1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2006, 2009, 2010, 2011, 2012, 2013, 2014, 2016 Free Software Foundation, Inc.
4 This program is free software: you can redistribute it and/or modify
5 it under the terms of the GNU General Public License as published by
6 the Free Software Foundation, either version 3 of the License, or
7 (at your option) any later version.
9 This program is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 GNU General Public License for more details.
14 You should have received a copy of the GNU General Public License
15 along with this program. If not, see <http://www.gnu.org/licenses/>. */
19 - How to calculate significance of some symmetric and directional measures?
20 - How to calculate ASE for symmetric Somers ' d?
21 - How to calculate ASE for Goodman and Kruskal's tau?
22 - How to calculate approx. T of symmetric uncertainty coefficient?
30 #include <gsl/gsl_cdf.h>
34 #include "data/case.h"
35 #include "data/casegrouper.h"
36 #include "data/casereader.h"
37 #include "data/data-out.h"
38 #include "data/dataset.h"
39 #include "data/dictionary.h"
40 #include "data/format.h"
41 #include "data/value-labels.h"
42 #include "data/variable.h"
43 #include "language/command.h"
44 #include "language/stats/freq.h"
45 #include "language/dictionary/split-file.h"
46 #include "language/lexer/lexer.h"
47 #include "language/lexer/variable-parser.h"
48 #include "libpspp/array.h"
49 #include "libpspp/assertion.h"
50 #include "libpspp/compiler.h"
51 #include "libpspp/hash-functions.h"
52 #include "libpspp/hmap.h"
53 #include "libpspp/hmapx.h"
54 #include "libpspp/message.h"
55 #include "libpspp/misc.h"
56 #include "libpspp/pool.h"
57 #include "libpspp/str.h"
58 #include "output/pivot-table.h"
59 #include "output/charts/barchart.h"
61 #include "gl/minmax.h"
62 #include "gl/xalloc-oversized.h"
63 #include "gl/xalloc.h"
67 #define _(msgid) gettext (msgid)
68 #define N_(msgid) msgid
70 /* Kinds of cells in the crosstabulation. */
72 C(COUNT, N_("Count"), PIVOT_RC_COUNT) \
73 C(EXPECTED, N_("Expected"), PIVOT_RC_OTHER) \
74 C(ROW, N_("Row %"), PIVOT_RC_PERCENT) \
75 C(COLUMN, N_("Column %"), PIVOT_RC_PERCENT) \
76 C(TOTAL, N_("Total %"), PIVOT_RC_PERCENT) \
77 C(RESIDUAL, N_("Residual"), PIVOT_RC_RESIDUAL) \
78 C(SRESIDUAL, N_("Std. Residual"), PIVOT_RC_RESIDUAL) \
79 C(ASRESIDUAL, N_("Adjusted Residual"), PIVOT_RC_RESIDUAL)
82 #define C(KEYWORD, STRING, RC) CRS_CL_##KEYWORD,
87 #define C(KEYWORD, STRING, RC) + 1
88 CRS_N_CELLS = CRS_CELLS
91 #define CRS_ALL_CELLS ((1u << CRS_N_CELLS) - 1)
93 /* Kinds of statistics. */
94 #define CRS_STATISTICS \
108 enum crs_statistic_index {
109 #define S(KEYWORD) CRS_ST_##KEYWORD##_INDEX,
113 enum crs_statistic_bit {
114 #define S(KEYWORD) CRS_ST_##KEYWORD = 1u << CRS_ST_##KEYWORD##_INDEX,
119 #define S(KEYWORD) + 1
120 CRS_N_STATISTICS = CRS_STATISTICS
123 #define CRS_ALL_STATISTICS ((1u << CRS_N_STATISTICS) - 1)
125 /* Number of chi-square statistics. */
128 /* Number of symmetric statistics. */
129 #define N_SYMMETRIC 9
131 /* Number of directional statistics. */
132 #define N_DIRECTIONAL 13
134 /* Indexes into the 'vars' member of struct crosstabulation and
135 struct crosstab member. */
138 ROW_VAR = 0, /* Row variable. */
139 COL_VAR = 1 /* Column variable. */
140 /* Higher indexes cause multiple tables to be output. */
145 const struct variable *var;
150 /* A crosstabulation of 2 or more variables. */
151 struct crosstabulation
153 struct crosstabs_proc *proc;
154 struct fmt_spec weight_format; /* Format for weight variable. */
155 double missing; /* Weight of missing cases. */
157 /* Variables (2 or more). */
159 struct xtab_var *vars;
161 /* Constants (0 or more). */
163 struct xtab_var *const_vars;
164 size_t *const_indexes;
168 struct freq **entries;
171 /* Number of statistically interesting columns/rows
172 (columns/rows with data in them). */
173 int ns_cols, ns_rows;
175 /* Matrix contents. */
176 double *mat; /* Matrix proper. */
177 double *row_tot; /* Row totals. */
178 double *col_tot; /* Column totals. */
179 double total; /* Grand total. */
182 /* Integer mode variable info. */
185 struct hmap_node hmap_node; /* In struct crosstabs_proc var_ranges map. */
186 const struct variable *var; /* The variable. */
187 int min; /* Minimum value. */
188 int max; /* Maximum value + 1. */
189 int count; /* max - min. */
192 struct crosstabs_proc
194 const struct dictionary *dict;
195 enum { INTEGER, GENERAL } mode;
196 enum mv_class exclude;
199 struct fmt_spec weight_format;
201 /* Variables specifies on VARIABLES. */
202 const struct variable **variables;
204 struct hmap var_ranges;
207 struct crosstabulation *pivots;
211 int n_cells; /* Number of cells requested. */
212 unsigned int cells; /* Bit k is 1 if cell k is requested. */
213 int a_cells[CRS_N_CELLS]; /* 0...n_cells-1 are the requested cells. */
215 /* Rounding of cells. */
216 bool round_case_weights; /* Round case weights? */
217 bool round_cells; /* If !round_case_weights, round cells? */
218 bool round_down; /* Round down? (otherwise to nearest) */
221 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
223 bool descending; /* True if descending sort order is requested. */
226 static bool parse_crosstabs_tables (struct lexer *, struct dataset *,
227 struct crosstabs_proc *);
228 static bool parse_crosstabs_variables (struct lexer *, struct dataset *,
229 struct crosstabs_proc *);
231 static const struct var_range *get_var_range (const struct crosstabs_proc *,
232 const struct variable *);
234 static bool should_tabulate_case (const struct crosstabulation *,
235 const struct ccase *, enum mv_class exclude);
236 static void tabulate_general_case (struct crosstabulation *, const struct ccase *,
238 static void tabulate_integer_case (struct crosstabulation *, const struct ccase *,
240 static void postcalc (struct crosstabs_proc *);
243 round_weight (const struct crosstabs_proc *proc, double weight)
245 return proc->round_down ? floor (weight) : floor (weight + 0.5);
248 #define FOR_EACH_POPULATED_COLUMN(C, XT) \
249 for (int C = next_populated_column (0, XT); \
250 C < (XT)->vars[COL_VAR].n_values; \
251 C = next_populated_column (C + 1, XT))
253 next_populated_column (int c, const struct crosstabulation *xt)
255 int n_columns = xt->vars[COL_VAR].n_values;
256 for (; c < n_columns; c++)
262 #define FOR_EACH_POPULATED_ROW(R, XT) \
263 for (int R = next_populated_row (0, XT); R < (XT)->vars[ROW_VAR].n_values; \
264 R = next_populated_row (R + 1, XT))
266 next_populated_row (int r, const struct crosstabulation *xt)
268 int n_rows = xt->vars[ROW_VAR].n_values;
269 for (; r < n_rows; r++)
275 /* Parses and executes the CROSSTABS procedure. */
277 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
279 int result = CMD_FAILURE;
281 struct crosstabs_proc proc = {
282 .dict = dataset_dict (ds),
287 .weight_format = *dict_get_weight_format (dataset_dict (ds)),
291 .var_ranges = HMAP_INITIALIZER (proc.var_ranges),
296 .cells = 1u << CRS_CL_COUNT,
297 /* n_cells and a_cells will be filled in later. */
299 .round_case_weights = false,
300 .round_cells = false,
307 bool show_tables = true;
309 lex_match (lexer, T_SLASH);
312 if (lex_match_id (lexer, "VARIABLES"))
314 if (!parse_crosstabs_variables (lexer, ds, &proc))
317 else if (lex_match_id (lexer, "MISSING"))
319 lex_match (lexer, T_EQUALS);
320 exclude_ofs = lex_ofs (lexer);
321 if (lex_match_id (lexer, "TABLE"))
322 proc.exclude = MV_ANY;
323 else if (lex_match_id (lexer, "INCLUDE"))
324 proc.exclude = MV_SYSTEM;
325 else if (lex_match_id (lexer, "REPORT"))
329 lex_error (lexer, NULL);
333 else if (lex_match_id (lexer, "COUNT"))
335 lex_match (lexer, T_EQUALS);
337 /* Default is CELL. */
338 proc.round_case_weights = false;
339 proc.round_cells = true;
341 while (lex_token (lexer) != T_SLASH && lex_token (lexer) != T_ENDCMD)
343 if (lex_match_id (lexer, "ASIS"))
345 proc.round_case_weights = false;
346 proc.round_cells = false;
348 else if (lex_match_id (lexer, "CASE"))
350 proc.round_case_weights = true;
351 proc.round_cells = false;
353 else if (lex_match_id (lexer, "CELL"))
355 proc.round_case_weights = false;
356 proc.round_cells = true;
358 else if (lex_match_id (lexer, "ROUND"))
359 proc.round_down = false;
360 else if (lex_match_id (lexer, "TRUNCATE"))
361 proc.round_down = true;
364 lex_error (lexer, NULL);
367 lex_match (lexer, T_COMMA);
370 else if (lex_match_id (lexer, "FORMAT"))
372 lex_match (lexer, T_EQUALS);
373 while (lex_token (lexer) != T_SLASH && lex_token (lexer) != T_ENDCMD)
375 if (lex_match_id (lexer, "AVALUE"))
376 proc.descending = false;
377 else if (lex_match_id (lexer, "DVALUE"))
378 proc.descending = true;
379 else if (lex_match_id (lexer, "TABLES"))
381 else if (lex_match_id (lexer, "NOTABLES"))
385 lex_error (lexer, NULL);
388 lex_match (lexer, T_COMMA);
391 else if (lex_match_id (lexer, "BARCHART"))
392 proc.barchart = true;
393 else if (lex_match_id (lexer, "CELLS"))
395 lex_match (lexer, T_EQUALS);
397 if (lex_match_id (lexer, "NONE"))
399 else if (lex_match (lexer, T_ALL))
400 proc.cells = CRS_ALL_CELLS;
404 while (lex_token (lexer) != T_SLASH && lex_token (lexer) != T_ENDCMD)
406 #define C(KEYWORD, STRING, RC) \
407 if (lex_match_id (lexer, #KEYWORD)) \
409 proc.cells |= 1u << CRS_CL_##KEYWORD; \
414 lex_error (lexer, NULL);
418 proc.cells = ((1u << CRS_CL_COUNT) | (1u << CRS_CL_ROW)
419 | (1u << CRS_CL_COLUMN) | (1u << CRS_CL_TOTAL));
422 else if (lex_match_id (lexer, "STATISTICS"))
424 lex_match (lexer, T_EQUALS);
426 if (lex_match_id (lexer, "NONE"))
428 else if (lex_match (lexer, T_ALL))
429 proc.statistics = CRS_ALL_STATISTICS;
433 while (lex_token (lexer) != T_SLASH && lex_token (lexer) != T_ENDCMD)
436 if (lex_match_id (lexer, #KEYWORD)) \
438 proc.statistics |= CRS_ST_##KEYWORD; \
443 lex_error (lexer, NULL);
446 if (!proc.statistics)
447 proc.statistics = CRS_ST_CHISQ;
