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_destroy (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)));
1247 pivot_table_set_weight_format (table, &proc->weight_format);
1248 table->omit_empty = true;
1250 struct pivot_dimension *statistics = pivot_dimension_create (
1251 table, PIVOT_AXIS_ROW, N_("Statistics"));
1258 static const struct statistic stats[CRS_CL_count] =
1260 [CRS_CL_COUNT] = { N_("Count"), PIVOT_RC_COUNT },
1261 [CRS_CL_ROW] = { N_("Row %"), PIVOT_RC_PERCENT },
1262 [CRS_CL_COLUMN] = { N_("Column %"), PIVOT_RC_PERCENT },
1263 [CRS_CL_TOTAL] = { N_("Total %"), PIVOT_RC_PERCENT },
1264 [CRS_CL_EXPECTED] = { N_("Expected"), PIVOT_RC_OTHER },
1265 [CRS_CL_RESIDUAL] = { N_("Residual"), PIVOT_RC_RESIDUAL },
1266 [CRS_CL_SRESIDUAL] = { N_("Std. Residual"), PIVOT_RC_RESIDUAL },
1267 [CRS_CL_ASRESIDUAL] = { N_("Adjusted Residual"), PIVOT_RC_RESIDUAL },
1269 for (size_t i = 0; i < CRS_CL_count; i++)
1270 if (proc->cells & (1u << i) && stats[i].label)
1271 crs_leaves[i] = pivot_category_create_leaf_rc (
1272 statistics->root, pivot_value_new_text (stats[i].label),
1275 for (size_t i = 0; i < xt->n_vars; i++)
1276 add_var_dimension (table, &xt->vars[i],
1277 i == COL_VAR ? PIVOT_AXIS_COLUMN : PIVOT_AXIS_ROW,
1283 static struct pivot_table *
1284 create_chisq_table (struct crosstabulation *xt)
1286 struct pivot_table *chisq = pivot_table_create (N_("Chi-Square Tests"));
1287 pivot_table_set_weight_format (chisq, &xt->weight_format);
1288 chisq->omit_empty = true;
1290 pivot_dimension_create (
1291 chisq, PIVOT_AXIS_ROW, N_("Statistics"),
1292 N_("Pearson Chi-Square"),
1293 N_("Likelihood Ratio"),
1294 N_("Fisher's Exact Test"),
1295 N_("Continuity Correction"),
1296 N_("Linear-by-Linear Association"),
1297 N_("N of Valid Cases"), PIVOT_RC_COUNT);
1299 pivot_dimension_create (
1300 chisq, PIVOT_AXIS_COLUMN, N_("Statistics"),
1301 N_("Value"), PIVOT_RC_OTHER,
1302 N_("df"), PIVOT_RC_COUNT,
1303 N_("Asymptotic Sig. (2-tailed)"), PIVOT_RC_SIGNIFICANCE,
1304 N_("Exact Sig. (2-tailed)"), PIVOT_RC_SIGNIFICANCE,
1305 N_("Exact Sig. (1-tailed)"), PIVOT_RC_SIGNIFICANCE);
1307 for (size_t i = 2; i < xt->n_vars; i++)
1308 add_var_dimension (chisq, &xt->vars[i], PIVOT_AXIS_ROW, false);
1313 /* Symmetric measures. */
1314 static struct pivot_table *
1315 create_sym_table (struct crosstabulation *xt)
1317 struct pivot_table *sym = pivot_table_create (N_("Symmetric Measures"));
1318 pivot_table_set_weight_format (sym, &xt->weight_format);
1319 sym->omit_empty = true;
1321 pivot_dimension_create (
1322 sym, PIVOT_AXIS_COLUMN, N_("Values"),
1323 N_("Value"), PIVOT_RC_OTHER,
1324 N_("Asymp. Std. Error"), PIVOT_RC_OTHER,
1325 N_("Approx. T"), PIVOT_RC_OTHER,
1326 N_("Approx. Sig."), PIVOT_RC_SIGNIFICANCE);
1328 struct pivot_dimension *statistics = pivot_dimension_create (
1329 sym, PIVOT_AXIS_ROW, N_("Statistics"));
1330 pivot_category_create_group (
1331 statistics->root, N_("Nominal by Nominal"),
1332 N_("Phi"), N_("Cramer's V"), N_("Contingency Coefficient"));
1333 pivot_category_create_group (
1334 statistics->root, N_("Ordinal by Ordinal"),
1335 N_("Kendall's tau-b"), N_("Kendall's tau-c"),
1336 N_("Gamma"), N_("Spearman Correlation"));
1337 pivot_category_create_group (
1338 statistics->root, N_("Interval by Interval"),
1340 pivot_category_create_group (
1341 statistics->root, N_("Measure of Agreement"),
1343 pivot_category_create_leaves (statistics->root, N_("N of Valid Cases"),
1346 for (size_t i = 2; i < xt->n_vars; i++)
1347 add_var_dimension (sym, &xt->vars[i], PIVOT_AXIS_ROW, false);
1352 /* Risk estimate. */
1353 static struct pivot_table *
1354 create_risk_table (struct crosstabulation *xt,
1355 struct pivot_dimension **risk_statistics)
1357 struct pivot_table *risk = pivot_table_create (N_("Risk Estimate"));
1358 pivot_table_set_weight_format (risk, &xt->weight_format);
1359 risk->omit_empty = true;
1361 struct pivot_dimension *values = pivot_dimension_create (
1362 risk, PIVOT_AXIS_COLUMN, N_("Values"),
1363 N_("Value"), PIVOT_RC_OTHER);
1364 pivot_category_create_group (
1365 values->root, N_("95% Confidence Interval"),
1366 N_("Lower"), PIVOT_RC_OTHER,
1367 N_("Upper"), PIVOT_RC_OTHER);
1369 *risk_statistics = pivot_dimension_create (
1370 risk, PIVOT_AXIS_ROW, N_("Statistics"));
1372 for (size_t i = 2; i < xt->n_vars; i++)
1373 add_var_dimension (risk, &xt->vars[i], PIVOT_AXIS_ROW, false);
1379 create_direct_stat (struct pivot_category *parent,
1380 const struct crosstabulation *xt,
1381 const char *name, bool symmetric)
1383 struct pivot_category *group = pivot_category_create_group (
1386 pivot_category_create_leaf (group, pivot_value_new_text (N_("Symmetric")));
1388 char *row_label = xasprintf (_("%s Dependent"),
