313 x->col_tot[col] += *mp;
1314 x->row_tot[row] += *mp;
1321 assert (mp == &x->mat[n_cols * n_rows]);
1325 for (col = 0; col < n_cols; col++)
1326 for (row = 0; row < n_rows; row++)
1327 if (x->mat[col + row * n_cols] != 0.0)
1335 for (col = 0; col < n_cols; col++)
1336 x->total += x->col_tot[col];
1340 add_var_dimension (struct pivot_table *table, const struct xtab_var *var,
1341 enum pivot_axis_type axis_type, bool total)
1343 struct pivot_dimension *d = pivot_dimension_create__ (
1344 table, axis_type, pivot_value_new_variable (var->var));
1346 struct pivot_footnote *missing_footnote = pivot_table_create_footnote (
1347 table, pivot_value_new_text (N_("Missing value")));
1349 struct pivot_category *group = pivot_category_create_group__ (
1350 d->root, pivot_value_new_variable (var->var));
1351 for (size_t j = 0; j < var->n_values; j++)
1353 struct pivot_value *value = pivot_value_new_var_value (
1354 var->var, &var->values[j]);
1355 if (var_is_value_missing (var->var, &var->values[j]))
1356 pivot_value_add_footnote (value, missing_footnote);
1357 pivot_category_create_leaf (group, value);
1361 pivot_category_create_leaf (d->root, pivot_value_new_text (N_("Total")));
1364 static struct pivot_table *
1365 create_crosstab_table (struct crosstabs_proc *proc, struct crosstabulation *xt,
1366 size_t crs_leaves[CRS_N_CELLS])
1369 struct string title = DS_EMPTY_INITIALIZER;
1370 for (size_t i = 0; i < xt->n_vars; i++)
1373 ds_put_cstr (&title, " × ");
1374 ds_put_cstr (&title, var_to_string (xt->vars[i].var));
1376 for (size_t i = 0; i < xt->n_consts; i++)
1378 const struct variable *var = xt->const_vars[i].var;
1379 const union value *value = &xt->entries[0]->values[2 + i];
1382 ds_put_format (&title, ", %s=", var_to_string (var));
1384 /* Insert the formatted value of VAR without any leading spaces. */
1385 s = data_out (value, var_get_encoding (var), var_get_print_format (var),
1386 settings_get_fmt_settings ());
1387 ds_put_cstr (&title, s + strspn (s, " "));
1390 struct pivot_table *table = pivot_table_create__ (
1391 pivot_value_new_user_text_nocopy (ds_steal_cstr (&title)),
1393 pivot_table_set_weight_format (table, &proc->weight_format);
1395 struct pivot_dimension *statistics = pivot_dimension_create (
1396 table, PIVOT_AXIS_ROW, N_("Statistics"));
1403 static const struct statistic stats[CRS_N_CELLS] =
1405 #define C(KEYWORD, STRING, RC) { STRING, RC },
1409 for (size_t i = 0; i < CRS_N_CELLS; i++)
1410 if (proc->cells & (1u << i) && stats[i].label)
1411 crs_leaves[i] = pivot_category_create_leaf_rc (
1412 statistics->root, pivot_value_new_text (stats[i].label),
1415 for (size_t i = 0; i < xt->n_vars; i++)
1416 add_var_dimension (table, &xt->vars[i],
1417 i == COL_VAR ? PIVOT_AXIS_COLUMN : PIVOT_AXIS_ROW,
1423 static struct pivot_table *
1424 create_chisq_table (struct crosstabulation *xt)
1426 struct pivot_table *chisq = pivot_table_create (N_("Chi-Square Tests"));
1427 pivot_table_set_weight_format (chisq, &xt->weight_format);
1429 pivot_dimension_create (
1430 chisq, PIVOT_AXIS_ROW, N_("Statistics"),
1431 N_("Pearson Chi-Square"),
1432 N_("Likelihood Ratio"),
1433 N_("Fisher's Exact Test"),
1434 N_("Continuity Correction"),
1435 N_("Linear-by-Linear Association"),
1436 N_("N of Valid Cases"), PIVOT_RC_COUNT);
1438 pivot_dimension_create (
1439 chisq, PIVOT_AXIS_COLUMN, N_("Statistics"),
1440 N_("Value"), PIVOT_RC_OTHER,
1441 N_("df"), PIVOT_RC_COUNT,
1442 N_("Asymptotic Sig. (2-tailed)"), PIVOT_RC_SIGNIFICANCE,
1443 N_("Exact Sig. (2-tailed)"), PIVOT_RC_SIGNIFICANCE,
1444 N_("Exact Sig. (1-tailed)"), PIVOT_RC_SIGNIFICANCE);
1446 for (size_t i = 2; i < xt->n_vars; i++)
1447 add_var_dimension (chisq, &xt->vars[i], PIVOT_AXIS_ROW, false);
1452 /* Symmetric measures. */
1453 static struct pivot_table *
1454 create_sym_table (struct crosstabulation *xt)
1456 struct pivot_table *sym = pivot_table_create (N_("Symmetric Measures"));
1457 pivot_table_set_weight_format (sym, &xt->weight_format);
1459 pivot_dimension_create (
1460 sym, PIVOT_AXIS_COLUMN, N_("Values"),
1461 N_("Value"), PIVOT_RC_OTHER,
1462 N_("Asymp. Std. Error"), PIVOT_RC_OTHER,
1463 N_("Approx. T"), PIVOT_RC_OTHER,
1464 N_("Approx. Sig."), PIVOT_RC_SIGNIFICANCE);
1466 struct pivot_dimension *statistics = pivot_dimension_create (
1467 sym, PIVOT_AXIS_ROW, N_("Statistics"));
1468 pivot_category_create_group (
1469 statistics->root, N_("Nominal by Nominal"),
1470 N_("Phi"), N_("Cramer's V"), N_("Contingency Coefficient"));
1471 pivot_category_create_group (
1472 statistics->root, N_("Ordinal by Ordinal"),
1473 N_("Kendall's tau-b"), N_("Kendall's tau-c"),
1474 N_("Gamma"), N_("Spearman Correlation"));
1475 pivot_category_create_group (
1476 statistics->root, N_("Interval by Interval"),
1478 pivot_category_create_group (
1479 statistics->root, N_("Measure of Agreement"),
1481 pivot_category_create_leaves (statistics->root, N_("N of Valid Cases"),
1484 for (size_t i = 2; i < xt->n_vars; i++)
1485 add_var_dimension (sym, &xt->vars[i], PIVOT_AXIS_ROW, false);
1490 /* Risk estimate. */
1491 static struct pivot_table *
