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/chart-item.h"
60 #include "output/charts/barchart.h"
62 #include "gl/minmax.h"
63 #include "gl/xalloc.h"
67 #define _(msgid) gettext (msgid)
68 #define N_(msgid) msgid
76 missing=miss:!table/include/report;
77 count=roundwhat:asis/case/!cell,
78 roundhow:!round/truncate;
79 +write[wr_]=none,cells,all;
80 +format=val:!avalue/dvalue,
82 tabl:!tables/notables,
86 +cells[cl_]=count,expected,row,column,total,residual,sresidual,
88 +statistics[st_]=chisq,phi,cc,lambda,uc,none,btau,ctau,risk,gamma,d,
94 /* Number of chi-square statistics. */
97 /* Number of symmetric statistics. */
100 /* Number of directional statistics. */
101 #define N_DIRECTIONAL 13
104 /* Indexes into the 'vars' member of struct crosstabulation and
105 struct crosstab member. */
108 ROW_VAR = 0, /* Row variable. */
109 COL_VAR = 1 /* Column variable. */
110 /* Higher indexes cause multiple tables to be output. */
115 const struct variable *var;
120 /* A crosstabulation of 2 or more variables. */
121 struct crosstabulation
123 struct crosstabs_proc *proc;
124 struct fmt_spec weight_format; /* Format for weight variable. */
125 double missing; /* Weight of missing cases. */
127 /* Variables (2 or more). */
129 struct xtab_var *vars;
131 /* Constants (0 or more). */
133 struct xtab_var *const_vars;
134 size_t *const_indexes;
138 struct freq **entries;
141 /* Number of statistically interesting columns/rows
142 (columns/rows with data in them). */
143 int ns_cols, ns_rows;
145 /* Matrix contents. */
146 double *mat; /* Matrix proper. */
147 double *row_tot; /* Row totals. */
148 double *col_tot; /* Column totals. */
149 double total; /* Grand total. */
152 /* Integer mode variable info. */
155 struct hmap_node hmap_node; /* In struct crosstabs_proc var_ranges map. */
156 const struct variable *var; /* The variable. */
157 int min; /* Minimum value. */
158 int max; /* Maximum value + 1. */
159 int count; /* max - min. */
162 struct crosstabs_proc
164 const struct dictionary *dict;
165 enum { INTEGER, GENERAL } mode;
166 enum mv_class exclude;
170 struct fmt_spec weight_format;
172 /* Variables specifies on VARIABLES. */
173 const struct variable **variables;
175 struct hmap var_ranges;
178 struct crosstabulation *pivots;
182 int n_cells; /* Number of cells requested. */
183 unsigned int cells; /* Bit k is 1 if cell k is requested. */
184 int a_cells[CRS_CL_count]; /* 0...n_cells-1 are the requested cells. */
186 /* Rounding of cells. */
187 bool round_case_weights; /* Round case weights? */
188 bool round_cells; /* If !round_case_weights, round cells? */
189 bool round_down; /* Round down? (otherwise to nearest) */
192 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
194 bool descending; /* True if descending sort order is requested. */
197 const struct var_range *get_var_range (const struct crosstabs_proc *,
198 const struct variable *);
200 static bool should_tabulate_case (const struct crosstabulation *,
201 const struct ccase *, enum mv_class exclude);
202 static void tabulate_general_case (struct crosstabulation *, const struct ccase *,
204 static void tabulate_integer_case (struct crosstabulation *, const struct ccase *,
206 static void postcalc (struct crosstabs_proc *);
209 round_weight (const struct crosstabs_proc *proc, double weight)
211 return proc->round_down ? floor (weight) : floor (weight + 0.5);
214 #define FOR_EACH_POPULATED_COLUMN(C, XT) \
215 for (int C = next_populated_column (0, XT); \
216 C < (XT)->vars[COL_VAR].n_values; \
217 C = next_populated_column (C + 1, XT))
219 next_populated_column (int c, const struct crosstabulation *xt)
221 int n_columns = xt->vars[COL_VAR].n_values;
222 for (; c < n_columns; c++)
228 #define FOR_EACH_POPULATED_ROW(R, XT) \
229 for (int R = next_populated_row (0, XT); R < (XT)->vars[ROW_VAR].n_values; \
230 R = next_populated_row (R + 1, XT))
232 next_populated_row (int r, const struct crosstabulation *xt)
234 int n_rows = xt->vars[ROW_VAR].n_values;
235 for (; r < n_rows; r++)
241 /* Parses and executes the CROSSTABS procedure. */
243 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
245 struct var_range *range, *next_range;
246 struct crosstabs_proc proc;
247 struct casegrouper *grouper;
248 struct casereader *input, *group;
249 struct cmd_crosstabs cmd;
250 struct crosstabulation *xt;
255 proc.dict = dataset_dict (ds);
256 proc.bad_warn = true;
257 proc.variables = NULL;
258 proc.n_variables = 0;
259 hmap_init (&proc.var_ranges);
262 proc.descending = false;
263 proc.weight_format = *dict_get_weight_format (dataset_dict (ds));
265 if (!parse_crosstabs (lexer, ds, &cmd, &proc))
267 result = CMD_FAILURE;
271 proc.mode = proc.n_variables ? INTEGER : GENERAL;
272 proc.barchart = cmd.sbc_barchart > 0;
274 proc.descending = cmd.val == CRS_DVALUE;
276 proc.round_case_weights = cmd.sbc_count && cmd.roundwhat == CRS_CASE;
277 proc.round_cells = cmd.sbc_count && cmd.roundwhat == CRS_CELL;
278 proc.round_down = cmd.roundhow == CRS_TRUNCATE;
282 proc.cells = 1u << CRS_CL_COUNT;
283 else if (cmd.a_cells[CRS_CL_ALL])
284 proc.cells = UINT_MAX;
288 for (i = 0; i < CRS_CL_count; i++)
290 proc.cells |= 1u << i;
292 proc.cells = ((1u << CRS_CL_COUNT)
294 | (1u << CRS_CL_COLUMN)
295 | (1u << CRS_CL_TOTAL));
297 proc.cells &= ((1u << CRS_CL_count) - 1);
298 proc.cells &= ~((1u << CRS_CL_NONE) | (1u << CRS_CL_ALL));
300 for (i = 0; i < CRS_CL_count; i++)
301 if (proc.cells & (1u << i))
302 proc.a_cells[proc.n_cells++] = i;
305 if (cmd.a_statistics[CRS_ST_ALL])
306 proc.statistics = UINT_MAX;
307 else if (cmd.sbc_statistics)
312 for (i = 0; i < CRS_ST_count; i++)
313 if (cmd.a_statistics[i])
314 proc.statistics |= 1u << i;
315 if (proc.statistics == 0)
316 proc.statistics |= 1u << CRS_ST_CHISQ;
322 proc.exclude = (cmd.miss == CRS_TABLE ? MV_ANY
323 : cmd.miss == CRS_INCLUDE ? MV_SYSTEM
325 if (proc.mode == GENERAL && proc.exclude == MV_NEVER)
327 msg (SE, _("Missing mode %s not allowed in general mode. "
328 "Assuming %s."), "REPORT", "MISSING=TABLE");
329 proc.exclude = MV_ANY;
333 proc.pivot = cmd.pivot == CRS_PIVOT;
335 input = casereader_create_filter_weight (proc_open (ds), dataset_dict (ds),
337 grouper = casegrouper_create_splits (input, dataset_dict (ds));
338 while (casegrouper_get_next_group (grouper, &group))
342 /* Output SPLIT FILE variables. */
343 c = casereader_peek (group, 0);
346 output_split_file_values (ds, c);
350 /* Initialize hash tables. */
351 for (xt = &proc.pivots[0]; xt < &proc.pivots[proc.n_pivots]; xt++)
352 hmap_init (&xt->data);
355 for (; (c = casereader_read (group)) != NULL; case_unref (c))
356 for (xt = &proc.pivots[0]; xt < &proc.pivots[proc.n_pivots]; xt++)
358 double weight = dict_get_case_weight (dataset_dict (ds), c,
360 if (cmd.roundwhat == CRS_CASE)
362 weight = round_weight (&proc, weight);
366 if (should_tabulate_case (xt, c, proc.exclude))
368 if (proc.mode == GENERAL)
369 tabulate_general_case (xt, c, weight);
371 tabulate_integer_case (xt, c, weight);
374 xt->missing += weight;
376 casereader_destroy (group);
381 ok = casegrouper_destroy (grouper);
382 ok = proc_commit (ds) && ok;
384 result = ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
387 free (proc.variables);
388 HMAP_FOR_EACH_SAFE (range, next_range, struct var_range, hmap_node,
391 hmap_delete (&proc.var_ranges, &range->hmap_node);
394 for (xt = &proc.pivots[0]; xt < &proc.pivots[proc.n_pivots]; xt++)
397 free (xt->const_vars);
398 free (xt->const_indexes);
405 /* Parses the TABLES subcommand. */
407 crs_custom_tables (struct lexer *lexer, struct dataset *ds,
408 struct cmd_crosstabs *cmd UNUSED, void *proc_)
410 struct crosstabs_proc *proc = proc_;
411 struct const_var_set *var_set;
413 const struct variable ***by = NULL;
415 size_t *by_nvar = NULL;
420 /* Ensure that this is a TABLES subcommand. */
421 if (!lex_match_id (lexer, "TABLES")
422 && (lex_token (lexer) != T_ID ||
423 dict_lookup_var (dataset_dict (ds), lex_tokcstr (lexer)) == NULL)
424 && lex_token (lexer) != T_ALL)
426 lex_match (lexer, T_EQUALS);
428 if (proc->variables != NULL)
429 var_set = const_var_set_create_from_array (proc->variables,
432 var_set = const_var_set_create_from_dict (dataset_dict (ds));
433 assert (var_set != NULL);
437 by = xnrealloc (by, n_by + 1, sizeof *by);
438 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
439 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
440 PV_NO_DUPLICATE | PV_NO_SCRATCH))
442 if (xalloc_oversized (nx, by_nvar[n_by]))
444 msg (SE, _("Too many cross-tabulation variables or dimensions."));
450 if (!lex_match (lexer, T_BY))
459 by_iter = xcalloc (n_by, sizeof *by_iter);
460 proc->pivots = xnrealloc (proc->pivots,
461 proc->n_pivots + nx, sizeof *proc->pivots);
462 for (i = 0; i < nx; i++)
464 struct crosstabulation *xt = &proc->pivots[proc->n_pivots++];
468 xt->weight_format = proc->weight_format;
471 xt->vars = xcalloc (n_by, sizeof *xt->vars);
473 xt->const_vars = NULL;
474 xt->const_indexes = NULL;
476 for (j = 0; j < n_by; j++)
477 xt->vars[j].var = by[j][by_iter[j]];
479 for (j = n_by - 1; j >= 0; j--)
481 if (++by_iter[j] < by_nvar[j])
490 /* All return paths lead here. */
491 for (i = 0; i < n_by; i++)
496 const_var_set_destroy (var_set);
501 /* Parses the VARIABLES subcommand. */
503 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
504 struct cmd_crosstabs *cmd UNUSED, void *proc_)
506 struct crosstabs_proc *proc = proc_;
509 msg (SE, _("%s must be specified before %s."), "VARIABLES", "TABLES");
513 lex_match (lexer, T_EQUALS);
517 size_t orig_nv = proc->n_variables;
522 if (!parse_variables_const (lexer, dataset_dict (ds),
523 &proc->variables, &proc->n_variables,
524 (PV_APPEND | PV_NUMERIC
525 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
528 if (!lex_force_match (lexer, T_LPAREN))
531 if (!lex_force_int (lexer))
533 min = lex_integer (lexer);
536 lex_match (lexer, T_COMMA);
538 if (!lex_force_int (lexer))
540 max = lex_integer (lexer);
543 msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
549 if (!lex_force_match (lexer, T_RPAREN))
552 for (i = orig_nv; i < proc->n_variables; i++)
554 const struct variable *var = proc->variables[i];
555 struct var_range *vr = xmalloc (sizeof *vr);
560 vr->count = max - min + 1;
561 hmap_insert (&proc->var_ranges, &vr->hmap_node,
562 hash_pointer (var, 0));
565 if (lex_token (lexer) == T_SLASH)
572 free (proc->variables);
573 proc->variables = NULL;
574 proc->n_variables = 0;
578 /* Data file processing. */
580 const struct var_range *
581 get_var_range (const struct crosstabs_proc *proc, const struct variable *var)
583 if (!hmap_is_empty (&proc->var_ranges))
585 const struct var_range *range;
587 HMAP_FOR_EACH_IN_BUCKET (range, struct var_range, hmap_node,
588 hash_pointer (var, 0), &proc->var_ranges)
589 if (range->var == var)
597 should_tabulate_case (const struct crosstabulation *xt, const struct ccase *c,
598 enum mv_class exclude)
601 for (j = 0; j < xt->n_vars; j++)
603 const struct variable *var = xt->vars[j].var;
604 const struct var_range *range = get_var_range (xt->proc, var);
606 if (var_is_value_missing (var, case_data (c, var), exclude))
611 double num = case_num (c, var);
612 if (num < range->min || num >= range->max + 1.)