1389 var_to_string (xt->vars[ROW_VAR].var));
1390 pivot_category_create_leaf (group, pivot_value_new_user_text_nocopy (
1393 char *col_label = xasprintf (_("%s Dependent"),
1394 var_to_string (xt->vars[COL_VAR].var));
1395 pivot_category_create_leaf (group, pivot_value_new_user_text_nocopy (
1399 /* Directional measures. */
1400 static struct pivot_table *
1401 create_direct_table (struct crosstabulation *xt)
1403 struct pivot_table *direct = pivot_table_create (N_("Directional Measures"));
1404 pivot_table_set_weight_format (direct, &xt->weight_format);
1405 direct->omit_empty = true;
1407 pivot_dimension_create (
1408 direct, PIVOT_AXIS_COLUMN, N_("Values"),
1409 N_("Value"), PIVOT_RC_OTHER,
1410 N_("Asymp. Std. Error"), PIVOT_RC_OTHER,
1411 N_("Approx. T"), PIVOT_RC_OTHER,
1412 N_("Approx. Sig."), PIVOT_RC_SIGNIFICANCE);
1414 struct pivot_dimension *statistics = pivot_dimension_create (
1415 direct, PIVOT_AXIS_ROW, N_("Statistics"));
1416 struct pivot_category *nn = pivot_category_create_group (
1417 statistics->root, N_("Nominal by Nominal"));
1418 create_direct_stat (nn, xt, N_("Lambda"), true);
1419 create_direct_stat (nn, xt, N_("Goodman and Kruskal tau"), false);
1420 create_direct_stat (nn, xt, N_("Uncertainty Coefficient"), true);
1421 struct pivot_category *oo = pivot_category_create_group (
1422 statistics->root, N_("Ordinal by Ordinal"));
1423 create_direct_stat (oo, xt, N_("Somers' d"), true);
1424 struct pivot_category *ni = pivot_category_create_group (
1425 statistics->root, N_("Nominal by Interval"));
1426 create_direct_stat (ni, xt, N_("Eta"), false);
1428 for (size_t i = 2; i < xt->n_vars; i++)
1429 add_var_dimension (direct, &xt->vars[i], PIVOT_AXIS_ROW, false);
1434 /* Delete missing rows and columns for statistical analysis when
1437 delete_missing (struct crosstabulation *xt)
1439 size_t n_rows = xt->vars[ROW_VAR].n_values;
1440 size_t n_cols = xt->vars[COL_VAR].n_values;
1443 for (r = 0; r < n_rows; r++)
1444 if (var_is_num_missing (xt->vars[ROW_VAR].var,
1445 xt->vars[ROW_VAR].values[r].f, MV_USER))
1447 for (c = 0; c < n_cols; c++)
1448 xt->mat[c + r * n_cols] = 0.;
1453 for (c = 0; c < n_cols; c++)
1454 if (var_is_num_missing (xt->vars[COL_VAR].var,
1455 xt->vars[COL_VAR].values[c].f, MV_USER))
1457 for (r = 0; r < n_rows; r++)
1458 xt->mat[c + r * n_cols] = 0.;
1464 find_crosstab (struct crosstabulation *xt, size_t *row0p, size_t *row1p)
1466 size_t row0 = *row1p;
1469 if (row0 >= xt->n_entries)
1472 for (row1 = row0 + 1; row1 < xt->n_entries; row1++)
1474 struct freq *a = xt->entries[row0];
1475 struct freq *b = xt->entries[row1];
1476 if (compare_table_entry_vars_3way (a, b, xt, 2, xt->n_vars) != 0)
1484 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1485 result. WIDTH_ points to an int which is either 0 for a
1486 numeric value or a string width for a string value. */
1488 compare_value_3way (const void *a_, const void *b_, const void *width_)
1490 const union value *a = a_;
1491 const union value *b = b_;
1492 const int *width = width_;
1494 return value_compare_3way (a, b, *width);
1497 /* Inverted version of the above */
1499 compare_value_3way_inv (const void *a_, const void *b_, const void *width_)
1501 return -compare_value_3way (a_, b_, width_);
1505 /* Given an array of ENTRY_CNT table_entry structures starting at
1506 ENTRIES, creates a sorted list of the values that the variable
1507 with index VAR_IDX takes on. Stores the array of the values in
1508 XT->values and the number of values in XT->n_values. */
1510 enum_var_values (const struct crosstabulation *xt, int var_idx,
1513 struct xtab_var *xv = &xt->vars[var_idx];
1514 const struct var_range *range = get_var_range (xt->proc, xv->var);
1518 xv->values = xnmalloc (range->count, sizeof *xv->values);
1519 xv->n_values = range->count;
1520 for (size_t i = 0; i < range->count; i++)
1521 xv->values[i].f = range->min + i;
1525 int width = var_get_width (xv->var);
1526 struct hmapx_node *node;
1527 const union value *iter;
1531 for (size_t i = 0; i < xt->n_entries; i++)
1533 const struct freq *te = xt->entries[i];
1534 const union value *value = &te->values[var_idx];
1535 size_t hash = value_hash (value, width, 0);
1537 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1538 if (value_equal (iter, value, width))
1541 hmapx_insert (&set, (union value *) value, hash);
1546 xv->n_values = hmapx_count (&set);
1547 xv->values = xnmalloc (xv->n_values, sizeof *xv->values);
1549 HMAPX_FOR_EACH (iter, node, &set)
1550 xv->values[i++] = *iter;
1551 hmapx_destroy (&set);
1553 sort (xv->values, xv->n_values, sizeof *xv->values,
1554 descending ? compare_value_3way_inv : compare_value_3way,