1492 create_risk_table (struct crosstabulation *xt,
1493 struct pivot_dimension **risk_statistics)
1495 struct pivot_table *risk = pivot_table_create (N_("Risk Estimate"));
1496 pivot_table_set_weight_format (risk, &xt->weight_format);
1498 struct pivot_dimension *values = pivot_dimension_create (
1499 risk, PIVOT_AXIS_COLUMN, N_("Values"),
1500 N_("Value"), PIVOT_RC_OTHER);
1501 pivot_category_create_group (
1502 /* xgettext:no-c-format */
1503 values->root, N_("95% Confidence Interval"),
1504 N_("Lower"), PIVOT_RC_OTHER,
1505 N_("Upper"), PIVOT_RC_OTHER);
1507 *risk_statistics = pivot_dimension_create (
1508 risk, PIVOT_AXIS_ROW, N_("Statistics"));
1510 for (size_t i = 2; i < xt->n_vars; i++)
1511 add_var_dimension (risk, &xt->vars[i], PIVOT_AXIS_ROW, false);
1517 create_direct_stat (struct pivot_category *parent,
1518 const struct crosstabulation *xt,
1519 const char *name, bool symmetric)
1521 struct pivot_category *group = pivot_category_create_group (
1524 pivot_category_create_leaf (group, pivot_value_new_text (N_("Symmetric")));
1526 char *row_label = xasprintf (_("%s Dependent"),
1527 var_to_string (xt->vars[ROW_VAR].var));
1528 pivot_category_create_leaf (group, pivot_value_new_user_text_nocopy (
1531 char *col_label = xasprintf (_("%s Dependent"),
1532 var_to_string (xt->vars[COL_VAR].var));
1533 pivot_category_create_leaf (group, pivot_value_new_user_text_nocopy (
1537 /* Directional measures. */
1538 static struct pivot_table *
1539 create_direct_table (struct crosstabulation *xt)
1541 struct pivot_table *direct = pivot_table_create (N_("Directional Measures"));
1542 pivot_table_set_weight_format (direct, &xt->weight_format);
1544 pivot_dimension_create (
1545 direct, PIVOT_AXIS_COLUMN, N_("Values"),
1546 N_("Value"), PIVOT_RC_OTHER,
1547 N_("Asymp. Std. Error"), PIVOT_RC_OTHER,
1548 N_("Approx. T"), PIVOT_RC_OTHER,
1549 N_("Approx. Sig."), PIVOT_RC_SIGNIFICANCE);
1551 struct pivot_dimension *statistics = pivot_dimension_create (
1552 direct, PIVOT_AXIS_ROW, N_("Statistics"));
1553 struct pivot_category *nn = pivot_category_create_group (
1554 statistics->root, N_("Nominal by Nominal"));
1555 create_direct_stat (nn, xt, N_("Lambda"), true);
1556 create_direct_stat (nn, xt, N_("Goodman and Kruskal tau"), false);
1557 create_direct_stat (nn, xt, N_("Uncertainty Coefficient"), true);
1558 struct pivot_category *oo = pivot_category_create_group (
1559 statistics->root, N_("Ordinal by Ordinal"));
1560 create_direct_stat (oo, xt, N_("Somers' d"), true);
1561 struct pivot_category *ni = pivot_category_create_group (
1562 statistics->root, N_("Nominal by Interval"));
1563 create_direct_stat (ni, xt, N_("Eta"), false);
1565 for (size_t i = 2; i < xt->n_vars; i++)
1566 add_var_dimension (direct, &xt->vars[i], PIVOT_AXIS_ROW, false);
1571 /* Delete missing rows and columns for statistical analysis when
1574 delete_missing (struct crosstabulation *xt)
1576 size_t n_rows = xt->vars[ROW_VAR].n_values;
1577 size_t n_cols = xt->vars[COL_VAR].n_values;
1580 for (r = 0; r < n_rows; r++)
1581 if (var_is_num_missing (xt->vars[ROW_VAR].var,
1582 xt->vars[ROW_VAR].values[r].f) == MV_USER)
1584 for (c = 0; c < n_cols; c++)
1585 xt->mat[c + r * n_cols] = 0.;
1590 for (c = 0; c < n_cols; c++)
1591 if (var_is_num_missing (xt->vars[COL_VAR].var,
1592 xt->vars[COL_VAR].values[c].f) == MV_USER)
1594 for (r = 0; r < n_rows; r++)
1595 xt->mat[c + r * n_cols] = 0.;
1601 find_crosstab (struct crosstabulation *xt, size_t *row0p, size_t *row1p)
1603 size_t row0 = *row1p;
1606 if (row0 >= xt->n_entries)
1609 for (row1 = row0 + 1; row1 < xt->n_entries; row1++)
1611 struct freq *a = xt->entries[row0];
1612 struct freq *b = xt->entries[row1];
1613 if (compare_table_entry_vars_3way (a, b, xt, 2, xt->n_vars) != 0)
1621 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1622 result. WIDTH_ points to an int which is either 0 for a
1623 numeric value or a string width for a string value. */
1625 compare_value_3way (const void *a_, const void *b_, const void *width_)
1627 const union value *a = a_;
1628 const union value *b = b_;
1629 const int *width = width_;
1631 return value_compare_3way (a, b, *width);
1634 /* Inverted version of the above */
1636 compare_value_3way_inv (const void *a_, const void *b_, const void *width_)
1638 return -compare_value_3way (a_, b_, width_);
1642 /* Given an array of ENTRY_CNT table_entry structures starting at
1643 ENTRIES, creates a sorted list of the values that the variable
1644 with index VAR_IDX takes on. Stores the array of the values in
1645 XT->values and the number of values in XT->n_values. */
1647 enum_var_values (const struct crosstabulation *xt, int var_idx,
1650 struct xtab_var *xv = &xt->vars[var_idx];
1651 const struct var_range *range = get_var_range (xt->proc, xv->var);
1655 xv->values = xnmalloc (range->count, sizeof *xv->values);
1656 xv->n_values = range->count;
1657 for (size_t i = 0; i < range->count; i++)
1658 xv->values[i].f = range->min + i;
1662 int width = var_get_width (xv->var);
1663 struct hmapx_node *node;
1664 const union value *iter;