620 tabulate_integer_case (struct crosstabulation *xt, const struct ccase *c,
628 for (j = 0; j < xt->n_vars; j++)
630 /* Throw away fractional parts of values. */
631 hash = hash_int (case_num (c, xt->vars[j].var), hash);
634 HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &xt->data)
636 for (j = 0; j < xt->n_vars; j++)
637 if ((int) case_num (c, xt->vars[j].var) != (int) te->values[j].f)
640 /* Found an existing entry. */
647 /* No existing entry. Create a new one. */
648 te = xmalloc (table_entry_size (xt->n_vars));
650 for (j = 0; j < xt->n_vars; j++)
651 te->values[j].f = (int) case_num (c, xt->vars[j].var);
652 hmap_insert (&xt->data, &te->node, hash);
656 tabulate_general_case (struct crosstabulation *xt, const struct ccase *c,
664 for (j = 0; j < xt->n_vars; j++)
666 const struct variable *var = xt->vars[j].var;
667 hash = value_hash (case_data (c, var), var_get_width (var), hash);
670 HMAP_FOR_EACH_WITH_HASH (te, struct freq, node, hash, &xt->data)
672 for (j = 0; j < xt->n_vars; j++)
674 const struct variable *var = xt->vars[j].var;
675 if (!value_equal (case_data (c, var), &te->values[j],
676 var_get_width (var)))
680 /* Found an existing entry. */
687 /* No existing entry. Create a new one. */
688 te = xmalloc (table_entry_size (xt->n_vars));
690 for (j = 0; j < xt->n_vars; j++)
692 const struct variable *var = xt->vars[j].var;
693 value_clone (&te->values[j], case_data (c, var), var_get_width (var));
695 hmap_insert (&xt->data, &te->node, hash);
698 /* Post-data reading calculations. */
700 static int compare_table_entry_vars_3way (const struct freq *a,
701 const struct freq *b,
702 const struct crosstabulation *xt,
704 static int compare_table_entry_3way (const void *ap_, const void *bp_,
706 static int compare_table_entry_3way_inv (const void *ap_, const void *bp_,
709 static void enum_var_values (const struct crosstabulation *, int var_idx,
711 static void free_var_values (const struct crosstabulation *, int var_idx);
712 static void output_crosstabulation (struct crosstabs_proc *,
713 struct crosstabulation *);
714 static void make_crosstabulation_subset (struct crosstabulation *xt,
715 size_t row0, size_t row1,
716 struct crosstabulation *subset);
717 static void make_summary_table (struct crosstabs_proc *);
718 static bool find_crosstab (struct crosstabulation *, size_t *row0p,
722 postcalc (struct crosstabs_proc *proc)
725 /* Round hash table entries, if requested
727 If this causes any of the cell counts to fall to zero, delete those
729 if (proc->round_cells)
730 for (struct crosstabulation *xt = proc->pivots;
731 xt < &proc->pivots[proc->n_pivots]; xt++)
733 struct freq *e, *next;
734 HMAP_FOR_EACH_SAFE (e, next, struct freq, node, &xt->data)
736 e->count = round_weight (proc, e->count);
739 hmap_delete (&xt->data, &e->node);
745 /* Convert hash tables into sorted arrays of entries. */
746 for (struct crosstabulation *xt = proc->pivots;
747 xt < &proc->pivots[proc->n_pivots]; xt++)
751 xt->n_entries = hmap_count (&xt->data);
752 xt->entries = xnmalloc (xt->n_entries, sizeof *xt->entries);
754 HMAP_FOR_EACH (e, struct freq, node, &xt->data)
755 xt->entries[i++] = e;
756 hmap_destroy (&xt->data);
758 sort (xt->entries, xt->n_entries, sizeof *xt->entries,
759 proc->descending ? compare_table_entry_3way_inv : compare_table_entry_3way,
764 make_summary_table (proc);
766 /* Output each pivot table. */
767 for (struct crosstabulation *xt = proc->pivots;
768 xt < &proc->pivots[proc->n_pivots]; xt++)
770 if (proc->pivot || xt->n_vars == 2)
771 output_crosstabulation (proc, xt);
774 size_t row0 = 0, row1 = 0;
775 while (find_crosstab (xt, &row0, &row1))
777 struct crosstabulation subset;
778 make_crosstabulation_subset (xt, row0, row1, &subset);
779 output_crosstabulation (proc, &subset);
780 free (subset.const_indexes);
785 const struct variable **vars = xcalloc (xt->n_vars, sizeof *vars);
786 for (size_t i = 0; i < xt->n_vars; i++)
787 vars[i] = xt->vars[i].var;
788 chart_item_submit (barchart_create (vars, xt->n_vars, _("Count"),
790 xt->entries, xt->n_entries));
795 /* Free output and prepare for next split file. */
796 for (struct crosstabulation *xt = proc->pivots;
797 xt < &proc->pivots[proc->n_pivots]; xt++)
801 /* Free the members that were allocated in this function(and the values
802 owned by the entries.