1560 free_var_values (const struct crosstabulation *xt, int var_idx)
1562 struct xtab_var *xv = &xt->vars[var_idx];
1568 /* Displays the crosstabulation table. */
1570 display_crosstabulation (struct crosstabs_proc *proc,
1571 struct crosstabulation *xt, struct pivot_table *table,
1572 size_t crs_leaves[CRS_CL_count])
1574 size_t n_rows = xt->vars[ROW_VAR].n_values;
1575 size_t n_cols = xt->vars[COL_VAR].n_values;
1577 size_t *indexes = xnmalloc (table->n_dimensions, sizeof *indexes);
1578 assert (xt->n_vars == 2);
1579 for (size_t i = 0; i < xt->n_consts; i++)
1580 indexes[i + 3] = xt->const_indexes[i];
1582 /* Put in the actual cells. */
1583 double *mp = xt->mat;
1584 for (size_t r = 0; r < n_rows; r++)
1586 if (!xt->row_tot[r] && proc->mode != INTEGER)
1589 indexes[ROW_VAR + 1] = r;
1590 for (size_t c = 0; c < n_cols; c++)
1592 if (!xt->col_tot[c] && proc->mode != INTEGER)
1595 indexes[COL_VAR + 1] = c;
1597 double expected_value = xt->row_tot[r] * xt->col_tot[c] / xt->total;
1598 double residual = *mp - expected_value;
1599 double sresidual = residual / sqrt (expected_value);
1600 double asresidual = (sresidual
1601 * (1. - xt->row_tot[r] / xt->total)
1602 * (1. - xt->col_tot[c] / xt->total));
1603 double entries[] = {
1604 [CRS_CL_COUNT] = *mp,
1605 [CRS_CL_ROW] = *mp / xt->row_tot[r] * 100.,
1606 [CRS_CL_COLUMN] = *mp / xt->col_tot[c] * 100.,
1607 [CRS_CL_TOTAL] = *mp / xt->total * 100.,
1608 [CRS_CL_EXPECTED] = expected_value,
1609 [CRS_CL_RESIDUAL] = residual,
1610 [CRS_CL_SRESIDUAL] = sresidual,
1611 [CRS_CL_ASRESIDUAL] = asresidual,
1613 for (size_t i = 0; i < proc->n_cells; i++)
1615 int cell = proc->a_cells[i];
1616 indexes[0] = crs_leaves[cell];
1617 pivot_table_put (table, indexes, table->n_dimensions,
1618 pivot_value_new_number (entries[cell]));
1626 for (size_t r = 0; r < n_rows; r++)
1628 if (!xt->row_tot[r] && proc->mode != INTEGER)
1631 double expected_value = xt->row_tot[r] / xt->total;
1632 double entries[] = {
1633 [CRS_CL_COUNT] = xt->row_tot[r],
1634 [CRS_CL_ROW] = 100.0,
1635 [CRS_CL_COLUMN] = expected_value * 100.,
1636 [CRS_CL_TOTAL] = expected_value * 100.,
1637 [CRS_CL_EXPECTED] = expected_value,
1638 [CRS_CL_RESIDUAL] = SYSMIS,
1639 [CRS_CL_SRESIDUAL] = SYSMIS,
1640 [CRS_CL_ASRESIDUAL] = SYSMIS,
1642 for (size_t i = 0; i < proc->n_cells; i++)
1644 int cell = proc->a_cells[i];
1645 double entry = entries[cell];
1646 if (entry != SYSMIS)
1648 indexes[ROW_VAR + 1] = r;
1649 indexes[COL_VAR + 1] = n_cols;
1650 indexes[0] = crs_leaves[cell];
1651 pivot_table_put (table, indexes, table->n_dimensions,
1652 pivot_value_new_number (entry));
1657 for (size_t c = 0; c <= n_cols; c++)
1659 if (c < n_cols && !xt->col_tot[c] && proc->mode != INTEGER)
1662 double ct = c < n_cols ? xt->col_tot[c] : xt->total;
1663 double expected_value = ct / xt->total;
1664 double entries[] = {
1665 [CRS_CL_COUNT] = ct,
1666 [CRS_CL_ROW] = expected_value * 100.0,
1667 [CRS_CL_COLUMN] = 100.0,
1668 [CRS_CL_TOTAL] = expected_value * 100.,
1669 [CRS_CL_EXPECTED] = expected_value,
1670 [CRS_CL_RESIDUAL] = SYSMIS,
1671 [CRS_CL_SRESIDUAL] = SYSMIS,
1672 [CRS_CL_ASRESIDUAL] = SYSMIS,
1674 for (size_t i = 0; i < proc->n_cells; i++)
1676 int cell = proc->a_cells[i];
1677 double entry = entries[cell];
1678 if (entry != SYSMIS)
1680 indexes[ROW_VAR + 1] = n_rows;
1681 indexes[COL_VAR + 1] = c;
1682 indexes[0] = crs_leaves[cell];
1683 pivot_table_put (table, indexes, table->n_dimensions,
1684 pivot_value_new_number (entry));
1692 static void calc_r (struct crosstabulation *,
1693 double *XT, double *Y, double *, double *, double *);
1694 static void calc_chisq (struct crosstabulation *,
1695 double[N_CHISQ], int[N_CHISQ], double *, double *);
1697 /* Display chi-square statistics. */
1699 display_chisq (struct crosstabulation *xt, struct pivot_table *chisq)
1701 double chisq_v[N_CHISQ];
1702 double fisher1, fisher2;
1704 calc_chisq (xt, chisq_v, df, &fisher1, &fisher2);
1706 size_t *indexes = xnmalloc (chisq->n_dimensions, sizeof *indexes);
1707 assert (xt->n_vars == 2);
1708 for (size_t i = 0; i < xt->n_consts; i++)
1709 indexes[i + 2] = xt->const_indexes[i];
1710 for (int i = 0; i < N_CHISQ; i++)
1714 double entries[5] = { SYSMIS, SYSMIS, SYSMIS, SYSMIS, SYSMIS };
1717 entries[3] = fisher2;
1718 entries[4] = fisher1;
1720 else if (chisq_v[i] != SYSMIS)
1722 entries[0] = chisq_v[i];
1724 entries[2] = gsl_cdf_chisq_Q (chisq_v[i], df[i]);
1727 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1728 if (entries[j] != SYSMIS)
1731 pivot_table_put (chisq, indexes, chisq->n_dimensions,
1732 pivot_value_new_number (entries[j]));
1738 pivot_table_put (chisq, indexes, chisq->n_dimensions,
1739 pivot_value_new_number (xt->total));
1744 static int calc_symmetric (struct crosstabs_proc *, struct crosstabulation *,