1668 for (size_t i = 0; i < xt->n_entries; i++)
1670 const struct freq *te = xt->entries[i];
1671 const union value *value = &te->values[var_idx];
1672 size_t hash = value_hash (value, width, 0);
1674 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1675 if (value_equal (iter, value, width))
1678 hmapx_insert (&set, (union value *) value, hash);
1683 xv->n_values = hmapx_count (&set);
1684 xv->values = xnmalloc (xv->n_values, sizeof *xv->values);
1686 HMAPX_FOR_EACH (iter, node, &set)
1687 xv->values[i++] = *iter;
1688 hmapx_destroy (&set);
1690 sort (xv->values, xv->n_values, sizeof *xv->values,
1691 descending ? compare_value_3way_inv : compare_value_3way,
1697 free_var_values (const struct crosstabulation *xt, int var_idx)
1699 struct xtab_var *xv = &xt->vars[var_idx];
1705 /* Displays the crosstabulation table. */
1707 display_crosstabulation (struct crosstabs_proc *proc,
1708 struct crosstabulation *xt, struct pivot_table *table,
1709 size_t crs_leaves[CRS_N_CELLS])
1711 size_t n_rows = xt->vars[ROW_VAR].n_values;
1712 size_t n_cols = xt->vars[COL_VAR].n_values;
1714 size_t *indexes = xnmalloc (table->n_dimensions, sizeof *indexes);
1715 assert (xt->n_vars == 2);
1716 for (size_t i = 0; i < xt->n_consts; i++)
1717 indexes[i + 3] = xt->const_indexes[i];
1719 /* Put in the actual cells. */
1720 double *mp = xt->mat;
1721 for (size_t r = 0; r < n_rows; r++)
1723 if (!xt->row_tot[r] && proc->mode != INTEGER)
1726 indexes[ROW_VAR + 1] = r;
1727 for (size_t c = 0; c < n_cols; c++)
1729 if (!xt->col_tot[c] && proc->mode != INTEGER)
1732 indexes[COL_VAR + 1] = c;
1734 double expected_value = xt->row_tot[r] * xt->col_tot[c] / xt->total;
1735 double residual = *mp - expected_value;
1736 double sresidual = residual / sqrt (expected_value);
1738 = residual / sqrt (expected_value
1739 * (1. - xt->row_tot[r] / xt->total)
1740 * (1. - xt->col_tot[c] / xt->total));
1741 double entries[CRS_N_CELLS] = {
1742 [CRS_CL_COUNT] = *mp,
1743 [CRS_CL_ROW] = *mp / xt->row_tot[r] * 100.,
1744 [CRS_CL_COLUMN] = *mp / xt->col_tot[c] * 100.,
1745 [CRS_CL_TOTAL] = *mp / xt->total * 100.,
1746 [CRS_CL_EXPECTED] = expected_value,
1747 [CRS_CL_RESIDUAL] = residual,
1748 [CRS_CL_SRESIDUAL] = sresidual,
1749 [CRS_CL_ASRESIDUAL] = asresidual,
1751 for (size_t i = 0; i < proc->n_cells; i++)
1753 int cell = proc->a_cells[i];
1754 indexes[0] = crs_leaves[cell];
1755 pivot_table_put (table, indexes, table->n_dimensions,
1756 pivot_value_new_number (entries[cell]));
1764 for (size_t r = 0; r < n_rows; r++)
1766 if (!xt->row_tot[r] && proc->mode != INTEGER)
1769 double expected_value = xt->row_tot[r] / xt->total;
1770 double entries[CRS_N_CELLS] = {
1771 [CRS_CL_COUNT] = xt->row_tot[r],
1772 [CRS_CL_ROW] = 100.0,
1773 [CRS_CL_COLUMN] = expected_value * 100.,
1774 [CRS_CL_TOTAL] = expected_value * 100.,
1775 [CRS_CL_EXPECTED] = expected_value,
1776 [CRS_CL_RESIDUAL] = SYSMIS,
1777 [CRS_CL_SRESIDUAL] = SYSMIS,
1778 [CRS_CL_ASRESIDUAL] = SYSMIS,
1780 for (size_t i = 0; i < proc->n_cells; i++)
1782 int cell = proc->a_cells[i];
1783 double entry = entries[cell];
1784 if (entry != SYSMIS)
1786 indexes[ROW_VAR + 1] = r;
1787 indexes[COL_VAR + 1] = n_cols;
1788 indexes[0] = crs_leaves[cell];
1789 pivot_table_put (table, indexes, table->n_dimensions,
1790 pivot_value_new_number (entry));
1795 for (size_t c = 0; c <= n_cols; c++)
1797 if (c < n_cols && !xt->col_tot[c] && proc->mode != INTEGER)
1800 double ct = c < n_cols ? xt->col_tot[c] : xt->total;
1801 double expected_value = ct / xt->total;
1802 double entries[CRS_N_CELLS] = {
1803 [CRS_CL_COUNT] = ct,
1804 [CRS_CL_ROW] = expected_value * 100.0,
1805 [CRS_CL_COLUMN] = 100.0,
1806 [CRS_CL_TOTAL] = expected_value * 100.,
1807 [CRS_CL_EXPECTED] = expected_value,
1808 [CRS_CL_RESIDUAL] = SYSMIS,
1809 [CRS_CL_SRESIDUAL] = SYSMIS,
1810 [CRS_CL_ASRESIDUAL] = SYSMIS,
1812 for (size_t i = 0; i < proc->n_cells; i++)
1814 int cell = proc->a_cells[i];
1815 double entry = entries[cell];
1816 if (entry != SYSMIS)
1818 indexes[ROW_VAR + 1] = n_rows;
1819 indexes[COL_VAR + 1] = c;
1820 indexes[0] = crs_leaves[cell];
1821 pivot_table_put (table, indexes, table->n_dimensions,
1822 pivot_value_new_number (entry));
1830 static void calc_r (struct crosstabulation *,
1831 double *XT, double *Y, double *, double *, double *);
1832 static void calc_chisq (struct crosstabulation *,
1833 double[N_CHISQ], int[N_CHISQ], double *, double *);
1835 /* Display chi-square statistics. */
1837 display_chisq (struct crosstabulation *xt, struct pivot_table *chisq)
1839 double chisq_v[N_CHISQ];
1840 double fisher1, fisher2;
1842 calc_chisq (xt, chisq_v, df, &fisher1, &fisher2);
1844 size_t *indexes = xnmalloc (chisq->n_dimensions, sizeof *indexes);
1845 assert (xt->n_vars == 2);
1846 for (size_t i = 0; i < xt->n_consts; i++)
1847 indexes[i + 2] = xt->const_indexes[i];
1848 for (int i = 0; i < N_CHISQ; i++)
1852 double entries[5] = { SYSMIS, SYSMIS, SYSMIS, SYSMIS, SYSMIS };
1855 entries[3] = fisher2;
1856 entries[4] = fisher1;
1858 else if (chisq_v[i] != SYSMIS)
1860 entries[0] = chisq_v[i];
1862 entries[2] = gsl_cdf_chisq_Q (chisq_v[i], df[i]);