450 else if (!parse_crosstabs_tables (lexer, ds, &proc))
453 if (!lex_match (lexer, T_SLASH))
456 if (!lex_end_of_command (lexer))
461 msg (SE, _("At least one crosstabulation must be requested (using "
462 "the TABLES subcommand)."));
469 for (int i = 0; i < CRS_N_CELLS; i++)
470 if (proc.cells & (1u << i))
471 proc.a_cells[proc.n_cells++] = i;
472 assert (proc.n_cells < CRS_N_CELLS);
474 /* Missing values. */
475 if (proc.mode == GENERAL && !proc.exclude)
477 lex_ofs_error (lexer, exclude_ofs, exclude_ofs,
478 _("Missing mode %s not allowed in general mode. "
479 "Assuming %s."), "REPORT", "MISSING=TABLE");
480 proc.exclude = MV_ANY;
483 struct casereader *input = casereader_create_filter_weight (proc_open (ds),
486 struct casegrouper *grouper = casegrouper_create_splits (input, dataset_dict (ds));
487 struct casereader *group;
488 while (casegrouper_get_next_group (grouper, &group))
492 /* Output SPLIT FILE variables. */
493 c = casereader_peek (group, 0);
496 output_split_file_values (ds, c);
500 /* Initialize hash tables. */
501 for (struct crosstabulation *xt = &proc.pivots[0];
502 xt < &proc.pivots[proc.n_pivots]; xt++)
503 hmap_init (&xt->data);
506 for (; (c = casereader_read (group)) != NULL; case_unref (c))
507 for (struct crosstabulation *xt = &proc.pivots[0];
508 xt < &proc.pivots[proc.n_pivots]; xt++)
510 double weight = dict_get_case_weight (dataset_dict (ds), c,
512 if (proc.round_case_weights)
514 weight = round_weight (&proc, weight);
518 if (should_tabulate_case (xt, c, proc.exclude))
520 if (proc.mode == GENERAL)
521 tabulate_general_case (xt, c, weight);
523 tabulate_integer_case (xt, c, weight);
526 xt->missing += weight;
528 casereader_destroy (group);
533 bool ok = casegrouper_destroy (grouper);
534 ok = proc_commit (ds) && ok;
536 result = ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
539 free (proc.variables);
541 struct var_range *range, *next_range;
542 HMAP_FOR_EACH_SAFE (range, next_range, struct var_range, hmap_node,
545 hmap_delete (&proc.var_ranges, &range->hmap_node);
548 for (struct crosstabulation *xt = &proc.pivots[0];
549 xt < &proc.pivots[proc.n_pivots]; xt++)
552 free (xt->const_vars);
553 free (xt->const_indexes);
560 /* Parses the TABLES subcommand. */
562 parse_crosstabs_tables (struct lexer *lexer, struct dataset *ds,
563 struct crosstabs_proc *proc)
565 const struct variable ***by = NULL;
566 size_t *by_nvar = NULL;
569 /* Ensure that this is a TABLES subcommand. */
570 if (!lex_match_id (lexer, "TABLES")
571 && (lex_token (lexer) != T_ID ||
572 dict_lookup_var (dataset_dict (ds), lex_tokcstr (lexer)) == NULL)
573 && lex_token (lexer) != T_ALL)
575 lex_error (lexer, NULL);
578 lex_match (lexer, T_EQUALS);
580 struct const_var_set *var_set
582 ? const_var_set_create_from_array (proc->variables,
584 : const_var_set_create_from_dict (dataset_dict (ds)));
590 by = xnrealloc (by, n_by + 1, sizeof *by);
591 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
592 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
593 PV_NO_DUPLICATE | PV_NO_SCRATCH))
595 if (xalloc_oversized (nx, by_nvar[n_by]))
597 msg (SE, _("Too many cross-tabulation variables or dimensions."));
603 if (!lex_match (lexer, T_BY))
612 int *by_iter = XCALLOC (n_by, int);
613 proc->pivots = xnrealloc (proc->pivots,
614 proc->n_pivots + nx, sizeof *proc->pivots);
615 for (int i = 0; i < nx; i++)
617 struct crosstabulation *xt = &proc->pivots[proc->n_pivots++];
619 *xt = (struct crosstabulation) {
621 .weight_format = proc->weight_format,
624 .vars = xcalloc (n_by, sizeof *xt->vars),
627 .const_indexes = NULL,
630 for (int j = 0; j < n_by; j++)
631 xt->vars[j].var = by[j][by_iter[j]];
633 for (int j = n_by - 1; j >= 0; j--)
635 if (++by_iter[j] < by_nvar[j])
644 /* All return paths lead here. */
645 for (int i = 0; i < n_by; i++)
650 const_var_set_destroy (var_set);
655 /* Parses the VARIABLES subcommand. */
657 parse_crosstabs_variables (struct lexer *lexer, struct dataset *ds,
658 struct crosstabs_proc *proc)
662 lex_next_error (lexer, -1, -1, _("%s must be specified before %s."),
663 "VARIABLES", "TABLES");
667 lex_match (lexer, T_EQUALS);
671 size_t orig_nv = proc->n_variables;
673 if (!parse_variables_const (lexer, dataset_dict (ds),
674 &proc->variables, &proc->n_variables,
675 (PV_APPEND | PV_NUMERIC
676 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
679 if (!lex_force_match (lexer, T_LPAREN))
682 if (!lex_force_int (lexer))
684 long min = lex_integer (lexer);
687 lex_match (lexer, T_COMMA);
689 if (!lex_force_int_range (lexer, NULL, min, LONG_MAX))
691 long max = lex_integer (lexer);
694 if (!lex_force_match (lexer, T_RPAREN))
697 for (size_t i = orig_nv; i < proc->n_variables; i++)
699 const struct variable *var = proc->variables[i];
700 struct var_range *vr = xmalloc (sizeof *vr);
705 vr->count = max - min + 1;
706 hmap_insert (&proc->var_ranges, &vr->hmap_node,
707 hash_pointer (var, 0));
710 if (lex_token (lexer) == T_SLASH)
714 proc->mode = INTEGER;
718 free (proc->variables);
719 proc->variables = NULL;
720 proc->n_variables = 0;
724 /* Data file processing. */
726 static const struct var_range *
727 get_var_range (const struct crosstabs_proc *proc, const struct variable *var)
729 if (!hmap_is_empty (&proc->var_ranges))
731 const struct var_range *range;
733 HMAP_FOR_EACH_IN_BUCKET (range, struct var_range, hmap_node,
734 hash_pointer (var, 0), &proc->var_ranges)
735 if (range->var == var)
743 should_tabulate_case (const struct crosstabulation *xt, const struct ccase *c,
744 enum mv_class exclude)
747 for (j = 0; j < xt->n_vars; j++)
749 const struct variable *var = xt->vars[j].var;
750 const struct var_range *range = get_var_range (xt->proc, var);
752 if (var_is_value_missing (var, case_data (c, var)) & exclude)
757 double num = case_num (c, var);
758 if (num < range->min || num >= range->max + 1.)
766 tabulate_integer_case (struct crosstabulation *xt, const struct ccase *c,
774 for (j = 0; j < xt->n_vars; j++)
776 /* Throw away fractional parts of values. */
777 hash = hash_int (case_num (c, xt->vars[j].var), hash);
780 HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &xt->data)
782 for (j = 0; j < xt->n_vars; j++)
783 if ((int) case_num (c, xt->vars[j].var) != (int) te->values[j].f)
786 /* Found an existing entry. */
793 /* No existing entry. Create a new one. */
794 te = xmalloc (table_entry_size (xt->n_vars));
796 for (j = 0; j < xt->n_vars; j++)
797 te->values[j].f = (int) case_num (c, xt->vars[j].var);
798 hmap_insert (&xt->data, &te->node, hash);
802 tabulate_general_case (struct crosstabulation *xt, const struct ccase *c,
810 for (j = 0; j < xt->n_vars; j++)
812 const struct variable *var = xt->vars[j].var;
813 hash = value_hash (case_data (c, var), var_get_width (var), hash);
816 HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &xt->data)
818 for (j = 0; j < xt->n_vars; j++)
820 const struct variable *var = xt->vars[j].var;
821 if (!value_equal (case_data (c, var), &te->values[j],
822 var_get_width (var)))
826 /* Found an existing entry. */
833 /* No existing entry. Create a new one. */
834 te = xmalloc (table_entry_size (xt->n_vars));
836 for (j = 0; j < xt->n_vars; j++)
838 const struct variable *var = xt->vars[j].var;
839 value_clone (&te->values[j], case_data (c, var), var_get_width (var));
841 hmap_insert (&xt->data, &te->node, hash);
844 /* Post-data reading calculations. */
846 static int compare_table_entry_vars_3way (const struct freq *a,
847 const struct freq *b,
848 const struct crosstabulation *xt,
850 static int compare_table_entry_3way (const void *ap_, const void *bp_,
852 static int compare_table_entry_3way_inv (const void *ap_, const void *bp_,
855 static void enum_var_values (const struct crosstabulation *, int var_idx,
857 static void free_var_values (const struct crosstabulation *, int var_idx);
858 static void output_crosstabulation (struct crosstabs_proc *,
859 struct crosstabulation *);
860 static void make_crosstabulation_subset (struct crosstabulation *xt,
861 size_t row0, size_t row1,
862 struct crosstabulation *subset);
863 static void make_summary_table (struct crosstabs_proc *);
864 static bool find_crosstab (struct crosstabulation *, size_t *row0p,
868 postcalc (struct crosstabs_proc *proc)
870 /* Round hash table entries, if requested
872 If this causes any of the cell counts to fall to zero, delete those
874 if (proc->round_cells)
875 for (struct crosstabulation *xt = proc->pivots;
876 xt < &proc->pivots[proc->n_pivots]; xt++)
878 struct freq *e, *next;
879 HMAP_FOR_EACH_SAFE (e, next, struct freq, node, &xt->data)
881 e->count = round_weight (proc, e->count);
884 hmap_delete (&xt->data, &e->node);
890 /* Convert hash tables into sorted arrays of entries. */
891 for (struct crosstabulation *xt = proc->pivots;
892 xt < &proc->pivots[proc->n_pivots]; xt++)
896 xt->n_entries = hmap_count (&xt->data);
897 xt->entries = xnmalloc (xt->n_entries, sizeof *xt->entries);
899 HMAP_FOR_EACH (e, struct freq, node, &xt->data)
900 xt->entries[i++] = e;
901 hmap_destroy (&xt->data);
903 sort (xt->entries, xt->n_entries, sizeof *xt->entries,
904 proc->descending ? compare_table_entry_3way_inv : compare_table_entry_3way,
909 make_summary_table (proc);
911 /* Output each pivot table. */
912 for (struct crosstabulation *xt = proc->pivots;
913 xt < &proc->pivots[proc->n_pivots]; xt++)
915 output_crosstabulation (proc, xt);
918 int n_vars = (xt->n_vars > 2 ? 2 : xt->n_vars);
919 const struct variable **vars = XCALLOC (n_vars, const struct variable*);
920 for (size_t i = 0; i < n_vars; i++)
921 vars[i] = xt->vars[i].var;
922 chart_submit (barchart_create (vars, n_vars, _("Count"),
924 xt->entries, xt->n_entries));
929 /* Free output and prepare for next split file. */
930 for (struct crosstabulation *xt = proc->pivots;
931 xt < &proc->pivots[proc->n_pivots]; xt++)
935 /* Free the members that were allocated in this function(and the values
936 owned by the entries.
