1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 1997-9, 2000, 2006, 2009 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/output.h>
60 #include <output/table.h>
67 #define _(msgid) gettext (msgid)
68 #define N_(msgid) msgid
76 missing=miss:!table/include/report;
77 +write[wr_]=none,cells,all;
78 +format=fmt:!labels/nolabels/novallabs,
81 tabl:!tables/notables,
84 +cells[cl_]=count,expected,row,column,total,residual,sresidual,
86 +statistics[st_]=chisq,phi,cc,lambda,uc,none,btau,ctau,risk,gamma,d,
92 /* Number of chi-square statistics. */
95 /* Number of symmetric statistics. */
98 /* Number of directional statistics. */
99 #define N_DIRECTIONAL 13
101 /* A single table entry for general mode. */
104 struct hmap_node node; /* Entry in hash table. */
105 double freq; /* Frequency count. */
106 union value values[1]; /* Values. */
110 table_entry_size (size_t n_values)
112 return (offsetof (struct table_entry, values)
113 + n_values * sizeof (union value));
116 /* Indexes into the 'vars' member of struct pivot_table and
117 struct crosstab member. */
120 ROW_VAR = 0, /* Row variable. */
121 COL_VAR = 1 /* Column variable. */
122 /* Higher indexes cause multiple tables to be output. */
125 /* A crosstabulation of 2 or more variables. */
128 struct fmt_spec weight_format; /* Format for weight variable. */
129 double missing; /* Weight of missing cases. */
131 /* Variables (2 or more). */
133 const struct variable **vars;
135 /* Constants (0 or more). */
137 const struct variable **const_vars;
138 union value *const_values;
142 struct table_entry **entries;
145 /* Column values, number of columns. */
149 /* Row values, number of rows. */
153 /* Number of statistically interesting columns/rows
154 (columns/rows with data in them). */
155 int ns_cols, ns_rows;
157 /* Matrix contents. */
158 double *mat; /* Matrix proper. */
159 double *row_tot; /* Row totals. */
160 double *col_tot; /* Column totals. */
161 double total; /* Grand total. */
164 /* Integer mode variable info. */
167 int min; /* Minimum value. */
168 int max; /* Maximum value + 1. */
169 int count; /* max - min. */
172 static inline struct var_range *
173 get_var_range (const struct variable *v)
175 return var_get_aux (v);
178 struct crosstabs_proc
180 const struct dictionary *dict;
181 enum { INTEGER, GENERAL } mode;
182 enum mv_class exclude;
185 struct fmt_spec weight_format;
187 /* Variables specifies on VARIABLES. */
188 const struct variable **variables;
192 struct pivot_table *pivots;
196 int n_cells; /* Number of cells requested. */
197 unsigned int cells; /* Bit k is 1 if cell k is requested. */
198 int a_cells[CRS_CL_count]; /* 0...n_cells-1 are the requested cells. */
201 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
205 init_proc (struct crosstabs_proc *proc, struct dataset *ds)
207 const struct variable *wv = dict_get_weight (dataset_dict (ds));
208 proc->dict = dataset_dict (ds);
209 proc->bad_warn = true;
210 proc->variables = NULL;
211 proc->n_variables = 0;
214 proc->weight_format = wv ? *var_get_print_format (wv) : F_8_0;
218 free_proc (struct crosstabs_proc *proc)
220 struct pivot_table *pt;
222 free (proc->variables);
223 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
226 free (pt->const_vars);
227 /* We must not call value_destroy on const_values because
228 it is a wild pointer; it never pointed to anything owned
231 The rest of the data was allocated and destroyed at a
232 lower level already. */
237 static int internal_cmd_crosstabs (struct lexer *lexer, struct dataset *ds,
238 struct crosstabs_proc *);
239 static bool should_tabulate_case (const struct pivot_table *,
240 const struct ccase *, enum mv_class exclude);
241 static void tabulate_general_case (struct pivot_table *, const struct ccase *,
243 static void tabulate_integer_case (struct pivot_table *, const struct ccase *,
245 static void postcalc (struct crosstabs_proc *);
246 static void submit (struct crosstabs_proc *, struct pivot_table *,
249 /* Parse and execute CROSSTABS, then clean up. */
251 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
253 struct crosstabs_proc proc;
256 init_proc (&proc, ds);
257 result = internal_cmd_crosstabs (lexer, ds, &proc);
263 /* Parses and executes the CROSSTABS procedure. */
265 internal_cmd_crosstabs (struct lexer *lexer, struct dataset *ds,
266 struct crosstabs_proc *proc)
268 struct casegrouper *grouper;
269 struct casereader *input, *group;
270 struct cmd_crosstabs cmd;
271 struct pivot_table *pt;
275 if (!parse_crosstabs (lexer, ds, &cmd, proc))
278 proc->mode = proc->n_variables ? INTEGER : GENERAL;
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;
291 if (proc->cells == 0)
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)
311 proc->statistics = 0;
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;
319 proc->statistics = 0;
322 proc->exclude = (cmd.miss == CRS_TABLE ? MV_ANY
323 : cmd.miss == CRS_INCLUDE ? MV_SYSTEM
325 if (proc->mode == GENERAL && proc->mode == MV_NEVER)
327 msg (SE, _("Missing mode REPORT not allowed in general mode. "
328 "Assuming MISSING=TABLE."));