804 The other pointer members are either both allocated and destroyed at a
805 lower level (in output_crosstabulation), or both allocated and
806 destroyed at a higher level (in crs_custom_tables and free_proc,
808 for (size_t i = 0; i < xt->n_vars; i++)
810 int width = var_get_width (xt->vars[i].var);
811 if (value_needs_init (width))
815 for (j = 0; j < xt->n_entries; j++)
816 value_destroy (&xt->entries[j]->values[i], width);
820 for (size_t i = 0; i < xt->n_entries; i++)
821 free (xt->entries[i]);
827 make_crosstabulation_subset (struct crosstabulation *xt, size_t row0,
828 size_t row1, struct crosstabulation *subset)
833 assert (xt->n_consts == 0);
835 subset->vars = xt->vars;
837 subset->n_consts = xt->n_vars - 2;
838 subset->const_vars = xt->vars + 2;
839 subset->const_indexes = xcalloc (subset->n_consts,
840 sizeof *subset->const_indexes);
841 for (size_t i = 0; i < subset->n_consts; i++)
843 const union value *value = &xt->entries[row0]->values[2 + i];
845 for (size_t j = 0; j < xt->vars[2 + i].n_values; j++)
846 if (value_equal (&xt->vars[2 + i].values[j], value,
847 var_get_width (xt->vars[2 + i].var)))
849 subset->const_indexes[i] = j;
856 subset->entries = &xt->entries[row0];
857 subset->n_entries = row1 - row0;
861 compare_table_entry_var_3way (const struct freq *a,
862 const struct freq *b,
863 const struct crosstabulation *xt,
866 return value_compare_3way (&a->values[idx], &b->values[idx],
867 var_get_width (xt->vars[idx].var));
871 compare_table_entry_vars_3way (const struct freq *a,
872 const struct freq *b,
873 const struct crosstabulation *xt,
878 for (i = idx1 - 1; i >= idx0; i--)
880 int cmp = compare_table_entry_var_3way (a, b, xt, i);
887 /* Compare the struct freq at *AP to the one at *BP and
888 return a strcmp()-type result. */
890 compare_table_entry_3way (const void *ap_, const void *bp_, const void *xt_)
892 const struct freq *const *ap = ap_;
893 const struct freq *const *bp = bp_;
894 const struct freq *a = *ap;
895 const struct freq *b = *bp;
896 const struct crosstabulation *xt = xt_;
899 cmp = compare_table_entry_vars_3way (a, b, xt, 2, xt->n_vars);
903 cmp = compare_table_entry_var_3way (a, b, xt, ROW_VAR);
907 return compare_table_entry_var_3way (a, b, xt, COL_VAR);
910 /* Inverted version of compare_table_entry_3way */
912 compare_table_entry_3way_inv (const void *ap_, const void *bp_, const void *xt_)
914 return -compare_table_entry_3way (ap_, bp_, xt_);
917 /* Output a table summarizing the cases processed. */
919 make_summary_table (struct crosstabs_proc *proc)
921 struct pivot_table *table = pivot_table_create (N_("Summary"));
922 pivot_table_set_weight_var (table, dict_get_weight (proc->dict));
924 pivot_dimension_create (table, PIVOT_AXIS_COLUMN, N_("Statistics"),
925 N_("N"), PIVOT_RC_COUNT,
926 N_("Percent"), PIVOT_RC_PERCENT);
928 struct pivot_dimension *cases = pivot_dimension_create (
929 table, PIVOT_AXIS_COLUMN, N_("Cases"),
930 N_("Valid"), N_("Missing"), N_("Total"));
931 cases->root->show_label = true;
933 struct pivot_dimension *tables = pivot_dimension_create (
934 table, PIVOT_AXIS_ROW, N_("Crosstabulation"));
935 for (struct crosstabulation *xt = &proc->pivots[0];
936 xt < &proc->pivots[proc->n_pivots]; xt++)
938 struct string name = DS_EMPTY_INITIALIZER;
939 for (size_t i = 0; i < xt->n_vars; i++)
942 ds_put_cstr (&name, " × ");
943 ds_put_cstr (&name, var_to_string (xt->vars[i].var));
946 int row = pivot_category_create_leaf (
948 pivot_value_new_user_text_nocopy (ds_steal_cstr (&name)));
951 for (size_t i = 0; i < xt->n_entries; i++)
952 valid += xt->entries[i]->count;
958 for (int i = 0; i < 3; i++)
960 pivot_table_put3 (table, 0, i, row, pivot_value_new_number (n[i]));
961 pivot_table_put3 (table, 1, i, row,
962 pivot_value_new_number (n[i] / n[2] * 100.0));
966 pivot_table_submit (table);
971 static struct pivot_table *create_crosstab_table (
972 struct crosstabs_proc *, struct crosstabulation *,
973 size_t crs_leaves[CRS_CL_count]);
974 static struct pivot_table *create_chisq_table (struct crosstabulation *);
975 static struct pivot_table *create_sym_table (struct crosstabulation *);
976 static struct pivot_table *create_risk_table (
977 struct crosstabulation *, struct pivot_dimension **risk_statistics);
978 static struct pivot_table *create_direct_table (struct crosstabulation *);
979 static void display_crosstabulation (struct crosstabs_proc *,
980 struct crosstabulation *,
981 struct pivot_table *,
982 size_t crs_leaves[CRS_CL_count]);
983 static void display_chisq (struct crosstabulation *, struct pivot_table *);
984 static void display_symmetric (struct crosstabs_proc *,
985 struct crosstabulation *, struct pivot_table *);
986 static void display_risk (struct crosstabulation *, struct pivot_table *,
987 struct pivot_dimension *risk_statistics);
988 static void display_directional (struct crosstabs_proc *,
989 struct crosstabulation *,
990 struct pivot_table *);
991 static void delete_missing (struct crosstabulation *);
992 static void build_matrix (struct crosstabulation *);
994 /* Output pivot table XT in the context of PROC. */
996 output_crosstabulation (struct crosstabs_proc *proc, struct crosstabulation *xt)
998 for (size_t i = 0; i < xt->n_vars; i++)
999 enum_var_values (xt, i, proc->descending);
1001 if (xt->vars[COL_VAR].n_values == 0)
1006 ds_init_cstr (&vars, var_to_string (xt->vars[0].var));
1007 for (i = 1; i < xt->n_vars; i++)
1008 ds_put_format (&vars, " × %s", var_to_string (xt->vars[i].var));
1010 /* TRANSLATORS: The %s here describes a crosstabulation. It takes the
1011 form "var1 * var2 * var3 * ...". */
1012 msg (SW, _("Crosstabulation %s contained no non-missing cases."),
1016 for (size_t i = 0; i < xt->n_vars; i++)
1017 free_var_values (xt, i);
1021 size_t crs_leaves[CRS_CL_count];
1022 struct pivot_table *table = (proc->cells
1023 ? create_crosstab_table (proc, xt, crs_leaves)
1025 struct pivot_table *chisq = (proc->statistics & (1u << CRS_ST_CHISQ)
1026 ? create_chisq_table (xt)
1028 struct pivot_table *sym
1029 = (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
1030 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
1031 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
1032 | (1u << CRS_ST_KAPPA))
1033 ? create_sym_table (xt)
1035 struct pivot_dimension *risk_statistics = NULL;
1036 struct pivot_table *risk = (proc->statistics & (1u << CRS_ST_RISK)
1037 ? create_risk_table (xt, &risk_statistics)
1039 struct pivot_table *direct
1040 = (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
1041 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA))
1042 ? create_direct_table (xt)
1047 while (find_crosstab (xt, &row0, &row1))
1049 struct crosstabulation x;
1051 make_crosstabulation_subset (xt, row0, row1, &x);
1053 size_t n_rows = x.vars[ROW_VAR].n_values;
1054 size_t n_cols = x.vars[COL_VAR].n_values;
1055 if (size_overflow_p (xtimes (xtimes (n_rows, n_cols), sizeof (double))))
1057 x.row_tot = xmalloc (n_rows * sizeof *x.row_tot);
1058 x.col_tot = xmalloc (n_cols * sizeof *x.col_tot);
1059 x.mat = xmalloc (n_rows * n_cols * sizeof *x.mat);
1063 /* Find the first variable that differs from the last subtable. */
1065 display_crosstabulation (proc, &x, table, crs_leaves);
1067 if (proc->exclude == MV_NEVER)
1068 delete_missing (&x);
1071 display_chisq (&x, chisq);
1074 display_symmetric (proc, &x, sym);
1076 display_risk (&x, risk, risk_statistics);
1078 display_directional (proc, &x, direct);
1083 free (x.const_indexes);
1087 pivot_table_submit (table);
1090 pivot_table_submit (chisq);
1093 pivot_table_submit (sym);
1097 if (!pivot_table_is_empty (risk))
1098 pivot_table_submit (risk);
1100 pivot_table_unref (risk);
1104 pivot_table_submit (direct);
1106 for (size_t i = 0; i < xt->n_vars; i++)
1107 free_var_values (xt, i);
1111 build_matrix (struct crosstabulation *x)
1113 const int col_var_width = var_get_width (x->vars[COL_VAR].var);
1114 const int row_var_width = var_get_width (x->vars[ROW_VAR].var);
1115 size_t n_rows = x->vars[ROW_VAR].n_values;
1116 size_t n_cols = x->vars[COL_VAR].n_values;
1123 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1125 const struct freq *te = *p;