1745 double[N_SYMMETRIC], double[N_SYMMETRIC],
1746 double[N_SYMMETRIC],
1747 double[3], double[3], double[3]);
1749 /* Display symmetric measures. */
1751 display_symmetric (struct crosstabs_proc *proc, struct crosstabulation *xt,
1752 struct pivot_table *sym)
1754 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1755 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1757 if (!calc_symmetric (proc, xt, sym_v, sym_ase, sym_t,
1758 somers_d_v, somers_d_ase, somers_d_t))
1761 size_t *indexes = xnmalloc (sym->n_dimensions, sizeof *indexes);
1762 assert (xt->n_vars == 2);
1763 for (size_t i = 0; i < xt->n_consts; i++)
1764 indexes[i + 2] = xt->const_indexes[i];
1766 for (int i = 0; i < N_SYMMETRIC; i++)
1768 if (sym_v[i] == SYSMIS)
1773 double entries[] = { sym_v[i], sym_ase[i], sym_t[i] };
1774 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1775 if (entries[j] != SYSMIS)
1778 pivot_table_put (sym, indexes, sym->n_dimensions,
1779 pivot_value_new_number (entries[j]));
1783 indexes[1] = N_SYMMETRIC;
1785 struct pivot_value *total = pivot_value_new_number (xt->total);
1786 pivot_value_set_rc (sym, total, PIVOT_RC_COUNT);
1787 pivot_table_put (sym, indexes, sym->n_dimensions, total);
1792 static bool calc_risk (struct crosstabulation *,
1793 double[], double[], double[], union value *,
1796 /* Display risk estimate. */
1798 display_risk (struct crosstabulation *xt, struct pivot_table *risk,
1799 struct pivot_dimension *risk_statistics)
1801 double risk_v[3], lower[3], upper[3], n_valid;
1803 if (!calc_risk (xt, risk_v, upper, lower, c, &n_valid))
1806 size_t *indexes = xnmalloc (risk->n_dimensions, sizeof *indexes);
1807 assert (xt->n_vars == 2);
1808 for (size_t i = 0; i < xt->n_consts; i++)
1809 indexes[i + 2] = xt->const_indexes[i];
1811 for (int i = 0; i < 3; i++)
1813 const struct variable *cv = xt->vars[COL_VAR].var;
1814 const struct variable *rv = xt->vars[ROW_VAR].var;
1816 if (risk_v[i] == SYSMIS)
1819 struct string label = DS_EMPTY_INITIALIZER;
1823 ds_put_format (&label, _("Odds Ratio for %s"), var_to_string (rv));
1824 ds_put_cstr (&label, " (");
1825 var_append_value_name (rv, &c[0], &label);
1826 ds_put_cstr (&label, " / ");
1827 var_append_value_name (rv, &c[1], &label);
1828 ds_put_cstr (&label, ")");
1832 ds_put_format (&label, _("For cohort %s = "), var_to_string (cv));
1833 var_append_value_name (cv, &xt->vars[ROW_VAR].values[i - 1], &label);
1837 indexes[1] = pivot_category_create_leaf (
1838 risk_statistics->root,
1839 pivot_value_new_user_text_nocopy (ds_steal_cstr (&label)));
1841 double entries[] = { risk_v[i], lower[i], upper[i] };
1842 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1845 pivot_table_put (risk, indexes, risk->n_dimensions,
1846 pivot_value_new_number (entries[i]));
1849 indexes[1] = pivot_category_create_leaf (
1850 risk_statistics->root,
1851 pivot_value_new_text (N_("N of Valid Cases")));
1853 pivot_table_put (risk, indexes, risk->n_dimensions,
1854 pivot_value_new_number (n_valid));
1858 static int calc_directional (struct crosstabs_proc *, struct crosstabulation *,
1859 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1860 double[N_DIRECTIONAL], double[N_DIRECTIONAL]);
1862 /* Display directional measures. */
1864 display_directional (struct crosstabs_proc *proc,
1865 struct crosstabulation *xt, struct pivot_table *direct)
1867 double direct_v[N_DIRECTIONAL];
1868 double direct_ase[N_DIRECTIONAL];
1869 double direct_t[N_DIRECTIONAL];
1870 double sig[N_DIRECTIONAL];
1871 if (!calc_directional (proc, xt, direct_v, direct_ase, direct_t, sig))
1874 size_t *indexes = xnmalloc (direct->n_dimensions, sizeof *indexes);
1875 assert (xt->n_vars == 2);
1876 for (size_t i = 0; i < xt->n_consts; i++)
1877 indexes[i + 2] = xt->const_indexes[i];
1879 for (int i = 0; i < N_DIRECTIONAL; i++)
1881 if (direct_v[i] == SYSMIS)
1886 double entries[] = {
1887 direct_v[i], direct_ase[i], direct_t[i], sig[i],
1889 for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
1890 if (entries[j] != SYSMIS)
1893 pivot_table_put (direct, indexes, direct->n_dimensions,
1894 pivot_value_new_number (entries[j]));
1901 /* Statistical calculations. */
1903 /* Returns the value of the logarithm of gamma (factorial) function for an integer
1906 log_gamma_int (double xt)
1911 for (i = 2; i < xt; i++)
1917 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
1919 static inline double
1920 Pr (int a, int b, int c, int d)
1922 return exp (log_gamma_int (a + b + 1.) - log_gamma_int (a + 1.)
1923 + log_gamma_int (c + d + 1.) - log_gamma_int (b + 1.)
1924 + log_gamma_int (a + c + 1.) - log_gamma_int (c + 1.)
1925 + log_gamma_int (b + d + 1.) - log_gamma_int (d + 1.)