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);
351 for (; (c = casereader_read (group)) != NULL; case_unref (c))
352 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
354 double weight = dict_get_case_weight (dataset_dict (ds), c,
356 if (should_tabulate_case (pt, c, proc->exclude))
358 if (proc->mode == GENERAL)
359 tabulate_general_case (pt, c, weight);
361 tabulate_integer_case (pt, c, weight);
364 pt->missing += weight;
366 casereader_destroy (group);
371 ok = casegrouper_destroy (grouper);
372 ok = proc_commit (ds) && ok;
374 return ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
377 /* Parses the TABLES subcommand. */
379 crs_custom_tables (struct lexer *lexer, struct dataset *ds,
380 struct cmd_crosstabs *cmd UNUSED, void *proc_)
382 struct crosstabs_proc *proc = proc_;
383 struct const_var_set *var_set;
385 const struct variable ***by = NULL;
387 size_t *by_nvar = NULL;
392 /* Ensure that this is a TABLES subcommand. */
393 if (!lex_match_id (lexer, "TABLES")
394 && (lex_token (lexer) != T_ID ||
395 dict_lookup_var (dataset_dict (ds), lex_tokid (lexer)) == NULL)
396 && lex_token (lexer) != T_ALL)
398 lex_match (lexer, '=');
400 if (proc->variables != NULL)
401 var_set = const_var_set_create_from_array (proc->variables,
404 var_set = const_var_set_create_from_dict (dataset_dict (ds));
405 assert (var_set != NULL);
409 by = xnrealloc (by, n_by + 1, sizeof *by);
410 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
411 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
412 PV_NO_DUPLICATE | PV_NO_SCRATCH))
414 if (xalloc_oversized (nx, by_nvar[n_by]))
416 msg (SE, _("Too many cross-tabulation variables or dimensions."));
422 if (!lex_match (lexer, T_BY))
426 lex_error (lexer, _("expecting BY"));
434 by_iter = xcalloc (n_by, sizeof *by_iter);
435 proc->pivots = xnrealloc (proc->pivots,
436 proc->n_pivots + nx, sizeof *proc->pivots);
437 for (i = 0; i < nx; i++)
439 struct pivot_table *pt = &proc->pivots[proc->n_pivots++];
442 pt->weight_format = proc->weight_format;
445 pt->vars = xmalloc (n_by * sizeof *pt->vars);
447 pt->const_vars = NULL;
448 pt->const_values = NULL;
449 hmap_init (&pt->data);
453 for (j = 0; j < n_by; j++)
454 pt->vars[j] = by[j][by_iter[j]];
456 for (j = n_by - 1; j >= 0; j--)
458 if (++by_iter[j] < by_nvar[j])
467 /* All return paths lead here. */
468 for (i = 0; i < n_by; i++)
473 const_var_set_destroy (var_set);
478 /* Parses the VARIABLES subcommand. */
480 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
481 struct cmd_crosstabs *cmd UNUSED, void *proc_)
483 struct crosstabs_proc *proc = proc_;
486 msg (SE, _("VARIABLES must be specified before TABLES."));
490 lex_match (lexer, '=');
494 size_t orig_nv = proc->n_variables;
499 if (!parse_variables_const (lexer, dataset_dict (ds),
500 &proc->variables, &proc->n_variables,
501 (PV_APPEND | PV_NUMERIC
502 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
505 if (lex_token (lexer) != '(')
507 lex_error (lexer, "expecting `('");
512 if (!lex_force_int (lexer))
514 min = lex_integer (lexer);
517 lex_match (lexer, ',');
519 if (!lex_force_int (lexer))
521 max = lex_integer (lexer);
524 msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
530 if (lex_token (lexer) != ')')
532 lex_error (lexer, "expecting `)'");
537 for (i = orig_nv; i < proc->n_variables; i++)
539 struct var_range *vr = xmalloc (sizeof *vr);
542 vr->count = max - min + 1;
543 var_attach_aux (proc->variables[i], vr, var_dtor_free);
546 if (lex_token (lexer) == '/')
553 free (proc->variables);
554 proc->variables = NULL;
555 proc->n_variables = 0;
559 /* Data file processing. */
562 should_tabulate_case (const struct pivot_table *pt, const struct ccase *c,
563 enum mv_class exclude)
566 for (j = 0; j < pt->n_vars; j++)
568 const struct variable *var = pt->vars[j];
569 struct var_range *range = get_var_range (var);
571 if (var_is_value_missing (var, case_data (c, var), exclude))
576 double num = case_num (c, var);
577 if (num < range->min || num > range->max)
585 tabulate_integer_case (struct pivot_table *pt, const struct ccase *c,
588 struct table_entry *te;
593 for (j = 0; j < pt->n_vars; j++)
595 /* Throw away fractional parts of values. */
596 hash = hash_int (case_num (c, pt->vars[j]), hash);
599 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
601 for (j = 0; j < pt->n_vars; j++)
602 if ((int) case_num (c, pt->vars[j]) != (int) te->values[j].f)
605 /* Found an existing entry. */
612 /* No existing entry. Create a new one. */
613 te = xmalloc (table_entry_size (pt->n_vars));
615 for (j = 0; j < pt->n_vars; j++)
616 te->values[j].f = (int) case_num (c, pt->vars[j]);
617 hmap_insert (&pt->data, &te->node, hash);
621 tabulate_general_case (struct pivot_table *pt, const struct ccase *c,
624 struct table_entry *te;
629 for (j = 0; j < pt->n_vars; j++)
631 const struct variable *var = pt->vars[j];
632 hash = value_hash (case_data (c, var), var_get_width (var), hash);
635 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
637 for (j = 0; j < pt->n_vars; j++)
639 const struct variable *var = pt->vars[j];