1127 while (!value_equal (&x->vars[ROW_VAR].values[row],
1128 &te->values[ROW_VAR], row_var_width))
1130 for (; col < n_cols; col++)
1136 while (!value_equal (&x->vars[COL_VAR].values[col],
1137 &te->values[COL_VAR], col_var_width))
1144 if (++col >= n_cols)
1150 while (mp < &x->mat[n_cols * n_rows])
1152 assert (mp == &x->mat[n_cols * n_rows]);
1154 /* Column totals, row totals, ns_rows. */
1156 for (col = 0; col < n_cols; col++)
1157 x->col_tot[col] = 0.0;
1158 for (row = 0; row < n_rows; row++)
1159 x->row_tot[row] = 0.0;
1161 for (row = 0; row < n_rows; row++)
1163 bool row_is_empty = true;
1164 for (col = 0; col < n_cols; col++)
1168 row_is_empty = false;
1169 x->col_tot[col] += *mp;
1170 x->row_tot[row] += *mp;
1177 assert (mp == &x->mat[n_cols * n_rows]);
1181 for (col = 0; col < n_cols; col++)
1182 for (row = 0; row < n_rows; row++)
1183 if (x->mat[col + row * n_cols] != 0.0)
1191 for (col = 0; col < n_cols; col++)
1192 x->total += x->col_tot[col];
1196 add_var_dimension (struct pivot_table *table, const struct xtab_var *var,
1197 enum pivot_axis_type axis_type, bool total)
1199 struct pivot_dimension *d = pivot_dimension_create__ (
1200 table, axis_type, pivot_value_new_variable (var->var));
1202 struct pivot_footnote *missing_footnote = pivot_table_create_footnote (
1203 table, pivot_value_new_text (N_("Missing value")));
1205 struct pivot_category *group = pivot_category_create_group__ (
1206 d->root, pivot_value_new_variable (var->var));
1207 for (size_t j = 0; j < var->n_values; j++)
1209 struct pivot_value *value = pivot_value_new_var_value (
1210 var->var, &var->values[j]);
1211 if (var_is_value_missing (var->var, &var->values[j], MV_ANY))
1212 pivot_value_add_footnote (value, missing_footnote);
1213 pivot_category_create_leaf (group, value);
1217 pivot_category_create_leaf (d->root, pivot_value_new_text (N_("Total")));
1220 static struct pivot_table *
1221 create_crosstab_table (struct crosstabs_proc *proc, struct crosstabulation *xt,
1222 size_t crs_leaves[CRS_CL_count])
1225 struct string title = DS_EMPTY_INITIALIZER;
1226 for (size_t i = 0; i < xt->n_vars; i++)
1229 ds_put_cstr (&title, " × ");
1230 ds_put_cstr (&title, var_to_string (xt->vars[i].var));
1232 for (size_t i = 0; i < xt->n_consts; i++)
1234 const struct variable *var = xt->const_vars[i].var;
1235 const union value *value = &xt->entries[0]->values[2 + i];
1238 ds_put_format (&title, ", %s=", var_to_string (var));
1240 /* Insert the formatted value of VAR without any leading spaces. */
1241 s = data_out (value, var_get_encoding (var), var_get_print_format (var));
1242 ds_put_cstr (&title, s + strspn (s, " "));
1245 struct pivot_table *table = pivot_table_create__ (
1246 pivot_value_new_user_text_nocopy (ds_steal_cstr (&title)),
1248 pivot_table_set_weight_format (table, &proc->weight_format);
1249 table->omit_empty = true;
1251 struct pivot_dimension *statistics = pivot_dimension_create (
1252 table, PIVOT_AXIS_ROW, N_("Statistics"));
1259 static const struct statistic stats[CRS_CL_count] =
1261 [CRS_CL_COUNT] = { N_("Count"), PIVOT_RC_COUNT },
1262 [CRS_CL_ROW] = { N_("Row %"), PIVOT_RC_PERCENT },
1263 [CRS_CL_COLUMN] = { N_("Column %"), PIVOT_RC_PERCENT },
1264 [CRS_CL_TOTAL] = { N_("Total %"), PIVOT_RC_PERCENT },
1265 [CRS_CL_EXPECTED] = { N_("Expected"), PIVOT_RC_OTHER },
1266 [CRS_CL_RESIDUAL] = { N_("Residual"), PIVOT_RC_RESIDUAL },
1267 [CRS_CL_SRESIDUAL] = { N_("Std. Residual"), PIVOT_RC_RESIDUAL },
1268 [CRS_CL_ASRESIDUAL] = { N_("Adjusted Residual"), PIVOT_RC_RESIDUAL },
1270 for (size_t i = 0; i < CRS_CL_count; i++)
1271 if (proc->cells & (1u << i) && stats[i].label)
1272 crs_leaves[i] = pivot_category_create_leaf_rc (
1273 statistics->root, pivot_value_new_text (stats[i].label),
1276 for (size_t i = 0; i < xt->n_vars; i++)
1277 add_var_dimension (table, &xt->vars[i],
1278 i == COL_VAR ? PIVOT_AXIS_COLUMN : PIVOT_AXIS_ROW,
1284 static struct pivot_table *
1285 create_chisq_table (struct crosstabulation *xt)
1287 struct pivot_table *chisq = pivot_table_create (N_("Chi-Square Tests"));
1288 pivot_table_set_weight_format (chisq, &xt->weight_format);
1289 chisq->omit_empty = true;
1291 pivot_dimension_create (
1292 chisq, PIVOT_AXIS_ROW, N_("Statistics"),
1293 N_("Pearson Chi-Square"),
1294 N_("Likelihood Ratio"),
1295 N_("Fisher's Exact Test"),
1296 N_("Continuity Correction"),
1297 N_("Linear-by-Linear Association"),
1298 N_("N of Valid Cases"), PIVOT_RC_COUNT);
1300 pivot_dimension_create (
1301 chisq, PIVOT_AXIS_COLUMN, N_("Statistics"),
1302 N_("Value"), PIVOT_RC_OTHER,
1303 N_("df"), PIVOT_RC_COUNT,
1304 N_("Asymptotic Sig. (2-tailed)"), PIVOT_RC_SIGNIFICANCE,
1305 N_("Exact Sig. (2-tailed)"), PIVOT_RC_SIGNIFICANCE,
1306 N_("Exact Sig. (1-tailed)"), PIVOT_RC_SIGNIFICANCE);
1308 for (size_t i = 2; i < xt->n_vars; i++)
1309 add_var_dimension (chisq, &xt->vars[i], PIVOT_AXIS_ROW, false);
1314 /* Symmetric measures. */
1315 static struct pivot_table *
1316 create_sym_table (struct crosstabulation *xt)
1318 struct pivot_table *sym = pivot_table_create (N_("Symmetric Measures"));
1319 pivot_table_set_weight_format (sym, &xt->weight_format);
1320 sym->omit_empty = true;
1322 pivot_dimension_create (
1323 sym, PIVOT_AXIS_COLUMN, N_("Values"),
1324 N_("Value"), PIVOT_RC_OTHER,
1325 N_("Asymp. Std. Error"), PIVOT_RC_OTHER,
1326 N_("Approx. T"), PIVOT_RC_OTHER,
1327 N_("Approx. Sig."), PIVOT_RC_SIGNIFICANCE);
1329 struct pivot_dimension *statistics = pivot_dimension_create (
1330 sym, PIVOT_AXIS_ROW, N_("Statistics"));
1331 pivot_category_create_group (
1332 statistics->root, N_("Nominal by Nominal"),
1333 N_("Phi"), N_("Cramer's V"), N_("Contingency Coefficient"));
1334 pivot_category_create_group (
1335 statistics->root, N_("Ordinal by Ordinal"),
1336 N_("Kendall's tau-b"), N_("Kendall's tau-c"),
1337 N_("Gamma"), N_("Spearman Correlation"));
1338 pivot_category_create_group (
1339 statistics->root, N_("Interval by Interval"),
1341 pivot_category_create_group (
1342 statistics->root, N_("Measure of Agreement"),
1344 pivot_category_create_leaves (statistics->root, N_("N of Valid Cases"),
1347 for (size_t i = 2; i < xt->n_vars; i++)
1348 add_var_dimension (sym, &xt->vars[i], PIVOT_AXIS_ROW, false);
1353 /* Risk estimate. */
1354 static struct pivot_table *
1355 create_risk_table (struct crosstabulation *xt,
1356 struct pivot_dimension **risk_statistics)
1358 struct pivot_table *risk = pivot_table_create (N_("Risk Estimate"));
1359 pivot_table_set_weight_format (risk, &xt->weight_format);
1360 risk->omit_empty = true;
1362 struct pivot_dimension *values = pivot_dimension_create (
1363 risk, PIVOT_AXIS_COLUMN, N_("Values"),
1364 N_("Value"), PIVOT_RC_OTHER);
1365 pivot_category_create_group (
1366 values->root, N_("95% Confidence Interval"),
1367 N_("Lower"), PIVOT_RC_OTHER,
1368 N_("Upper"), PIVOT_RC_OTHER);
1370 *risk_statistics = pivot_dimension_create (
1371 risk, PIVOT_AXIS_ROW, N_("Statistics"));
1373 for (size_t i = 2; i < xt->n_vars; i++)
1374 add_var_dimension (risk, &xt->vars[i], PIVOT_AXIS_ROW, false);
1380 create_direct_stat (struct pivot_category *parent,
1381 const struct crosstabulation *xt,
1382 const char *name, bool symmetric)
1384 struct pivot_category *group = pivot_category_create_group (
1387 pivot_category_create_leaf (group, pivot_value_new_text (N_("Symmetric")));
1389 char *row_label = xasprintf (_("%s Dependent"),
1390 var_to_string (xt->vars[ROW_VAR].var));
1391 pivot_category_create_leaf (group, pivot_value_new_user_text_nocopy (
1394 char *col_label = xasprintf (_("%s Dependent"),
1395 var_to_string (xt->vars[COL_VAR].var));
1396 pivot_category_create_leaf (group, pivot_value_new_user_text_nocopy (
1400 /* Directional measures. */
1401 static struct pivot_table *
1402 create_direct_table (struct crosstabulation *xt)
1404 struct pivot_table *direct = pivot_table_create (N_("Directional Measures"));
1405 pivot_table_set_weight_format (direct, &xt->weight_format);
1406 direct->omit_empty = true;
1408 pivot_dimension_create (
1409 direct, PIVOT_AXIS_COLUMN, N_("Values"),
1410 N_("Value"), PIVOT_RC_OTHER,
1411 N_("Asymp. Std. Error"), PIVOT_RC_OTHER,
1412 N_("Approx. T"), PIVOT_RC_OTHER,
1413 N_("Approx. Sig."), PIVOT_RC_SIGNIFICANCE);