938 The other pointer members are either both allocated and destroyed at a
939 lower level (in output_crosstabulation), or both allocated and
940 destroyed at a higher level (in crs_custom_tables and free_proc,
942 for (size_t i = 0; i < xt->n_vars; i++)
944 int width = var_get_width (xt->vars[i].var);
945 if (value_needs_init (width))
949 for (j = 0; j < xt->n_entries; j++)
950 value_destroy (&xt->entries[j]->values[i], width);
954 for (size_t i = 0; i < xt->n_entries; i++)
955 free (xt->entries[i]);
961 make_crosstabulation_subset (struct crosstabulation *xt, size_t row0,
962 size_t row1, struct crosstabulation *subset)
967 assert (xt->n_consts == 0);
969 subset->vars = xt->vars;
971 subset->n_consts = xt->n_vars - 2;
972 subset->const_vars = xt->vars + 2;
973 subset->const_indexes = xcalloc (subset->n_consts,
974 sizeof *subset->const_indexes);
975 for (size_t i = 0; i < subset->n_consts; i++)
977 const union value *value = &xt->entries[row0]->values[2 + i];
979 for (size_t j = 0; j < xt->vars[2 + i].n_values; j++)
980 if (value_equal (&xt->vars[2 + i].values[j], value,
981 var_get_width (xt->vars[2 + i].var)))
983 subset->const_indexes[i] = j;
990 subset->entries = &xt->entries[row0];
991 subset->n_entries = row1 - row0;
995 compare_table_entry_var_3way (const struct freq *a,
996 const struct freq *b,
997 const struct crosstabulation *xt,
1000 return value_compare_3way (&a->values[idx], &b->values[idx],
1001 var_get_width (xt->vars[idx].var));
1005 compare_table_entry_vars_3way (const struct freq *a,
1006 const struct freq *b,
1007 const struct crosstabulation *xt,
1012 for (i = idx1 - 1; i >= idx0; i--)
1014 int cmp = compare_table_entry_var_3way (a, b, xt, i);
1021 /* Compare the struct freq at *AP to the one at *BP and
1022 return a strcmp()-type result. */
1024 compare_table_entry_3way (const void *ap_, const void *bp_, const void *xt_)
1026 const struct freq *const *ap = ap_;
1027 const struct freq *const *bp = bp_;
1028 const struct freq *a = *ap;
1029 const struct freq *b = *bp;
1030 const struct crosstabulation *xt = xt_;
1033 cmp = compare_table_entry_vars_3way (a, b, xt, 2, xt->n_vars);
1037 cmp = compare_table_entry_var_3way (a, b, xt, ROW_VAR);
1041 return compare_table_entry_var_3way (a, b, xt, COL_VAR);
1044 /* Inverted version of compare_table_entry_3way */
1046 compare_table_entry_3way_inv (const void *ap_, const void *bp_, const void *xt_)
1048 return -compare_table_entry_3way (ap_, bp_, xt_);
1051 /* Output a table summarizing the cases processed. */
1053 make_summary_table (struct crosstabs_proc *proc)
1055 struct pivot_table *table = pivot_table_create (N_("Summary"));
1056 pivot_table_set_weight_var (table, dict_get_weight (proc->dict));
1058 pivot_dimension_create (table, PIVOT_AXIS_COLUMN, N_("Statistics"),
1059 N_("N"), PIVOT_RC_COUNT,
1060 N_("Percent"), PIVOT_RC_PERCENT);
1062 struct pivot_dimension *cases = pivot_dimension_create (
1063 table, PIVOT_AXIS_COLUMN, N_("Cases"),
1064 N_("Valid"), N_("Missing"), N_("Total"));
1065 cases->root->show_label = true;
1067 struct pivot_dimension *tables = pivot_dimension_create (
1068 table, PIVOT_AXIS_ROW, N_("Crosstabulation"));
1069 for (struct crosstabulation *xt = &proc->pivots[0];
1070 xt < &proc->pivots[proc->n_pivots]; xt++)
1072 struct string name = DS_EMPTY_INITIALIZER;
1073 for (size_t i = 0; i < xt->n_vars; i++)
1076 ds_put_cstr (&name, " × ");
1077 ds_put_cstr (&name, var_to_string (xt->vars[i].var));
1080 int row = pivot_category_create_leaf (
1082 pivot_value_new_user_text_nocopy (ds_steal_cstr (&name)));
1085 for (size_t i = 0; i < xt->n_entries; i++)
1086 valid += xt->entries[i]->count;
1092 for (int i = 0; i < 3; i++)
1094 pivot_table_put3 (table, 0, i, row, pivot_value_new_number (n[i]));
1095 pivot_table_put3 (table, 1, i, row,
1096 pivot_value_new_number (n[i] / n[2] * 100.0));
1100 pivot_table_submit (table);
1105 static struct pivot_table *create_crosstab_table (
1106 struct crosstabs_proc *, struct crosstabulation *,
1107 size_t crs_leaves[CRS_N_CELLS]);
1108 static struct pivot_table *create_chisq_table (struct crosstabulation *);
1109 static struct pivot_table *create_sym_table (struct crosstabulation *);
1110 static struct pivot_table *create_risk_table (
1111 struct crosstabulation *, struct pivot_dimension **risk_statistics);
1112 static struct pivot_table *create_direct_table (struct crosstabulation *);
1113 static void display_crosstabulation (struct crosstabs_proc *,
1114 struct crosstabulation *,
1115 struct pivot_table *,
1116 size_t crs_leaves[CRS_N_CELLS]);
1117 static void display_chisq (struct crosstabulation *, struct pivot_table *);
1118 static void display_symmetric (struct crosstabs_proc *,
1119 struct crosstabulation *, struct pivot_table *);
1120 static void display_risk (struct crosstabulation *, struct pivot_table *,
1121 struct pivot_dimension *risk_statistics);
1122 static void display_directional (struct crosstabs_proc *,
1123 struct crosstabulation *,
1124 struct pivot_table *);
1125 static void delete_missing (struct crosstabulation *);
1126 static void build_matrix (struct crosstabulation *);
1128 /* Output pivot table XT in the context of PROC. */
1130 output_crosstabulation (struct crosstabs_proc *proc, struct crosstabulation *xt)
1132 for (size_t i = 0; i < xt->n_vars; i++)
1133 enum_var_values (xt, i, proc->descending);
1135 if (xt->vars[COL_VAR].n_values == 0)
1140 ds_init_cstr (&vars, var_to_string (xt->vars[0].var));
1141 for (i = 1; i < xt->n_vars; i++)
1142 ds_put_format (&vars, " × %s", var_to_string (xt->vars[i].var));
1144 /* TRANSLATORS: The %s here describes a crosstabulation. It takes the
1145 form "var1 * var2 * var3 * ...". */
1146 msg (SW, _("Crosstabulation %s contained no non-missing cases."),
1150 for (size_t i = 0; i < xt->n_vars; i++)
1151 free_var_values (xt, i);
1155 size_t crs_leaves[CRS_N_CELLS];
1156 struct pivot_table *table = (proc->cells
1157 ? create_crosstab_table (proc, xt, crs_leaves)
1159 struct pivot_table *chisq = (proc->statistics & CRS_ST_CHISQ
1160 ? create_chisq_table (xt)
1162 struct pivot_table *sym
1163 = (proc->statistics & (CRS_ST_PHI | CRS_ST_CC | CRS_ST_BTAU | CRS_ST_CTAU
1164 | CRS_ST_GAMMA | CRS_ST_CORR | CRS_ST_KAPPA)
1165 ? create_sym_table (xt)
1167 struct pivot_dimension *risk_statistics = NULL;
1168 struct pivot_table *risk = (proc->statistics & CRS_ST_RISK
1169 ? create_risk_table (xt, &risk_statistics)
1171 struct pivot_table *direct
1172 = (proc->statistics & (CRS_ST_LAMBDA | CRS_ST_UC | CRS_ST_D | CRS_ST_ETA)
1173 ? create_direct_table (xt)
1178 while (find_crosstab (xt, &row0, &row1))
1180 struct crosstabulation x;
1182 make_crosstabulation_subset (xt, row0, row1, &x);
1184 size_t n_rows = x.vars[ROW_VAR].n_values;
1185 size_t n_cols = x.vars[COL_VAR].n_values;
1186 if (size_overflow_p (xtimes (xtimes (n_rows, n_cols), sizeof (double))))
1188 x.row_tot = xmalloc (n_rows * sizeof *x.row_tot);
1189 x.col_tot = xmalloc (n_cols * sizeof *x.col_tot);
1190 x.mat = xmalloc (n_rows * n_cols * sizeof *x.mat);
1194 /* Find the first variable that differs from the last subtable. */
1196 display_crosstabulation (proc, &x, table, crs_leaves);
1198 if (proc->exclude == 0)
1199 delete_missing (&x);
1202 display_chisq (&x, chisq);
1205 display_symmetric (proc, &x, sym);
1207 display_risk (&x, risk, risk_statistics);
1209 display_directional (proc, &x, direct);
1214 free (x.const_indexes);
1218 pivot_table_submit (table);
1221 pivot_table_submit (chisq);
1224 pivot_table_submit (sym);
1228 if (!pivot_table_is_empty (risk))
1229 pivot_table_submit (risk);
1231 pivot_table_unref (risk);
1235 pivot_table_submit (direct);
1237 for (size_t i = 0; i < xt->n_vars; i++)
1238 free_var_values (xt, i);
1242 build_matrix (struct crosstabulation *x)
1244 const int col_var_width = var_get_width (x->vars[COL_VAR].var);
1245 const int row_var_width = var_get_width (x->vars[ROW_VAR].var);
1246 size_t n_rows = x->vars[ROW_VAR].n_values;
1247 size_t n_cols = x->vars[COL_VAR].n_values;
