1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2006, 2009, 2010 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 - Pearson's R (but not Spearman!) is off a little.
20 - T values for Spearman's R and Pearson's R are wrong.
21 - How to calculate significance of symmetric and directional measures?
22 - Asymmetric ASEs and T values for lambda are wrong.
23 - ASE of Goodman and Kruskal's tau is not calculated.
24 - ASE of symmetric somers' d is wrong.
25 - Approx. T of uncertainty coefficient is wrong.
32 #include <gsl/gsl_cdf.h>
36 #include <data/case.h>
37 #include <data/casegrouper.h>
38 #include <data/casereader.h>
39 #include <data/data-out.h>
40 #include <data/dictionary.h>
41 #include <data/format.h>
42 #include <data/procedure.h>
43 #include <data/value-labels.h>
44 #include <data/variable.h>
45 #include <language/command.h>
46 #include <language/dictionary/split-file.h>
47 #include <language/lexer/lexer.h>
48 #include <language/lexer/variable-parser.h>
49 #include <libpspp/array.h>
50 #include <libpspp/assertion.h>
51 #include <libpspp/compiler.h>
52 #include <libpspp/hash.h>
53 #include <libpspp/hmap.h>
54 #include <libpspp/hmapx.h>
55 #include <libpspp/message.h>
56 #include <libpspp/misc.h>
57 #include <libpspp/pool.h>
58 #include <libpspp/str.h>
59 #include <output/tab.h>
66 #define _(msgid) gettext (msgid)
67 #define N_(msgid) msgid
75 missing=miss:!table/include/report;
76 +write[wr_]=none,cells,all;
77 +format=fmt:!labels/nolabels/novallabs,
80 tabl:!tables/notables,
83 +cells[cl_]=count,expected,row,column,total,residual,sresidual,
85 +statistics[st_]=chisq,phi,cc,lambda,uc,none,btau,ctau,risk,gamma,d,
91 /* Number of chi-square statistics. */
94 /* Number of symmetric statistics. */
97 /* Number of directional statistics. */
98 #define N_DIRECTIONAL 13
100 /* A single table entry for general mode. */
103 struct hmap_node node; /* Entry in hash table. */
104 double freq; /* Frequency count. */
105 union value values[1]; /* Values. */
109 table_entry_size (size_t n_values)
111 return (offsetof (struct table_entry, values)
112 + n_values * sizeof (union value));
115 /* Indexes into the 'vars' member of struct pivot_table and
116 struct crosstab member. */
119 ROW_VAR = 0, /* Row variable. */
120 COL_VAR = 1 /* Column variable. */
121 /* Higher indexes cause multiple tables to be output. */
124 /* A crosstabulation of 2 or more variables. */
127 struct fmt_spec weight_format; /* Format for weight variable. */
128 double missing; /* Weight of missing cases. */
130 /* Variables (2 or more). */
132 const struct variable **vars;
134 /* Constants (0 or more). */
136 const struct variable **const_vars;
137 union value *const_values;
141 struct table_entry **entries;
144 /* Column values, number of columns. */
148 /* Row values, number of rows. */
152 /* Number of statistically interesting columns/rows
153 (columns/rows with data in them). */
154 int ns_cols, ns_rows;
156 /* Matrix contents. */
157 double *mat; /* Matrix proper. */
158 double *row_tot; /* Row totals. */
159 double *col_tot; /* Column totals. */
160 double total; /* Grand total. */
163 /* Integer mode variable info. */
166 int min; /* Minimum value. */
167 int max; /* Maximum value + 1. */
168 int count; /* max - min. */
171 static inline struct var_range *
172 get_var_range (const struct variable *v)
174 return var_get_aux (v);
177 struct crosstabs_proc
179 const struct dictionary *dict;
180 enum { INTEGER, GENERAL } mode;
181 enum mv_class exclude;
184 struct fmt_spec weight_format;
186 /* Variables specifies on VARIABLES. */
187 const struct variable **variables;
191 struct pivot_table *pivots;
195 int n_cells; /* Number of cells requested. */
196 unsigned int cells; /* Bit k is 1 if cell k is requested. */
197 int a_cells[CRS_CL_count]; /* 0...n_cells-1 are the requested cells. */
200 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
203 static bool should_tabulate_case (const struct pivot_table *,
204 const struct ccase *, enum mv_class exclude);
205 static void tabulate_general_case (struct pivot_table *, const struct ccase *,
207 static void tabulate_integer_case (struct pivot_table *, const struct ccase *,
209 static void postcalc (struct crosstabs_proc *);
210 static void submit (struct pivot_table *, struct tab_table *);
212 /* Parses and executes the CROSSTABS procedure. */
214 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
216 const struct variable *wv = dict_get_weight (dataset_dict (ds));
217 struct crosstabs_proc proc;
218 struct casegrouper *grouper;
219 struct casereader *input, *group;
220 struct cmd_crosstabs cmd;
221 struct pivot_table *pt;
226 proc.dict = dataset_dict (ds);
227 proc.bad_warn = true;
228 proc.variables = NULL;
229 proc.n_variables = 0;
232 proc.weight_format = wv ? *var_get_print_format (wv) : F_8_0;
234 if (!parse_crosstabs (lexer, ds, &cmd, &proc))
236 result = CMD_FAILURE;
240 proc.mode = proc.n_variables ? INTEGER : GENERAL;
244 proc.cells = 1u << CRS_CL_COUNT;
245 else if (cmd.a_cells[CRS_CL_ALL])
246 proc.cells = UINT_MAX;
250 for (i = 0; i < CRS_CL_count; i++)
252 proc.cells |= 1u << i;
254 proc.cells = ((1u << CRS_CL_COUNT)
256 | (1u << CRS_CL_COLUMN)
257 | (1u << CRS_CL_TOTAL));
259 proc.cells &= ((1u << CRS_CL_count) - 1);
260 proc.cells &= ~((1u << CRS_CL_NONE) | (1u << CRS_CL_ALL));
262 for (i = 0; i < CRS_CL_count; i++)
263 if (proc.cells & (1u << i))
264 proc.a_cells[proc.n_cells++] = i;
267 if (cmd.a_statistics[CRS_ST_ALL])
268 proc.statistics = UINT_MAX;
269 else if (cmd.sbc_statistics)
274 for (i = 0; i < CRS_ST_count; i++)
275 if (cmd.a_statistics[i])
276 proc.statistics |= 1u << i;
277 if (proc.statistics == 0)
278 proc.statistics |= 1u << CRS_ST_CHISQ;
284 proc.exclude = (cmd.miss == CRS_TABLE ? MV_ANY
285 : cmd.miss == CRS_INCLUDE ? MV_SYSTEM
287 if (proc.mode == GENERAL && proc.mode == MV_NEVER)
289 msg (SE, _("Missing mode REPORT not allowed in general mode. "
290 "Assuming MISSING=TABLE."));
295 proc.pivot = cmd.pivot == CRS_PIVOT;
297 input = casereader_create_filter_weight (proc_open (ds), dataset_dict (ds),
299 grouper = casegrouper_create_splits (input, dataset_dict (ds));
300 while (casegrouper_get_next_group (grouper, &group))
304 /* Output SPLIT FILE variables. */
305 c = casereader_peek (group, 0);
308 output_split_file_values (ds, c);
312 /* Initialize hash tables. */
313 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
314 hmap_init (&pt->data);
317 for (; (c = casereader_read (group)) != NULL; case_unref (c))
318 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
320 double weight = dict_get_case_weight (dataset_dict (ds), c,
322 if (should_tabulate_case (pt, c, proc.exclude))
324 if (proc.mode == GENERAL)
325 tabulate_general_case (pt, c, weight);
327 tabulate_integer_case (pt, c, weight);
330 pt->missing += weight;
332 casereader_destroy (group);
337 ok = casegrouper_destroy (grouper);
338 ok = proc_commit (ds) && ok;
340 result = ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
343 free (proc.variables);
344 for (pt = &proc.pivots[0]; pt < &proc.pivots[proc.n_pivots]; pt++)
347 free (pt->const_vars);
348 /* We must not call value_destroy on const_values because
349 it is a wild pointer; it never pointed to anything owned
352 The rest of the data was allocated and destroyed at a
353 lower level already. */
360 /* Parses the TABLES subcommand. */
362 crs_custom_tables (struct lexer *lexer, struct dataset *ds,
363 struct cmd_crosstabs *cmd UNUSED, void *proc_)
365 struct crosstabs_proc *proc = proc_;
366 struct const_var_set *var_set;
368 const struct variable ***by = NULL;
370 size_t *by_nvar = NULL;
375 /* Ensure that this is a TABLES subcommand. */
376 if (!lex_match_id (lexer, "TABLES")
377 && (lex_token (lexer) != T_ID ||