640 if (!value_equal (case_data (c, var), &te->values[j],
641 var_get_width (var)))
645 /* Found an existing entry. */
652 /* No existing entry. Create a new one. */
653 te = xmalloc (table_entry_size (pt->n_vars));
655 for (j = 0; j < pt->n_vars; j++)
657 const struct variable *var = pt->vars[j];
658 int width = var_get_width (var);
659 value_init (&te->values[j], width);
660 value_copy (&te->values[j], case_data (c, var), width);
662 hmap_insert (&pt->data, &te->node, hash);
665 /* Post-data reading calculations. */
667 static int compare_table_entry_vars_3way (const struct table_entry *a,
668 const struct table_entry *b,
669 const struct pivot_table *pt,
671 static int compare_table_entry_3way (const void *ap_, const void *bp_,
673 static void enum_var_values (const struct pivot_table *, int var_idx,
674 union value **valuesp, int *n_values);
675 static void output_pivot_table (struct crosstabs_proc *,
676 struct pivot_table *);
677 static void make_pivot_table_subset (struct pivot_table *pt,
678 size_t row0, size_t row1,
679 struct pivot_table *subset);
680 static void make_summary_table (struct crosstabs_proc *);
681 static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
684 postcalc (struct crosstabs_proc *proc)
686 struct pivot_table *pt;
688 /* Convert hash tables into sorted arrays of entries. */
689 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
691 struct table_entry *e;
694 pt->n_entries = hmap_count (&pt->data);
695 pt->entries = xnmalloc (pt->n_entries, sizeof *pt->entries);
697 HMAP_FOR_EACH (e, struct table_entry, node, &pt->data)
698 pt->entries[i++] = e;
699 hmap_destroy (&pt->data);
701 sort (pt->entries, pt->n_entries, sizeof *pt->entries,
702 compare_table_entry_3way, pt);
705 make_summary_table (proc);
707 /* Output each pivot table. */
708 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
710 if (proc->pivot || pt->n_vars == 2)
711 output_pivot_table (proc, pt);
714 size_t row0 = 0, row1 = 0;
715 while (find_crosstab (pt, &row0, &row1))
717 struct pivot_table subset;
718 make_pivot_table_subset (pt, row0, row1, &subset);
719 output_pivot_table (proc, &subset);
724 /* Free output and prepare for next split file. */
725 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
731 /* Free only the members that were allocated in this
732 function. The other pointer members are either both
733 allocated and destroyed at a lower level (in
734 output_pivot_table), or both allocated and destroyed at
735 a higher level (in crs_custom_tables and free_proc,
737 for (i = 0; i < pt->n_entries; i++)
738 free (pt->entries[i]);
744 make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
745 struct pivot_table *subset)
750 assert (pt->n_consts == 0);
751 subset->missing = pt->missing;
753 subset->vars = pt->vars;
754 subset->n_consts = pt->n_vars - 2;
755 subset->const_vars = pt->vars + 2;
756 subset->const_values = &pt->entries[row0]->values[2];
758 subset->entries = &pt->entries[row0];
759 subset->n_entries = row1 - row0;
763 compare_table_entry_var_3way (const struct table_entry *a,
764 const struct table_entry *b,
765 const struct pivot_table *pt,
768 return value_compare_3way (&a->values[idx], &b->values[idx],
769 var_get_width (pt->vars[idx]));
773 compare_table_entry_vars_3way (const struct table_entry *a,
774 const struct table_entry *b,
775 const struct pivot_table *pt,
780 for (i = idx1 - 1; i >= idx0; i--)
782 int cmp = compare_table_entry_var_3way (a, b, pt, i);
789 /* Compare the struct table_entry at *AP to the one at *BP and
790 return a strcmp()-type result. */
792 compare_table_entry_3way (const void *ap_, const void *bp_, const void *pt_)
794 const struct table_entry *const *ap = ap_;
795 const struct table_entry *const *bp = bp_;
796 const struct table_entry *a = *ap;
797 const struct table_entry *b = *bp;
798 const struct pivot_table *pt = pt_;
801 cmp = compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars);
805 cmp = compare_table_entry_var_3way (a, b, pt, ROW_VAR);
809 return compare_table_entry_var_3way (a, b, pt, COL_VAR);
813 find_first_difference (const struct pivot_table *pt, size_t row)
816 return pt->n_vars - 1;
819 const struct table_entry *a = pt->entries[row];
820 const struct table_entry *b = pt->entries[row - 1];
823 for (col = pt->n_vars - 1; col >= 0; col--)
824 if (compare_table_entry_var_3way (a, b, pt, col))
830 /* Output a table summarizing the cases processed. */
832 make_summary_table (struct crosstabs_proc *proc)
834 struct tab_table *summary;
835 struct pivot_table *pt;
839 summary = tab_create (7, 3 + proc->n_pivots, 1);
840 tab_title (summary, _("Summary."));
841 tab_headers (summary, 1, 0, 3, 0);
842 tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
843 tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
844 tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
845 tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
846 tab_hline (summary, TAL_1, 1, 6, 1);
847 tab_hline (summary, TAL_1, 1, 6, 2);
848 tab_vline (summary, TAL_1, 3, 1, 1);
849 tab_vline (summary, TAL_1, 5, 1, 1);
850 for (i = 0; i < 3; i++)
852 tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