1926 - log_gamma_int (a + b + c + d + 1.));
1929 /* Swap the contents of A and B. */
1931 swap (int *a, int *b)
1938 /* Calculate significance for Fisher's exact test as specified in
1939 _SPSS Statistical Algorithms_, Appendix 5. */
1941 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
1946 if (MIN (c, d) < MIN (a, b))
1947 swap (&a, &c), swap (&b, &d);
1948 if (MIN (b, d) < MIN (a, c))
1949 swap (&a, &b), swap (&c, &d);
1953 swap (&a, &b), swap (&c, &d);
1955 swap (&a, &c), swap (&b, &d);
1958 pn1 = Pr (a, b, c, d);
1960 for (xt = 1; xt <= a; xt++)
1962 *fisher1 += Pr (a - xt, b + xt, c + xt, d - xt);
1965 *fisher2 = *fisher1;
1967 for (xt = 1; xt <= b; xt++)
1969 double p = Pr (a + xt, b - xt, c - xt, d + xt);
1975 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
1976 columns with values COLS and N_ROWS rows with values ROWS. Values
1977 in the matrix sum to xt->total. */
1979 calc_chisq (struct crosstabulation *xt,
1980 double chisq[N_CHISQ], int df[N_CHISQ],
1981 double *fisher1, double *fisher2)
1983 chisq[0] = chisq[1] = 0.;
1984 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
1985 *fisher1 = *fisher2 = SYSMIS;
1987 df[0] = df[1] = (xt->ns_cols - 1) * (xt->ns_rows - 1);
1989 if (xt->ns_rows <= 1 || xt->ns_cols <= 1)
1991 chisq[0] = chisq[1] = SYSMIS;
1995 size_t n_cols = xt->vars[COL_VAR].n_values;
1996 FOR_EACH_POPULATED_ROW (r, xt)
1997 FOR_EACH_POPULATED_COLUMN (c, xt)
1999 const double expected = xt->row_tot[r] * xt->col_tot[c] / xt->total;
2000 const double freq = xt->mat[n_cols * r + c];
2001 const double residual = freq - expected;
2003 chisq[0] += residual * residual / expected;
2005 chisq[1] += freq * log (expected / freq);
2016 /* Calculate Yates and Fisher exact test. */
2017 if (xt->ns_cols == 2 && xt->ns_rows == 2)
2019 double f11, f12, f21, f22;
2025 FOR_EACH_POPULATED_COLUMN (c, xt)
2033 f11 = xt->mat[nz_cols[0]];
2034 f12 = xt->mat[nz_cols[1]];
2035 f21 = xt->mat[nz_cols[0] + n_cols];
2036 f22 = xt->mat[nz_cols[1] + n_cols];
2041 const double xt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * xt->total;
2044 chisq[3] = (xt->total * pow2 (xt_)
2045 / (f11 + f12) / (f21 + f22)
2046 / (f11 + f21) / (f12 + f22));
2054 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2057 /* Calculate Mantel-Haenszel. */
2058 if (var_is_numeric (xt->vars[ROW_VAR].var)
2059 && var_is_numeric (xt->vars[COL_VAR].var))
2061 double r, ase_0, ase_1;
2062 calc_r (xt, (double *) xt->vars[ROW_VAR].values,
2063 (double *) xt->vars[COL_VAR].values,
2064 &r, &ase_0, &ase_1);
2066 chisq[4] = (xt->total - 1.) * r * r;
2071 /* Calculate the value of Pearson's r. r is stored into R, its T value into
2072 T, and standard error into ERROR. The row and column values must be
2073 passed in XT and Y. */
2075 calc_r (struct crosstabulation *xt,
2076 double *XT, double *Y, double *r, double *t, double *error)
2078 size_t n_rows = xt->vars[ROW_VAR].n_values;
2079 size_t n_cols = xt->vars[COL_VAR].n_values;
2080 double SX, SY, S, T;
2082 double sum_XYf, sum_X2Y2f;
2083 double sum_Xr, sum_X2r;
2084 double sum_Yc, sum_Y2c;
2087 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < n_rows; i++)
2088 for (j = 0; j < n_cols; j++)
2090 double fij = xt->mat[j + i * n_cols];
2091 double product = XT[i] * Y[j];
2092 double temp = fij * product;
2094 sum_X2Y2f += temp * product;
2097 for (sum_Xr = sum_X2r = 0., i = 0; i < n_rows; i++)
2099 sum_Xr += XT[i] * xt->row_tot[i];
2100 sum_X2r += pow2 (XT[i]) * xt->row_tot[i];
2102 Xbar = sum_Xr / xt->total;
2104 for (sum_Yc = sum_Y2c = 0., i = 0; i < n_cols; i++)
2106 sum_Yc += Y[i] * xt->col_tot[i];
2107 sum_Y2c += Y[i] * Y[i] * xt->col_tot[i];
2109 Ybar = sum_Yc / xt->total;
2111 S = sum_XYf - sum_Xr * sum_Yc / xt->total;
2112 SX = sum_X2r - pow2 (sum_Xr) / xt->total;
2113 SY = sum_Y2c - pow2 (sum_Yc) / xt->total;
2116 *t = *r / sqrt (1 - pow2 (*r)) * sqrt (xt->total - 2);
2121 for (s = c = 0., i = 0; i < n_rows; i++)
2122 for (j = 0; j < n_cols; j++)
2124 double Xresid, Yresid;
2127 Xresid = XT[i] - Xbar;
2128 Yresid = Y[j] - Ybar;
2129 temp = (T * Xresid * Yresid
2131 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2132 y = xt->mat[j + i * n_cols] * temp * temp - c;
2137 *error = sqrt (s) / (T * T);
2141 /* Calculate symmetric statistics and their asymptotic standard
2142 errors. Returns 0 if none could be calculated. */
2144 calc_symmetric (struct crosstabs_proc *proc, struct crosstabulation *xt,
2145 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2146 double t[N_SYMMETRIC],
2147 double somers_d_v[3], double somers_d_ase[3],
2148 double somers_d_t[3])
2150 size_t n_rows = xt->vars[ROW_VAR].n_values;
2151 size_t n_cols = xt->vars[COL_VAR].n_values;
2154 q = MIN (xt->ns_rows, xt->ns_cols);
2158 for (i = 0; i < N_SYMMETRIC; i++)
2159 v[i] = ase[i] = t[i] = SYSMIS;
2161 /* Phi, Cramer's V, contingency coefficient. */
2162 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2164 double Xp = 0.; /* Pearson chi-square. */
2166 FOR_EACH_POPULATED_ROW (r, xt)
2167 FOR_EACH_POPULATED_COLUMN (c, xt)
2169 double expected = xt->row_tot[r] * xt->col_tot[c] / xt->total;
2170 double freq = xt->mat[n_cols * r + c];
2171 double residual = freq - expected;
2173 Xp += residual * residual / expected;
2176 if (proc->statistics & (1u << CRS_ST_PHI))
2178 v[0] = sqrt (Xp / xt->total);
2179 v[1] = sqrt (Xp / (xt->total * (q - 1)));
2181 if (proc->statistics & (1u << CRS_ST_CC))
2182 v[2] = sqrt (Xp / (Xp + xt->total));
2185 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2186 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2191 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2195 Dr = Dc = pow2 (xt->total);