378 dict_lookup_var (dataset_dict (ds), lex_tokid (lexer)) == NULL)
379 && lex_token (lexer) != T_ALL)
381 lex_match (lexer, '=');
383 if (proc->variables != NULL)
384 var_set = const_var_set_create_from_array (proc->variables,
387 var_set = const_var_set_create_from_dict (dataset_dict (ds));
388 assert (var_set != NULL);
392 by = xnrealloc (by, n_by + 1, sizeof *by);
393 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
394 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
395 PV_NO_DUPLICATE | PV_NO_SCRATCH))
397 if (xalloc_oversized (nx, by_nvar[n_by]))
399 msg (SE, _("Too many cross-tabulation variables or dimensions."));
405 if (!lex_match (lexer, T_BY))
409 lex_force_match (lexer, T_BY);
417 by_iter = xcalloc (n_by, sizeof *by_iter);
418 proc->pivots = xnrealloc (proc->pivots,
419 proc->n_pivots + nx, sizeof *proc->pivots);
420 for (i = 0; i < nx; i++)
422 struct pivot_table *pt = &proc->pivots[proc->n_pivots++];
425 pt->weight_format = proc->weight_format;
428 pt->vars = xmalloc (n_by * sizeof *pt->vars);
430 pt->const_vars = NULL;
431 pt->const_values = NULL;
433 for (j = 0; j < n_by; j++)
434 pt->vars[j] = by[j][by_iter[j]];
436 for (j = n_by - 1; j >= 0; j--)
438 if (++by_iter[j] < by_nvar[j])
447 /* All return paths lead here. */
448 for (i = 0; i < n_by; i++)
453 const_var_set_destroy (var_set);
458 /* Parses the VARIABLES subcommand. */
460 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
461 struct cmd_crosstabs *cmd UNUSED, void *proc_)
463 struct crosstabs_proc *proc = proc_;
466 msg (SE, _("VARIABLES must be specified before TABLES."));
470 lex_match (lexer, '=');
474 size_t orig_nv = proc->n_variables;
479 if (!parse_variables_const (lexer, dataset_dict (ds),
480 &proc->variables, &proc->n_variables,
481 (PV_APPEND | PV_NUMERIC
482 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
485 if (!lex_force_match (lexer, '('))
488 if (!lex_force_int (lexer))
490 min = lex_integer (lexer);
493 lex_match (lexer, ',');
495 if (!lex_force_int (lexer))
497 max = lex_integer (lexer);
500 msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
506 if (!lex_force_match (lexer, ')'))
509 for (i = orig_nv; i < proc->n_variables; i++)
511 struct var_range *vr = xmalloc (sizeof *vr);
514 vr->count = max - min + 1;
515 var_attach_aux (proc->variables[i], vr, var_dtor_free);
518 if (lex_token (lexer) == '/')
525 free (proc->variables);
526 proc->variables = NULL;
527 proc->n_variables = 0;
531 /* Data file processing. */
534 should_tabulate_case (const struct pivot_table *pt, const struct ccase *c,
535 enum mv_class exclude)
538 for (j = 0; j < pt->n_vars; j++)
540 const struct variable *var = pt->vars[j];
541 struct var_range *range = get_var_range (var);
543 if (var_is_value_missing (var, case_data (c, var), exclude))
548 double num = case_num (c, var);
549 if (num < range->min || num > range->max)
557 tabulate_integer_case (struct pivot_table *pt, const struct ccase *c,
560 struct table_entry *te;
565 for (j = 0; j < pt->n_vars; j++)
567 /* Throw away fractional parts of values. */
568 hash = hash_int (case_num (c, pt->vars[j]), hash);
571 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
573 for (j = 0; j < pt->n_vars; j++)
574 if ((int) case_num (c, pt->vars[j]) != (int) te->values[j].f)
577 /* Found an existing entry. */
584 /* No existing entry. Create a new one. */
585 te = xmalloc (table_entry_size (pt->n_vars));
587 for (j = 0; j < pt->n_vars; j++)
588 te->values[j].f = (int) case_num (c, pt->vars[j]);
589 hmap_insert (&pt->data, &te->node, hash);
593 tabulate_general_case (struct pivot_table *pt, const struct ccase *c,
596 struct table_entry *te;
601 for (j = 0; j < pt->n_vars; j++)
603 const struct variable *var = pt->vars[j];
604 hash = value_hash (case_data (c, var), var_get_width (var), hash);
607 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
609 for (j = 0; j < pt->n_vars; j++)
611 const struct variable *var = pt->vars[j];
612 if (!value_equal (case_data (c, var), &te->values[j],
613 var_get_width (var)))
617 /* Found an existing entry. */
624 /* No existing entry. Create a new one. */
625 te = xmalloc (table_entry_size (pt->n_vars));
627 for (j = 0; j < pt->n_vars; j++)
629 const struct variable *var = pt->vars[j];
630 value_clone (&te->values[j], case_data (c, var), var_get_width (var));
632 hmap_insert (&pt->data, &te->node, hash);
635 /* Post-data reading calculations. */
637 static int compare_table_entry_vars_3way (const struct table_entry *a,
638 const struct table_entry *b,
639 const struct pivot_table *pt,
641 static int compare_table_entry_3way (const void *ap_, const void *bp_,
643 static void enum_var_values (const struct pivot_table *, int var_idx,
644 union value **valuesp, int *n_values);
645 static void output_pivot_table (struct crosstabs_proc *,
646 struct pivot_table *);
647 static void make_pivot_table_subset (struct pivot_table *pt,
648 size_t row0, size_t row1,
649 struct pivot_table *subset);
650 static void make_summary_table (struct crosstabs_proc *);
651 static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
654 postcalc (struct crosstabs_proc *proc)
656 struct pivot_table *pt;
658 /* Convert hash tables into sorted arrays of entries. */
659 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
661 struct table_entry *e;
664 pt->n_entries = hmap_count (&pt->data);
665 pt->entries = xnmalloc (pt->n_entries, sizeof *pt->entries);
667 HMAP_FOR_EACH (e, struct table_entry, node, &pt->data)
668 pt->entries[i++] = e;
669 hmap_destroy (&pt->data);
671 sort (pt->entries, pt->n_entries, sizeof *pt->entries,
672 compare_table_entry_3way, pt);
675 make_summary_table (proc);
677 /* Output each pivot table. */
678 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
680 if (proc->pivot || pt->n_vars == 2)
681 output_pivot_table (proc, pt);
684 size_t row0 = 0, row1 = 0;
685 while (find_crosstab (pt, &row0, &row1))
687 struct pivot_table subset;
688 make_pivot_table_subset (pt, row0, row1, &subset);
689 output_pivot_table (proc, &subset);
694 /* Free output and prepare for next split file. */
695 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
701 /* Free only the members that were allocated in this
702 function. The other pointer members are either both
703 allocated and destroyed at a lower level (in
704 output_pivot_table), or both allocated and destroyed at
705 a higher level (in crs_custom_tables and free_proc,
707 for (i = 0; i < pt->n_entries; i++)
708 free (pt->entries[i]);
714 make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
715 struct pivot_table *subset)
720 assert (pt->n_consts == 0);
721 subset->missing = pt->missing;
723 subset->vars = pt->vars;
724 subset->n_consts = pt->n_vars - 2;
725 subset->const_vars = pt->vars + 2;
726 subset->const_values = &pt->entries[row0]->values[2];
728 subset->entries = &pt->entries[row0];
729 subset->n_entries = row1 - row0;
733 compare_table_entry_var_3way (const struct table_entry *a,
734 const struct table_entry *b,
735 const struct pivot_table *pt,
738 return value_compare_3way (&a->values[idx], &b->values[idx],
739 var_get_width (pt->vars[idx]));
743 compare_table_entry_vars_3way (const struct table_entry *a,
744 const struct table_entry *b,
745 const struct pivot_table *pt,
750 for (i = idx1 - 1; i >= idx0; i--)
752 int cmp = compare_table_entry_var_3way (a, b, pt, i);
759 /* Compare the struct table_entry at *AP to the one at *BP and
760 return a strcmp()-type result. */
762 compare_table_entry_3way (const void *ap_, const void *bp_, const void *pt_)
764 const struct table_entry *const *ap = ap_;
765 const struct table_entry *const *bp = bp_;
766 const struct table_entry *a = *ap;
767 const struct table_entry *b = *bp;
768 const struct pivot_table *pt = pt_;