1865 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1866 if (entries[j] != SYSMIS)
1869 pivot_table_put (chisq, indexes, chisq->n_dimensions,
1870 pivot_value_new_number (entries[j]));
1876 pivot_table_put (chisq, indexes, chisq->n_dimensions,
1877 pivot_value_new_number (xt->total));
1882 static int calc_symmetric (struct crosstabs_proc *, struct crosstabulation *,
1883 double[N_SYMMETRIC], double[N_SYMMETRIC],
1884 double[N_SYMMETRIC],
1885 double[3], double[3], double[3]);
1887 /* Display symmetric measures. */
1889 display_symmetric (struct crosstabs_proc *proc, struct crosstabulation *xt,
1890 struct pivot_table *sym)
1892 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1893 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1895 if (!calc_symmetric (proc, xt, sym_v, sym_ase, sym_t,
1896 somers_d_v, somers_d_ase, somers_d_t))
1899 size_t *indexes = xnmalloc (sym->n_dimensions, sizeof *indexes);
1900 assert (xt->n_vars == 2);
1901 for (size_t i = 0; i < xt->n_consts; i++)
1902 indexes[i + 2] = xt->const_indexes[i];
1904 for (int i = 0; i < N_SYMMETRIC; i++)
1906 if (sym_v[i] == SYSMIS)
1911 double entries[] = { sym_v[i], sym_ase[i], sym_t[i] };
1912 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1913 if (entries[j] != SYSMIS)
1916 pivot_table_put (sym, indexes, sym->n_dimensions,
1917 pivot_value_new_number (entries[j]));
1921 indexes[1] = N_SYMMETRIC;
1923 struct pivot_value *total = pivot_value_new_number (xt->total);
1924 pivot_value_set_rc (sym, total, PIVOT_RC_COUNT);
1925 pivot_table_put (sym, indexes, sym->n_dimensions, total);
1930 static bool calc_risk (struct crosstabulation *,
1931 double[], double[], double[], union value *,
1934 /* Display risk estimate. */
1936 display_risk (struct crosstabulation *xt, struct pivot_table *risk,
1937 struct pivot_dimension *risk_statistics)
1939 double risk_v[3], lower[3], upper[3], n_valid;
1941 if (!calc_risk (xt, risk_v, upper, lower, c, &n_valid))
1943 assert (risk_statistics);
1945 size_t *indexes = xnmalloc (risk->n_dimensions, sizeof *indexes);
1946 assert (xt->n_vars == 2);
1947 for (size_t i = 0; i < xt->n_consts; i++)
1948 indexes[i + 2] = xt->const_indexes[i];
1950 for (int i = 0; i < 3; i++)
1952 const struct variable *cv = xt->vars[COL_VAR].var;
1953 const struct variable *rv = xt->vars[ROW_VAR].var;
1955 if (risk_v[i] == SYSMIS)
1958 struct string label = DS_EMPTY_INITIALIZER;
1962 ds_put_format (&label, _("Odds Ratio for %s"), var_to_string (rv));
1963 ds_put_cstr (&label, " (");
1964 var_append_value_name (rv, &c[0], &label);
1965 ds_put_cstr (&label, " / ");
1966 var_append_value_name (rv, &c[1], &label);
1967 ds_put_cstr (&label, ")");
1971 ds_put_format (&label, _("For cohort %s = "), var_to_string (cv));
1972 var_append_value_name (cv, &xt->vars[ROW_VAR].values[i - 1], &label);
1976 indexes[1] = pivot_category_create_leaf (
1977 risk_statistics->root,
1978 pivot_value_new_user_text_nocopy (ds_steal_cstr (&label)));
1980 double entries[] = { risk_v[i], lower[i], upper[i] };
1981 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1984 pivot_table_put (risk, indexes, risk->n_dimensions,
1985 pivot_value_new_number (entries[i]));
1988 indexes[1] = pivot_category_create_leaf (
1989 risk_statistics->root,
1990 pivot_value_new_text (N_("N of Valid Cases")));
1992 pivot_table_put (risk, indexes, risk->n_dimensions,
1993 pivot_value_new_number (n_valid));
1997 static int calc_directional (struct crosstabs_proc *, struct crosstabulation *,
1998 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1999 double[N_DIRECTIONAL], double[N_DIRECTIONAL]);
2001 /* Display directional measures. */
2003 display_directional (struct crosstabs_proc *proc,
2004 struct crosstabulation *xt, struct pivot_table *direct)
2006 double direct_v[N_DIRECTIONAL];
2007 double direct_ase[N_DIRECTIONAL];
2008 double direct_t[N_DIRECTIONAL];
2009 double sig[N_DIRECTIONAL];
2010 if (!calc_directional (proc, xt, direct_v, direct_ase, direct_t, sig))
2013 size_t *indexes = xnmalloc (direct->n_dimensions, sizeof *indexes);
2014 assert (xt->n_vars == 2);
2015 for (size_t i = 0; i < xt->n_consts; i++)
2016 indexes[i + 2] = xt->const_indexes[i];
2018 for (int i = 0; i < N_DIRECTIONAL; i++)
2020 if (direct_v[i] == SYSMIS)
2025 double entries[] = {
2026 direct_v[i], direct_ase[i], direct_t[i], sig[i],
2028 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
2029 if (entries[j] != SYSMIS)
2032 pivot_table_put (direct, indexes, direct->n_dimensions,
2033 pivot_value_new_number (entries[j]));
2040 /* Statistical calculations. */
2042 /* Returns the value of the logarithm of gamma (factorial) function for an integer
2045 log_gamma_int (double xt)
2050 for (i = 2; i < xt; i++)
2056 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2058 static inline double
2059 Pr (int a, int b, int c, int d)
2061 return exp (log_gamma_int (a + b + 1.) - log_gamma_int (a + 1.)
2062 + log_gamma_int (c + d + 1.) - log_gamma_int (b + 1.)
2063 + log_gamma_int (a + c + 1.) - log_gamma_int (c + 1.)
2064 + log_gamma_int (b + d + 1.) - log_gamma_int (d + 1.)