853 tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
855 tab_offset (summary, 0, 3);
857 ds_init_empty (&name);
858 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
864 tab_hline (summary, TAL_1, 0, 6, 0);
867 for (i = 0; i < pt->n_vars; i++)
870 ds_put_cstr (&name, " * ");
871 ds_put_cstr (&name, var_to_string (pt->vars[i]));
873 tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
876 for (i = 0; i < pt->n_entries; i++)
877 valid += pt->entries[i]->freq;
882 for (i = 0; i < 3; i++)
884 tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i],
885 &proc->weight_format);
886 tab_text_format (summary, i * 2 + 2, 0, TAB_RIGHT, "%.1f%%",
890 tab_next_row (summary);
894 submit (proc, NULL, summary);
899 static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
900 struct pivot_table *);
901 static struct tab_table *create_chisq_table (struct pivot_table *);
902 static struct tab_table *create_sym_table (struct pivot_table *);
903 static struct tab_table *create_risk_table (struct pivot_table *);
904 static struct tab_table *create_direct_table (struct pivot_table *);
905 static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
906 struct tab_table *, int first_difference);
907 static void display_crosstabulation (struct crosstabs_proc *,
908 struct pivot_table *,
910 static void display_chisq (struct pivot_table *, struct tab_table *,
911 bool *showed_fisher);
912 static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
914 static void display_risk (struct pivot_table *, struct tab_table *);
915 static void display_directional (struct crosstabs_proc *, struct pivot_table *,
917 static void crosstabs_dim (struct tab_table *, struct outp_driver *,
919 static void table_value_missing (struct crosstabs_proc *proc,
920 struct tab_table *table, int c, int r,
921 unsigned char opt, const union value *v,
922 const struct variable *var);
923 static void delete_missing (struct pivot_table *);
924 static void build_matrix (struct pivot_table *);
926 /* Output pivot table beginning at PB and continuing until PE,
927 exclusive. For efficiency, *MATP is a pointer to a matrix that can
928 hold *MAXROWS entries. */
930 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
932 struct tab_table *table = NULL; /* Crosstabulation table. */
933 struct tab_table *chisq = NULL; /* Chi-square table. */
934 bool showed_fisher = false;
935 struct tab_table *sym = NULL; /* Symmetric measures table. */
936 struct tab_table *risk = NULL; /* Risk estimate table. */
937 struct tab_table *direct = NULL; /* Directional measures table. */
940 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols);
943 table = create_crosstab_table (proc, pt);
944 if (proc->statistics & (1u << CRS_ST_CHISQ))
945 chisq = create_chisq_table (pt);
946 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
947 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
948 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
949 | (1u << CRS_ST_KAPPA)))
950 sym = create_sym_table (pt);
951 if (proc->statistics & (1u << CRS_ST_RISK))
952 risk = create_risk_table (pt);
953 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
954 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
955 direct = create_direct_table (pt);
958 while (find_crosstab (pt, &row0, &row1))
960 struct pivot_table x;
961 int first_difference;
963 make_pivot_table_subset (pt, row0, row1, &x);
965 /* Find all the row variable values. */
966 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows);
968 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
971 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
972 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
973 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
975 /* Allocate table space for the matrix. */
977 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
978 tab_realloc (table, -1,
979 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
980 tab_nr (table) * pt->n_entries / x.n_entries));
984 /* Find the first variable that differs from the last subtable. */
985 first_difference = find_first_difference (pt, row0);
988 display_dimensions (proc, &x, table, first_difference);
989 display_crosstabulation (proc, &x, table);
992 if (proc->exclude == MV_NEVER)
997 display_dimensions (proc, &x, chisq, first_difference);
998 display_chisq (&x, chisq, &showed_fisher);
1002 display_dimensions (proc, &x, sym, first_difference);
1003 display_symmetric (proc, &x, sym);
1007 display_dimensions (proc, &x, risk, first_difference);
1008 display_risk (&x, risk);
1012 display_dimensions (proc, &x, direct, first_difference);
1013 display_directional (proc, &x, direct);
1016 /* Free the parts of x that are not owned by pt. In
1017 particular we must not free x.cols, which is the same as
1018 pt->cols, which is freed at the end of this function. */
1026 submit (proc, NULL, table);
1031 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
1032 submit (proc, pt, chisq);
1035 submit (proc, pt, sym);
1036 submit (proc, pt, risk);
1037 submit (proc, pt, direct);
1043 build_matrix (struct pivot_table *x)