771 cmp = compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars);
775 cmp = compare_table_entry_var_3way (a, b, pt, ROW_VAR);
779 return compare_table_entry_var_3way (a, b, pt, COL_VAR);
783 find_first_difference (const struct pivot_table *pt, size_t row)
786 return pt->n_vars - 1;
789 const struct table_entry *a = pt->entries[row];
790 const struct table_entry *b = pt->entries[row - 1];
793 for (col = pt->n_vars - 1; col >= 0; col--)
794 if (compare_table_entry_var_3way (a, b, pt, col))
800 /* Output a table summarizing the cases processed. */
802 make_summary_table (struct crosstabs_proc *proc)
804 struct tab_table *summary;
805 struct pivot_table *pt;
809 summary = tab_create (7, 3 + proc->n_pivots);
810 tab_title (summary, _("Summary."));
811 tab_headers (summary, 1, 0, 3, 0);
812 tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
813 tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
814 tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
815 tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
816 tab_hline (summary, TAL_1, 1, 6, 1);
817 tab_hline (summary, TAL_1, 1, 6, 2);
818 tab_vline (summary, TAL_1, 3, 1, 1);
819 tab_vline (summary, TAL_1, 5, 1, 1);
820 for (i = 0; i < 3; i++)
822 tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
823 tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
825 tab_offset (summary, 0, 3);
827 ds_init_empty (&name);
828 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
834 tab_hline (summary, TAL_1, 0, 6, 0);
837 for (i = 0; i < pt->n_vars; i++)
840 ds_put_cstr (&name, " * ");
841 ds_put_cstr (&name, var_to_string (pt->vars[i]));
843 tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
846 for (i = 0; i < pt->n_entries; i++)
847 valid += pt->entries[i]->freq;
852 for (i = 0; i < 3; i++)
854 tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i],
855 &proc->weight_format);
856 tab_text_format (summary, i * 2 + 2, 0, TAB_RIGHT, "%.1f%%",
860 tab_next_row (summary);
864 submit (NULL, summary);
869 static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
870 struct pivot_table *);
871 static struct tab_table *create_chisq_table (struct pivot_table *);
872 static struct tab_table *create_sym_table (struct pivot_table *);
873 static struct tab_table *create_risk_table (struct pivot_table *);
874 static struct tab_table *create_direct_table (struct pivot_table *);
875 static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
876 struct tab_table *, int first_difference);
877 static void display_crosstabulation (struct crosstabs_proc *,
878 struct pivot_table *,
880 static void display_chisq (struct pivot_table *, struct tab_table *,
881 bool *showed_fisher);
882 static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
884 static void display_risk (struct pivot_table *, struct tab_table *);
885 static void display_directional (struct crosstabs_proc *, struct pivot_table *,
887 static void table_value_missing (struct crosstabs_proc *proc,
888 struct tab_table *table, int c, int r,
889 unsigned char opt, const union value *v,
890 const struct variable *var);
891 static void delete_missing (struct pivot_table *);
892 static void build_matrix (struct pivot_table *);
894 /* Output pivot table beginning at PB and continuing until PE,
895 exclusive. For efficiency, *MATP is a pointer to a matrix that can
896 hold *MAXROWS entries. */
898 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
900 struct tab_table *table = NULL; /* Crosstabulation table. */
901 struct tab_table *chisq = NULL; /* Chi-square table. */
902 bool showed_fisher = false;
903 struct tab_table *sym = NULL; /* Symmetric measures table. */
904 struct tab_table *risk = NULL; /* Risk estimate table. */
905 struct tab_table *direct = NULL; /* Directional measures table. */
908 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols);
911 table = create_crosstab_table (proc, pt);
912 if (proc->statistics & (1u << CRS_ST_CHISQ))
913 chisq = create_chisq_table (pt);
914 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
915 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
916 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
917 | (1u << CRS_ST_KAPPA)))
918 sym = create_sym_table (pt);
919 if (proc->statistics & (1u << CRS_ST_RISK))
920 risk = create_risk_table (pt);
921 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
922 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
923 direct = create_direct_table (pt);
926 while (find_crosstab (pt, &row0, &row1))
928 struct pivot_table x;
929 int first_difference;
931 make_pivot_table_subset (pt, row0, row1, &x);
933 /* Find all the row variable values. */
934 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows);
936 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
939 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
940 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
941 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
943 /* Allocate table space for the matrix. */
945 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
946 tab_realloc (table, -1,
947 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
948 tab_nr (table) * pt->n_entries / x.n_entries));
952 /* Find the first variable that differs from the last subtable. */
953 first_difference = find_first_difference (pt, row0);
956 display_dimensions (proc, &x, table, first_difference);
957 display_crosstabulation (proc, &x, table);
960 if (proc->exclude == MV_NEVER)
965 display_dimensions (proc, &x, chisq, first_difference);
966 display_chisq (&x, chisq, &showed_fisher);
970 display_dimensions (proc, &x, sym, first_difference);
971 display_symmetric (proc, &x, sym);
975 display_dimensions (proc, &x, risk, first_difference);
976 display_risk (&x, risk);
980 display_dimensions (proc, &x, direct, first_difference);
981 display_directional (proc, &x, direct);
984 /* Free the parts of x that are not owned by pt. In
985 particular we must not free x.cols, which is the same as
986 pt->cols, which is freed at the end of this function. */
994 submit (NULL, table);
999 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
1005 submit (pt, direct);
1011 build_matrix (struct pivot_table *x)
1013 const int col_var_width = var_get_width (x->vars[COL_VAR]);
1014 const int row_var_width = var_get_width (x->vars[ROW_VAR]);
1017 struct table_entry **p;
1021 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1023 const struct table_entry *te = *p;
1025 while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
1027 for (; col < x->n_cols; col++)
1033 while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
1040 if (++col >= x->n_cols)
1046 while (mp < &x->mat[x->n_cols * x->n_rows])
1048 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1050 /* Column totals, row totals, ns_rows. */
1052 for (col = 0; col < x->n_cols; col++)
1053 x->col_tot[col] = 0.0;
1054 for (row = 0; row < x->n_rows; row++)
1055 x->row_tot[row] = 0.0;
1057 for (row = 0; row < x->n_rows; row++)
1059 bool row_is_empty = true;
1060 for (col = 0; col < x->n_cols; col++)
1064 row_is_empty = false;
1065 x->col_tot[col] += *mp;
1066 x->row_tot[row] += *mp;
1073 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1077 for (col = 0; col < x->n_cols; col++)
1078 for (row = 0; row < x->n_rows; row++)
1079 if (x->mat[col + row * x->n_cols] != 0.0)
1087 for (col = 0; col < x->n_cols; col++)
1088 x->total += x->col_tot[col];
1091 static struct tab_table *
1092 create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1099 static const struct tuple names[] =
1101 {CRS_CL_COUNT, N_("count")},
1102 {CRS_CL_ROW, N_("row %")},
1103 {CRS_CL_COLUMN, N_("column %")},
1104 {CRS_CL_TOTAL, N_("total %")},
1105 {CRS_CL_EXPECTED, N_("expected")},
1106 {CRS_CL_RESIDUAL, N_("residual")},
1107 {CRS_CL_SRESIDUAL, N_("std. resid.")},