1254 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1256 const struct freq *te = *p;
1258 while (!value_equal (&x->vars[ROW_VAR].values[row],
1259 &te->values[ROW_VAR], row_var_width))
1261 for (; col < n_cols; col++)
1267 while (!value_equal (&x->vars[COL_VAR].values[col],
1268 &te->values[COL_VAR], col_var_width))
1275 if (++col >= n_cols)
1281 while (mp < &x->mat[n_cols * n_rows])
1283 assert (mp == &x->mat[n_cols * n_rows]);
1285 /* Column totals, row totals, ns_rows. */
1287 for (col = 0; col < n_cols; col++)
1288 x->col_tot[col] = 0.0;
1289 for (row = 0; row < n_rows; row++)
1290 x->row_tot[row] = 0.0;
1292 for (row = 0; row < n_rows; row++)
1294 bool row_is_empty = true;
1295 for (col = 0; col < n_cols; col++)
1299 row_is_empty = false;
1300 x->col_tot[col] += *mp;
1301 x->row_tot[row] += *mp;
1308 assert (mp == &x->mat[n_cols * n_rows]);
1312 for (col = 0; col < n_cols; col++)
1313 for (row = 0; row < n_rows; row++)
1314 if (x->mat[col + row * n_cols] != 0.0)
1322 for (col = 0; col < n_cols; col++)
1323 x->total += x->col_tot[col];
1327 add_var_dimension (struct pivot_table *table, const struct xtab_var *var,
1328 enum pivot_axis_type axis_type, bool total)
1330 struct pivot_dimension *d = pivot_dimension_create__ (
1331 table, axis_type, pivot_value_new_variable (var->var));
1333 struct pivot_footnote *missing_footnote = pivot_table_create_footnote (
1334 table, pivot_value_new_text (N_("Missing value")));
1336 struct pivot_category *group = pivot_category_create_group__ (
1337 d->root, pivot_value_new_variable (var->var));
1338 for (size_t j = 0; j < var->n_values; j++)
1340 struct pivot_value *value = pivot_value_new_var_value (
1341 var->var, &var->values[j]);
1342 if (var_is_value_missing (var->var, &var->values[j]))
1343 pivot_value_add_footnote (value, missing_footnote);
1344 pivot_category_create_leaf (group, value);
1348 pivot_category_create_leaf (d->root, pivot_value_new_text (N_("Total")));
1351 static struct pivot_table *
1352 create_crosstab_table (struct crosstabs_proc *proc, struct crosstabulation *xt,
1353 size_t crs_leaves[CRS_N_CELLS])
1356 struct string title = DS_EMPTY_INITIALIZER;
1357 for (size_t i = 0; i < xt->n_vars; i++)
1360 ds_put_cstr (&title, " × ");
1361 ds_put_cstr (&title, var_to_string (xt->vars[i].var));
1363 for (size_t i = 0; i < xt->n_consts; i++)
1365 const struct variable *var = xt->const_vars[i].var;
1366 const union value *value = &xt->entries[0]->values[2 + i];
1369 ds_put_format (&title, ", %s=", var_to_string (var));
1371 /* Insert the formatted value of VAR without any leading spaces. */
1372 s = data_out (value, var_get_encoding (var), var_get_print_format (var),
1373 settings_get_fmt_settings ());
1374 ds_put_cstr (&title, s + strspn (s, " "));
1377 struct pivot_table *table = pivot_table_create__ (
1378 pivot_value_new_user_text_nocopy (ds_steal_cstr (&title)),
1380 pivot_table_set_weight_format (table, &proc->weight_format);
1382 struct pivot_dimension *statistics = pivot_dimension_create (
1383 table, PIVOT_AXIS_ROW, N_("Statistics"));
1390 static const struct statistic stats[CRS_N_CELLS] =
1392 #define C(KEYWORD, STRING, RC) { STRING, RC },
1396 for (size_t i = 0; i < CRS_N_CELLS; i++)
1397 if (proc->cells & (1u << i) && stats[i].label)
1398 crs_leaves[i] = pivot_category_create_leaf_rc (
1399 statistics->root, pivot_value_new_text (stats[i].label),
1402 for (size_t i = 0; i < xt->n_vars; i++)
1403 add_var_dimension (table, &xt->vars[i],
1404 i == COL_VAR ? PIVOT_AXIS_COLUMN : PIVOT_AXIS_ROW,
1410 static struct pivot_table *
1411 create_chisq_table (struct crosstabulation *xt)
1413 struct pivot_table *chisq = pivot_table_create (N_("Chi-Square Tests"));
1414 pivot_table_set_weight_format (chisq, &xt->weight_format);
1416 pivot_dimension_create (
1417 chisq, PIVOT_AXIS_ROW, N_("Statistics"),
1418 N_("Pearson Chi-Square"),
1419 N_("Likelihood Ratio"),
1420 N_("Fisher's Exact Test"),
1421 N_("Continuity Correction"),
1422 N_("Linear-by-Linear Association"),
1423 N_("N of Valid Cases"), PIVOT_RC_COUNT);
1425 pivot_dimension_create (
1426 chisq, PIVOT_AXIS_COLUMN, N_("Statistics"),
1427 N_("Value"), PIVOT_RC_OTHER,
1428 N_("df"), PIVOT_RC_COUNT,
1429 N_("Asymptotic Sig. (2-tailed)"), PIVOT_RC_SIGNIFICANCE,
1430 N_("Exact Sig. (2-tailed)"), PIVOT_RC_SIGNIFICANCE,
1431 N_("Exact Sig. (1-tailed)"), PIVOT_RC_SIGNIFICANCE);
1433 for (size_t i = 2; i < xt->n_vars; i++)
1434 add_var_dimension (chisq, &xt->vars[i], PIVOT_AXIS_ROW, false);
1439 /* Symmetric measures. */
1440 static struct pivot_table *
1441 create_sym_table (struct crosstabulation *xt)
1443 struct pivot_table *sym = pivot_table_create (N_("Symmetric Measures"));
1444 pivot_table_set_weight_format (sym, &xt->weight_format);
1446 pivot_dimension_create (
1447 sym, PIVOT_AXIS_COLUMN, N_("Values"),
1448 N_("Value"), PIVOT_RC_OTHER,
1449 N_("Asymp. Std. Error"), PIVOT_RC_OTHER,
1450 N_("Approx. T"), PIVOT_RC_OTHER,
1451 N_("Approx. Sig."), PIVOT_RC_SIGNIFICANCE);
1453 struct pivot_dimension *statistics = pivot_dimension_create (
1454 sym, PIVOT_AXIS_ROW, N_("Statistics"));
1455 pivot_category_create_group (
1456 statistics->root, N_("Nominal by Nominal"),
1457 N_("Phi"), N_("Cramer's V"), N_("Contingency Coefficient"));
1458 pivot_category_create_group (
1459 statistics->root, N_("Ordinal by Ordinal"),
1460 N_("Kendall's tau-b"), N_("Kendall's tau-c"),
1461 N_("Gamma"), N_("Spearman Correlation"));
1462 pivot_category_create_group (
1463 statistics->root, N_("Interval by Interval"),
1465 pivot_category_create_group (
1466 statistics->root, N_("Measure of Agreement"),
1468 pivot_category_create_leaves (statistics->root, N_("N of Valid Cases"),
1471 for (size_t i = 2; i < xt->n_vars; i++)
1472 add_var_dimension (sym, &xt->vars[i], PIVOT_AXIS_ROW, false);
1477 /* Risk estimate. */
1478 static struct pivot_table *
1479 create_risk_table (struct crosstabulation *xt,
1480 struct pivot_dimension **risk_statistics)
1482 struct pivot_table *risk = pivot_table_create (N_("Risk Estimate"));
1483 pivot_table_set_weight_format (risk, &xt->weight_format);
1485 struct pivot_dimension *values = pivot_dimension_create (
1486 risk, PIVOT_AXIS_COLUMN, N_("Values"),
1487 N_("Value"), PIVOT_RC_OTHER);
1488 pivot_category_create_group (
1489 /* xgettext:no-c-format */
1490 values->root, N_("95% Confidence Interval"),
1491 N_("Lower"), PIVOT_RC_OTHER,
1492 N_("Upper"), PIVOT_RC_OTHER);
1494 *risk_statistics = pivot_dimension_create (
1495 risk, PIVOT_AXIS_ROW, N_("Statistics"));
1497 for (size_t i = 2; i < xt->n_vars; i++)
1498 add_var_dimension (risk, &xt->vars[i], PIVOT_AXIS_ROW, false);
1504 create_direct_stat (struct pivot_category *parent,
1505 const struct crosstabulation *xt,
1506 const char *name, bool symmetric)
1508 struct pivot_category *group = pivot_category_create_group (
1511 pivot_category_create_leaf (group, pivot_value_new_text (N_("Symmetric")));
1513 char *row_label = xasprintf (_("%s Dependent"),
1514 var_to_string (xt->vars[ROW_VAR].var));
1515 pivot_category_create_leaf (group, pivot_value_new_user_text_nocopy (
1518 char *col_label = xasprintf (_("%s Dependent"),
1519 var_to_string (xt->vars[COL_VAR].var));
1520 pivot_category_create_leaf (group, pivot_value_new_user_text_nocopy (
1524 /* Directional measures. */
1525 static struct pivot_table *
1526 create_direct_table (struct crosstabulation *xt)
1528 struct pivot_table *direct = pivot_table_create (N_("Directional Measures"));
1529 pivot_table_set_weight_format (direct, &xt->weight_format);
1531 pivot_dimension_create (
1532 direct, PIVOT_AXIS_COLUMN, N_("Values"),
1533 N_("Value"), PIVOT_RC_OTHER,
1534 N_("Asymp. Std. Error"), PIVOT_RC_OTHER,
1535 N_("Approx. T"), PIVOT_RC_OTHER,
1536 N_("Approx. Sig."), PIVOT_RC_SIGNIFICANCE);
1538 struct pivot_dimension *statistics = pivot_dimension_create (
1539 direct, PIVOT_AXIS_ROW, N_("Statistics"));
1540 struct pivot_category *nn = pivot_category_create_group (
1541 statistics->root, N_("Nominal by Nominal"));