2065 - log_gamma_int (a + b + c + d + 1.));
2068 /* Swap the contents of A and B. */
2070 swap (int *a, int *b)
2077 /* Calculate significance for Fisher's exact test as specified in
2078 _SPSS Statistical Algorithms_, Appendix 5. */
2080 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2085 if (MIN (c, d) < MIN (a, b))
2086 swap (&a, &c), swap (&b, &d);
2087 if (MIN (b, d) < MIN (a, c))
2088 swap (&a, &b), swap (&c, &d);
2092 swap (&a, &b), swap (&c, &d);
2094 swap (&a, &c), swap (&b, &d);
2097 pn1 = Pr (a, b, c, d);
2099 for (xt = 1; xt <= a; xt++)
2101 *fisher1 += Pr (a - xt, b + xt, c + xt, d - xt);
2104 *fisher2 = *fisher1;
2106 for (xt = 1; xt <= b; xt++)
2108 double p = Pr (a + xt, b - xt, c - xt, d + xt);
2114 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2115 columns with values COLS and N_ROWS rows with values ROWS. Values
2116 in the matrix sum to xt->total. */
2118 calc_chisq (struct crosstabulation *xt,
2119 double chisq[N_CHISQ], int df[N_CHISQ],
2120 double *fisher1, double *fisher2)
2122 chisq[0] = chisq[1] = 0.;
2123 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2124 *fisher1 = *fisher2 = SYSMIS;
2126 df[0] = df[1] = (xt->ns_cols - 1) * (xt->ns_rows - 1);
2128 if (xt->ns_rows <= 1 || xt->ns_cols <= 1)
2130 chisq[0] = chisq[1] = SYSMIS;
2134 size_t n_cols = xt->vars[COL_VAR].n_values;
2135 FOR_EACH_POPULATED_ROW (r, xt)
2136 FOR_EACH_POPULATED_COLUMN (c, xt)
2138 const double expected = xt->row_tot[r] * xt->col_tot[c] / xt->total;
2139 const double freq = xt->mat[n_cols * r + c];
2140 const double residual = freq - expected;
2142 chisq[0] += residual * residual / expected;
2144 chisq[1] += freq * log (expected / freq);
2155 /* Calculate Yates and Fisher exact test. */
2156 if (xt->ns_cols == 2 && xt->ns_rows == 2)
2158 double f11, f12, f21, f22;
2164 FOR_EACH_POPULATED_COLUMN (c, xt)
2172 f11 = xt->mat[nz_cols[0]];
2173 f12 = xt->mat[nz_cols[1]];
2174 f21 = xt->mat[nz_cols[0] + n_cols];
2175 f22 = xt->mat[nz_cols[1] + n_cols];
2180 const double xt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * xt->total;
2183 chisq[3] = (xt->total * pow2 (xt_)
2184 / (f11 + f12) / (f21 + f22)
2185 / (f11 + f21) / (f12 + f22));
2193 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2196 /* Calculate Mantel-Haenszel. */
2197 if (var_is_numeric (xt->vars[ROW_VAR].var)
2198 && var_is_numeric (xt->vars[COL_VAR].var))
2200 double r, ase_0, ase_1;
2201 calc_r (xt, (double *) xt->vars[ROW_VAR].values,
2202 (double *) xt->vars[COL_VAR].values,
2203 &r, &ase_0, &ase_1);
2205 chisq[4] = (xt->total - 1.) * r * r;
2210 /* Calculate the value of Pearson's r. r is stored into R, its T value into
2211 T, and standard error into ERROR. The row and column values must be
2212 passed in XT and Y. */
2214 calc_r (struct crosstabulation *xt,
2215 double *XT, double *Y, double *r, double *t, double *error)
2217 size_t n_rows = xt->vars[ROW_VAR].n_values;
2218 size_t n_cols = xt->vars[COL_VAR].n_values;
2219 double SX, SY, S, T;
2221 double sum_XYf, sum_X2Y2f;
2222 double sum_Xr, sum_X2r;
2223 double sum_Yc, sum_Y2c;
2226 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < n_rows; i++)
2227 for (j = 0; j < n_cols; j++)
2229 double fij = xt->mat[j + i * n_cols];
2230 double product = XT[i] * Y[j];
2231 double temp = fij * product;
2233 sum_X2Y2f += temp * product;
2236 for (sum_Xr = sum_X2r = 0., i = 0; i < n_rows; i++)
2238 sum_Xr += XT[i] * xt->row_tot[i];
2239 sum_X2r += pow2 (XT[i]) * xt->row_tot[i];
2241 Xbar = sum_Xr / xt->total;
2243 for (sum_Yc = sum_Y2c = 0., i = 0; i < n_cols; i++)
2245 sum_Yc += Y[i] * xt->col_tot[i];
2246 sum_Y2c += Y[i] * Y[i] * xt->col_tot[i];
2248 Ybar = sum_Yc / xt->total;
2250 S = sum_XYf - sum_Xr * sum_Yc / xt->total;
2251 SX = sum_X2r - pow2 (sum_Xr) / xt->total;
2252 SY = sum_Y2c - pow2 (sum_Yc) / xt->total;
2255 *t = *r / sqrt (1 - pow2 (*r)) * sqrt (xt->total - 2);
2260 for (s = c = 0., i = 0; i < n_rows; i++)
2261 for (j = 0; j < n_cols; j++)
2263 double Xresid, Yresid;
2266 Xresid = XT[i] - Xbar;
2267 Yresid = Y[j] - Ybar;
2268 temp = (T * Xresid * Yresid
2270 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2271 y = xt->mat[j + i * n_cols] * temp * temp - c;
2276 *error = sqrt (s) / (T * T);
2280 /* Calculate symmetric statistics and their asymptotic standard
2281 errors. Returns 0 if none could be calculated. */
2283 calc_symmetric (struct crosstabs_proc *proc, struct crosstabulation *xt,
2284 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2285 double t[N_SYMMETRIC],
2286 double somers_d_v[3], double somers_d_ase[3],
2287 double somers_d_t[3])
2289 size_t n_rows = xt->vars[ROW_VAR].n_values;
2290 size_t n_cols = xt->vars[COL_VAR].n_values;
2293 q = MIN (xt->ns_rows, xt->ns_cols);
2297 for (i = 0; i < N_SYMMETRIC; i++)
2298 v[i] = ase[i] = t[i] = SYSMIS;
2300 /* Phi, Cramer's V, contingency coefficient. */
2301 if (proc->statistics & (CRS_ST_PHI | CRS_ST_CC))
2303 double Xp = 0.; /* Pearson chi-square. */
2305 FOR_EACH_POPULATED_ROW (r, xt)
2306 FOR_EACH_POPULATED_COLUMN (c, xt)
2308 double expected = xt->row_tot[r] * xt->col_tot[c] / xt->total;
2309 double freq = xt->mat[n_cols * r + c];
2310 double residual = freq - expected;
2312 Xp += residual * residual / expected;
2315 if (proc->statistics & CRS_ST_PHI)
2317 v[0] = sqrt (Xp / xt->total);
2318 v[1] = sqrt (Xp / (xt->total * (q - 1)));
2320 if (proc->statistics & CRS_ST_CC)
2321 v[2] = sqrt (Xp / (Xp + xt->total));
2324 if (proc->statistics & (CRS_ST_BTAU | CRS_ST_CTAU
2325 | CRS_ST_GAMMA | CRS_ST_D))