1108 {CRS_CL_ASRESIDUAL, N_("adj. resid.")},
1110 const int n_names = sizeof names / sizeof *names;
1111 const struct tuple *t;
1113 struct tab_table *table;
1114 struct string title;
1115 struct pivot_table x;
1119 make_pivot_table_subset (pt, 0, 0, &x);
1121 table = tab_create (x.n_consts + 1 + x.n_cols + 1,
1122 (x.n_entries / x.n_cols) * 3 / 2 * proc->n_cells + 10);
1123 tab_headers (table, x.n_consts + 1, 0, 2, 0);
1125 /* First header line. */
1126 tab_joint_text (table, x.n_consts + 1, 0,
1127 (x.n_consts + 1) + (x.n_cols - 1), 0,
1128 TAB_CENTER | TAT_TITLE, var_get_name (x.vars[COL_VAR]));
1130 tab_hline (table, TAL_1, x.n_consts + 1,
1131 x.n_consts + 2 + x.n_cols - 2, 1);
1133 /* Second header line. */
1134 for (i = 2; i < x.n_consts + 2; i++)
1135 tab_joint_text (table, x.n_consts + 2 - i - 1, 0,
1136 x.n_consts + 2 - i - 1, 1,
1137 TAB_RIGHT | TAT_TITLE, var_to_string (x.vars[i]));
1138 tab_text (table, x.n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1139 var_get_name (x.vars[ROW_VAR]));
1140 for (i = 0; i < x.n_cols; i++)
1141 table_value_missing (proc, table, x.n_consts + 2 + i - 1, 1, TAB_RIGHT,
1142 &x.cols[i], x.vars[COL_VAR]);
1143 tab_text (table, x.n_consts + 2 + x.n_cols - 1, 1, TAB_CENTER, _("Total"));
1145 tab_hline (table, TAL_1, 0, x.n_consts + 2 + x.n_cols - 1, 2);
1146 tab_vline (table, TAL_1, x.n_consts + 2 + x.n_cols - 1, 0, 1);
1149 ds_init_empty (&title);
1150 for (i = 0; i < x.n_consts + 2; i++)
1153 ds_put_cstr (&title, " * ");
1154 ds_put_cstr (&title, var_get_name (x.vars[i]));
1156 for (i = 0; i < pt->n_consts; i++)
1158 const struct variable *var = pt->const_vars[i];
1162 ds_put_format (&title, ", %s=", var_get_name (var));
1164 /* Insert the formatted value of the variable, then trim
1165 leading spaces in what was just inserted. */
1166 ofs = ds_length (&title);
1167 s = data_out (&pt->const_values[i], var_get_encoding (var),
1168 var_get_print_format (var));
1169 ds_put_cstr (&title, s);
1171 ds_remove (&title, ofs, ss_cspan (ds_substr (&title, ofs, SIZE_MAX),
1175 ds_put_cstr (&title, " [");
1177 for (t = names; t < &names[n_names]; t++)
1178 if (proc->cells & (1u << t->value))
1181 ds_put_cstr (&title, ", ");
1182 ds_put_cstr (&title, gettext (t->name));
1184 ds_put_cstr (&title, "].");
1186 tab_title (table, "%s", ds_cstr (&title));
1187 ds_destroy (&title);
1189 tab_offset (table, 0, 2);
1193 static struct tab_table *
1194 create_chisq_table (struct pivot_table *pt)
1196 struct tab_table *chisq;
1198 chisq = tab_create (6 + (pt->n_vars - 2),
1199 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10);
1200 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1202 tab_title (chisq, _("Chi-square tests."));
1204 tab_offset (chisq, pt->n_vars - 2, 0);
1205 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1206 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1207 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1208 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1209 _("Asymp. Sig. (2-tailed)"));
1210 tab_text_format (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1211 _("Exact Sig. (%d-tailed)"), 2);
1212 tab_text_format (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1213 _("Exact Sig. (%d-tailed)"), 1);
1214 tab_offset (chisq, 0, 1);
1219 /* Symmetric measures. */
1220 static struct tab_table *
1221 create_sym_table (struct pivot_table *pt)
1223 struct tab_table *sym;
1225 sym = tab_create (6 + (pt->n_vars - 2),
1226 pt->n_entries / pt->n_cols * 7 + 10);
1227 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1228 tab_title (sym, _("Symmetric measures."));
1230 tab_offset (sym, pt->n_vars - 2, 0);
1231 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1232 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1233 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1234 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1235 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1236 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1237 tab_offset (sym, 0, 1);
1242 /* Risk estimate. */
1243 static struct tab_table *
1244 create_risk_table (struct pivot_table *pt)
1246 struct tab_table *risk;
1248 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10);
1249 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1250 tab_title (risk, _("Risk estimate."));
1252 tab_offset (risk, pt->n_vars - 2, 0);
1253 tab_joint_text_format (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE,
1254 _("95%% Confidence Interval"));
1255 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1256 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1257 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1258 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1259 tab_hline (risk, TAL_1, 2, 3, 1);
1260 tab_vline (risk, TAL_1, 2, 0, 1);
1261 tab_offset (risk, 0, 2);
1266 /* Directional measures. */
1267 static struct tab_table *
1268 create_direct_table (struct pivot_table *pt)
1270 struct tab_table *direct;
1272 direct = tab_create (7 + (pt->n_vars - 2),
1273 pt->n_entries / pt->n_cols * 7 + 10);
1274 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1275 tab_title (direct, _("Directional measures."));
1277 tab_offset (direct, pt->n_vars - 2, 0);
1278 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1279 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1280 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1281 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1282 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1283 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1284 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1285 tab_offset (direct, 0, 1);
1291 /* Delete missing rows and columns for statistical analysis when
1294 delete_missing (struct pivot_table *pt)
1298 for (r = 0; r < pt->n_rows; r++)
1299 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1301 for (c = 0; c < pt->n_cols; c++)
1302 pt->mat[c + r * pt->n_cols] = 0.;
1307 for (c = 0; c < pt->n_cols; c++)
1308 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1310 for (r = 0; r < pt->n_rows; r++)
1311 pt->mat[c + r * pt->n_cols] = 0.;
1316 /* Prepare table T for submission, and submit it. */
1318 submit (struct pivot_table *pt, struct tab_table *t)
1325 tab_resize (t, -1, 0);
1326 if (tab_nr (t) == tab_t (t))
1328 table_unref (&t->table);
1331 tab_offset (t, 0, 0);
1333 for (i = 2; i < pt->n_vars; i++)
1334 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1335 var_to_string (pt->vars[i]));
1336 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1337 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1339 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1341 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1347 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1349 size_t row0 = *row1p;
1352 if (row0 >= pt->n_entries)
1355 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1357 struct table_entry *a = pt->entries[row0];
1358 struct table_entry *b = pt->entries[row1];
1359 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1367 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1368 result. WIDTH_ points to an int which is either 0 for a
1369 numeric value or a string width for a string value. */
1371 compare_value_3way (const void *a_, const void *b_, const void *width_)
1373 const union value *a = a_;
1374 const union value *b = b_;
1375 const int *width = width_;
1377 return value_compare_3way (a, b, *width);
1380 /* Given an array of ENTRY_CNT table_entry structures starting at
1381 ENTRIES, creates a sorted list of the values that the variable
1382 with index VAR_IDX takes on. The values are returned as a
1383 malloc()'d array stored in *VALUES, with the number of values
1384 stored in *VALUE_CNT.