1542 create_direct_stat (nn, xt, N_("Lambda"), true);
1543 create_direct_stat (nn, xt, N_("Goodman and Kruskal tau"), false);
1544 create_direct_stat (nn, xt, N_("Uncertainty Coefficient"), true);
1545 struct pivot_category *oo = pivot_category_create_group (
1546 statistics->root, N_("Ordinal by Ordinal"));
1547 create_direct_stat (oo, xt, N_("Somers' d"), true);
1548 struct pivot_category *ni = pivot_category_create_group (
1549 statistics->root, N_("Nominal by Interval"));
1550 create_direct_stat (ni, xt, N_("Eta"), false);
1552 for (size_t i = 2; i < xt->n_vars; i++)
1553 add_var_dimension (direct, &xt->vars[i], PIVOT_AXIS_ROW, false);
1558 /* Delete missing rows and columns for statistical analysis when
1561 delete_missing (struct crosstabulation *xt)
1563 size_t n_rows = xt->vars[ROW_VAR].n_values;
1564 size_t n_cols = xt->vars[COL_VAR].n_values;
1567 for (r = 0; r < n_rows; r++)
1568 if (var_is_num_missing (xt->vars[ROW_VAR].var,
1569 xt->vars[ROW_VAR].values[r].f) == MV_USER)
1571 for (c = 0; c < n_cols; c++)
1572 xt->mat[c + r * n_cols] = 0.;
1577 for (c = 0; c < n_cols; c++)
1578 if (var_is_num_missing (xt->vars[COL_VAR].var,
1579 xt->vars[COL_VAR].values[c].f) == MV_USER)
1581 for (r = 0; r < n_rows; r++)
1582 xt->mat[c + r * n_cols] = 0.;
1588 find_crosstab (struct crosstabulation *xt, size_t *row0p, size_t *row1p)
1590 size_t row0 = *row1p;
1593 if (row0 >= xt->n_entries)
1596 for (row1 = row0 + 1; row1 < xt->n_entries; row1++)
1598 struct freq *a = xt->entries[row0];
1599 struct freq *b = xt->entries[row1];
1600 if (compare_table_entry_vars_3way (a, b, xt, 2, xt->n_vars) != 0)
1608 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1609 result. WIDTH_ points to an int which is either 0 for a
1610 numeric value or a string width for a string value. */
1612 compare_value_3way (const void *a_, const void *b_, const void *width_)
1614 const union value *a = a_;
1615 const union value *b = b_;
1616 const int *width = width_;
1618 return value_compare_3way (a, b, *width);
1621 /* Inverted version of the above */
1623 compare_value_3way_inv (const void *a_, const void *b_, const void *width_)
1625 return -compare_value_3way (a_, b_, width_);
1629 /* Given an array of ENTRY_CNT table_entry structures starting at
1630 ENTRIES, creates a sorted list of the values that the variable
1631 with index VAR_IDX takes on. Stores the array of the values in
1632 XT->values and the number of values in XT->n_values. */
1634 enum_var_values (const struct crosstabulation *xt, int var_idx,
1637 struct xtab_var *xv = &xt->vars[var_idx];
1638 const struct var_range *range = get_var_range (xt->proc, xv->var);
1642 xv->values = xnmalloc (range->count, sizeof *xv->values);
1643 xv->n_values = range->count;
1644 for (size_t i = 0; i < range->count; i++)
1645 xv->values[i].f = range->min + i;
1649 int width = var_get_width (xv->var);
1650 struct hmapx_node *node;
1651 const union value *iter;
1655 for (size_t i = 0; i < xt->n_entries; i++)
1657 const struct freq *te = xt->entries[i];
1658 const union value *value = &te->values[var_idx];
1659 size_t hash = value_hash (value, width, 0);
1661 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1662 if (value_equal (iter, value, width))
1665 hmapx_insert (&set, (union value *) value, hash);
1670 xv->n_values = hmapx_count (&set);
1671 xv->values = xnmalloc (xv->n_values, sizeof *xv->values);
1673 HMAPX_FOR_EACH (iter, node, &set)
1674 xv->values[i++] = *iter;
1675 hmapx_destroy (&set);
1677 sort (xv->values, xv->n_values, sizeof *xv->values,
1678 descending ? compare_value_3way_inv : compare_value_3way,
1684 free_var_values (const struct crosstabulation *xt, int var_idx)
1686 struct xtab_var *xv = &xt->vars[var_idx];
1692 /* Displays the crosstabulation table. */
1694 display_crosstabulation (struct crosstabs_proc *proc,
1695 struct crosstabulation *xt, struct pivot_table *table,
1696 size_t crs_leaves[CRS_N_CELLS])
1698 size_t n_rows = xt->vars[ROW_VAR].n_values;
1699 size_t n_cols = xt->vars[COL_VAR].n_values;
1701 size_t *indexes = xnmalloc (table->n_dimensions, sizeof *indexes);
1702 assert (xt->n_vars == 2);
1703 for (size_t i = 0; i < xt->n_consts; i++)
1704 indexes[i + 3] = xt->const_indexes[i];
1706 /* Put in the actual cells. */
1707 double *mp = xt->mat;
1708 for (size_t r = 0; r < n_rows; r++)
1710 if (!xt->row_tot[r] && proc->mode != INTEGER)
1713 indexes[ROW_VAR + 1] = r;
1714 for (size_t c = 0; c < n_cols; c++)
1716 if (!xt->col_tot[c] && proc->mode != INTEGER)
1719 indexes[COL_VAR + 1] = c;
1721 double expected_value = xt->row_tot[r] * xt->col_tot[c] / xt->total;
1722 double residual = *mp - expected_value;
1723 double sresidual = residual / sqrt (expected_value);
1725 = residual / sqrt (expected_value
1726 * (1. - xt->row_tot[r] / xt->total)
1727 * (1. - xt->col_tot[c] / xt->total));
1728 double entries[CRS_N_CELLS] = {
1729 [CRS_CL_COUNT] = *mp,
1730 [CRS_CL_ROW] = *mp / xt->row_tot[r] * 100.,
1731 [CRS_CL_COLUMN] = *mp / xt->col_tot[c] * 100.,
1732 [CRS_CL_TOTAL] = *mp / xt->total * 100.,
1733 [CRS_CL_EXPECTED] = expected_value,
1734 [CRS_CL_RESIDUAL] = residual,
1735 [CRS_CL_SRESIDUAL] = sresidual,
1736 [CRS_CL_ASRESIDUAL] = asresidual,
1738 for (size_t i = 0; i < proc->n_cells; i++)
1740 int cell = proc->a_cells[i];
1741 indexes[0] = crs_leaves[cell];
1742 pivot_table_put (table, indexes, table->n_dimensions,
1743 pivot_value_new_number (entries[cell]));
1751 for (size_t r = 0; r < n_rows; r++)
1753 if (!xt->row_tot[r] && proc->mode != INTEGER)
1756 double expected_value = xt->row_tot[r] / xt->total;
1757 double entries[CRS_N_CELLS] = {
1758 [CRS_CL_COUNT] = xt->row_tot[r],
1759 [CRS_CL_ROW] = 100.0,
1760 [CRS_CL_COLUMN] = expected_value * 100.,
1761 [CRS_CL_TOTAL] = expected_value * 100.,
1762 [CRS_CL_EXPECTED] = expected_value,
1763 [CRS_CL_RESIDUAL] = SYSMIS,
1764 [CRS_CL_SRESIDUAL] = SYSMIS,
1765 [CRS_CL_ASRESIDUAL] = SYSMIS,
1767 for (size_t i = 0; i < proc->n_cells; i++)
1769 int cell = proc->a_cells[i];
1770 double entry = entries[cell];
1771 if (entry != SYSMIS)
1773 indexes[ROW_VAR + 1] = r;
1774 indexes[COL_VAR + 1] = n_cols;
1775 indexes[0] = crs_leaves[cell];
1776 pivot_table_put (table, indexes, table->n_dimensions,
1777 pivot_value_new_number (entry));
1782 for (size_t c = 0; c <= n_cols; c++)
1784 if (c < n_cols && !xt->col_tot[c] && proc->mode != INTEGER)
1787 double ct = c < n_cols ? xt->col_tot[c] : xt->total;
1788 double expected_value = ct / xt->total;
1789 double entries[CRS_N_CELLS] = {
1790 [CRS_CL_COUNT] = ct,
1791 [CRS_CL_ROW] = expected_value * 100.0,
1792 [CRS_CL_COLUMN] = 100.0,
1793 [CRS_CL_TOTAL] = expected_value * 100.,
1794 [CRS_CL_EXPECTED] = expected_value,
1795 [CRS_CL_RESIDUAL] = SYSMIS,
1796 [CRS_CL_SRESIDUAL] = SYSMIS,
1797 [CRS_CL_ASRESIDUAL] = SYSMIS,
1799 for (size_t i = 0; i < proc->n_cells; i++)
1801 int cell = proc->a_cells[i];
1802 double entry = entries[cell];
1803 if (entry != SYSMIS)
1805 indexes[ROW_VAR + 1] = n_rows;
1806 indexes[COL_VAR + 1] = c;
1807 indexes[0] = crs_leaves[cell];
1808 pivot_table_put (table, indexes, table->n_dimensions,
1809 pivot_value_new_number (entry));
1817 static void calc_r (struct crosstabulation *,
1818 double *XT, double *Y, double *, double *, double *);
1819 static void calc_chisq (struct crosstabulation *,
1820 double[N_CHISQ], int[N_CHISQ], double *, double *);
1822 /* Display chi-square statistics. */
1824 display_chisq (struct crosstabulation *xt, struct pivot_table *chisq)
1826 double chisq_v[N_CHISQ];
1827 double fisher1, fisher2;
1829 calc_chisq (xt, chisq_v, df, &fisher1, &fisher2);
1831 size_t *indexes = xnmalloc (chisq->n_dimensions, sizeof *indexes);
1832 assert (xt->n_vars == 2);
1833 for (size_t i = 0; i < xt->n_consts; i++)
1834 indexes[i + 2] = xt->const_indexes[i];
1835 for (int i = 0; i < N_CHISQ; i++)
1839 double entries[5] = { SYSMIS, SYSMIS, SYSMIS, SYSMIS, SYSMIS };
1842 entries[3] = fisher2;
1843 entries[4] = fisher1;
1845 else if (chisq_v[i] != SYSMIS)
1847 entries[0] = chisq_v[i];