1045 const int col_var_width = var_get_width (x->vars[COL_VAR]);
1046 const int row_var_width = var_get_width (x->vars[ROW_VAR]);
1049 struct table_entry **p;
1053 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1055 const struct table_entry *te = *p;
1057 while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
1059 for (; col < x->n_cols; col++)
1065 while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
1072 if (++col >= x->n_cols)
1078 while (mp < &x->mat[x->n_cols * x->n_rows])
1080 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1082 /* Column totals, row totals, ns_rows. */
1084 for (col = 0; col < x->n_cols; col++)
1085 x->col_tot[col] = 0.0;
1086 for (row = 0; row < x->n_rows; row++)
1087 x->row_tot[row] = 0.0;
1089 for (row = 0; row < x->n_rows; row++)
1091 bool row_is_empty = true;
1092 for (col = 0; col < x->n_cols; col++)
1096 row_is_empty = false;
1097 x->col_tot[col] += *mp;
1098 x->row_tot[row] += *mp;
1105 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1109 for (col = 0; col < x->n_cols; col++)
1110 for (row = 0; row < x->n_rows; row++)
1111 if (x->mat[col + row * x->n_cols] != 0.0)
1119 for (col = 0; col < x->n_cols; col++)
1120 x->total += x->col_tot[col];
1123 static struct tab_table *
1124 create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1131 static const struct tuple names[] =
1133 {CRS_CL_COUNT, N_("count")},
1134 {CRS_CL_ROW, N_("row %")},
1135 {CRS_CL_COLUMN, N_("column %")},
1136 {CRS_CL_TOTAL, N_("total %")},
1137 {CRS_CL_EXPECTED, N_("expected")},
1138 {CRS_CL_RESIDUAL, N_("residual")},
1139 {CRS_CL_SRESIDUAL, N_("std. resid.")},
1140 {CRS_CL_ASRESIDUAL, N_("adj. resid.")},
1142 const int n_names = sizeof names / sizeof *names;
1143 const struct tuple *t;
1145 struct tab_table *table;
1146 struct string title;
1149 table = tab_create (pt->n_consts + 1 + pt->n_cols + 1,
1150 (pt->n_entries / pt->n_cols) * 3 / 2 * proc->n_cells + 10,
1152 tab_headers (table, pt->n_consts + 1, 0, 2, 0);
1154 /* First header line. */
1155 tab_joint_text (table, pt->n_consts + 1, 0,
1156 (pt->n_consts + 1) + (pt->n_cols - 1), 0,
1157 TAB_CENTER | TAT_TITLE, var_get_name (pt->vars[COL_VAR]));
1159 tab_hline (table, TAL_1, pt->n_consts + 1,
1160 pt->n_consts + 2 + pt->n_cols - 2, 1);
1162 /* Second header line. */
1163 for (i = 2; i < pt->n_consts + 2; i++)
1164 tab_joint_text (table, pt->n_consts + 2 - i - 1, 0,
1165 pt->n_consts + 2 - i - 1, 1,
1166 TAB_RIGHT | TAT_TITLE, var_to_string (pt->vars[i]));
1167 tab_text (table, pt->n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1168 var_get_name (pt->vars[ROW_VAR]));
1169 for (i = 0; i < pt->n_cols; i++)
1170 table_value_missing (proc, table, pt->n_consts + 2 + i - 1, 1, TAB_RIGHT,
1171 &pt->cols[i], pt->vars[COL_VAR]);
1172 tab_text (table, pt->n_consts + 2 + pt->n_cols - 1, 1, TAB_CENTER, _("Total"));
1174 tab_hline (table, TAL_1, 0, pt->n_consts + 2 + pt->n_cols - 1, 2);
1175 tab_vline (table, TAL_1, pt->n_consts + 2 + pt->n_cols - 1, 0, 1);
1178 ds_init_empty (&title);
1179 for (i = 0; i < pt->n_consts + 2; i++)
1182 ds_put_cstr (&title, " * ");
1183 ds_put_cstr (&title, var_get_name (pt->vars[i]));
1185 for (i = 0; i < pt->n_consts; i++)
1187 const struct variable *var = pt->const_vars[i];
1191 ds_put_format (&title, ", %s=", var_get_name (var));
1193 /* Insert the formatted value of the variable, then trim
1194 leading spaces in what was just inserted. */
1195 ofs = ds_length (&title);
1196 s = data_out (&pt->const_values[i], dict_get_encoding (proc->dict), var_get_print_format (var));
1197 ds_put_cstr (&title, s);
1199 ds_remove (&title, ofs, ss_cspan (ds_substr (&title, ofs, SIZE_MAX),
1203 ds_put_cstr (&title, " [");
1205 for (t = names; t < &names[n_names]; t++)
1206 if (proc->cells & (1u << t->value))
1209 ds_put_cstr (&title, ", ");
1210 ds_put_cstr (&title, gettext (t->name));
1212 ds_put_cstr (&title, "].");
1214 tab_title (table, "%s", ds_cstr (&title));
1215 ds_destroy (&title);
1217 tab_offset (table, 0, 2);
1221 static struct tab_table *
1222 create_chisq_table (struct pivot_table *pt)
1224 struct tab_table *chisq;
1226 chisq = tab_create (6 + (pt->n_vars - 2),
1227 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10,
1229 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1231 tab_title (chisq, _("Chi-square tests."));
1233 tab_offset (chisq, pt->n_vars - 2, 0);
1234 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1235 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1236 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1237 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1238 _("Asymp. Sig. (2-sided)"));
1239 tab_text (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1240 _("Exact Sig. (2-sided)"));
1241 tab_text (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1242 _("Exact Sig. (1-sided)"));
1243 tab_offset (chisq, 0, 1);
1248 /* Symmetric measures. */
1249 static struct tab_table *
1250 create_sym_table (struct pivot_table *pt)
1252 struct tab_table *sym;
1254 sym = tab_create (6 + (pt->n_vars - 2),
1255 pt->n_entries / pt->n_cols * 7 + 10, 1);