1387 enum_var_values (const struct pivot_table *pt, int var_idx,
1388 union value **valuesp, int *n_values)
1390 const struct variable *var = pt->vars[var_idx];
1391 struct var_range *range = get_var_range (var);
1392 union value *values;
1397 values = *valuesp = xnmalloc (range->count, sizeof *values);
1398 *n_values = range->count;
1399 for (i = 0; i < range->count; i++)
1400 values[i].f = range->min + i;
1404 int width = var_get_width (var);
1405 struct hmapx_node *node;
1406 const union value *iter;
1410 for (i = 0; i < pt->n_entries; i++)
1412 const struct table_entry *te = pt->entries[i];
1413 const union value *value = &te->values[var_idx];
1414 size_t hash = value_hash (value, width, 0);
1416 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1417 if (value_equal (iter, value, width))
1420 hmapx_insert (&set, (union value *) value, hash);
1425 *n_values = hmapx_count (&set);
1426 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1428 HMAPX_FOR_EACH (iter, node, &set)
1429 values[i++] = *iter;
1430 hmapx_destroy (&set);
1432 sort (values, *n_values, sizeof *values, compare_value_3way, &width);
1436 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1437 from V, displayed with print format spec from variable VAR. When
1438 in REPORT missing-value mode, missing values have an M appended. */
1440 table_value_missing (struct crosstabs_proc *proc,
1441 struct tab_table *table, int c, int r, unsigned char opt,
1442 const union value *v, const struct variable *var)
1444 const char *label = var_lookup_value_label (var, v);
1446 tab_text (table, c, r, TAB_LEFT, label);
1449 const struct fmt_spec *print = var_get_print_format (var);
1450 if (proc->exclude == MV_NEVER && var_is_value_missing (var, v, MV_USER))
1452 char *s = data_out (v, dict_get_encoding (proc->dict), print);
1453 tab_text_format (table, c, r, opt, "%sM", s + strspn (s, " "));
1457 tab_value (table, c, r, opt, v, proc->dict, print);
1461 /* Draws a line across TABLE at the current row to indicate the most
1462 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1463 that changed, and puts the values that changed into the table. TB
1464 and PT must be the corresponding table_entry and crosstab,
1467 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1468 struct tab_table *table, int first_difference)
1470 tab_hline (table, TAL_1, pt->n_consts + pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1472 for (; first_difference >= 2; first_difference--)
1473 table_value_missing (proc, table, pt->n_consts + pt->n_vars - first_difference - 1, 0,
1474 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1475 pt->vars[first_difference]);
1478 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1479 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1480 additionally suffixed with a letter `M'. */
1482 format_cell_entry (struct tab_table *table, int c, int r, double value,
1483 char suffix, bool mark_missing, const struct dictionary *dict)
1485 const struct fmt_spec f = {FMT_F, 10, 1};
1492 s = data_out (&v, dict_get_encoding (dict), &f);
1496 suffixes[suffix_len++] = suffix;
1498 suffixes[suffix_len++] = 'M';
1499 suffixes[suffix_len] = '\0';
1501 tab_text_format (table, c, r, TAB_RIGHT, "%s%s",
1502 s + strspn (s, " "), suffixes);
1507 /* Displays the crosstabulation table. */
1509 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1510 struct tab_table *table)
1516 for (r = 0; r < pt->n_rows; r++)
1517 table_value_missing (proc, table, pt->n_consts + pt->n_vars - 2,
1518 r * proc->n_cells, TAB_RIGHT, &pt->rows[r],
1521 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1522 TAB_LEFT, _("Total"));
1524 /* Put in the actual cells. */
1526 tab_offset (table, pt->n_consts + pt->n_vars - 1, -1);
1527 for (r = 0; r < pt->n_rows; r++)
1529 if (proc->n_cells > 1)
1530 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1531 for (c = 0; c < pt->n_cols; c++)
1533 bool mark_missing = false;
1534 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1535 if (proc->exclude == MV_NEVER
1536 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1537 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1539 mark_missing = true;
1540 for (i = 0; i < proc->n_cells; i++)
1545 switch (proc->a_cells[i])
1551 v = *mp / pt->row_tot[r] * 100.;
1555 v = *mp / pt->col_tot[c] * 100.;
1559 v = *mp / pt->total * 100.;
1562 case CRS_CL_EXPECTED:
1565 case CRS_CL_RESIDUAL:
1566 v = *mp - expected_value;
1568 case CRS_CL_SRESIDUAL:
1569 v = (*mp - expected_value) / sqrt (expected_value);
1571 case CRS_CL_ASRESIDUAL:
1572 v = ((*mp - expected_value)
1573 / sqrt (expected_value
1574 * (1. - pt->row_tot[r] / pt->total)
1575 * (1. - pt->col_tot[c] / pt->total)));
1580 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1586 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1590 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1591 for (r = 0; r < pt->n_rows; r++)
1593 bool mark_missing = false;
1595 if (proc->exclude == MV_NEVER
1596 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1597 mark_missing = true;
1599 for (i = 0; i < proc->n_cells; i++)
1604 switch (proc->a_cells[i])
1614 v = pt->row_tot[r] / pt->total * 100.;
1618 v = pt->row_tot[r] / pt->total * 100.;
1621 case CRS_CL_EXPECTED:
1622 case CRS_CL_RESIDUAL:
1623 case CRS_CL_SRESIDUAL:
1624 case CRS_CL_ASRESIDUAL:
1631 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing, proc->dict);
1632 tab_next_row (table);
1636 /* Column totals, grand total. */
1638 if (proc->n_cells > 1)
1639 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1640 for (c = 0; c <= pt->n_cols; c++)
1642 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1643 bool mark_missing = false;
1646 if (proc->exclude == MV_NEVER && c < pt->n_cols
1647 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1648 mark_missing = true;
1650 for (i = 0; i < proc->n_cells; i++)
1655 switch (proc->a_cells[i])
1661 v = ct / pt->total * 100.;
1669 v = ct / pt->total * 100.;
1672 case CRS_CL_EXPECTED:
1673 case CRS_CL_RESIDUAL:
1674 case CRS_CL_SRESIDUAL:
1675 case CRS_CL_ASRESIDUAL:
1681 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1686 tab_offset (table, -1, tab_row (table) + last_row);
1687 tab_offset (table, 0, -1);
1690 static void calc_r (struct pivot_table *,
1691 double *PT, double *Y, double *, double *, double *);
1692 static void calc_chisq (struct pivot_table *,
1693 double[N_CHISQ], int[N_CHISQ], double *, double *);
1695 /* Display chi-square statistics. */
1697 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1698 bool *showed_fisher)
1700 static const char *chisq_stats[N_CHISQ] =
1702 N_("Pearson Chi-Square"),
1703 N_("Likelihood Ratio"),
1704 N_("Fisher's Exact Test"),
1705 N_("Continuity Correction"),
1706 N_("Linear-by-Linear Association"),
1708 double chisq_v[N_CHISQ];
1709 double fisher1, fisher2;
1714 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1716 tab_offset (chisq, pt->n_vars - 2, -1);
1718 for (i = 0; i < N_CHISQ; i++)
1720 if ((i != 2 && chisq_v[i] == SYSMIS)
1721 || (i == 2 && fisher1 == SYSMIS))
1724 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1727 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL);
1728 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], &pt->weight_format);
1729 tab_double (chisq, 3, 0, TAB_RIGHT,
1730 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL);
1734 *showed_fisher = true;
1735 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL);
1736 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL);
1738 tab_next_row (chisq);
1741 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1742 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1743 tab_next_row (chisq);
1745 tab_offset (chisq, 0, -1);
1748 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1749 double[N_SYMMETRIC], double[N_SYMMETRIC],