1849 entries[2] = gsl_cdf_chisq_Q (chisq_v[i], df[i]);
1852 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1853 if (entries[j] != SYSMIS)
1856 pivot_table_put (chisq, indexes, chisq->n_dimensions,
1857 pivot_value_new_number (entries[j]));
1863 pivot_table_put (chisq, indexes, chisq->n_dimensions,
1864 pivot_value_new_number (xt->total));
1869 static int calc_symmetric (struct crosstabs_proc *, struct crosstabulation *,
1870 double[N_SYMMETRIC], double[N_SYMMETRIC],
1871 double[N_SYMMETRIC],
1872 double[3], double[3], double[3]);
1874 /* Display symmetric measures. */
1876 display_symmetric (struct crosstabs_proc *proc, struct crosstabulation *xt,
1877 struct pivot_table *sym)
1879 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1880 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1882 if (!calc_symmetric (proc, xt, sym_v, sym_ase, sym_t,
1883 somers_d_v, somers_d_ase, somers_d_t))
1886 size_t *indexes = xnmalloc (sym->n_dimensions, sizeof *indexes);
1887 assert (xt->n_vars == 2);
1888 for (size_t i = 0; i < xt->n_consts; i++)
1889 indexes[i + 2] = xt->const_indexes[i];
1891 for (int i = 0; i < N_SYMMETRIC; i++)
1893 if (sym_v[i] == SYSMIS)
1898 double entries[] = { sym_v[i], sym_ase[i], sym_t[i] };
1899 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1900 if (entries[j] != SYSMIS)
1903 pivot_table_put (sym, indexes, sym->n_dimensions,
1904 pivot_value_new_number (entries[j]));
1908 indexes[1] = N_SYMMETRIC;
1910 struct pivot_value *total = pivot_value_new_number (xt->total);
1911 pivot_value_set_rc (sym, total, PIVOT_RC_COUNT);
1912 pivot_table_put (sym, indexes, sym->n_dimensions, total);
1917 static bool calc_risk (struct crosstabulation *,
1918 double[], double[], double[], union value *,
1921 /* Display risk estimate. */
1923 display_risk (struct crosstabulation *xt, struct pivot_table *risk,
1924 struct pivot_dimension *risk_statistics)
1926 double risk_v[3], lower[3], upper[3], n_valid;
1928 if (!calc_risk (xt, risk_v, upper, lower, c, &n_valid))
1930 assert (risk_statistics);
1932 size_t *indexes = xnmalloc (risk->n_dimensions, sizeof *indexes);
1933 assert (xt->n_vars == 2);
1934 for (size_t i = 0; i < xt->n_consts; i++)
1935 indexes[i + 2] = xt->const_indexes[i];
1937 for (int i = 0; i < 3; i++)
1939 const struct variable *cv = xt->vars[COL_VAR].var;
1940 const struct variable *rv = xt->vars[ROW_VAR].var;
1942 if (risk_v[i] == SYSMIS)
1945 struct string label = DS_EMPTY_INITIALIZER;
1949 ds_put_format (&label, _("Odds Ratio for %s"), var_to_string (rv));
1950 ds_put_cstr (&label, " (");
1951 var_append_value_name (rv, &c[0], &label);
1952 ds_put_cstr (&label, " / ");
1953 var_append_value_name (rv, &c[1], &label);
1954 ds_put_cstr (&label, ")");
1958 ds_put_format (&label, _("For cohort %s = "), var_to_string (cv));
1959 var_append_value_name (cv, &xt->vars[ROW_VAR].values[i - 1], &label);
1963 indexes[1] = pivot_category_create_leaf (
1964 risk_statistics->root,
1965 pivot_value_new_user_text_nocopy (ds_steal_cstr (&label)));
1967 double entries[] = { risk_v[i], lower[i], upper[i] };
1968 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1971 pivot_table_put (risk, indexes, risk->n_dimensions,
1972 pivot_value_new_number (entries[i]));
1975 indexes[1] = pivot_category_create_leaf (
1976 risk_statistics->root,
1977 pivot_value_new_text (N_("N of Valid Cases")));
1979 pivot_table_put (risk, indexes, risk->n_dimensions,
1980 pivot_value_new_number (n_valid));
1984 static int calc_directional (struct crosstabs_proc *, struct crosstabulation *,
1985 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1986 double[N_DIRECTIONAL], double[N_DIRECTIONAL]);
1988 /* Display directional measures. */
1990 display_directional (struct crosstabs_proc *proc,
1991 struct crosstabulation *xt, struct pivot_table *direct)
1993 double direct_v[N_DIRECTIONAL];
1994 double direct_ase[N_DIRECTIONAL];
1995 double direct_t[N_DIRECTIONAL];
1996 double sig[N_DIRECTIONAL];
1997 if (!calc_directional (proc, xt, direct_v, direct_ase, direct_t, sig))
2000 size_t *indexes = xnmalloc (direct->n_dimensions, sizeof *indexes);
2001 assert (xt->n_vars == 2);
2002 for (size_t i = 0; i < xt->n_consts; i++)
2003 indexes[i + 2] = xt->const_indexes[i];
2005 for (int i = 0; i < N_DIRECTIONAL; i++)
2007 if (direct_v[i] == SYSMIS)
2012 double entries[] = {
2013 direct_v[i], direct_ase[i], direct_t[i], sig[i],
2015 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
2016 if (entries[j] != SYSMIS)
2019 pivot_table_put (direct, indexes, direct->n_dimensions,
2020 pivot_value_new_number (entries[j]));
2027 /* Statistical calculations. */
2029 /* Returns the value of the logarithm of gamma (factorial) function for an integer
2032 log_gamma_int (double xt)
2037 for (i = 2; i < xt; i++)
2043 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2045 static inline double
2046 Pr (int a, int b, int c, int d)
2048 return exp (log_gamma_int (a + b + 1.) - log_gamma_int (a + 1.)
2049 + log_gamma_int (c + d + 1.) - log_gamma_int (b + 1.)
2050 + log_gamma_int (a + c + 1.) - log_gamma_int (c + 1.)
2051 + log_gamma_int (b + d + 1.) - log_gamma_int (d + 1.)
2052 - log_gamma_int (a + b + c + d + 1.));
2055 /* Swap the contents of A and B. */
2057 swap (int *a, int *b)
2064 /* Calculate significance for Fisher's exact test as specified in
2065 _SPSS Statistical Algorithms_, Appendix 5. */
2067 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 pn1 = Pr (a, b, c, d);
2086 for (xt = 1; xt <= a; xt++)
2088 *fisher1 += Pr (a - xt, b + xt, c + xt, d - xt);
2091 *fisher2 = *fisher1;
2093 for (xt = 1; xt <= b; xt++)
2095 double p = Pr (a + xt, b - xt, c - xt, d + xt);
2101 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2102 columns with values COLS and N_ROWS rows with values ROWS. Values
2103 in the matrix sum to xt->total. */
2105 calc_chisq (struct crosstabulation *xt,
2106 double chisq[N_CHISQ], int df[N_CHISQ],
2107 double *fisher1, double *fisher2)
2109 chisq[0] = chisq[1] = 0.;
2110 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2111 *fisher1 = *fisher2 = SYSMIS;
2113 df[0] = df[1] = (xt->ns_cols - 1) * (xt->ns_rows - 1);
2115 if (xt->ns_rows <= 1 || xt->ns_cols <= 1)
2117 chisq[0] = chisq[1] = SYSMIS;
2121 size_t n_cols = xt->vars[COL_VAR].n_values;
2122 FOR_EACH_POPULATED_ROW (r, xt)
2123 FOR_EACH_POPULATED_COLUMN (c, xt)
2125 const double expected = xt->row_tot[r] * xt->col_tot[c] / xt->total;
2126 const double freq = xt->mat[n_cols * r + c];
2127 const double residual = freq - expected;
2129 chisq[0] += residual * residual / expected;
2131 chisq[1] += freq * log (expected / freq);
2142 /* Calculate Yates and Fisher exact test. */
2143 if (xt->ns_cols == 2 && xt->ns_rows == 2)
2145 double f11, f12, f21, f22;
2151 FOR_EACH_POPULATED_COLUMN (c, xt)
2159 f11 = xt->mat[nz_cols[0]];
2160 f12 = xt->mat[nz_cols[1]];
2161 f21 = xt->mat[nz_cols[0] + n_cols];
2162 f22 = xt->mat[nz_cols[1] + n_cols];
2167 const double xt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * xt->total;
2170 chisq[3] = (xt->total * pow2 (xt_)
2171 / (f11 + f12) / (f21 + f22)
2172 / (f11 + f21) / (f12 + f22));
2180 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2183 /* Calculate Mantel-Haenszel. */
2184 if (var_is_numeric (xt->vars[ROW_VAR].var)
2185 && var_is_numeric (xt->vars[COL_VAR].var))
2187 double r, ase_0, ase_1;
2188 calc_r (xt, (double *) xt->vars[ROW_VAR].values,
2189 (double *) xt->vars[COL_VAR].values,
2190 &r, &ase_0, &ase_1);
2192 chisq[4] = (xt->total - 1.) * r * r;
2197 /* Calculate the value of Pearson's r. r is stored into R, its T value into
2198 T, and standard error into ERROR. The row and column values must be
2199 passed in XT and Y. */
2201 calc_r (struct crosstabulation *xt,
2202 double *XT, double *Y, double *r, double *t, double *error)
2204 size_t n_rows = xt->vars[ROW_VAR].n_values;
2205 size_t n_cols = xt->vars[COL_VAR].n_values;
2206 double SX, SY, S, T;
2208 double sum_XYf, sum_X2Y2f;
2209 double sum_Xr, sum_X2r;
2210 double sum_Yc, sum_Y2c;