1415 struct pivot_dimension *statistics = pivot_dimension_create (
1416 direct, PIVOT_AXIS_ROW, N_("Statistics"));
1417 struct pivot_category *nn = pivot_category_create_group (
1418 statistics->root, N_("Nominal by Nominal"));
1419 create_direct_stat (nn, xt, N_("Lambda"), true);
1420 create_direct_stat (nn, xt, N_("Goodman and Kruskal tau"), false);
1421 create_direct_stat (nn, xt, N_("Uncertainty Coefficient"), true);
1422 struct pivot_category *oo = pivot_category_create_group (
1423 statistics->root, N_("Ordinal by Ordinal"));
1424 create_direct_stat (oo, xt, N_("Somers' d"), true);
1425 struct pivot_category *ni = pivot_category_create_group (
1426 statistics->root, N_("Nominal by Interval"));
1427 create_direct_stat (ni, xt, N_("Eta"), false);
1429 for (size_t i = 2; i < xt->n_vars; i++)
1430 add_var_dimension (direct, &xt->vars[i], PIVOT_AXIS_ROW, false);
1435 /* Delete missing rows and columns for statistical analysis when
1438 delete_missing (struct crosstabulation *xt)
1440 size_t n_rows = xt->vars[ROW_VAR].n_values;
1441 size_t n_cols = xt->vars[COL_VAR].n_values;
1444 for (r = 0; r < n_rows; r++)
1445 if (var_is_num_missing (xt->vars[ROW_VAR].var,
1446 xt->vars[ROW_VAR].values[r].f, MV_USER))
1448 for (c = 0; c < n_cols; c++)
1449 xt->mat[c + r * n_cols] = 0.;
1454 for (c = 0; c < n_cols; c++)
1455 if (var_is_num_missing (xt->vars[COL_VAR].var,
1456 xt->vars[COL_VAR].values[c].f, MV_USER))
1458 for (r = 0; r < n_rows; r++)
1459 xt->mat[c + r * n_cols] = 0.;
1465 find_crosstab (struct crosstabulation *xt, size_t *row0p, size_t *row1p)
1467 size_t row0 = *row1p;
1470 if (row0 >= xt->n_entries)
1473 for (row1 = row0 + 1; row1 < xt->n_entries; row1++)
1475 struct freq *a = xt->entries[row0];
1476 struct freq *b = xt->entries[row1];
1477 if (compare_table_entry_vars_3way (a, b, xt, 2, xt->n_vars) != 0)
1485 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1486 result. WIDTH_ points to an int which is either 0 for a
1487 numeric value or a string width for a string value. */
1489 compare_value_3way (const void *a_, const void *b_, const void *width_)
1491 const union value *a = a_;
1492 const union value *b = b_;
1493 const int *width = width_;
1495 return value_compare_3way (a, b, *width);
1498 /* Inverted version of the above */
1500 compare_value_3way_inv (const void *a_, const void *b_, const void *width_)
1502 return -compare_value_3way (a_, b_, width_);
1506 /* Given an array of ENTRY_CNT table_entry structures starting at
1507 ENTRIES, creates a sorted list of the values that the variable
1508 with index VAR_IDX takes on. Stores the array of the values in
1509 XT->values and the number of values in XT->n_values. */
1511 enum_var_values (const struct crosstabulation *xt, int var_idx,
1514 struct xtab_var *xv = &xt->vars[var_idx];
1515 const struct var_range *range = get_var_range (xt->proc, xv->var);
1519 xv->values = xnmalloc (range->count, sizeof *xv->values);
1520 xv->n_values = range->count;
1521 for (size_t i = 0; i < range->count; i++)
1522 xv->values[i].f = range->min + i;
1526 int width = var_get_width (xv->var);
1527 struct hmapx_node *node;
1528 const union value *iter;
1532 for (size_t i = 0; i < xt->n_entries; i++)
1534 const struct freq *te = xt->entries[i];
1535 const union value *value = &te->values[var_idx];
1536 size_t hash = value_hash (value, width, 0);
1538 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1539 if (value_equal (iter, value, width))
1542 hmapx_insert (&set, (union value *) value, hash);
1547 xv->n_values = hmapx_count (&set);
1548 xv->values = xnmalloc (xv->n_values, sizeof *xv->values);
1550 HMAPX_FOR_EACH (iter, node, &set)
1551 xv->values[i++] = *iter;
1552 hmapx_destroy (&set);
1554 sort (xv->values, xv->n_values, sizeof *xv->values,
1555 descending ? compare_value_3way_inv : compare_value_3way,
1561 free_var_values (const struct crosstabulation *xt, int var_idx)
1563 struct xtab_var *xv = &xt->vars[var_idx];
1569 /* Displays the crosstabulation table. */
1571 display_crosstabulation (struct crosstabs_proc *proc,
1572 struct crosstabulation *xt, struct pivot_table *table,
1573 size_t crs_leaves[CRS_CL_count])
1575 size_t n_rows = xt->vars[ROW_VAR].n_values;
1576 size_t n_cols = xt->vars[COL_VAR].n_values;
1578 size_t *indexes = xnmalloc (table->n_dimensions, sizeof *indexes);
1579 assert (xt->n_vars == 2);
1580 for (size_t i = 0; i < xt->n_consts; i++)
1581 indexes[i + 3] = xt->const_indexes[i];
1583 /* Put in the actual cells. */
1584 double *mp = xt->mat;
1585 for (size_t r = 0; r < n_rows; r++)
1587 if (!xt->row_tot[r] && proc->mode != INTEGER)
1590 indexes[ROW_VAR + 1] = r;
1591 for (size_t c = 0; c < n_cols; c++)
1593 if (!xt->col_tot[c] && proc->mode != INTEGER)
1596 indexes[COL_VAR + 1] = c;
1598 double expected_value = xt->row_tot[r] * xt->col_tot[c] / xt->total;
1599 double residual = *mp - expected_value;
1600 double sresidual = residual / sqrt (expected_value);
1601 double asresidual = (sresidual
1602 * (1. - xt->row_tot[r] / xt->total)
1603 * (1. - xt->col_tot[c] / xt->total));
1604 double entries[] = {
1605 [CRS_CL_COUNT] = *mp,
1606 [CRS_CL_ROW] = *mp / xt->row_tot[r] * 100.,
1607 [CRS_CL_COLUMN] = *mp / xt->col_tot[c] * 100.,
1608 [CRS_CL_TOTAL] = *mp / xt->total * 100.,
1609 [CRS_CL_EXPECTED] = expected_value,
1610 [CRS_CL_RESIDUAL] = residual,
1611 [CRS_CL_SRESIDUAL] = sresidual,
1612 [CRS_CL_ASRESIDUAL] = asresidual,
1614 for (size_t i = 0; i < proc->n_cells; i++)
1616 int cell = proc->a_cells[i];
1617 indexes[0] = crs_leaves[cell];
1618 pivot_table_put (table, indexes, table->n_dimensions,
1619 pivot_value_new_number (entries[cell]));
1627 for (size_t r = 0; r < n_rows; r++)
1629 if (!xt->row_tot[r] && proc->mode != INTEGER)
1632 double expected_value = xt->row_tot[r] / xt->total;
1633 double entries[] = {
1634 [CRS_CL_COUNT] = xt->row_tot[r],
1635 [CRS_CL_ROW] = 100.0,
1636 [CRS_CL_COLUMN] = expected_value * 100.,
1637 [CRS_CL_TOTAL] = expected_value * 100.,
1638 [CRS_CL_EXPECTED] = expected_value,
1639 [CRS_CL_RESIDUAL] = SYSMIS,
1640 [CRS_CL_SRESIDUAL] = SYSMIS,
1641 [CRS_CL_ASRESIDUAL] = SYSMIS,
1643 for (size_t i = 0; i < proc->n_cells; i++)
1645 int cell = proc->a_cells[i];
1646 double entry = entries[cell];
1647 if (entry != SYSMIS)
1649 indexes[ROW_VAR + 1] = r;
1650 indexes[COL_VAR + 1] = n_cols;
1651 indexes[0] = crs_leaves[cell];
1652 pivot_table_put (table, indexes, table->n_dimensions,
1653 pivot_value_new_number (entry));
1658 for (size_t c = 0; c <= n_cols; c++)
1660 if (c < n_cols && !xt->col_tot[c] && proc->mode != INTEGER)
1663 double ct = c < n_cols ? xt->col_tot[c] : xt->total;
1664 double expected_value = ct / xt->total;
1665 double entries[] = {
1666 [CRS_CL_COUNT] = ct,
1667 [CRS_CL_ROW] = expected_value * 100.0,
1668 [CRS_CL_COLUMN] = 100.0,
1669 [CRS_CL_TOTAL] = expected_value * 100.,
1670 [CRS_CL_EXPECTED] = expected_value,
1671 [CRS_CL_RESIDUAL] = SYSMIS,
1672 [CRS_CL_SRESIDUAL] = SYSMIS,
1673 [CRS_CL_ASRESIDUAL] = SYSMIS,
1675 for (size_t i = 0; i < proc->n_cells; i++)
1677 int cell = proc->a_cells[i];
1678 double entry = entries[cell];
1679 if (entry != SYSMIS)
1681 indexes[ROW_VAR + 1] = n_rows;
1682 indexes[COL_VAR + 1] = c;
1683 indexes[0] = crs_leaves[cell];
1684 pivot_table_put (table, indexes, table->n_dimensions,
1685 pivot_value_new_number (entry));
1693 static void calc_r (struct crosstabulation *,
1694 double *XT, double *Y, double *, double *, double *);
1695 static void calc_chisq (struct crosstabulation *,
1696 double[N_CHISQ], int[N_CHISQ], double *, double *);
1698 /* Display chi-square statistics. */
1700 display_chisq (struct crosstabulation *xt, struct pivot_table *chisq)
1702 double chisq_v[N_CHISQ];
1703 double fisher1, fisher2;
1705 calc_chisq (xt, chisq_v, df, &fisher1, &fisher2);
1707 size_t *indexes = xnmalloc (chisq->n_dimensions, sizeof *indexes);
1708 assert (xt->n_vars == 2);
1709 for (size_t i = 0; i < xt->n_consts; i++)
1710 indexes[i + 2] = xt->const_indexes[i];
1711 for (int i = 0; i < N_CHISQ; i++)
1715 double entries[5] = { SYSMIS, SYSMIS, SYSMIS, SYSMIS, SYSMIS };
1718 entries[3] = fisher2;
1719 entries[4] = fisher1;
1721 else if (chisq_v[i] != SYSMIS)