1750 double[N_SYMMETRIC],
1751 double[3], double[3], double[3]);
1753 /* Display symmetric measures. */
1755 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1756 struct tab_table *sym)
1758 static const char *categories[] =
1760 N_("Nominal by Nominal"),
1761 N_("Ordinal by Ordinal"),
1762 N_("Interval by Interval"),
1763 N_("Measure of Agreement"),
1766 static const char *stats[N_SYMMETRIC] =
1770 N_("Contingency Coefficient"),
1771 N_("Kendall's tau-b"),
1772 N_("Kendall's tau-c"),
1774 N_("Spearman Correlation"),
1779 static const int stats_categories[N_SYMMETRIC] =
1781 0, 0, 0, 1, 1, 1, 1, 2, 3,
1785 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1786 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1789 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1790 somers_d_v, somers_d_ase, somers_d_t))
1793 tab_offset (sym, pt->n_vars - 2, -1);
1795 for (i = 0; i < N_SYMMETRIC; i++)
1797 if (sym_v[i] == SYSMIS)
1800 if (stats_categories[i] != last_cat)
1802 last_cat = stats_categories[i];
1803 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1806 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1807 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL);
1808 if (sym_ase[i] != SYSMIS)
1809 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL);
1810 if (sym_t[i] != SYSMIS)
1811 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL);
1812 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL);*/
1816 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1817 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1820 tab_offset (sym, 0, -1);
1823 static int calc_risk (struct pivot_table *,
1824 double[], double[], double[], union value *);
1826 /* Display risk estimate. */
1828 display_risk (struct pivot_table *pt, struct tab_table *risk)
1831 double risk_v[3], lower[3], upper[3];
1835 if (!calc_risk (pt, risk_v, upper, lower, c))
1838 tab_offset (risk, pt->n_vars - 2, -1);
1840 for (i = 0; i < 3; i++)
1842 const struct variable *cv = pt->vars[COL_VAR];
1843 const struct variable *rv = pt->vars[ROW_VAR];
1844 int cvw = var_get_width (cv);
1845 int rvw = var_get_width (rv);
1847 if (risk_v[i] == SYSMIS)
1853 if (var_is_numeric (cv))
1854 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1855 var_get_name (cv), c[0].f, c[1].f);
1857 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1859 cvw, value_str (&c[0], cvw),
1860 cvw, value_str (&c[1], cvw));
1864 if (var_is_numeric (rv))
1865 sprintf (buf, _("For cohort %s = %g"),
1866 var_get_name (rv), pt->rows[i - 1].f);
1868 sprintf (buf, _("For cohort %s = %.*s"),
1870 rvw, value_str (&pt->rows[i - 1], rvw));
1874 tab_text (risk, 0, 0, TAB_LEFT, buf);
1875 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL);
1876 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL);
1877 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL);
1878 tab_next_row (risk);
1881 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1882 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1883 tab_next_row (risk);
1885 tab_offset (risk, 0, -1);
1888 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1889 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1890 double[N_DIRECTIONAL]);
1892 /* Display directional measures. */
1894 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
1895 struct tab_table *direct)
1897 static const char *categories[] =
1899 N_("Nominal by Nominal"),
1900 N_("Ordinal by Ordinal"),
1901 N_("Nominal by Interval"),
1904 static const char *stats[] =
1907 N_("Goodman and Kruskal tau"),
1908 N_("Uncertainty Coefficient"),
1913 static const char *types[] =
1920 static const int stats_categories[N_DIRECTIONAL] =
1922 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
1925 static const int stats_stats[N_DIRECTIONAL] =
1927 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
1930 static const int stats_types[N_DIRECTIONAL] =
1932 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
1935 static const int *stats_lookup[] =
1942 static const char **stats_names[] =
1954 double direct_v[N_DIRECTIONAL];
1955 double direct_ase[N_DIRECTIONAL];
1956 double direct_t[N_DIRECTIONAL];
1960 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t))
1963 tab_offset (direct, pt->n_vars - 2, -1);
1965 for (i = 0; i < N_DIRECTIONAL; i++)
1967 if (direct_v[i] == SYSMIS)
1973 for (j = 0; j < 3; j++)
1974 if (last[j] != stats_lookup[j][i])
1977 tab_hline (direct, TAL_1, j, 6, 0);
1982 int k = last[j] = stats_lookup[j][i];
1987 string = var_get_name (pt->vars[0]);
1989 string = var_get_name (pt->vars[1]);
1991 tab_text_format (direct, j, 0, TAB_LEFT,
1992 gettext (stats_names[j][k]), string);
1997 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL);
1998 if (direct_ase[i] != SYSMIS)
1999 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL);
2000 if (direct_t[i] != SYSMIS)
2001 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL);
2002 /*tab_double (direct, 6, 0, TAB_RIGHT, normal_sig (direct_v[i]), NULL);*/
2003 tab_next_row (direct);
2006 tab_offset (direct, 0, -1);
2009 /* Statistical calculations. */
2011 /* Returns the value of the gamma (factorial) function for an integer
2014 gamma_int (double pt)
2019 for (i = 2; i < pt; i++)
2024 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2026 static inline double
2027 Pr (int a, int b, int c, int d)
2029 return (gamma_int (a + b + 1.) / gamma_int (a + 1.)
2030 * gamma_int (c + d + 1.) / gamma_int (b + 1.)
2031 * gamma_int (a + c + 1.) / gamma_int (c + 1.)
2032 * gamma_int (b + d + 1.) / gamma_int (d + 1.)
2033 / gamma_int (a + b + c + d + 1.));
2036 /* Swap the contents of A and B. */
2038 swap (int *a, int *b)
2045 /* Calculate significance for Fisher's exact test as specified in
2046 _SPSS Statistical Algorithms_, Appendix 5. */
2048 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2052 if (MIN (c, d) < MIN (a, b))
2053 swap (&a, &c), swap (&b, &d);
2054 if (MIN (b, d) < MIN (a, c))
2055 swap (&a, &b), swap (&c, &d);
2059 swap (&a, &b), swap (&c, &d);
2061 swap (&a, &c), swap (&b, &d);
2065 for (pt = 0; pt <= a; pt++)
2066 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2068 *fisher2 = *fisher1;
2069 for (pt = 1; pt <= b; pt++)
2070 *fisher2 += Pr (a + pt, b - pt, c - pt, d + pt);
2073 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2074 columns with values COLS and N_ROWS rows with values ROWS. Values
2075 in the matrix sum to pt->total. */
2077 calc_chisq (struct pivot_table *pt,
2078 double chisq[N_CHISQ], int df[N_CHISQ],
2079 double *fisher1, double *fisher2)
2083 chisq[0] = chisq[1] = 0.;
2084 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2085 *fisher1 = *fisher2 = SYSMIS;
2087 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2089 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2091 chisq[0] = chisq[1] = SYSMIS;
2095 for (r = 0; r < pt->n_rows; r++)
2096 for (c = 0; c < pt->n_cols; c++)
2098 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2099 const double freq = pt->mat[pt->n_cols * r + c];
2100 const double residual = freq - expected;
2102 chisq[0] += residual * residual / expected;
2104 chisq[1] += freq * log (expected / freq);
2115 /* Calculate Yates and Fisher exact test. */
2116 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2118 double f11, f12, f21, f22;
2124 for (i = j = 0; i < pt->n_cols; i++)
2125 if (pt->col_tot[i] != 0.)
2134 f11 = pt->mat[nz_cols[0]];
2135 f12 = pt->mat[nz_cols[1]];
2136 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2137 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2142 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2145 chisq[3] = (pt->total * pow2 (pt_)
2146 / (f11 + f12) / (f21 + f22)
2147 / (f11 + f21) / (f12 + f22));
2155 if (f11 < 5. || f12 < 5. || f21 < 5. || f22 < 5.)