2213 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < n_rows; i++)
2214 for (j = 0; j < n_cols; j++)
2216 double fij = xt->mat[j + i * n_cols];
2217 double product = XT[i] * Y[j];
2218 double temp = fij * product;
2220 sum_X2Y2f += temp * product;
2223 for (sum_Xr = sum_X2r = 0., i = 0; i < n_rows; i++)
2225 sum_Xr += XT[i] * xt->row_tot[i];
2226 sum_X2r += pow2 (XT[i]) * xt->row_tot[i];
2228 Xbar = sum_Xr / xt->total;
2230 for (sum_Yc = sum_Y2c = 0., i = 0; i < n_cols; i++)
2232 sum_Yc += Y[i] * xt->col_tot[i];
2233 sum_Y2c += Y[i] * Y[i] * xt->col_tot[i];
2235 Ybar = sum_Yc / xt->total;
2237 S = sum_XYf - sum_Xr * sum_Yc / xt->total;
2238 SX = sum_X2r - pow2 (sum_Xr) / xt->total;
2239 SY = sum_Y2c - pow2 (sum_Yc) / xt->total;
2242 *t = *r / sqrt (1 - pow2 (*r)) * sqrt (xt->total - 2);
2247 for (s = c = 0., i = 0; i < n_rows; i++)
2248 for (j = 0; j < n_cols; j++)
2250 double Xresid, Yresid;
2253 Xresid = XT[i] - Xbar;
2254 Yresid = Y[j] - Ybar;
2255 temp = (T * Xresid * Yresid
2257 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2258 y = xt->mat[j + i * n_cols] * temp * temp - c;
2263 *error = sqrt (s) / (T * T);
2267 /* Calculate symmetric statistics and their asymptotic standard
2268 errors. Returns 0 if none could be calculated. */
2270 calc_symmetric (struct crosstabs_proc *proc, struct crosstabulation *xt,
2271 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2272 double t[N_SYMMETRIC],
2273 double somers_d_v[3], double somers_d_ase[3],
2274 double somers_d_t[3])
2276 size_t n_rows = xt->vars[ROW_VAR].n_values;
2277 size_t n_cols = xt->vars[COL_VAR].n_values;
2280 q = MIN (xt->ns_rows, xt->ns_cols);
2284 for (i = 0; i < N_SYMMETRIC; i++)
2285 v[i] = ase[i] = t[i] = SYSMIS;
2287 /* Phi, Cramer's V, contingency coefficient. */
2288 if (proc->statistics & (CRS_ST_PHI | CRS_ST_CC))
2290 double Xp = 0.; /* Pearson chi-square. */
2292 FOR_EACH_POPULATED_ROW (r, xt)
2293 FOR_EACH_POPULATED_COLUMN (c, xt)
2295 double expected = xt->row_tot[r] * xt->col_tot[c] / xt->total;
2296 double freq = xt->mat[n_cols * r + c];
2297 double residual = freq - expected;
2299 Xp += residual * residual / expected;
2302 if (proc->statistics & CRS_ST_PHI)
2304 v[0] = sqrt (Xp / xt->total);
2305 v[1] = sqrt (Xp / (xt->total * (q - 1)));
2307 if (proc->statistics & CRS_ST_CC)
2308 v[2] = sqrt (Xp / (Xp + xt->total));
2311 if (proc->statistics & (CRS_ST_BTAU | CRS_ST_CTAU
2312 | CRS_ST_GAMMA | CRS_ST_D))
2317 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2321 Dr = Dc = pow2 (xt->total);
2322 for (r = 0; r < n_rows; r++)
2323 Dr -= pow2 (xt->row_tot[r]);
2324 for (c = 0; c < n_cols; c++)
2325 Dc -= pow2 (xt->col_tot[c]);
2327 cum = xnmalloc (n_cols * n_rows, sizeof *cum);
2328 for (c = 0; c < n_cols; c++)
2332 for (r = 0; r < n_rows; r++)
2333 cum[c + r * n_cols] = ct += xt->mat[c + r * n_cols];
2342 for (i = 0; i < n_rows; i++)
2346 for (j = 1; j < n_cols; j++)
2347 Cij += xt->col_tot[j] - cum[j + i * n_cols];
2350 for (j = 1; j < n_cols; j++)
2351 Dij += cum[j + (i - 1) * n_cols];
2355 double fij = xt->mat[j + i * n_cols];
2361 assert (j < n_cols);
2363 Cij -= xt->col_tot[j] - cum[j + i * n_cols];
2364 Dij += xt->col_tot[j - 1] - cum[j - 1 + i * n_cols];
2368 Cij += cum[j - 1 + (i - 1) * n_cols];
2369 Dij -= cum[j + (i - 1) * n_cols];
2375 if (proc->statistics & CRS_ST_BTAU)
2376 v[3] = (P - Q) / sqrt (Dr * Dc);
2377 if (proc->statistics & CRS_ST_CTAU)
2378 v[4] = (q * (P - Q)) / (pow2 (xt->total) * (q - 1));
2379 if (proc->statistics & CRS_ST_GAMMA)
2380 v[5] = (P - Q) / (P + Q);
2382 /* ASE for tau-b, tau-c, gamma. Calculations could be
2383 eliminated here, at expense of memory. */
2388 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2389 for (i = 0; i < n_rows; i++)
2393 for (j = 1; j < n_cols; j++)
2394 Cij += xt->col_tot[j] - cum[j + i * n_cols];
2397 for (j = 1; j < n_cols; j++)
2398 Dij += cum[j + (i - 1) * n_cols];
2402 double fij = xt->mat[j + i * n_cols];
2404 if (proc->statistics & CRS_ST_BTAU)
2406 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2407 + v[3] * (xt->row_tot[i] * Dc
2408 + xt->col_tot[j] * Dr));
2409 btau_cum += fij * temp * temp;
2413 const double temp = Cij - Dij;
2414 ctau_cum += fij * temp * temp;
2417 if (proc->statistics & CRS_ST_GAMMA)
2419 const double temp = Q * Cij - P * Dij;
2420 gamma_cum += fij * temp * temp;
2423 if (proc->statistics & CRS_ST_D)
2425 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2426 - (P - Q) * (xt->total - xt->row_tot[i]));
2427 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2428 - (Q - P) * (xt->total - xt->col_tot[j]));
2433 assert (j < n_cols);
2435 Cij -= xt->col_tot[j] - cum[j + i * n_cols];
2436 Dij += xt->col_tot[j - 1] - cum[j - 1 + i * n_cols];
2440 Cij += cum[j - 1 + (i - 1) * n_cols];
2441 Dij -= cum[j + (i - 1) * n_cols];
2447 btau_var = ((btau_cum
2448 - (xt->total * pow2 (xt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2450 if (proc->statistics & CRS_ST_BTAU)
2452 ase[3] = sqrt (btau_var);
2453 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / xt->total)
2456 if (proc->statistics & CRS_ST_CTAU)
2458 ase[4] = ((2 * q / ((q - 1) * pow2 (xt->total)))
2459 * sqrt (ctau_cum - (P - Q) * (P - Q) / xt->total));
2460 t[4] = v[4] / ase[4];
2462 if (proc->statistics & CRS_ST_GAMMA)
2464 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2465 t[5] = v[5] / (2. / (P + Q)
2466 * sqrt (ctau_cum - (P - Q) * (P - Q) / xt->total));
2468 if (proc->statistics & CRS_ST_D)
2470 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2471 somers_d_ase[0] = SYSMIS;
2472 somers_d_t[0] = (somers_d_v[0]
2474 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2475 somers_d_v[1] = (P - Q) / Dc;
2476 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2477 somers_d_t[1] = (somers_d_v[1]
2479 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2480 somers_d_v[2] = (P - Q) / Dr;
2481 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2482 somers_d_t[2] = (somers_d_v[2]
2484 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2490 /* Spearman correlation, Pearson's r. */
2491 if (proc->statistics & CRS_ST_CORR)
2493 double *R = xmalloc (sizeof *R * n_rows);
2494 double *C = xmalloc (sizeof *C * n_cols);
2497 double y, t, c = 0., s = 0.;
2502 R[i] = s + (xt->row_tot[i] + 1.) / 2.;
2503 y = xt->row_tot[i] - c;
2509 assert (i < n_rows);
2514 double y, t, c = 0., s = 0.;
2519 C[j] = s + (xt->col_tot[j] + 1.) / 2;
2520 y = xt->col_tot[j] - c;
2526 assert (j < n_cols);
2530 calc_r (xt, R, C, &v[6], &t[6], &ase[6]);
2535 calc_r (xt, (double *) xt->vars[ROW_VAR].values,
2536 (double *) xt->vars[COL_VAR].values,
2537 &v[7], &t[7], &ase[7]);
2540 /* Cohen's kappa. */
2541 if (proc->statistics & CRS_ST_KAPPA && xt->ns_rows == xt->ns_cols)
2543 double ase_under_h0;
2544 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2547 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2548 i < xt->ns_rows; i++, j++)
2552 while (xt->col_tot[j] == 0.)
2555 prod = xt->row_tot[i] * xt->col_tot[j];
2556 sum = xt->row_tot[i] + xt->col_tot[j];
2558 sum_fii += xt->mat[j + i * n_cols];
2560 sum_fiiri_ci += xt->mat[j + i * n_cols] * sum;
2561 sum_riciri_ci += prod * sum;
2563 for (sum_fijri_ci2 = 0., i = 0; i < xt->ns_rows; i++)
2564 for (j = 0; j < xt->ns_cols; j++)
2566 double sum = xt->row_tot[i] + xt->col_tot[j];
2567 sum_fijri_ci2 += xt->mat[j + i * n_cols] * sum * sum;
2570 v[8] = (xt->total * sum_fii - sum_rici) / (pow2 (xt->total) - sum_rici);
2572 ase_under_h0 = sqrt ((pow2 (xt->total) * sum_rici
2573 + sum_rici * sum_rici
2574 - xt->total * sum_riciri_ci)
2575 / (xt->total * (pow2 (xt->total) - sum_rici) * (pow2 (xt->total) - sum_rici)));
2577 ase[8] = sqrt (xt->total * (((sum_fii * (xt->total - sum_fii))
2578 / pow2 (pow2 (xt->total) - sum_rici))
2579 + ((2. * (xt->total - sum_fii)
2580 * (2. * sum_fii * sum_rici
2581 - xt->total * sum_fiiri_ci))
2582 / pow3 (pow2 (xt->total) - sum_rici))
2583 + (pow2 (xt->total - sum_fii)
2584 * (xt->total * sum_fijri_ci2 - 4.