1256 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1257 tab_title (sym, _("Symmetric measures."));
1259 tab_offset (sym, pt->n_vars - 2, 0);
1260 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1261 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1262 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1263 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1264 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1265 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1266 tab_offset (sym, 0, 1);
1271 /* Risk estimate. */
1272 static struct tab_table *
1273 create_risk_table (struct pivot_table *pt)
1275 struct tab_table *risk;
1277 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10,
1279 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1280 tab_title (risk, _("Risk estimate."));
1282 tab_offset (risk, pt->n_vars - 2, 0);
1283 tab_joint_text_format (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE,
1284 _("95%% Confidence Interval"));
1285 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1286 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1287 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1288 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1289 tab_hline (risk, TAL_1, 2, 3, 1);
1290 tab_vline (risk, TAL_1, 2, 0, 1);
1291 tab_offset (risk, 0, 2);
1296 /* Directional measures. */
1297 static struct tab_table *
1298 create_direct_table (struct pivot_table *pt)
1300 struct tab_table *direct;
1302 direct = tab_create (7 + (pt->n_vars - 2),
1303 pt->n_entries / pt->n_cols * 7 + 10, 1);
1304 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1305 tab_title (direct, _("Directional measures."));
1307 tab_offset (direct, pt->n_vars - 2, 0);
1308 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1309 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1310 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1311 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1312 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1313 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1314 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1315 tab_offset (direct, 0, 1);
1321 /* Delete missing rows and columns for statistical analysis when
1324 delete_missing (struct pivot_table *pt)
1328 for (r = 0; r < pt->n_rows; r++)
1329 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1331 for (c = 0; c < pt->n_cols; c++)
1332 pt->mat[c + r * pt->n_cols] = 0.;
1337 for (c = 0; c < pt->n_cols; c++)
1338 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1340 for (r = 0; r < pt->n_rows; r++)
1341 pt->mat[c + r * pt->n_cols] = 0.;
1346 /* Prepare table T for submission, and submit it. */
1348 submit (struct crosstabs_proc *proc, struct pivot_table *pt,
1349 struct tab_table *t)
1356 tab_resize (t, -1, 0);
1357 if (tab_nr (t) == tab_t (t))
1362 tab_offset (t, 0, 0);
1364 for (i = 2; i < pt->n_vars; i++)
1365 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1366 var_to_string (pt->vars[i]));
1367 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1368 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1370 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1372 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1373 tab_dim (t, crosstabs_dim, proc);
1377 /* Sets the widths of all the columns and heights of all the rows in
1378 table T for driver D. */
1380 crosstabs_dim (struct tab_table *t, struct outp_driver *d, void *proc_)
1382 struct crosstabs_proc *proc = proc_;
1385 /* Width of a numerical column. */
1386 int c = outp_string_width (d, "0.000000", OUTP_PROPORTIONAL);
1387 if (proc->exclude == MV_NEVER)
1388 c += outp_string_width (d, "M", OUTP_PROPORTIONAL);
1390 /* Set width for header columns. */
1396 w = d->width - c * (t->nc - t->l);
1397 for (i = 0; i <= t->nc; i++)
1401 if (w < d->prop_em_width * 8)
1402 w = d->prop_em_width * 8;
1404 if (w > d->prop_em_width * 15)
1405 w = d->prop_em_width * 15;
1407 for (i = 0; i < t->l; i++)
1411 for (i = t->l; i < t->nc; i++)
1414 for (i = 0; i < t->nr; i++)
1415 t->h[i] = tab_natural_height (t, d, i);
1419 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1421 size_t row0 = *row1p;
1424 if (row0 >= pt->n_entries)
1427 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1429 struct table_entry *a = pt->entries[row0];
1430 struct table_entry *b = pt->entries[row1];
1431 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1439 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1440 result. WIDTH_ points to an int which is either 0 for a
1441 numeric value or a string width for a string value. */
1443 compare_value_3way (const void *a_, const void *b_, const void *width_)
1445 const union value *a = a_;
1446 const union value *b = b_;
1447 const int *width = width_;
1449 return value_compare_3way (a, b, *width);
1452 /* Given an array of ENTRY_CNT table_entry structures starting at
1453 ENTRIES, creates a sorted list of the values that the variable
1454 with index VAR_IDX takes on. The values are returned as a
1455 malloc()'d array stored in *VALUES, with the number of values
1456 stored in *VALUE_CNT.