2330 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2334 Dr = Dc = pow2 (xt->total);
2335 for (r = 0; r < n_rows; r++)
2336 Dr -= pow2 (xt->row_tot[r]);
2337 for (c = 0; c < n_cols; c++)
2338 Dc -= pow2 (xt->col_tot[c]);
2340 cum = xnmalloc (n_cols * n_rows, sizeof *cum);
2341 for (c = 0; c < n_cols; c++)
2345 for (r = 0; r < n_rows; r++)
2346 cum[c + r * n_cols] = ct += xt->mat[c + r * n_cols];
2355 for (i = 0; i < n_rows; i++)
2359 for (j = 1; j < n_cols; j++)
2360 Cij += xt->col_tot[j] - cum[j + i * n_cols];
2363 for (j = 1; j < n_cols; j++)
2364 Dij += cum[j + (i - 1) * n_cols];
2368 double fij = xt->mat[j + i * n_cols];
2374 assert (j < n_cols);
2376 Cij -= xt->col_tot[j] - cum[j + i * n_cols];
2377 Dij += xt->col_tot[j - 1] - cum[j - 1 + i * n_cols];
2381 Cij += cum[j - 1 + (i - 1) * n_cols];
2382 Dij -= cum[j + (i - 1) * n_cols];
2388 if (proc->statistics & CRS_ST_BTAU)
2389 v[3] = (P - Q) / sqrt (Dr * Dc);
2390 if (proc->statistics & CRS_ST_CTAU)
2391 v[4] = (q * (P - Q)) / (pow2 (xt->total) * (q - 1));
2392 if (proc->statistics & CRS_ST_GAMMA)
2393 v[5] = (P - Q) / (P + Q);
2395 /* ASE for tau-b, tau-c, gamma. Calculations could be
2396 eliminated here, at expense of memory. */
2401 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2402 for (i = 0; i < n_rows; i++)
2406 for (j = 1; j < n_cols; j++)
2407 Cij += xt->col_tot[j] - cum[j + i * n_cols];
2410 for (j = 1; j < n_cols; j++)
2411 Dij += cum[j + (i - 1) * n_cols];
2415 double fij = xt->mat[j + i * n_cols];
2417 if (proc->statistics & CRS_ST_BTAU)
2419 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2420 + v[3] * (xt->row_tot[i] * Dc
2421 + xt->col_tot[j] * Dr));
2422 btau_cum += fij * temp * temp;
2426 const double temp = Cij - Dij;
2427 ctau_cum += fij * temp * temp;
2430 if (proc->statistics & CRS_ST_GAMMA)
2432 const double temp = Q * Cij - P * Dij;
2433 gamma_cum += fij * temp * temp;
2436 if (proc->statistics & CRS_ST_D)
2438 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2439 - (P - Q) * (xt->total - xt->row_tot[i]));
2440 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2441 - (Q - P) * (xt->total - xt->col_tot[j]));
2446 assert (j < n_cols);
2448 Cij -= xt->col_tot[j] - cum[j + i * n_cols];
2449 Dij += xt->col_tot[j - 1] - cum[j - 1 + i * n_cols];
2453 Cij += cum[j - 1 + (i - 1) * n_cols];
2454 Dij -= cum[j + (i - 1) * n_cols];
2460 btau_var = ((btau_cum
2461 - (xt->total * pow2 (xt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2463 if (proc->statistics & CRS_ST_BTAU)
2465 ase[3] = sqrt (btau_var);
2466 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / xt->total)
2469 if (proc->statistics & CRS_ST_CTAU)
2471 ase[4] = ((2 * q / ((q - 1) * pow2 (xt->total)))
2472 * sqrt (ctau_cum - (P - Q) * (P - Q) / xt->total));
2473 t[4] = v[4] / ase[4];
2475 if (proc->statistics & CRS_ST_GAMMA)
2477 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2478 t[5] = v[5] / (2. / (P + Q)
2479 * sqrt (ctau_cum - (P - Q) * (P - Q) / xt->total));
2481 if (proc->statistics & CRS_ST_D)
2483 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2484 somers_d_ase[0] = SYSMIS;
2485 somers_d_t[0] = (somers_d_v[0]
2487 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2488 somers_d_v[1] = (P - Q) / Dc;
2489 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2490 somers_d_t[1] = (somers_d_v[1]
2492 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2493 somers_d_v[2] = (P - Q) / Dr;
2494 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2495 somers_d_t[2] = (somers_d_v[2]
2497 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2503 /* Spearman correlation, Pearson's r. */
2504 if (proc->statistics & CRS_ST_CORR)
2506 double *R = xmalloc (sizeof *R * n_rows);
2507 double *C = xmalloc (sizeof *C * n_cols);
2510 double y, t, c = 0., s = 0.;
2515 R[i] = s + (xt->row_tot[i] + 1.) / 2.;
2516 y = xt->row_tot[i] - c;
2522 assert (i < n_rows);
2527 double y, t, c = 0., s = 0.;
2532 C[j] = s + (xt->col_tot[j] + 1.) / 2;
2533 y = xt->col_tot[j] - c;
2539 assert (j < n_cols);
2543 calc_r (xt, R, C, &v[6], &t[6], &ase[6]);
2548 calc_r (xt, (double *) xt->vars[ROW_VAR].values,
2549 (double *) xt->vars[COL_VAR].values,
2550 &v[7], &t[7], &ase[7]);
2553 /* Cohen's kappa. */
2554 if (proc->statistics & CRS_ST_KAPPA && xt->ns_rows == xt->ns_cols)
2556 double ase_under_h0;
2557 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2560 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2561 i < xt->ns_rows; i++, j++)
2565 while (xt->col_tot[j] == 0.)
2568 prod = xt->row_tot[i] * xt->col_tot[j];
2569 sum = xt->row_tot[i] + xt->col_tot[j];
2571 sum_fii += xt->mat[j + i * n_cols];
2573 sum_fiiri_ci += xt->mat[j + i * n_cols] * sum;
2574 sum_riciri_ci += prod * sum;
2576 for (sum_fijri_ci2 = 0., i = 0; i < xt->ns_rows; i++)
2577 for (j = 0; j < xt->ns_cols; j++)
2579 double sum = xt->row_tot[i] + xt->col_tot[j];
2580 sum_fijri_ci2 += xt->mat[j + i * n_cols] * sum * sum;
2583 v[8] = (xt->total * sum_fii - sum_rici) / (pow2 (xt->total) - sum_rici);
2585 ase_under_h0 = sqrt ((pow2 (xt->total) * sum_rici
2586 + sum_rici * sum_rici
2587 - xt->total * sum_riciri_ci)
2588 / (xt->total * (pow2 (xt->total) - sum_rici) * (pow2 (xt->total) - sum_rici)));
2590 ase[8] = sqrt (xt->total * (((sum_fii * (xt->total - sum_fii))
2591 / pow2 (pow2 (xt->total) - sum_rici))
2592 + ((2. * (xt->total - sum_fii)
2593 * (2. * sum_fii * sum_rici
2594 - xt->total * sum_fiiri_ci))
2595 / pow3 (pow2 (xt->total) - sum_rici))
2596 + (pow2 (xt->total - sum_fii)
2597 * (xt->total * sum_fijri_ci2 - 4.