2196 for (r = 0; r < n_rows; r++)
2197 Dr -= pow2 (xt->row_tot[r]);
2198 for (c = 0; c < n_cols; c++)
2199 Dc -= pow2 (xt->col_tot[c]);
2201 cum = xnmalloc (n_cols * n_rows, sizeof *cum);
2202 for (c = 0; c < n_cols; c++)
2206 for (r = 0; r < n_rows; r++)
2207 cum[c + r * n_cols] = ct += xt->mat[c + r * n_cols];
2216 for (i = 0; i < n_rows; i++)
2220 for (j = 1; j < n_cols; j++)
2221 Cij += xt->col_tot[j] - cum[j + i * n_cols];
2224 for (j = 1; j < n_cols; j++)
2225 Dij += cum[j + (i - 1) * n_cols];
2229 double fij = xt->mat[j + i * n_cols];
2235 assert (j < n_cols);
2237 Cij -= xt->col_tot[j] - cum[j + i * n_cols];
2238 Dij += xt->col_tot[j - 1] - cum[j - 1 + i * n_cols];
2242 Cij += cum[j - 1 + (i - 1) * n_cols];
2243 Dij -= cum[j + (i - 1) * n_cols];
2249 if (proc->statistics & (1u << CRS_ST_BTAU))
2250 v[3] = (P - Q) / sqrt (Dr * Dc);
2251 if (proc->statistics & (1u << CRS_ST_CTAU))
2252 v[4] = (q * (P - Q)) / (pow2 (xt->total) * (q - 1));
2253 if (proc->statistics & (1u << CRS_ST_GAMMA))
2254 v[5] = (P - Q) / (P + Q);
2256 /* ASE for tau-b, tau-c, gamma. Calculations could be
2257 eliminated here, at expense of memory. */
2262 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2263 for (i = 0; i < n_rows; i++)
2267 for (j = 1; j < n_cols; j++)
2268 Cij += xt->col_tot[j] - cum[j + i * n_cols];
2271 for (j = 1; j < n_cols; j++)
2272 Dij += cum[j + (i - 1) * n_cols];
2276 double fij = xt->mat[j + i * n_cols];
2278 if (proc->statistics & (1u << CRS_ST_BTAU))
2280 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2281 + v[3] * (xt->row_tot[i] * Dc
2282 + xt->col_tot[j] * Dr));
2283 btau_cum += fij * temp * temp;
2287 const double temp = Cij - Dij;
2288 ctau_cum += fij * temp * temp;
2291 if (proc->statistics & (1u << CRS_ST_GAMMA))
2293 const double temp = Q * Cij - P * Dij;
2294 gamma_cum += fij * temp * temp;
2297 if (proc->statistics & (1u << CRS_ST_D))
2299 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2300 - (P - Q) * (xt->total - xt->row_tot[i]));
2301 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2302 - (Q - P) * (xt->total - xt->col_tot[j]));
2307 assert (j < n_cols);
2309 Cij -= xt->col_tot[j] - cum[j + i * n_cols];
2310 Dij += xt->col_tot[j - 1] - cum[j - 1 + i * n_cols];
2314 Cij += cum[j - 1 + (i - 1) * n_cols];
2315 Dij -= cum[j + (i - 1) * n_cols];
2321 btau_var = ((btau_cum
2322 - (xt->total * pow2 (xt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2324 if (proc->statistics & (1u << CRS_ST_BTAU))
2326 ase[3] = sqrt (btau_var);
2327 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / xt->total)
2330 if (proc->statistics & (1u << CRS_ST_CTAU))
2332 ase[4] = ((2 * q / ((q - 1) * pow2 (xt->total)))
2333 * sqrt (ctau_cum - (P - Q) * (P - Q) / xt->total));
2334 t[4] = v[4] / ase[4];
2336 if (proc->statistics & (1u << CRS_ST_GAMMA))
2338 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2339 t[5] = v[5] / (2. / (P + Q)
2340 * sqrt (ctau_cum - (P - Q) * (P - Q) / xt->total));
2342 if (proc->statistics & (1u << CRS_ST_D))
2344 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2345 somers_d_ase[0] = SYSMIS;
2346 somers_d_t[0] = (somers_d_v[0]
2348 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2349 somers_d_v[1] = (P - Q) / Dc;
2350 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2351 somers_d_t[1] = (somers_d_v[1]
2353 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2354 somers_d_v[2] = (P - Q) / Dr;
2355 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2356 somers_d_t[2] = (somers_d_v[2]
2358 * sqrt (ctau_cum - pow2 (P - Q) / xt->total)));
2364 /* Spearman correlation, Pearson's r. */
2365 if (proc->statistics & (1u << CRS_ST_CORR))
2367 double *R = xmalloc (sizeof *R * n_rows);
2368 double *C = xmalloc (sizeof *C * n_cols);
2371 double y, t, c = 0., s = 0.;
2376 R[i] = s + (xt->row_tot[i] + 1.) / 2.;
2377 y = xt->row_tot[i] - c;
2383 assert (i < n_rows);
2388 double y, t, c = 0., s = 0.;
2393 C[j] = s + (xt->col_tot[j] + 1.) / 2;
2394 y = xt->col_tot[j] - c;
2400 assert (j < n_cols);
2404 calc_r (xt, R, C, &v[6], &t[6], &ase[6]);
2409 calc_r (xt, (double *) xt->vars[ROW_VAR].values,
2410 (double *) xt->vars[COL_VAR].values,
2411 &v[7], &t[7], &ase[7]);
2414 /* Cohen's kappa. */
2415 if (proc->statistics & (1u << CRS_ST_KAPPA) && xt->ns_rows == xt->ns_cols)
2417 double ase_under_h0;
2418 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2421 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2422 i < xt->ns_rows; i++, j++)
2426 while (xt->col_tot[j] == 0.)
2429 prod = xt->row_tot[i] * xt->col_tot[j];
2430 sum = xt->row_tot[i] + xt->col_tot[j];
2432 sum_fii += xt->mat[j + i * n_cols];
2434 sum_fiiri_ci += xt->mat[j + i * n_cols] * sum;
2435 sum_riciri_ci += prod * sum;
2437 for (sum_fijri_ci2 = 0., i = 0; i < xt->ns_rows; i++)
2438 for (j = 0; j < xt->ns_cols; j++)
2440 double sum = xt->row_tot[i] + xt->col_tot[j];
2441 sum_fijri_ci2 += xt->mat[j + i * n_cols] * sum * sum;
2444 v[8] = (xt->total * sum_fii - sum_rici) / (pow2 (xt->total) - sum_rici);
2446 ase_under_h0 = sqrt ((pow2 (xt->total) * sum_rici
2447 + sum_rici * sum_rici
2448 - xt->total * sum_riciri_ci)
2449 / (xt->total * (pow2 (xt->total) - sum_rici) * (pow2 (xt->total) - sum_rici)));
2451 ase[8] = sqrt (xt->total * (((sum_fii * (xt->total - sum_fii))
2452 / pow2 (pow2 (xt->total) - sum_rici))
2453 + ((2. * (xt->total - sum_fii)
2454 * (2. * sum_fii * sum_rici
2455 - xt->total * sum_fiiri_ci))
2456 / pow3 (pow2 (xt->total) - sum_rici))
2457 + (pow2 (xt->total - sum_fii)
2458 * (xt->total * sum_fijri_ci2 - 4.