1723 entries[0] = chisq_v[i];
1725 entries[2] = gsl_cdf_chisq_Q (chisq_v[i], df[i]);
1728 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1729 if (entries[j] != SYSMIS)
1732 pivot_table_put (chisq, indexes, chisq->n_dimensions,
1733 pivot_value_new_number (entries[j]));
1739 pivot_table_put (chisq, indexes, chisq->n_dimensions,
1740 pivot_value_new_number (xt->total));
1745 static int calc_symmetric (struct crosstabs_proc *, struct crosstabulation *,
1746 double[N_SYMMETRIC], double[N_SYMMETRIC],
1747 double[N_SYMMETRIC],
1748 double[3], double[3], double[3]);
1750 /* Display symmetric measures. */
1752 display_symmetric (struct crosstabs_proc *proc, struct crosstabulation *xt,
1753 struct pivot_table *sym)
1755 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1756 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1758 if (!calc_symmetric (proc, xt, sym_v, sym_ase, sym_t,
1759 somers_d_v, somers_d_ase, somers_d_t))
1762 size_t *indexes = xnmalloc (sym->n_dimensions, sizeof *indexes);
1763 assert (xt->n_vars == 2);
1764 for (size_t i = 0; i < xt->n_consts; i++)
1765 indexes[i + 2] = xt->const_indexes[i];
1767 for (int i = 0; i < N_SYMMETRIC; i++)
1769 if (sym_v[i] == SYSMIS)
1774 double entries[] = { sym_v[i], sym_ase[i], sym_t[i] };
1775 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1776 if (entries[j] != SYSMIS)
1779 pivot_table_put (sym, indexes, sym->n_dimensions,
1780 pivot_value_new_number (entries[j]));
1784 indexes[1] = N_SYMMETRIC;
1786 struct pivot_value *total = pivot_value_new_number (xt->total);
1787 pivot_value_set_rc (sym, total, PIVOT_RC_COUNT);
1788 pivot_table_put (sym, indexes, sym->n_dimensions, total);
1793 static bool calc_risk (struct crosstabulation *,
1794 double[], double[], double[], union value *,
1797 /* Display risk estimate. */
1799 display_risk (struct crosstabulation *xt, struct pivot_table *risk,
1800 struct pivot_dimension *risk_statistics)
1802 double risk_v[3], lower[3], upper[3], n_valid;
1804 if (!calc_risk (xt, risk_v, upper, lower, c, &n_valid))
1807 size_t *indexes = xnmalloc (risk->n_dimensions, sizeof *indexes);
1808 assert (xt->n_vars == 2);
1809 for (size_t i = 0; i < xt->n_consts; i++)
1810 indexes[i + 2] = xt->const_indexes[i];
1812 for (int i = 0; i < 3; i++)
1814 const struct variable *cv = xt->vars[COL_VAR].var;
1815 const struct variable *rv = xt->vars[ROW_VAR].var;
1817 if (risk_v[i] == SYSMIS)
1820 struct string label = DS_EMPTY_INITIALIZER;
1824 ds_put_format (&label, _("Odds Ratio for %s"), var_to_string (rv));
1825 ds_put_cstr (&label, " (");
1826 var_append_value_name (rv, &c[0], &label);
1827 ds_put_cstr (&label, " / ");
1828 var_append_value_name (rv, &c[1], &label);
1829 ds_put_cstr (&label, ")");
1833 ds_put_format (&label, _("For cohort %s = "), var_to_string (cv));
1834 var_append_value_name (cv, &xt->vars[ROW_VAR].values[i - 1], &label);
1838 indexes[1] = pivot_category_create_leaf (
1839 risk_statistics->root,
1840 pivot_value_new_user_text_nocopy (ds_steal_cstr (&label)));
1842 double entries[] = { risk_v[i], lower[i], upper[i] };
1843 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1846 pivot_table_put (risk, indexes, risk->n_dimensions,
1847 pivot_value_new_number (entries[i]));
1850 indexes[1] = pivot_category_create_leaf (
1851 risk_statistics->root,
1852 pivot_value_new_text (N_("N of Valid Cases")));
1854 pivot_table_put (risk, indexes, risk->n_dimensions,
1855 pivot_value_new_number (n_valid));
1859 static int calc_directional (struct crosstabs_proc *, struct crosstabulation *,
1860 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1861 double[N_DIRECTIONAL], double[N_DIRECTIONAL]);
1863 /* Display directional measures. */
1865 display_directional (struct crosstabs_proc *proc,
1866 struct crosstabulation *xt, struct pivot_table *direct)
1868 double direct_v[N_DIRECTIONAL];
1869 double direct_ase[N_DIRECTIONAL];
1870 double direct_t[N_DIRECTIONAL];
1871 double sig[N_DIRECTIONAL];
1872 if (!calc_directional (proc, xt, direct_v, direct_ase, direct_t, sig))
1875 size_t *indexes = xnmalloc (direct->n_dimensions, sizeof *indexes);
1876 assert (xt->n_vars == 2);
1877 for (size_t i = 0; i < xt->n_consts; i++)
1878 indexes[i + 2] = xt->const_indexes[i];
1880 for (int i = 0; i < N_DIRECTIONAL; i++)
1882 if (direct_v[i] == SYSMIS)
1887 double entries[] = {
1888 direct_v[i], direct_ase[i], direct_t[i], sig[i],
1890 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1891 if (entries[j] != SYSMIS)
1894 pivot_table_put (direct, indexes, direct->n_dimensions,
1895 pivot_value_new_number (entries[j]));
1902 /* Statistical calculations. */
1904 /* Returns the value of the logarithm of gamma (factorial) function for an integer
1907 log_gamma_int (double xt)
1912 for (i = 2; i < xt; i++)
1918 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
1920 static inline double
1921 Pr (int a, int b, int c, int d)
1923 return exp (log_gamma_int (a + b + 1.) - log_gamma_int (a + 1.)
1924 + log_gamma_int (c + d + 1.) - log_gamma_int (b + 1.)
1925 + log_gamma_int (a + c + 1.) - log_gamma_int (c + 1.)
1926 + log_gamma_int (b + d + 1.) - log_gamma_int (d + 1.)
1927 - log_gamma_int (a + b + c + d + 1.));
1930 /* Swap the contents of A and B. */
1932 swap (int *a, int *b)
1939 /* Calculate significance for Fisher's exact test as specified in
1940 _SPSS Statistical Algorithms_, Appendix 5. */
1942 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
1947 if (MIN (c, d) < MIN (a, b))
1948 swap (&a, &c), swap (&b, &d);
1949 if (MIN (b, d) < MIN (a, c))
1950 swap (&a, &b), swap (&c, &d);
1954 swap (&a, &b), swap (&c, &d);
1956 swap (&a, &c), swap (&b, &d);
1959 pn1 = Pr (a, b, c, d);
1961 for (xt = 1; xt <= a; xt++)
1963 *fisher1 += Pr (a - xt, b + xt, c + xt, d - xt);
1966 *fisher2 = *fisher1;
1968 for (xt = 1; xt <= b; xt++)
1970 double p = Pr (a + xt, b - xt, c - xt, d + xt);
1976 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
1977 columns with values COLS and N_ROWS rows with values ROWS. Values
1978 in the matrix sum to xt->total. */
1980 calc_chisq (struct crosstabulation *xt,
1981 double chisq[N_CHISQ], int df[N_CHISQ],
1982 double *fisher1, double *fisher2)
1984 chisq[0] = chisq[1] = 0.;
1985 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
1986 *fisher1 = *fisher2 = SYSMIS;
1988 df[0] = df[1] = (xt->ns_cols - 1) * (xt->ns_rows - 1);
1990 if (xt->ns_rows <= 1 || xt->ns_cols <= 1)
1992 chisq[0] = chisq[1] = SYSMIS;
1996 size_t n_cols = xt->vars[COL_VAR].n_values;
1997 FOR_EACH_POPULATED_ROW (r, xt)
1998 FOR_EACH_POPULATED_COLUMN (c, xt)
2000 const double expected = xt->row_tot[r] * xt->col_tot[c] / xt->total;
2001 const double freq = xt->mat[n_cols * r + c];
2002 const double residual = freq - expected;
2004 chisq[0] += residual * residual / expected;
2006 chisq[1] += freq * log (expected / freq);
2017 /* Calculate Yates and Fisher exact test. */
2018 if (xt->ns_cols == 2 && xt->ns_rows == 2)
2020 double f11, f12, f21, f22;
2026 FOR_EACH_POPULATED_COLUMN (c, xt)
2034 f11 = xt->mat[nz_cols[0]];
2035 f12 = xt->mat[nz_cols[1]];
2036 f21 = xt->mat[nz_cols[0] + n_cols];
2037 f22 = xt->mat[nz_cols[1] + n_cols];
2042 const double xt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * xt->total;
2045 chisq[3] = (xt->total * pow2 (xt_)
2046 / (f11 + f12) / (f21 + f22)
2047 / (f11 + f21) / (f12 + f22));
2055 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2058 /* Calculate Mantel-Haenszel. */
2059 if (var_is_numeric (xt->vars[ROW_VAR].var)
2060 && var_is_numeric (xt->vars[COL_VAR].var))
2062 double r, ase_0, ase_1;
2063 calc_r (xt, (double *) xt->vars[ROW_VAR].values,
2064 (double *) xt->vars[COL_VAR].values,
2065 &r, &ase_0, &ase_1);
2067 chisq[4] = (xt->total - 1.) * r * r;
2072 /* Calculate the value of Pearson's r. r is stored into R, its T value into
2073 T, and standard error into ERROR. The row and column values must be
2074 passed in XT and Y. */
2076 calc_r (struct crosstabulation *xt,
2077 double *XT, double *Y, double *r, double *t, double *error)
2079 size_t n_rows = xt->vars[ROW_VAR].n_values;
2080 size_t n_cols = xt->vars[COL_VAR].n_values;
2081 double SX, SY, S, T;
2083 double sum_XYf, sum_X2Y2f;