2156 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2159 /* Calculate Mantel-Haenszel. */
2160 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2162 double r, ase_0, ase_1;
2163 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2165 chisq[4] = (pt->total - 1.) * r * r;
2170 /* Calculate the value of Pearson's r. r is stored into R, ase_1 into
2171 ASE_1, and ase_0 into ASE_0. The row and column values must be
2172 passed in PT and Y. */
2174 calc_r (struct pivot_table *pt,
2175 double *PT, double *Y, double *r, double *ase_0, double *ase_1)
2177 double SX, SY, S, T;
2179 double sum_XYf, sum_X2Y2f;
2180 double sum_Xr, sum_X2r;
2181 double sum_Yc, sum_Y2c;
2184 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2185 for (j = 0; j < pt->n_cols; j++)
2187 double fij = pt->mat[j + i * pt->n_cols];
2188 double product = PT[i] * Y[j];
2189 double temp = fij * product;
2191 sum_X2Y2f += temp * product;
2194 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2196 sum_Xr += PT[i] * pt->row_tot[i];
2197 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2199 Xbar = sum_Xr / pt->total;
2201 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2203 sum_Yc += Y[i] * pt->col_tot[i];
2204 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2206 Ybar = sum_Yc / pt->total;
2208 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2209 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2210 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2213 *ase_0 = sqrt ((sum_X2Y2f - pow2 (sum_XYf) / pt->total) / (sum_X2r * sum_Y2c));
2218 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2219 for (j = 0; j < pt->n_cols; j++)
2221 double Xresid, Yresid;
2224 Xresid = PT[i] - Xbar;
2225 Yresid = Y[j] - Ybar;
2226 temp = (T * Xresid * Yresid
2228 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2229 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2234 *ase_1 = sqrt (s) / (T * T);
2238 /* Calculate symmetric statistics and their asymptotic standard
2239 errors. Returns 0 if none could be calculated. */
2241 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2242 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2243 double t[N_SYMMETRIC],
2244 double somers_d_v[3], double somers_d_ase[3],
2245 double somers_d_t[3])
2249 q = MIN (pt->ns_rows, pt->ns_cols);
2253 for (i = 0; i < N_SYMMETRIC; i++)
2254 v[i] = ase[i] = t[i] = SYSMIS;
2256 /* Phi, Cramer's V, contingency coefficient. */
2257 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2259 double Xp = 0.; /* Pearson chi-square. */
2262 for (r = 0; r < pt->n_rows; r++)
2263 for (c = 0; c < pt->n_cols; c++)
2265 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2266 const double freq = pt->mat[pt->n_cols * r + c];
2267 const double residual = freq - expected;
2269 Xp += residual * residual / expected;
2272 if (proc->statistics & (1u << CRS_ST_PHI))
2274 v[0] = sqrt (Xp / pt->total);
2275 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2277 if (proc->statistics & (1u << CRS_ST_CC))
2278 v[2] = sqrt (Xp / (Xp + pt->total));
2281 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2282 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2287 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2291 Dr = Dc = pow2 (pt->total);
2292 for (r = 0; r < pt->n_rows; r++)
2293 Dr -= pow2 (pt->row_tot[r]);
2294 for (c = 0; c < pt->n_cols; c++)
2295 Dc -= pow2 (pt->col_tot[c]);
2297 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2298 for (c = 0; c < pt->n_cols; c++)
2302 for (r = 0; r < pt->n_rows; r++)
2303 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2312 for (i = 0; i < pt->n_rows; i++)
2316 for (j = 1; j < pt->n_cols; j++)
2317 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2320 for (j = 1; j < pt->n_cols; j++)
2321 Dij += cum[j + (i - 1) * pt->n_cols];
2325 double fij = pt->mat[j + i * pt->n_cols];
2329 if (++j == pt->n_cols)
2331 assert (j < pt->n_cols);
2333 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2334 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2338 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2339 Dij -= cum[j + (i - 1) * pt->n_cols];
2345 if (proc->statistics & (1u << CRS_ST_BTAU))
2346 v[3] = (P - Q) / sqrt (Dr * Dc);
2347 if (proc->statistics & (1u << CRS_ST_CTAU))
2348 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2349 if (proc->statistics & (1u << CRS_ST_GAMMA))
2350 v[5] = (P - Q) / (P + Q);
2352 /* ASE for tau-b, tau-c, gamma. Calculations could be
2353 eliminated here, at expense of memory. */
2358 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2359 for (i = 0; i < pt->n_rows; i++)
2363 for (j = 1; j < pt->n_cols; j++)
2364 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2367 for (j = 1; j < pt->n_cols; j++)
2368 Dij += cum[j + (i - 1) * pt->n_cols];
2372 double fij = pt->mat[j + i * pt->n_cols];
2374 if (proc->statistics & (1u << CRS_ST_BTAU))
2376 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2377 + v[3] * (pt->row_tot[i] * Dc
2378 + pt->col_tot[j] * Dr));
2379 btau_cum += fij * temp * temp;
2383 const double temp = Cij - Dij;
2384 ctau_cum += fij * temp * temp;
2387 if (proc->statistics & (1u << CRS_ST_GAMMA))
2389 const double temp = Q * Cij - P * Dij;
2390 gamma_cum += fij * temp * temp;
2393 if (proc->statistics & (1u << CRS_ST_D))
2395 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2396 - (P - Q) * (pt->total - pt->row_tot[i]));
2397 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2398 - (Q - P) * (pt->total - pt->col_tot[j]));
2401 if (++j == pt->n_cols)
2403 assert (j < pt->n_cols);
2405 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2406 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2410 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2411 Dij -= cum[j + (i - 1) * pt->n_cols];
2417 btau_var = ((btau_cum
2418 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2420 if (proc->statistics & (1u << CRS_ST_BTAU))
2422 ase[3] = sqrt (btau_var);
2423 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2426 if (proc->statistics & (1u << CRS_ST_CTAU))
2428 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2429 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2430 t[4] = v[4] / ase[4];
2432 if (proc->statistics & (1u << CRS_ST_GAMMA))
2434 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2435 t[5] = v[5] / (2. / (P + Q)
2436 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2438 if (proc->statistics & (1u << CRS_ST_D))
2440 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2441 somers_d_ase[0] = 2. * btau_var / (Dr + Dc) * sqrt (Dr * Dc);
2442 somers_d_t[0] = (somers_d_v[0]
2444 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2445 somers_d_v[1] = (P - Q) / Dc;
2446 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2447 somers_d_t[1] = (somers_d_v[1]
2449 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2450 somers_d_v[2] = (P - Q) / Dr;
2451 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2452 somers_d_t[2] = (somers_d_v[2]
2454 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2460 /* Spearman correlation, Pearson's r. */
2461 if (proc->statistics & (1u << CRS_ST_CORR))
2463 double *R = xmalloc (sizeof *R * pt->n_rows);
2464 double *C = xmalloc (sizeof *C * pt->n_cols);
2467 double y, t, c = 0., s = 0.;
2472 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2473 y = pt->row_tot[i] - c;
2477 if (++i == pt->n_rows)
2479 assert (i < pt->n_rows);
2484 double y, t, c = 0., s = 0.;
2489 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2490 y = pt->col_tot[j] - c;
2494 if (++j == pt->n_cols)
2496 assert (j < pt->n_cols);
2500 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2506 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2510 /* Cohen's kappa. */
2511 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2513 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2516 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2517 i < pt->ns_rows; i++, j++)
2521 while (pt->col_tot[j] == 0.)
2524 prod = pt->row_tot[i] * pt->col_tot[j];
2525 sum = pt->row_tot[i] + pt->col_tot[j];
2527 sum_fii += pt->mat[j + i * pt->n_cols];
2529 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2530 sum_riciri_ci += prod * sum;
2532 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2533 for (j = 0; j < pt->ns_cols; j++)
2535 double sum = pt->row_tot[i] + pt->col_tot[j];
2536 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2539 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2541 ase[8] = sqrt ((pow2 (pt->total) * sum_rici
2542 + sum_rici * sum_rici
2543 - pt->total * sum_riciri_ci)
2544 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2546 t[8] = v[8] / sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2547 / pow2 (pow2 (pt->total) - sum_rici))
2548 + ((2. * (pt->total - sum_fii)
2549 * (2. * sum_fii * sum_rici
2550 - pt->total * sum_fiiri_ci))
2551 / cube (pow2 (pt->total) - sum_rici))
2552 + (pow2 (pt->total - sum_fii)
2553 * (pt->total * sum_fijri_ci2 - 4.
2554 * sum_rici * sum_rici)
2555 / pow4 (pow2 (pt->total) - sum_rici))));
2557 t[8] = v[8] / ase[8];
2564 /* Calculate risk estimate. */
2566 calc_risk (struct pivot_table *pt,
2567 double *value, double *upper, double *lower, union value *c)
2569 double f11, f12, f21, f22;
2575 for (i = 0; i < 3; i++)
2576 value[i] = upper[i] = lower[i] = SYSMIS;
2579 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2586 for (i = j = 0; i < pt->n_cols; i++)
2587 if (pt->col_tot[i] != 0.)