2459 * sum_rici * sum_rici)
2460 / pow4 (pow2 (xt->total) - sum_rici))));
2462 t[8] = v[8] / ase_under_h0;
2468 /* Calculate risk estimate. */
2470 calc_risk (struct crosstabulation *xt,
2471 double *value, double *upper, double *lower, union value *c,
2474 size_t n_cols = xt->vars[COL_VAR].n_values;
2475 double f11, f12, f21, f22;
2478 for (int i = 0; i < 3; i++)
2479 value[i] = upper[i] = lower[i] = SYSMIS;
2481 if (xt->ns_rows != 2 || xt->ns_cols != 2)
2485 /* Find populated columns. */
2488 FOR_EACH_POPULATED_COLUMN (c, xt)
2492 /* Find populated rows. */
2495 FOR_EACH_POPULATED_ROW (r, xt)
2499 f11 = xt->mat[nz_cols[0] + n_cols * nz_rows[0]];
2500 f12 = xt->mat[nz_cols[1] + n_cols * nz_rows[0]];
2501 f21 = xt->mat[nz_cols[0] + n_cols * nz_rows[1]];
2502 f22 = xt->mat[nz_cols[1] + n_cols * nz_rows[1]];
2503 *n_valid = f11 + f12 + f21 + f22;
2505 c[0] = xt->vars[COL_VAR].values[nz_cols[0]];
2506 c[1] = xt->vars[COL_VAR].values[nz_cols[1]];
2509 value[0] = (f11 * f22) / (f12 * f21);
2510 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2511 lower[0] = value[0] * exp (-1.960 * v);
2512 upper[0] = value[0] * exp (1.960 * v);
2514 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2515 v = sqrt ((f12 / (f11 * (f11 + f12)))
2516 + (f22 / (f21 * (f21 + f22))));
2517 lower[1] = value[1] * exp (-1.960 * v);
2518 upper[1] = value[1] * exp (1.960 * v);
2520 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2521 v = sqrt ((f11 / (f12 * (f11 + f12)))
2522 + (f21 / (f22 * (f21 + f22))));
2523 lower[2] = value[2] * exp (-1.960 * v);
2524 upper[2] = value[2] * exp (1.960 * v);
2529 /* Calculate directional measures. */
2531 calc_directional (struct crosstabs_proc *proc, struct crosstabulation *xt,
2532 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2533 double t[N_DIRECTIONAL], double sig[N_DIRECTIONAL])
2535 size_t n_rows = xt->vars[ROW_VAR].n_values;
2536 size_t n_cols = xt->vars[COL_VAR].n_values;
2537 for (int i = 0; i < N_DIRECTIONAL; i++)
2538 v[i] = ase[i] = t[i] = sig[i] = SYSMIS;
2541 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2543 /* Find maximum for each row and their sum. */
2544 double *fim = xnmalloc (n_rows, sizeof *fim);
2545 int *fim_index = xnmalloc (n_rows, sizeof *fim_index);
2546 double sum_fim = 0.0;
2547 for (int i = 0; i < n_rows; i++)
2549 double max = xt->mat[i * n_cols];
2552 for (int j = 1; j < n_cols; j++)
2553 if (xt->mat[j + i * n_cols] > max)
2555 max = xt->mat[j + i * n_cols];
2561 fim_index[i] = index;
2564 /* Find maximum for each column. */
2565 double *fmj = xnmalloc (n_cols, sizeof *fmj);
2566 int *fmj_index = xnmalloc (n_cols, sizeof *fmj_index);
2567 double sum_fmj = 0.0;
2568 for (int j = 0; j < n_cols; j++)
2570 double max = xt->mat[j];
2573 for (int i = 1; i < n_rows; i++)
2574 if (xt->mat[j + i * n_cols] > max)
2576 max = xt->mat[j + i * n_cols];
2582 fmj_index[j] = index;
2585 /* Find maximum row total. */
2586 double rm = xt->row_tot[0];
2588 for (int i = 1; i < n_rows; i++)
2589 if (xt->row_tot[i] > rm)
2591 rm = xt->row_tot[i];
2595 /* Find maximum column total. */
2596 double cm = xt->col_tot[0];
2598 for (int j = 1; j < n_cols; j++)
2599 if (xt->col_tot[j] > cm)
2601 cm = xt->col_tot[j];
2605 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * xt->total - rm - cm);
2606 v[1] = (sum_fmj - rm) / (xt->total - rm);
2607 v[2] = (sum_fim - cm) / (xt->total - cm);
2609 /* ASE1 for Y given XT. */
2612 for (int i = 0; i < n_rows; i++)
2613 if (cm_index == fim_index[i])
2615 ase[2] = sqrt ((xt->total - sum_fim) * (sum_fim + cm - 2. * accum)
2616 / pow3 (xt->total - cm));
2619 /* ASE0 for Y given XT. */
2622 for (int i = 0; i < n_rows; i++)
2623 if (cm_index != fim_index[i])
2624 accum += (xt->mat[i * n_cols + fim_index[i]]
2625 + xt->mat[i * n_cols + cm_index]);
2626 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / xt->total) / (xt->total - cm));
2629 /* ASE1 for XT given Y. */
2632 for (int j = 0; j < n_cols; j++)
2633 if (rm_index == fmj_index[j])
2635 ase[1] = sqrt ((xt->total - sum_fmj) * (sum_fmj + rm - 2. * accum)
2636 / pow3 (xt->total - rm));
2639 /* ASE0 for XT given Y. */
2642 for (int j = 0; j < n_cols; j++)
2643 if (rm_index != fmj_index[j])
2644 accum += (xt->mat[j + n_cols * fmj_index[j]]
2645 + xt->mat[j + n_cols * rm_index]);
2646 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / xt->total) / (xt->total - rm));
2649 /* Symmetric ASE0 and ASE1. */
2651 double accum0 = 0.0;
2652 double accum1 = 0.0;
2653 for (int i = 0; i < n_rows; i++)
2654 for (int j = 0; j < n_cols; j++)