2084 double sum_Xr, sum_X2r;
2085 double sum_Yc, sum_Y2c;
2088 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < n_rows; i++)
2089 for (j = 0; j < n_cols; j++)
2091 double fij = xt->mat[j + i * n_cols];
2092 double product = XT[i] * Y[j];
2093 double temp = fij * product;
2095 sum_X2Y2f += temp * product;
2098 for (sum_Xr = sum_X2r = 0., i = 0; i < n_rows; i++)
2100 sum_Xr += XT[i] * xt->row_tot[i];
2101 sum_X2r += pow2 (XT[i]) * xt->row_tot[i];
2103 Xbar = sum_Xr / xt->total;
2105 for (sum_Yc = sum_Y2c = 0., i = 0; i < n_cols; i++)
2107 sum_Yc += Y[i] * xt->col_tot[i];
2108 sum_Y2c += Y[i] * Y[i] * xt->col_tot[i];
2110 Ybar = sum_Yc / xt->total;
2112 S = sum_XYf - sum_Xr * sum_Yc / xt->total;
2113 SX = sum_X2r - pow2 (sum_Xr) / xt->total;
2114 SY = sum_Y2c - pow2 (sum_Yc) / xt->total;
2117 *t = *r / sqrt (1 - pow2 (*r)) * sqrt (xt->total - 2);
2122 for (s = c = 0., i = 0; i < n_rows; i++)
2123 for (j = 0; j < n_cols; j++)
2125 double Xresid, Yresid;
2128 Xresid = XT[i] - Xbar;
2129 Yresid = Y[j] - Ybar;
2130 temp = (T * Xresid * Yresid
2132 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2133 y = xt->mat[j + i * n_cols] * temp * temp - c;
2138 *error = sqrt (s) / (T * T);
2142 /* Calculate symmetric statistics and their asymptotic standard
2143 errors. Returns 0 if none could be calculated. */
2145 calc_symmetric (struct crosstabs_proc *proc, struct crosstabulation *xt,
2146 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2147 double t[N_SYMMETRIC],
2148 double somers_d_v[3], double somers_d_ase[3],
2149 double somers_d_t[3])
2151 size_t n_rows = xt->vars[ROW_VAR].n_values;
2152 size_t n_cols = xt->vars[COL_VAR].n_values;
2155 q = MIN (xt->ns_rows, xt->ns_cols);
2159 for (i = 0; i < N_SYMMETRIC; i++)
2160 v[i] = ase[i] = t[i] = SYSMIS;
2162 /* Phi, Cramer's V, contingency coefficient. */
2163 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2165 double Xp = 0.; /* Pearson chi-square. */
2167 FOR_EACH_POPULATED_ROW (r, xt)
2168 FOR_EACH_POPULATED_COLUMN (c, xt)
2170 double expected = xt->row_tot[r] * xt->col_tot[c] / xt->total;
2171 double freq = xt->mat[n_cols * r + c];
2172 double residual = freq - expected;
2174 Xp += residual * residual / expected;
2177 if (proc->statistics & (1u << CRS_ST_PHI))
2179 v[0] = sqrt (Xp / xt->total);
2180 v[1] = sqrt (Xp / (xt->total * (q - 1)));
2182 if (proc->statistics & (1u << CRS_ST_CC))
2183 v[2] = sqrt (Xp / (Xp + xt->total));
2186 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2187 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2192 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2196 Dr = Dc = pow2 (xt->total);
2197 for (r = 0; r < n_rows; r++)
2198 Dr -= pow2 (xt->row_tot[r]);
2199 for (c = 0; c < n_cols; c++)
2200 Dc -= pow2 (xt->col_tot[c]);
2202 cum = xnmalloc (n_cols * n_rows, sizeof *cum);
2203 for (c = 0; c < n_cols; c++)
2207 for (r = 0; r < n_rows; r++)
2208 cum[c + r * n_cols] = ct += xt->mat[c + r * n_cols];
2217 for (i = 0; i < n_rows; i++)
2221 for (j = 1; j < n_cols; j++)
2222 Cij += xt->col_tot[j] - cum[j + i * n_cols];
2225 for (j = 1; j < n_cols; j++)
2226 Dij += cum[j + (i - 1) * n_cols];
2230 double fij = xt->mat[j + i * n_cols];
2236 assert (j < n_cols);
2238 Cij -= xt->col_tot[j] - cum[j + i * n_cols];
2239 Dij += xt->col_tot[j - 1] - cum[j - 1 + i * n_cols];
2243 Cij += cum[j - 1 + (i - 1) * n_cols];
2244 Dij -= cum[j + (i - 1) * n_cols];
2250 if (proc->statistics & (1u << CRS_ST_BTAU))
2251 v[3] = (P - Q) / sqrt (Dr * Dc);
2252 if (proc->statistics & (1u << CRS_ST_CTAU))
2253 v[4] = (q * (P - Q)) / (pow2 (xt->total) * (q - 1));
2254 if (proc->statistics & (1u << CRS_ST_GAMMA))
2255 v[5] = (P - Q) / (P + Q);
2257 /* ASE for tau-b, tau-c, gamma. Calculations could be
2258 eliminated here, at expense of memory. */
2263 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2264 for (i = 0; i < n_rows; i++)
2268 for (j = 1; j < n_cols; j++)
2269 Cij += xt->col_tot[j] - cum[j + i * n_cols];
2272 for (j = 1; j < n_cols; j++)
2273 Dij += cum[j + (i - 1) * n_cols];
2277 double fij = xt->mat[j + i * n_cols];
2279 if (proc->statistics & (1u << CRS_ST_BTAU))
2281 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2282 + v[3] * (xt->row_tot[i] * Dc
2283 + xt->col_tot[j] * Dr));
2284 btau_cum += fij * temp * temp;
2288 const double temp = Cij - Dij;
2289 ctau_cum += fij * temp * temp;
2292 if (proc->statistics & (1u << CRS_ST_GAMMA))
2294 const double temp = Q * Cij - P * Dij;
2295 gamma_cum += fij * temp * temp;
2298 if (proc->statistics & (1u << CRS_ST_D))
2300 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2301 - (P - Q) * (xt->total - xt->row_tot[i]));
2302 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2303 - (Q - P) * (xt->total - xt->col_tot[j]));
2308 assert (j < n_cols);
2310 Cij -= xt->col_tot[j] - cum[j + i * n_cols];
2311 Dij += xt->col_tot[j - 1] - cum[j - 1 + i * n_cols];
2315 Cij += cum[j - 1 + (i - 1) * n_cols];
2316 Dij -= cum[j + (i - 1) * n_cols];
2322 btau_var = ((btau_cum
2323 - (xt->total * pow2 (xt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2325 if (proc->statistics & (1u << CRS_ST_BTAU))
2327 ase[3] = sqrt (btau_var);
2328 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / xt->total)
2331 if (proc->statistics & (1u << CRS_ST_CTAU))
2333 ase[4] = ((2 * q / ((q - 1) * pow2 (xt->total)))
2334 * sqrt (ctau_cum - (P - Q) * (P - Q) / xt->total));
2335 t[4] = v[4] / ase[4];
2337 if (proc->statistics & (1u << CRS_ST_GAMMA))
2339 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2340 t[5] = v[5] / (2. / (P + Q)
2341 * sqrt (ctau_cum - (P - Q) * (P - Q) / xt->total));
2343 if (proc->statistics & (1u << CRS_ST_D))
2345 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2346 somers_d_ase[0] = SYSMIS;
2347 somers_d_t[0] = (somers_d_v[0]
2349 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2350 somers_d_v[1] = (P - Q) / Dc;
2351 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2352 somers_d_t[1] = (somers_d_v[1]
2354 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2355 somers_d_v[2] = (P - Q) / Dr;
2356 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2357 somers_d_t[2] = (somers_d_v[2]
2359 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2365 /* Spearman correlation, Pearson's r. */
2366 if (proc->statistics & (1u << CRS_ST_CORR))
2368 double *R = xmalloc (sizeof *R * n_rows);
2369 double *C = xmalloc (sizeof *C * n_cols);
2372 double y, t, c = 0., s = 0.;
2377 R[i] = s + (xt->row_tot[i] + 1.) / 2.;
2378 y = xt->row_tot[i] - c;
2384 assert (i < n_rows);
2389 double y, t, c = 0., s = 0.;
2394 C[j] = s + (xt->col_tot[j] + 1.) / 2;
2395 y = xt->col_tot[j] - c;
2401 assert (j < n_cols);
2405 calc_r (xt, R, C, &v[6], &t[6], &ase[6]);
2410 calc_r (xt, (double *) xt->vars[ROW_VAR].values,
2411 (double *) xt->vars[COL_VAR].values,
2412 &v[7], &t[7], &ase[7]);
2415 /* Cohen's kappa. */
2416 if (proc->statistics & (1u << CRS_ST_KAPPA) && xt->ns_rows == xt->ns_cols)
2418 double ase_under_h0;
2419 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2422 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2423 i < xt->ns_rows; i++, j++)
2427 while (xt->col_tot[j] == 0.)
2430 prod = xt->row_tot[i] * xt->col_tot[j];
2431 sum = xt->row_tot[i] + xt->col_tot[j];
2433 sum_fii += xt->mat[j + i * n_cols];
2435 sum_fiiri_ci += xt->mat[j + i * n_cols] * sum;
2436 sum_riciri_ci += prod * sum;
2438 for (sum_fijri_ci2 = 0., i = 0; i < xt->ns_rows; i++)
2439 for (j = 0; j < xt->ns_cols; j++)
2441 double sum = xt->row_tot[i] + xt->col_tot[j];
2442 sum_fijri_ci2 += xt->mat[j + i * n_cols] * sum * sum;
2445 v[8] = (xt->total * sum_fii - sum_rici) / (pow2 (xt->total) - sum_rici);
2447 ase_under_h0 = sqrt ((pow2 (xt->total) * sum_rici
2448 + sum_rici * sum_rici
2449 - xt->total * sum_riciri_ci)
2450 / (xt->total * (pow2 (xt->total) - sum_rici) * (pow2 (xt->total) - sum_rici)));
2452 ase[8] = sqrt (xt->total * (((sum_fii * (xt->total - sum_fii))
2453 / pow2 (pow2 (xt->total) - sum_rici))
2454 + ((2. * (xt->total - sum_fii)
2455 * (2. * sum_fii * sum_rici
2456 - xt->total * sum_fiiri_ci))
2457 / pow3 (pow2 (xt->total) - sum_rici))
2458 + (pow2 (xt->total - sum_fii)
2459 * (xt->total * sum_fijri_ci2 - 4.