2596 f11 = pt->mat[nz_cols[0]];
2597 f12 = pt->mat[nz_cols[1]];
2598 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2599 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2601 c[0] = pt->cols[nz_cols[0]];
2602 c[1] = pt->cols[nz_cols[1]];
2605 value[0] = (f11 * f22) / (f12 * f21);
2606 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2607 lower[0] = value[0] * exp (-1.960 * v);
2608 upper[0] = value[0] * exp (1.960 * v);
2610 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2611 v = sqrt ((f12 / (f11 * (f11 + f12)))
2612 + (f22 / (f21 * (f21 + f22))));
2613 lower[1] = value[1] * exp (-1.960 * v);
2614 upper[1] = value[1] * exp (1.960 * v);
2616 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2617 v = sqrt ((f11 / (f12 * (f11 + f12)))
2618 + (f21 / (f22 * (f21 + f22))));
2619 lower[2] = value[2] * exp (-1.960 * v);
2620 upper[2] = value[2] * exp (1.960 * v);
2625 /* Calculate directional measures. */
2627 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2628 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2629 double t[N_DIRECTIONAL])
2634 for (i = 0; i < N_DIRECTIONAL; i++)
2635 v[i] = ase[i] = t[i] = SYSMIS;
2639 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2641 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2642 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2643 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2644 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2645 double sum_fim, sum_fmj;
2647 int rm_index, cm_index;
2650 /* Find maximum for each row and their sum. */
2651 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2653 double max = pt->mat[i * pt->n_cols];
2656 for (j = 1; j < pt->n_cols; j++)
2657 if (pt->mat[j + i * pt->n_cols] > max)
2659 max = pt->mat[j + i * pt->n_cols];
2663 sum_fim += fim[i] = max;
2664 fim_index[i] = index;
2667 /* Find maximum for each column. */
2668 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2670 double max = pt->mat[j];
2673 for (i = 1; i < pt->n_rows; i++)
2674 if (pt->mat[j + i * pt->n_cols] > max)
2676 max = pt->mat[j + i * pt->n_cols];
2680 sum_fmj += fmj[j] = max;
2681 fmj_index[j] = index;
2684 /* Find maximum row total. */
2685 rm = pt->row_tot[0];
2687 for (i = 1; i < pt->n_rows; i++)
2688 if (pt->row_tot[i] > rm)
2690 rm = pt->row_tot[i];
2694 /* Find maximum column total. */
2695 cm = pt->col_tot[0];
2697 for (j = 1; j < pt->n_cols; j++)
2698 if (pt->col_tot[j] > cm)
2700 cm = pt->col_tot[j];
2704 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2705 v[1] = (sum_fmj - rm) / (pt->total - rm);
2706 v[2] = (sum_fim - cm) / (pt->total - cm);
2708 /* ASE1 for Y given PT. */
2712 for (accum = 0., i = 0; i < pt->n_rows; i++)
2713 for (j = 0; j < pt->n_cols; j++)
2715 const int deltaj = j == cm_index;
2716 accum += (pt->mat[j + i * pt->n_cols]
2717 * pow2 ((j == fim_index[i])
2722 ase[2] = sqrt (accum - pt->total * v[0]) / (pt->total - cm);
2725 /* ASE0 for Y given PT. */
2729 for (accum = 0., i = 0; i < pt->n_rows; i++)
2730 if (cm_index != fim_index[i])
2731 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2732 + pt->mat[i * pt->n_cols + cm_index]);
2733 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2736 /* ASE1 for PT given Y. */
2740 for (accum = 0., i = 0; i < pt->n_rows; i++)
2741 for (j = 0; j < pt->n_cols; j++)
2743 const int deltaj = i == rm_index;
2744 accum += (pt->mat[j + i * pt->n_cols]
2745 * pow2 ((i == fmj_index[j])
2750 ase[1] = sqrt (accum - pt->total * v[0]) / (pt->total - rm);
2753 /* ASE0 for PT given Y. */
2757 for (accum = 0., j = 0; j < pt->n_cols; j++)
2758 if (rm_index != fmj_index[j])
2759 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2760 + pt->mat[j + pt->n_cols * rm_index]);
2761 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2764 /* Symmetric ASE0 and ASE1. */
2769 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2770 for (j = 0; j < pt->n_cols; j++)
2772 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2773 int temp1 = (i == rm_index) + (j == cm_index);
2774 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2775 accum1 += (pt->mat[j + i * pt->n_cols]
2776 * pow2 (temp0 + (v[0] - 1.) * temp1));
2778 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2779 t[0] = v[0] / (sqrt (accum0 - pow2 ((sum_fim + sum_fmj - cm - rm) / pt->total))
2780 / (2. * pt->total - rm - cm));
2789 double sum_fij2_ri, sum_fij2_ci;
2790 double sum_ri2, sum_cj2;
2792 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2793 for (j = 0; j < pt->n_cols; j++)
2795 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2796 sum_fij2_ri += temp / pt->row_tot[i];
2797 sum_fij2_ci += temp / pt->col_tot[j];
2800 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2801 sum_ri2 += pow2 (pt->row_tot[i]);
2803 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2804 sum_cj2 += pow2 (pt->col_tot[j]);
2806 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2807 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2811 if (proc->statistics & (1u << CRS_ST_UC))
2813 double UX, UY, UXY, P;
2814 double ase1_yx, ase1_xy, ase1_sym;
2817 for (UX = 0., i = 0; i < pt->n_rows; i++)
2818 if (pt->row_tot[i] > 0.)
2819 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2821 for (UY = 0., j = 0; j < pt->n_cols; j++)
2822 if (pt->col_tot[j] > 0.)
2823 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2825 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2826 for (j = 0; j < pt->n_cols; j++)
2828 double entry = pt->mat[j + i * pt->n_cols];
2833 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2834 UXY -= entry / pt->total * log (entry / pt->total);
2837 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2838 for (j = 0; j < pt->n_cols; j++)
2840 double entry = pt->mat[j + i * pt->n_cols];
2845 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2846 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2847 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2848 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2849 ase1_sym += entry * pow2 ((UXY
2850 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2851 - (UX + UY) * log (entry / pt->total));
2854 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2855 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2856 t[5] = v[5] / ((2. / (pt->total * (UX + UY)))
2857 * sqrt (P - pow2 (UX + UY - UXY) / pt->total));
2859 v[6] = (UX + UY - UXY) / UX;
2860 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2861 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2863 v[7] = (UX + UY - UXY) / UY;
2864 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2865 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2869 if (proc->statistics & (1u << CRS_ST_D))
2871 double v_dummy[N_SYMMETRIC];
2872 double ase_dummy[N_SYMMETRIC];
2873 double t_dummy[N_SYMMETRIC];
2874 double somers_d_v[3];
2875 double somers_d_ase[3];
2876 double somers_d_t[3];
2878 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2879 somers_d_v, somers_d_ase, somers_d_t))
2882 for (i = 0; i < 3; i++)
2884 v[8 + i] = somers_d_v[i];
2885 ase[8 + i] = somers_d_ase[i];
2886 t[8 + i] = somers_d_t[i];
2892 if (proc->statistics & (1u << CRS_ST_ETA))
2895 double sum_Xr, sum_X2r;
2899 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2901 sum_Xr += pt->rows[i].f * pt->row_tot[i];
2902 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
2904 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2906 for (SXW = 0., j = 0; j < pt->n_cols; j++)
2910 for (cum = 0., i = 0; i < pt->n_rows; i++)
2912 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
2913 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
2916 SXW -= cum * cum / pt->col_tot[j];
2918 v[11] = sqrt (1. - SXW / SX);
2922 double sum_Yc, sum_Y2c;
2926 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2928 sum_Yc += pt->cols[i].f * pt->col_tot[i];
2929 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
2931 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
2933 for (SYW = 0., i = 0; i < pt->n_rows; i++)
2937 for (cum = 0., j = 0; j < pt->n_cols; j++)
2939 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
2940 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
2943 SYW -= cum * cum / pt->row_tot[i];
2945 v[12] = sqrt (1. - SYW / SY);