2598 * sum_rici * sum_rici)
2599 / pow4 (pow2 (xt->total) - sum_rici))));
2601 t[8] = v[8] / ase_under_h0;
2607 /* Calculate risk estimate. */
2609 calc_risk (struct crosstabulation *xt,
2610 double *value, double *upper, double *lower, union value *c,
2613 size_t n_cols = xt->vars[COL_VAR].n_values;
2614 double f11, f12, f21, f22;
2617 for (int i = 0; i < 3; i++)
2618 value[i] = upper[i] = lower[i] = SYSMIS;
2620 if (xt->ns_rows != 2 || xt->ns_cols != 2)
2624 /* Find populated columns. */
2627 FOR_EACH_POPULATED_COLUMN (c, xt)
2631 /* Find populated rows. */
2634 FOR_EACH_POPULATED_ROW (r, xt)
2638 f11 = xt->mat[nz_cols[0] + n_cols * nz_rows[0]];
2639 f12 = xt->mat[nz_cols[1] + n_cols * nz_rows[0]];
2640 f21 = xt->mat[nz_cols[0] + n_cols * nz_rows[1]];
2641 f22 = xt->mat[nz_cols[1] + n_cols * nz_rows[1]];
2642 *n_valid = f11 + f12 + f21 + f22;
2644 c[0] = xt->vars[COL_VAR].values[nz_cols[0]];
2645 c[1] = xt->vars[COL_VAR].values[nz_cols[1]];
2648 value[0] = (f11 * f22) / (f12 * f21);
2649 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2650 lower[0] = value[0] * exp (-1.960 * v);
2651 upper[0] = value[0] * exp (1.960 * v);
2653 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2654 v = sqrt ((f12 / (f11 * (f11 + f12)))
2655 + (f22 / (f21 * (f21 + f22))));
2656 lower[1] = value[1] * exp (-1.960 * v);
2657 upper[1] = value[1] * exp (1.960 * v);
2659 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2660 v = sqrt ((f11 / (f12 * (f11 + f12)))
2661 + (f21 / (f22 * (f21 + f22))));
2662 lower[2] = value[2] * exp (-1.960 * v);
2663 upper[2] = value[2] * exp (1.960 * v);
2668 /* Calculate directional measures. */
2670 calc_directional (struct crosstabs_proc *proc, struct crosstabulation *xt,
2671 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2672 double t[N_DIRECTIONAL], double sig[N_DIRECTIONAL])
2674 size_t n_rows = xt->vars[ROW_VAR].n_values;
2675 size_t n_cols = xt->vars[COL_VAR].n_values;
2676 for (int i = 0; i < N_DIRECTIONAL; i++)
2677 v[i] = ase[i] = t[i] = sig[i] = SYSMIS;
2680 if (proc->statistics & CRS_ST_LAMBDA)
2682 /* Find maximum for each row and their sum. */
2683 double *fim = xnmalloc (n_rows, sizeof *fim);
2684 int *fim_index = xnmalloc (n_rows, sizeof *fim_index);
2685 double sum_fim = 0.0;
2686 for (int i = 0; i < n_rows; i++)
2688 double max = xt->mat[i * n_cols];
2691 for (int j = 1; j < n_cols; j++)
2692 if (xt->mat[j + i * n_cols] > max)
2694 max = xt->mat[j + i * n_cols];
2700 fim_index[i] = index;
2703 /* Find maximum for each column. */
2704 double *fmj = xnmalloc (n_cols, sizeof *fmj);
2705 int *fmj_index = xnmalloc (n_cols, sizeof *fmj_index);
2706 double sum_fmj = 0.0;
2707 for (int j = 0; j < n_cols; j++)
2709 double max = xt->mat[j];
2712 for (int i = 1; i < n_rows; i++)
2713 if (xt->mat[j + i * n_cols] > max)
2715 max = xt->mat[j + i * n_cols];
2721 fmj_index[j] = index;
2724 /* Find maximum row total. */
2725 double rm = xt->row_tot[0];
2727 for (int i = 1; i < n_rows; i++)
2728 if (xt->row_tot[i] > rm)
2730 rm = xt->row_tot[i];
2734 /* Find maximum column total. */
2735 double cm = xt->col_tot[0];
2737 for (int j = 1; j < n_cols; j++)
2738 if (xt->col_tot[j] > cm)
2740 cm = xt->col_tot[j];
2744 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * xt->total - rm - cm);
2745 v[1] = (sum_fmj - rm) / (xt->total - rm);
2746 v[2] = (sum_fim - cm) / (xt->total - cm);
2748 /* ASE1 for Y given XT. */
2751 for (int i = 0; i < n_rows; i++)
2752 if (cm_index == fim_index[i])
2754 ase[2] = sqrt ((xt->total - sum_fim) * (sum_fim + cm - 2. * accum)
2755 / pow3 (xt->total - cm));
2758 /* ASE0 for Y given XT. */
2761 for (int i = 0; i < n_rows; i++)
2762 if (cm_index != fim_index[i])
2763 accum += (xt->mat[i * n_cols + fim_index[i]]
2764 + xt->mat[i * n_cols + cm_index]);
2765 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / xt->total) / (xt->total - cm));
2768 /* ASE1 for XT given Y. */
2771 for (int j = 0; j < n_cols; j++)
2772 if (rm_index == fmj_index[j])
2774 ase[1] = sqrt ((xt->total - sum_fmj) * (sum_fmj + rm - 2. * accum)
2775 / pow3 (xt->total - rm));
2778 /* ASE0 for XT given Y. */
2781 for (int j = 0; j < n_cols; j++)
2782 if (rm_index != fmj_index[j])
2783 accum += (xt->mat[j + n_cols * fmj_index[j]]
2784 + xt->mat[j + n_cols * rm_index]);
2785 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / xt->total) / (xt->total - rm));
2788 /* Symmetric ASE0 and ASE1. */
2790 double accum0 = 0.0;
2791 double accum1 = 0.0;
2792 for (int i = 0; i < n_rows; i++)
2793 for (int j = 0; j < n_cols; j++)