1459 enum_var_values (const struct pivot_table *pt, int var_idx,
1460 union value **valuesp, int *n_values)
1462 const struct variable *var = pt->vars[var_idx];
1463 struct var_range *range = get_var_range (var);
1464 union value *values;
1469 values = *valuesp = xnmalloc (range->count, sizeof *values);
1470 *n_values = range->count;
1471 for (i = 0; i < range->count; i++)
1472 values[i].f = range->min + i;
1476 int width = var_get_width (var);
1477 struct hmapx_node *node;
1478 const union value *iter;
1482 for (i = 0; i < pt->n_entries; i++)
1484 const struct table_entry *te = pt->entries[i];
1485 const union value *value = &te->values[var_idx];
1486 size_t hash = value_hash (value, width, 0);
1488 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1489 if (value_equal (iter, value, width))
1492 hmapx_insert (&set, (union value *) value, hash);
1497 *n_values = hmapx_count (&set);
1498 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1500 HMAPX_FOR_EACH (iter, node, &set)
1501 values[i++] = *iter;
1502 hmapx_destroy (&set);
1504 sort (values, *n_values, sizeof *values, compare_value_3way, &width);
1508 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1509 from V, displayed with print format spec from variable VAR. When
1510 in REPORT missing-value mode, missing values have an M appended. */
1512 table_value_missing (struct crosstabs_proc *proc,
1513 struct tab_table *table, int c, int r, unsigned char opt,
1514 const union value *v, const struct variable *var)
1517 const struct fmt_spec *print = var_get_print_format (var);
1519 const char *label = var_lookup_value_label (var, v);
1522 tab_text (table, c, r, TAB_LEFT, label);
1526 s = ss_cstr (data_out_pool (v, dict_get_encoding (proc->dict), print,
1528 if (proc->exclude == MV_NEVER && var_is_num_missing (var, v->f, MV_USER))
1529 s.string[s.length++] = 'M';
1530 while (s.length && *s.string == ' ')
1535 tab_raw (table, c, r, opt, &s);
1538 /* Draws a line across TABLE at the current row to indicate the most
1539 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1540 that changed, and puts the values that changed into the table. TB
1541 and PT must be the corresponding table_entry and crosstab,
1544 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1545 struct tab_table *table, int first_difference)
1547 tab_hline (table, TAL_1, pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1549 for (; first_difference >= 2; first_difference--)
1550 table_value_missing (proc, table, pt->n_vars - first_difference - 1, 0,
1551 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1552 pt->vars[first_difference]);
1555 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1556 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1557 additionally suffixed with a letter `M'. */
1559 format_cell_entry (struct tab_table *table, int c, int r, double value,
1560 char suffix, bool mark_missing, const struct dictionary *dict)
1562 const struct fmt_spec f = {FMT_F, 10, 1};
1567 s = ss_cstr (data_out_pool (&v, dict_get_encoding (dict), &f, table->container));
1569 while (*s.string == ' ')
1575 s.string[s.length++] = suffix;
1577 s.string[s.length++] = 'M';
1579 tab_raw (table, c, r, TAB_RIGHT, &s);
1582 /* Displays the crosstabulation table. */
1584 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1585 struct tab_table *table)
1591 for (r = 0; r < pt->n_rows; r++)
1592 table_value_missing (proc, table, pt->n_vars - 2, r * proc->n_cells,
1593 TAB_RIGHT, &pt->rows[r], pt->vars[ROW_VAR]);
1595 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1596 TAB_LEFT, _("Total"));
1598 /* Put in the actual cells. */
1600 tab_offset (table, pt->n_vars - 1, -1);
1601 for (r = 0; r < pt->n_rows; r++)
1603 if (proc->n_cells > 1)
1604 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1605 for (c = 0; c < pt->n_cols; c++)
1607 bool mark_missing = false;
1608 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1609 if (proc->exclude == MV_NEVER
1610 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1611 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1613 mark_missing = true;
1614 for (i = 0; i < proc->n_cells; i++)
1619 switch (proc->a_cells[i])
1625 v = *mp / pt->row_tot[r] * 100.;
1629 v = *mp / pt->col_tot[c] * 100.;
1633 v = *mp / pt->total * 100.;
1636 case CRS_CL_EXPECTED:
1639 case CRS_CL_RESIDUAL:
1640 v = *mp - expected_value;
1642 case CRS_CL_SRESIDUAL:
1643 v = (*mp - expected_value) / sqrt (expected_value);
1645 case CRS_CL_ASRESIDUAL:
1646 v = ((*mp - expected_value)
1647 / sqrt (expected_value
1648 * (1. - pt->row_tot[r] / pt->total)
1649 * (1. - pt->col_tot[c] / pt->total)));
1654 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1660 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1664 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1665 for (r = 0; r < pt->n_rows; r++)
1667 bool mark_missing = false;
1669 if (proc->exclude == MV_NEVER
1670 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1671 mark_missing = true;
1673 for (i = 0; i < proc->n_cells; i++)
1678 switch (proc->a_cells[i])
1688 v = pt->row_tot[r] / pt->total * 100.;
1692 v = pt->row_tot[r] / pt->total * 100.;
1695 case CRS_CL_EXPECTED:
1696 case CRS_CL_RESIDUAL:
1697 case CRS_CL_SRESIDUAL:
1698 case CRS_CL_ASRESIDUAL:
1705 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing, proc->dict);
1706 tab_next_row (table);
1710 /* Column totals, grand total. */
1712 if (proc->n_cells > 1)
1713 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1714 for (c = 0; c <= pt->n_cols; c++)
1716 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1717 bool mark_missing = false;
1720 if (proc->exclude == MV_NEVER && c < pt->n_cols
1721 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1722 mark_missing = true;
1724 for (i = 0; i < proc->n_cells; i++)
1729 switch (proc->a_cells[i])
1735 v = ct / pt->total * 100.;
1743 v = ct / pt->total * 100.;
1746 case CRS_CL_EXPECTED:
1747 case CRS_CL_RESIDUAL:
1748 case CRS_CL_SRESIDUAL:
1749 case CRS_CL_ASRESIDUAL:
1755 format_cell_entry (table, c, i, v, suffix, mark_missing, proc->dict);
1760 tab_offset (table, -1, tab_row (table) + last_row);
1761 tab_offset (table, 0, -1);
1764 static void calc_r (struct pivot_table *,
1765 double *PT, double *Y, double *, double *, double *);
1766 static void calc_chisq (struct pivot_table *,
1767 double[N_CHISQ], int[N_CHISQ], double *, double *);