2656 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2657 int temp1 = (i == rm_index) + (j == cm_index);
2658 accum0 += xt->mat[j + i * n_cols] * pow2 (temp0 - temp1);
2659 accum1 += (xt->mat[j + i * n_cols]
2660 * pow2 (temp0 + (v[0] - 1.) * temp1));
2662 ase[0] = sqrt (accum1 - 4. * xt->total * v[0] * v[0]) / (2. * xt->total - rm - cm);
2663 t[0] = v[0] / (sqrt (accum0 - pow2 (sum_fim + sum_fmj - cm - rm) / xt->total)
2664 / (2. * xt->total - rm - cm));
2667 for (int i = 0; i < 3; i++)
2668 sig[i] = 2 * gsl_cdf_ugaussian_Q (t[i]);
2677 double sum_fij2_ri = 0.0;
2678 double sum_fij2_ci = 0.0;
2679 FOR_EACH_POPULATED_ROW (i, xt)
2680 FOR_EACH_POPULATED_COLUMN (j, xt)
2682 double temp = pow2 (xt->mat[j + i * n_cols]);
2683 sum_fij2_ri += temp / xt->row_tot[i];
2684 sum_fij2_ci += temp / xt->col_tot[j];
2687 double sum_ri2 = 0.0;
2688 for (int i = 0; i < n_rows; i++)
2689 sum_ri2 += pow2 (xt->row_tot[i]);
2691 double sum_cj2 = 0.0;
2692 for (int j = 0; j < n_cols; j++)
2693 sum_cj2 += pow2 (xt->col_tot[j]);
2695 v[3] = (xt->total * sum_fij2_ci - sum_ri2) / (pow2 (xt->total) - sum_ri2);
2696 v[4] = (xt->total * sum_fij2_ri - sum_cj2) / (pow2 (xt->total) - sum_cj2);
2700 if (proc->statistics & (1u << CRS_ST_UC))
2703 FOR_EACH_POPULATED_ROW (i, xt)
2704 UX -= xt->row_tot[i] / xt->total * log (xt->row_tot[i] / xt->total);
2707 FOR_EACH_POPULATED_COLUMN (j, xt)
2708 UY -= xt->col_tot[j] / xt->total * log (xt->col_tot[j] / xt->total);
2712 for (int i = 0; i < n_rows; i++)
2713 for (int j = 0; j < n_cols; j++)
2715 double entry = xt->mat[j + i * n_cols];
2720 P += entry * pow2 (log (xt->col_tot[j] * xt->row_tot[i] / (xt->total * entry)));
2721 UXY -= entry / xt->total * log (entry / xt->total);
2724 double ase1_yx = 0.0;
2725 double ase1_xy = 0.0;
2726 double ase1_sym = 0.0;
2727 for (int i = 0; i < n_rows; i++)
2728 for (int j = 0; j < n_cols; j++)
2730 double entry = xt->mat[j + i * n_cols];
2735 ase1_yx += entry * pow2 (UY * log (entry / xt->row_tot[i])
2736 + (UX - UXY) * log (xt->col_tot[j] / xt->total));
2737 ase1_xy += entry * pow2 (UX * log (entry / xt->col_tot[j])
2738 + (UY - UXY) * log (xt->row_tot[i] / xt->total));
2739 ase1_sym += entry * pow2 ((UXY
2740 * log (xt->row_tot[i] * xt->col_tot[j] / pow2 (xt->total)))
2741 - (UX + UY) * log (entry / xt->total));
2744 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2745 ase[5] = (2. / (xt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2748 v[6] = (UX + UY - UXY) / UX;
2749 ase[6] = sqrt (ase1_xy) / (xt->total * UX * UX);
2750 t[6] = v[6] / (sqrt (P - xt->total * pow2 (UX + UY - UXY)) / (xt->total * UX));
2752 v[7] = (UX + UY - UXY) / UY;
2753 ase[7] = sqrt (ase1_yx) / (xt->total * UY * UY);
2754 t[7] = v[7] / (sqrt (P - xt->total * pow2 (UX + UY - UXY)) / (xt->total * UY));
2758 if (proc->statistics & (1u << CRS_ST_D))
2760 double v_dummy[N_SYMMETRIC];
2761 double ase_dummy[N_SYMMETRIC];
2762 double t_dummy[N_SYMMETRIC];
2763 double somers_d_v[3];
2764 double somers_d_ase[3];
2765 double somers_d_t[3];
2767 if (calc_symmetric (proc, xt, v_dummy, ase_dummy, t_dummy,
2768 somers_d_v, somers_d_ase, somers_d_t))
2770 for (int i = 0; i < 3; i++)
2772 v[8 + i] = somers_d_v[i];
2773 ase[8 + i] = somers_d_ase[i];
2774 t[8 + i] = somers_d_t[i];
2775 sig[8 + i] = 2 * gsl_cdf_ugaussian_Q (fabs (somers_d_t[i]));
2781 if (proc->statistics & (1u << CRS_ST_ETA))
2784 double sum_Xr = 0.0;
2785 double sum_X2r = 0.0;
2786 for (int i = 0; i < n_rows; i++)
2788 sum_Xr += xt->vars[ROW_VAR].values[i].f * xt->row_tot[i];
2789 sum_X2r += pow2 (xt->vars[ROW_VAR].values[i].f) * xt->row_tot[i];
2791 double SX = sum_X2r - pow2 (sum_Xr) / xt->total;
2794 FOR_EACH_POPULATED_COLUMN (j, xt)
2798 for (int i = 0; i < n_rows; i++)
2800 SXW += (pow2 (xt->vars[ROW_VAR].values[i].f)
2801 * xt->mat[j + i * n_cols]);
2802 cum += (xt->vars[ROW_VAR].values[i].f
2803 * xt->mat[j + i * n_cols]);
2806 SXW -= cum * cum / xt->col_tot[j];
2808 v[11] = sqrt (1. - SXW / SX);
2811 double sum_Yc = 0.0;
2812 double sum_Y2c = 0.0;
2813 for (int i = 0; i < n_cols; i++)
2815 sum_Yc += xt->vars[COL_VAR].values[i].f * xt->col_tot[i];
2816 sum_Y2c += pow2 (xt->vars[COL_VAR].values[i].f) * xt->col_tot[i];
2818 double SY = sum_Y2c - pow2 (sum_Yc) / xt->total;
2821 FOR_EACH_POPULATED_ROW (i, xt)
2824 for (int j = 0; j < n_cols; j++)
2826 SYW += (pow2 (xt->vars[COL_VAR].values[j].f)
2827 * xt->mat[j + i * n_cols]);
2828 cum += (xt->vars[COL_VAR].values[j].f
2829 * xt->mat[j + i * n_cols]);
2832 SYW -= cum * cum / xt->row_tot[i];
2834 v[12] = sqrt (1. - SYW / SY);