2460 * sum_rici * sum_rici)
2461 / pow4 (pow2 (xt->total) - sum_rici))));
2463 t[8] = v[8] / ase_under_h0;
2469 /* Calculate risk estimate. */
2471 calc_risk (struct crosstabulation *xt,
2472 double *value, double *upper, double *lower, union value *c,
2475 size_t n_cols = xt->vars[COL_VAR].n_values;
2476 double f11, f12, f21, f22;
2479 for (int i = 0; i < 3; i++)
2480 value[i] = upper[i] = lower[i] = SYSMIS;
2482 if (xt->ns_rows != 2 || xt->ns_cols != 2)
2486 /* Find populated columns. */
2489 FOR_EACH_POPULATED_COLUMN (c, xt)
2493 /* Find populated rows. */
2496 FOR_EACH_POPULATED_ROW (r, xt)
2500 f11 = xt->mat[nz_cols[0] + n_cols * nz_rows[0]];
2501 f12 = xt->mat[nz_cols[1] + n_cols * nz_rows[0]];
2502 f21 = xt->mat[nz_cols[0] + n_cols * nz_rows[1]];
2503 f22 = xt->mat[nz_cols[1] + n_cols * nz_rows[1]];
2504 *n_valid = f11 + f12 + f21 + f22;
2506 c[0] = xt->vars[COL_VAR].values[nz_cols[0]];
2507 c[1] = xt->vars[COL_VAR].values[nz_cols[1]];
2510 value[0] = (f11 * f22) / (f12 * f21);
2511 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2512 lower[0] = value[0] * exp (-1.960 * v);
2513 upper[0] = value[0] * exp (1.960 * v);
2515 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2516 v = sqrt ((f12 / (f11 * (f11 + f12)))
2517 + (f22 / (f21 * (f21 + f22))));
2518 lower[1] = value[1] * exp (-1.960 * v);
2519 upper[1] = value[1] * exp (1.960 * v);
2521 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2522 v = sqrt ((f11 / (f12 * (f11 + f12)))
2523 + (f21 / (f22 * (f21 + f22))));
2524 lower[2] = value[2] * exp (-1.960 * v);
2525 upper[2] = value[2] * exp (1.960 * v);
2530 /* Calculate directional measures. */
2532 calc_directional (struct crosstabs_proc *proc, struct crosstabulation *xt,
2533 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2534 double t[N_DIRECTIONAL], double sig[N_DIRECTIONAL])
2536 size_t n_rows = xt->vars[ROW_VAR].n_values;
2537 size_t n_cols = xt->vars[COL_VAR].n_values;
2538 for (int i = 0; i < N_DIRECTIONAL; i++)
2539 v[i] = ase[i] = t[i] = sig[i] = SYSMIS;
2542 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2544 /* Find maximum for each row and their sum. */
2545 double *fim = xnmalloc (n_rows, sizeof *fim);
2546 int *fim_index = xnmalloc (n_rows, sizeof *fim_index);
2547 double sum_fim = 0.0;
2548 for (int i = 0; i < n_rows; i++)
2550 double max = xt->mat[i * n_cols];
2553 for (int j = 1; j < n_cols; j++)
2554 if (xt->mat[j + i * n_cols] > max)
2556 max = xt->mat[j + i * n_cols];
2562 fim_index[i] = index;
2565 /* Find maximum for each column. */
2566 double *fmj = xnmalloc (n_cols, sizeof *fmj);
2567 int *fmj_index = xnmalloc (n_cols, sizeof *fmj_index);
2568 double sum_fmj = 0.0;
2569 for (int j = 0; j < n_cols; j++)
2571 double max = xt->mat[j];
2574 for (int i = 1; i < n_rows; i++)
2575 if (xt->mat[j + i * n_cols] > max)
2577 max = xt->mat[j + i * n_cols];
2583 fmj_index[j] = index;
2586 /* Find maximum row total. */
2587 double rm = xt->row_tot[0];
2589 for (int i = 1; i < n_rows; i++)
2590 if (xt->row_tot[i] > rm)
2592 rm = xt->row_tot[i];
2596 /* Find maximum column total. */
2597 double cm = xt->col_tot[0];
2599 for (int j = 1; j < n_cols; j++)
2600 if (xt->col_tot[j] > cm)
2602 cm = xt->col_tot[j];
2606 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * xt->total - rm - cm);
2607 v[1] = (sum_fmj - rm) / (xt->total - rm);
2608 v[2] = (sum_fim - cm) / (xt->total - cm);
2610 /* ASE1 for Y given XT. */
2613 for (int i = 0; i < n_rows; i++)
2614 if (cm_index == fim_index[i])
2616 ase[2] = sqrt ((xt->total - sum_fim) * (sum_fim + cm - 2. * accum)
2617 / pow3 (xt->total - cm));
2620 /* ASE0 for Y given XT. */
2623 for (int i = 0; i < n_rows; i++)
2624 if (cm_index != fim_index[i])
2625 accum += (xt->mat[i * n_cols + fim_index[i]]
2626 + xt->mat[i * n_cols + cm_index]);
2627 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / xt->total) / (xt->total - cm));
2630 /* ASE1 for XT given Y. */
2633 for (int j = 0; j < n_cols; j++)
2634 if (rm_index == fmj_index[j])
2636 ase[1] = sqrt ((xt->total - sum_fmj) * (sum_fmj + rm - 2. * accum)
2637 / pow3 (xt->total - rm));
2640 /* ASE0 for XT given Y. */
2643 for (int j = 0; j < n_cols; j++)
2644 if (rm_index != fmj_index[j])
2645 accum += (xt->mat[j + n_cols * fmj_index[j]]
2646 + xt->mat[j + n_cols * rm_index]);
2647 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / xt->total) / (xt->total - rm));
2650 /* Symmetric ASE0 and ASE1. */
2652 double accum0 = 0.0;
2653 double accum1 = 0.0;
2654 for (int i = 0; i < n_rows; i++)
2655 for (int j = 0; j < n_cols; j++)
2657 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2658 int temp1 = (i == rm_index) + (j == cm_index);
2659 accum0 += xt->mat[j + i * n_cols] * pow2 (temp0 - temp1);
2660 accum1 += (xt->mat[j + i * n_cols]
2661 * pow2 (temp0 + (v[0] - 1.) * temp1));
2663 ase[0] = sqrt (accum1 - 4. * xt->total * v[0] * v[0]) / (2. * xt->total - rm - cm);
2664 t[0] = v[0] / (sqrt (accum0 - pow2 (sum_fim + sum_fmj - cm - rm) / xt->total)
2665 / (2. * xt->total - rm - cm));
2668 for (int i = 0; i < 3; i++)
2669 sig[i] = 2 * gsl_cdf_ugaussian_Q (t[i]);
2678 double sum_fij2_ri = 0.0;
2679 double sum_fij2_ci = 0.0;
2680 FOR_EACH_POPULATED_ROW (i, xt)
2681 FOR_EACH_POPULATED_COLUMN (j, xt)
2683 double temp = pow2 (xt->mat[j + i * n_cols]);
2684 sum_fij2_ri += temp / xt->row_tot[i];
2685 sum_fij2_ci += temp / xt->col_tot[j];
2688 double sum_ri2 = 0.0;
2689 for (int i = 0; i < n_rows; i++)
2690 sum_ri2 += pow2 (xt->row_tot[i]);
2692 double sum_cj2 = 0.0;
2693 for (int j = 0; j < n_cols; j++)
2694 sum_cj2 += pow2 (xt->col_tot[j]);
2696 v[3] = (xt->total * sum_fij2_ci - sum_ri2) / (pow2 (xt->total) - sum_ri2);
2697 v[4] = (xt->total * sum_fij2_ri - sum_cj2) / (pow2 (xt->total) - sum_cj2);
2701 if (proc->statistics & (1u << CRS_ST_UC))
2704 FOR_EACH_POPULATED_ROW (i, xt)
2705 UX -= xt->row_tot[i] / xt->total * log (xt->row_tot[i] / xt->total);
2708 FOR_EACH_POPULATED_COLUMN (j, xt)
2709 UY -= xt->col_tot[j] / xt->total * log (xt->col_tot[j] / xt->total);
2713 for (int i = 0; i < n_rows; i++)
2714 for (int j = 0; j < n_cols; j++)
2716 double entry = xt->mat[j + i * n_cols];
2721 P += entry * pow2 (log (xt->col_tot[j] * xt->row_tot[i] / (xt->total * entry)));
2722 UXY -= entry / xt->total * log (entry / xt->total);
2725 double ase1_yx = 0.0;
2726 double ase1_xy = 0.0;
2727 double ase1_sym = 0.0;
2728 for (int i = 0; i < n_rows; i++)
2729 for (int j = 0; j < n_cols; j++)
2731 double entry = xt->mat[j + i * n_cols];
2736 ase1_yx += entry * pow2 (UY * log (entry / xt->row_tot[i])
2737 + (UX - UXY) * log (xt->col_tot[j] / xt->total));
2738 ase1_xy += entry * pow2 (UX * log (entry / xt->col_tot[j])
2739 + (UY - UXY) * log (xt->row_tot[i] / xt->total));
2740 ase1_sym += entry * pow2 ((UXY
2741 * log (xt->row_tot[i] * xt->col_tot[j] / pow2 (xt->total)))
2742 - (UX + UY) * log (entry / xt->total));
2745 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2746 ase[5] = (2. / (xt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2749 v[6] = (UX + UY - UXY) / UX;
2750 ase[6] = sqrt (ase1_xy) / (xt->total * UX * UX);
2751 t[6] = v[6] / (sqrt (P - xt->total * pow2 (UX + UY - UXY)) / (xt->total * UX));
2753 v[7] = (UX + UY - UXY) / UY;
2754 ase[7] = sqrt (ase1_yx) / (xt->total * UY * UY);
2755 t[7] = v[7] / (sqrt (P - xt->total * pow2 (UX + UY - UXY)) / (xt->total * UY));
2759 if (proc->statistics & (1u << CRS_ST_D))
2761 double v_dummy[N_SYMMETRIC];
2762 double ase_dummy[N_SYMMETRIC];
2763 double t_dummy[N_SYMMETRIC];
2764 double somers_d_v[3];
2765 double somers_d_ase[3];
2766 double somers_d_t[3];
2768 if (calc_symmetric (proc, xt, v_dummy, ase_dummy, t_dummy,
2769 somers_d_v, somers_d_ase, somers_d_t))
2771 for (int i = 0; i < 3; i++)
2773 v[8 + i] = somers_d_v[i];
2774 ase[8 + i] = somers_d_ase[i];
2775 t[8 + i] = somers_d_t[i];
2776 sig[8 + i] = 2 * gsl_cdf_ugaussian_Q (fabs (somers_d_t[i]));
2782 if (proc->statistics & (1u << CRS_ST_ETA))
2785 double sum_Xr = 0.0;
2786 double sum_X2r = 0.0;
2787 for (int i = 0; i < n_rows; i++)
2789 sum_Xr += xt->vars[ROW_VAR].values[i].f * xt->row_tot[i];
2790 sum_X2r += pow2 (xt->vars[ROW_VAR].values[i].f) * xt->row_tot[i];
2792 double SX = sum_X2r - pow2 (sum_Xr) / xt->total;
2795 FOR_EACH_POPULATED_COLUMN (j, xt)
2799 for (int i = 0; i < n_rows; i++)
2801 SXW += (pow2 (xt->vars[ROW_VAR].values[i].f)
2802 * xt->mat[j + i * n_cols]);
2803 cum += (xt->vars[ROW_VAR].values[i].f
2804 * xt->mat[j + i * n_cols]);
2807 SXW -= cum * cum / xt->col_tot[j];
2809 v[11] = sqrt (1. - SXW / SX);
2812 double sum_Yc = 0.0;
2813 double sum_Y2c = 0.0;
2814 for (int i = 0; i < n_cols; i++)
2816 sum_Yc += xt->vars[COL_VAR].values[i].f * xt->col_tot[i];
2817 sum_Y2c += pow2 (xt->vars[COL_VAR].values[i].f) * xt->col_tot[i];
2819 double SY = sum_Y2c - pow2 (sum_Yc) / xt->total;
2822 FOR_EACH_POPULATED_ROW (i, xt)
2825 for (int j = 0; j < n_cols; j++)
2827 SYW += (pow2 (xt->vars[COL_VAR].values[j].f)
2828 * xt->mat[j + i * n_cols]);
2829 cum += (xt->vars[COL_VAR].values[j].f
2830 * xt->mat[j + i * n_cols]);
2833 SYW -= cum * cum / xt->row_tot[i];
2835 v[12] = sqrt (1. - SYW / SY);