2795 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2796 int temp1 = (i == rm_index) + (j == cm_index);
2797 accum0 += xt->mat[j + i * n_cols] * pow2 (temp0 - temp1);
2798 accum1 += (xt->mat[j + i * n_cols]
2799 * pow2 (temp0 + (v[0] - 1.) * temp1));
2801 ase[0] = sqrt (accum1 - 4. * xt->total * v[0] * v[0]) / (2. * xt->total - rm - cm);
2802 t[0] = v[0] / (sqrt (accum0 - pow2 (sum_fim + sum_fmj - cm - rm) / xt->total)
2803 / (2. * xt->total - rm - cm));
2806 for (int i = 0; i < 3; i++)
2807 sig[i] = 2 * gsl_cdf_ugaussian_Q (t[i]);
2816 double sum_fij2_ri = 0.0;
2817 double sum_fij2_ci = 0.0;
2818 FOR_EACH_POPULATED_ROW (i, xt)
2819 FOR_EACH_POPULATED_COLUMN (j, xt)
2821 double temp = pow2 (xt->mat[j + i * n_cols]);
2822 sum_fij2_ri += temp / xt->row_tot[i];
2823 sum_fij2_ci += temp / xt->col_tot[j];
2826 double sum_ri2 = 0.0;
2827 for (int i = 0; i < n_rows; i++)
2828 sum_ri2 += pow2 (xt->row_tot[i]);
2830 double sum_cj2 = 0.0;
2831 for (int j = 0; j < n_cols; j++)
2832 sum_cj2 += pow2 (xt->col_tot[j]);
2834 v[3] = (xt->total * sum_fij2_ci - sum_ri2) / (pow2 (xt->total) - sum_ri2);
2835 v[4] = (xt->total * sum_fij2_ri - sum_cj2) / (pow2 (xt->total) - sum_cj2);
2839 if (proc->statistics & CRS_ST_UC)
2842 FOR_EACH_POPULATED_ROW (i, xt)
2843 UX -= xt->row_tot[i] / xt->total * log (xt->row_tot[i] / xt->total);
2846 FOR_EACH_POPULATED_COLUMN (j, xt)
2847 UY -= xt->col_tot[j] / xt->total * log (xt->col_tot[j] / xt->total);
2851 for (int i = 0; i < n_rows; i++)
2852 for (int j = 0; j < n_cols; j++)
2854 double entry = xt->mat[j + i * n_cols];
2859 P += entry * pow2 (log (xt->col_tot[j] * xt->row_tot[i] / (xt->total * entry)));
2860 UXY -= entry / xt->total * log (entry / xt->total);
2863 double ase1_yx = 0.0;
2864 double ase1_xy = 0.0;
2865 double ase1_sym = 0.0;
2866 for (int i = 0; i < n_rows; i++)
2867 for (int j = 0; j < n_cols; j++)
2869 double entry = xt->mat[j + i * n_cols];
2874 ase1_yx += entry * pow2 (UY * log (entry / xt->row_tot[i])
2875 + (UX - UXY) * log (xt->col_tot[j] / xt->total));
2876 ase1_xy += entry * pow2 (UX * log (entry / xt->col_tot[j])
2877 + (UY - UXY) * log (xt->row_tot[i] / xt->total));
2878 ase1_sym += entry * pow2 ((UXY
2879 * log (xt->row_tot[i] * xt->col_tot[j] / pow2 (xt->total)))
2880 - (UX + UY) * log (entry / xt->total));
2883 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2884 ase[5] = (2. / (xt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2887 v[6] = (UX + UY - UXY) / UX;
2888 ase[6] = sqrt (ase1_xy) / (xt->total * UX * UX);
2889 t[6] = v[6] / (sqrt (P - xt->total * pow2 (UX + UY - UXY)) / (xt->total * UX));
2891 v[7] = (UX + UY - UXY) / UY;
2892 ase[7] = sqrt (ase1_yx) / (xt->total * UY * UY);
2893 t[7] = v[7] / (sqrt (P - xt->total * pow2 (UX + UY - UXY)) / (xt->total * UY));
2897 if (proc->statistics & CRS_ST_D)
2899 double v_dummy[N_SYMMETRIC];
2900 double ase_dummy[N_SYMMETRIC];
2901 double t_dummy[N_SYMMETRIC];
2902 double somers_d_v[3];
2903 double somers_d_ase[3];
2904 double somers_d_t[3];
2906 if (calc_symmetric (proc, xt, v_dummy, ase_dummy, t_dummy,
2907 somers_d_v, somers_d_ase, somers_d_t))
2909 for (int i = 0; i < 3; i++)
2911 v[8 + i] = somers_d_v[i];
2912 ase[8 + i] = somers_d_ase[i];
2913 t[8 + i] = somers_d_t[i];
2914 sig[8 + i] = 2 * gsl_cdf_ugaussian_Q (fabs (somers_d_t[i]));
2920 if (proc->statistics & CRS_ST_ETA)
2923 double sum_Xr = 0.0;
2924 double sum_X2r = 0.0;
2925 for (int i = 0; i < n_rows; i++)
2927 sum_Xr += xt->vars[ROW_VAR].values[i].f * xt->row_tot[i];
2928 sum_X2r += pow2 (xt->vars[ROW_VAR].values[i].f) * xt->row_tot[i];
2930 double SX = sum_X2r - pow2 (sum_Xr) / xt->total;
2933 FOR_EACH_POPULATED_COLUMN (j, xt)
2937 for (int i = 0; i < n_rows; i++)
2939 SXW += (pow2 (xt->vars[ROW_VAR].values[i].f)
2940 * xt->mat[j + i * n_cols]);
2941 cum += (xt->vars[ROW_VAR].values[i].f
2942 * xt->mat[j + i * n_cols]);
2945 SXW -= cum * cum / xt->col_tot[j];
2947 v[11] = sqrt (1. - SXW / SX);
2950 double sum_Yc = 0.0;
2951 double sum_Y2c = 0.0;
2952 for (int i = 0; i < n_cols; i++)
2954 sum_Yc += xt->vars[COL_VAR].values[i].f * xt->col_tot[i];
2955 sum_Y2c += pow2 (xt->vars[COL_VAR].values[i].f) * xt->col_tot[i];
2957 double SY = sum_Y2c - pow2 (sum_Yc) / xt->total;
2960 FOR_EACH_POPULATED_ROW (i, xt)
2963 for (int j = 0; j < n_cols; j++)
2965 SYW += (pow2 (xt->vars[COL_VAR].values[j].f)
2966 * xt->mat[j + i * n_cols]);
2967 cum += (xt->vars[COL_VAR].values[j].f
2968 * xt->mat[j + i * n_cols]);
2971 SYW -= cum * cum / xt->row_tot[i];
2973 v[12] = sqrt (1. - SYW / SY);