2585 * sum_rici * sum_rici)
2586 / pow4 (pow2 (xt->total) - sum_rici))));
2588 t[8] = v[8] / ase_under_h0;
2594 /* Calculate risk estimate. */
2596 calc_risk (struct crosstabulation *xt,
2597 double *value, double *upper, double *lower, union value *c,
2600 size_t n_cols = xt->vars[COL_VAR].n_values;
2601 double f11, f12, f21, f22;
2604 for (int i = 0; i < 3; i++)
2605 value[i] = upper[i] = lower[i] = SYSMIS;
2607 if (xt->ns_rows != 2 || xt->ns_cols != 2)
2611 /* Find populated columns. */
2614 FOR_EACH_POPULATED_COLUMN (c, xt)
2618 /* Find populated rows. */
2621 FOR_EACH_POPULATED_ROW (r, xt)
2625 f11 = xt->mat[nz_cols[0] + n_cols * nz_rows[0]];
2626 f12 = xt->mat[nz_cols[1] + n_cols * nz_rows[0]];
2627 f21 = xt->mat[nz_cols[0] + n_cols * nz_rows[1]];
2628 f22 = xt->mat[nz_cols[1] + n_cols * nz_rows[1]];
2629 *n_valid = f11 + f12 + f21 + f22;
2631 c[0] = xt->vars[COL_VAR].values[nz_cols[0]];
2632 c[1] = xt->vars[COL_VAR].values[nz_cols[1]];
2635 value[0] = (f11 * f22) / (f12 * f21);
2636 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2637 lower[0] = value[0] * exp (-1.960 * v);
2638 upper[0] = value[0] * exp (1.960 * v);
2640 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2641 v = sqrt ((f12 / (f11 * (f11 + f12)))
2642 + (f22 / (f21 * (f21 + f22))));
2643 lower[1] = value[1] * exp (-1.960 * v);
2644 upper[1] = value[1] * exp (1.960 * v);
2646 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2647 v = sqrt ((f11 / (f12 * (f11 + f12)))
2648 + (f21 / (f22 * (f21 + f22))));
2649 lower[2] = value[2] * exp (-1.960 * v);
2650 upper[2] = value[2] * exp (1.960 * v);
2655 /* Calculate directional measures. */
2657 calc_directional (struct crosstabs_proc *proc, struct crosstabulation *xt,
2658 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2659 double t[N_DIRECTIONAL], double sig[N_DIRECTIONAL])
2661 size_t n_rows = xt->vars[ROW_VAR].n_values;
2662 size_t n_cols = xt->vars[COL_VAR].n_values;
2663 for (int i = 0; i < N_DIRECTIONAL; i++)
2664 v[i] = ase[i] = t[i] = sig[i] = SYSMIS;
2667 if (proc->statistics & CRS_ST_LAMBDA)
2669 /* Find maximum for each row and their sum. */
2670 double *fim = xnmalloc (n_rows, sizeof *fim);
2671 int *fim_index = xnmalloc (n_rows, sizeof *fim_index);
2672 double sum_fim = 0.0;
2673 for (int i = 0; i < n_rows; i++)
2675 double max = xt->mat[i * n_cols];
2678 for (int j = 1; j < n_cols; j++)
2679 if (xt->mat[j + i * n_cols] > max)
2681 max = xt->mat[j + i * n_cols];
2687 fim_index[i] = index;
2690 /* Find maximum for each column. */
2691 double *fmj = xnmalloc (n_cols, sizeof *fmj);
2692 int *fmj_index = xnmalloc (n_cols, sizeof *fmj_index);
2693 double sum_fmj = 0.0;
2694 for (int j = 0; j < n_cols; j++)
2696 double max = xt->mat[j];
2699 for (int i = 1; i < n_rows; i++)
2700 if (xt->mat[j + i * n_cols] > max)
2702 max = xt->mat[j + i * n_cols];
2708 fmj_index[j] = index;
2711 /* Find maximum row total. */
2712 double rm = xt->row_tot[0];
2714 for (int i = 1; i < n_rows; i++)
2715 if (xt->row_tot[i] > rm)
2717 rm = xt->row_tot[i];
2721 /* Find maximum column total. */
2722 double cm = xt->col_tot[0];
2724 for (int j = 1; j < n_cols; j++)
2725 if (xt->col_tot[j] > cm)
2727 cm = xt->col_tot[j];
2731 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * xt->total - rm - cm);
2732 v[1] = (sum_fmj - rm) / (xt->total - rm);
2733 v[2] = (sum_fim - cm) / (xt->total - cm);
2735 /* ASE1 for Y given XT. */
2738 for (int i = 0; i < n_rows; i++)
2739 if (cm_index == fim_index[i])
2741 ase[2] = sqrt ((xt->total - sum_fim) * (sum_fim + cm - 2. * accum)
2742 / pow3 (xt->total - cm));
2745 /* ASE0 for Y given XT. */
2748 for (int i = 0; i < n_rows; i++)
2749 if (cm_index != fim_index[i])
2750 accum += (xt->mat[i * n_cols + fim_index[i]]
2751 + xt->mat[i * n_cols + cm_index]);
2752 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / xt->total) / (xt->total - cm));
2755 /* ASE1 for XT given Y. */
2758 for (int j = 0; j < n_cols; j++)
2759 if (rm_index == fmj_index[j])
2761 ase[1] = sqrt ((xt->total - sum_fmj) * (sum_fmj + rm - 2. * accum)
2762 / pow3 (xt->total - rm));
2765 /* ASE0 for XT given Y. */
2768 for (int j = 0; j < n_cols; j++)
2769 if (rm_index != fmj_index[j])
2770 accum += (xt->mat[j + n_cols * fmj_index[j]]
2771 + xt->mat[j + n_cols * rm_index]);
2772 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / xt->total) / (xt->total - rm));
2775 /* Symmetric ASE0 and ASE1. */
2777 double accum0 = 0.0;
2778 double accum1 = 0.0;
2779 for (int i = 0; i < n_rows; i++)
2780 for (int j = 0; j < n_cols; j++)
2782 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2783 int temp1 = (i == rm_index) + (j == cm_index);
2784 accum0 += xt->mat[j + i * n_cols] * pow2 (temp0 - temp1);
2785 accum1 += (xt->mat[j + i * n_cols]
2786 * pow2 (temp0 + (v[0] - 1.) * temp1));
2788 ase[0] = sqrt (accum1 - 4. * xt->total * v[0] * v[0]) / (2. * xt->total - rm - cm);
2789 t[0] = v[0] / (sqrt (accum0 - pow2 (sum_fim + sum_fmj - cm - rm) / xt->total)
2790 / (2. * xt->total - rm - cm));
2793 for (int i = 0; i < 3; i++)
2794 sig[i] = 2 * gsl_cdf_ugaussian_Q (t[i]);
2803 double sum_fij2_ri = 0.0;
2804 double sum_fij2_ci = 0.0;
2805 FOR_EACH_POPULATED_ROW (i, xt)
2806 FOR_EACH_POPULATED_COLUMN (j, xt)
2808 double temp = pow2 (xt->mat[j + i * n_cols]);
2809 sum_fij2_ri += temp / xt->row_tot[i];
2810 sum_fij2_ci += temp / xt->col_tot[j];
2813 double sum_ri2 = 0.0;
2814 for (int i = 0; i < n_rows; i++)
2815 sum_ri2 += pow2 (xt->row_tot[i]);
2817 double sum_cj2 = 0.0;
2818 for (int j = 0; j < n_cols; j++)
2819 sum_cj2 += pow2 (xt->col_tot[j]);
2821 v[3] = (xt->total * sum_fij2_ci - sum_ri2) / (pow2 (xt->total) - sum_ri2);
2822 v[4] = (xt->total * sum_fij2_ri - sum_cj2) / (pow2 (xt->total) - sum_cj2);
2826 if (proc->statistics & CRS_ST_UC)
2829 FOR_EACH_POPULATED_ROW (i, xt)
2830 UX -= xt->row_tot[i] / xt->total * log (xt->row_tot[i] / xt->total);
2833 FOR_EACH_POPULATED_COLUMN (j, xt)
2834 UY -= xt->col_tot[j] / xt->total * log (xt->col_tot[j] / xt->total);
2838 for (int i = 0; i < n_rows; i++)
2839 for (int j = 0; j < n_cols; j++)
2841 double entry = xt->mat[j + i * n_cols];
2846 P += entry * pow2 (log (xt->col_tot[j] * xt->row_tot[i] / (xt->total * entry)));
2847 UXY -= entry / xt->total * log (entry / xt->total);
2850 double ase1_yx = 0.0;
2851 double ase1_xy = 0.0;
2852 double ase1_sym = 0.0;
2853 for (int i = 0; i < n_rows; i++)
2854 for (int j = 0; j < n_cols; j++)
2856 double entry = xt->mat[j + i * n_cols];
2861 ase1_yx += entry * pow2 (UY * log (entry / xt->row_tot[i])
2862 + (UX - UXY) * log (xt->col_tot[j] / xt->total));
2863 ase1_xy += entry * pow2 (UX * log (entry / xt->col_tot[j])
2864 + (UY - UXY) * log (xt->row_tot[i] / xt->total));
2865 ase1_sym += entry * pow2 ((UXY
2866 * log (xt->row_tot[i] * xt->col_tot[j] / pow2 (xt->total)))
2867 - (UX + UY) * log (entry / xt->total));
2870 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2871 ase[5] = (2. / (xt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2874 v[6] = (UX + UY - UXY) / UX;
2875 ase[6] = sqrt (ase1_xy) / (xt->total * UX * UX);
2876 t[6] = v[6] / (sqrt (P - xt->total * pow2 (UX + UY - UXY)) / (xt->total * UX));
2878 v[7] = (UX + UY - UXY) / UY;
2879 ase[7] = sqrt (ase1_yx) / (xt->total * UY * UY);
2880 t[7] = v[7] / (sqrt (P - xt->total * pow2 (UX + UY - UXY)) / (xt->total * UY));
2884 if (proc->statistics & CRS_ST_D)
2886 double v_dummy[N_SYMMETRIC];
2887 double ase_dummy[N_SYMMETRIC];
2888 double t_dummy[N_SYMMETRIC];
2889 double somers_d_v[3];
2890 double somers_d_ase[3];
2891 double somers_d_t[3];
2893 if (calc_symmetric (proc, xt, v_dummy, ase_dummy, t_dummy,
2894 somers_d_v, somers_d_ase, somers_d_t))
2896 for (int i = 0; i < 3; i++)
2898 v[8 + i] = somers_d_v[i];
2899 ase[8 + i] = somers_d_ase[i];
2900 t[8 + i] = somers_d_t[i];
2901 sig[8 + i] = 2 * gsl_cdf_ugaussian_Q (fabs (somers_d_t[i]));
2907 if (proc->statistics & CRS_ST_ETA)
2910 double sum_Xr = 0.0;
2911 double sum_X2r = 0.0;
2912 for (int i = 0; i < n_rows; i++)
2914 sum_Xr += xt->vars[ROW_VAR].values[i].f * xt->row_tot[i];
2915 sum_X2r += pow2 (xt->vars[ROW_VAR].values[i].f) * xt->row_tot[i];
2917 double SX = sum_X2r - pow2 (sum_Xr) / xt->total;
2920 FOR_EACH_POPULATED_COLUMN (j, xt)
2924 for (int i = 0; i < n_rows; i++)
2926 SXW += (pow2 (xt->vars[ROW_VAR].values[i].f)
2927 * xt->mat[j + i * n_cols]);
2928 cum += (xt->vars[ROW_VAR].values[i].f
2929 * xt->mat[j + i * n_cols]);
2932 SXW -= cum * cum / xt->col_tot[j];
2934 v[11] = sqrt (1. - SXW / SX);
2937 double sum_Yc = 0.0;
2938 double sum_Y2c = 0.0;
2939 for (int i = 0; i < n_cols; i++)
2941 sum_Yc += xt->vars[COL_VAR].values[i].f * xt->col_tot[i];
2942 sum_Y2c += pow2 (xt->vars[COL_VAR].values[i].f) * xt->col_tot[i];
2944 double SY = sum_Y2c - pow2 (sum_Yc) / xt->total;
2947 FOR_EACH_POPULATED_ROW (i, xt)
2950 for (int j = 0; j < n_cols; j++)
2952 SYW += (pow2 (xt->vars[COL_VAR].values[j].f)
2953 * xt->mat[j + i * n_cols]);
2954 cum += (xt->vars[COL_VAR].values[j].f
2955 * xt->mat[j + i * n_cols]);
2958 SYW -= cum * cum / xt->row_tot[i];
2960 v[12] = sqrt (1. - SYW / SY);