1769 /* Display chi-square statistics. */
1771 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1772 bool *showed_fisher)
1774 static const char *chisq_stats[N_CHISQ] =
1776 N_("Pearson Chi-Square"),
1777 N_("Likelihood Ratio"),
1778 N_("Fisher's Exact Test"),
1779 N_("Continuity Correction"),
1780 N_("Linear-by-Linear Association"),
1782 double chisq_v[N_CHISQ];
1783 double fisher1, fisher2;
1788 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1790 tab_offset (chisq, pt->n_vars - 2, -1);
1792 for (i = 0; i < N_CHISQ; i++)
1794 if ((i != 2 && chisq_v[i] == SYSMIS)
1795 || (i == 2 && fisher1 == SYSMIS))
1798 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1801 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL);
1802 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], &pt->weight_format);
1803 tab_double (chisq, 3, 0, TAB_RIGHT,
1804 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL);
1808 *showed_fisher = true;
1809 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL);
1810 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL);
1812 tab_next_row (chisq);
1815 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1816 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1817 tab_next_row (chisq);
1819 tab_offset (chisq, 0, -1);
1822 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1823 double[N_SYMMETRIC], double[N_SYMMETRIC],
1824 double[N_SYMMETRIC],
1825 double[3], double[3], double[3]);
1827 /* Display symmetric measures. */
1829 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1830 struct tab_table *sym)
1832 static const char *categories[] =
1834 N_("Nominal by Nominal"),
1835 N_("Ordinal by Ordinal"),
1836 N_("Interval by Interval"),
1837 N_("Measure of Agreement"),
1840 static const char *stats[N_SYMMETRIC] =
1844 N_("Contingency Coefficient"),
1845 N_("Kendall's tau-b"),
1846 N_("Kendall's tau-c"),
1848 N_("Spearman Correlation"),
1853 static const int stats_categories[N_SYMMETRIC] =
1855 0, 0, 0, 1, 1, 1, 1, 2, 3,
1859 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1860 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1863 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1864 somers_d_v, somers_d_ase, somers_d_t))
1867 tab_offset (sym, pt->n_vars - 2, -1);
1869 for (i = 0; i < N_SYMMETRIC; i++)
1871 if (sym_v[i] == SYSMIS)
1874 if (stats_categories[i] != last_cat)
1876 last_cat = stats_categories[i];
1877 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1880 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1881 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL);
1882 if (sym_ase[i] != SYSMIS)
1883 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL);
1884 if (sym_t[i] != SYSMIS)
1885 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL);
1886 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL);*/
1890 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1891 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1894 tab_offset (sym, 0, -1);
1897 static int calc_risk (struct pivot_table *,
1898 double[], double[], double[], union value *);
1900 /* Display risk estimate. */
1902 display_risk (struct pivot_table *pt, struct tab_table *risk)
1905 double risk_v[3], lower[3], upper[3];
1909 if (!calc_risk (pt, risk_v, upper, lower, c))
1912 tab_offset (risk, pt->n_vars - 2, -1);
1914 for (i = 0; i < 3; i++)
1916 const struct variable *cv = pt->vars[COL_VAR];
1917 const struct variable *rv = pt->vars[ROW_VAR];
1918 int cvw = var_get_width (cv);
1919 int rvw = var_get_width (rv);
1921 if (risk_v[i] == SYSMIS)
1927 if (var_is_numeric (cv))
1928 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1929 var_get_name (cv), c[0].f, c[1].f);
1931 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1933 cvw, value_str (&c[0], cvw),
1934 cvw, value_str (&c[1], cvw));
1938 if (var_is_numeric (rv))
1939 sprintf (buf, _("For cohort %s = %g"),
1940 var_get_name (rv), pt->rows[i - 1].f);
1942 sprintf (buf, _("For cohort %s = %.*s"),
1944 rvw, value_str (&pt->rows[i - 1], rvw));
1948 tab_text (risk, 0, 0, TAB_LEFT, buf);
1949 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL);
1950 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL);
1951 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL);
1952 tab_next_row (risk);
1955 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1956 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1957 tab_next_row (risk);
1959 tab_offset (risk, 0, -1);
1962 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1963 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
1964 double[N_DIRECTIONAL]);
1966 /* Display directional measures. */
1968 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
1969 struct tab_table *direct)
1971 static const char *categories[] =
1973 N_("Nominal by Nominal"),
1974 N_("Ordinal by Ordinal"),
1975 N_("Nominal by Interval"),
1978 static const char *stats[] =
1981 N_("Goodman and Kruskal tau"),
1982 N_("Uncertainty Coefficient"),
1987 static const char *types[] =
1994 static const int stats_categories[N_DIRECTIONAL] =
1996 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
1999 static const int stats_stats[N_DIRECTIONAL] =
2001 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
2004 static const int stats_types[N_DIRECTIONAL] =
2006 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
2009 static const int *stats_lookup[] =
2016 static const char **stats_names[] =
2028 double direct_v[N_DIRECTIONAL];
2029 double direct_ase[N_DIRECTIONAL];
2030 double direct_t[N_DIRECTIONAL];
2034 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t))
2037 tab_offset (direct, pt->n_vars - 2, -1);
2039 for (i = 0; i < N_DIRECTIONAL; i++)
2041 if (direct_v[i] == SYSMIS)
2047 for (j = 0; j < 3; j++)
2048 if (last[j] != stats_lookup[j][i])
2051 tab_hline (direct, TAL_1, j, 6, 0);
2056 int k = last[j] = stats_lookup[j][i];
2061 string = var_get_name (pt->vars[0]);
2063 string = var_get_name (pt->vars[1]);
2065 tab_text_format (direct, j, 0, TAB_LEFT,
2066 gettext (stats_names[j][k]), string);
2071 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL);
2072 if (direct_ase[i] != SYSMIS)
2073 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL);
2074 if (direct_t[i] != SYSMIS)
2075 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL);
2076 /*tab_double (direct, 6, 0, TAB_RIGHT, normal_sig (direct_v[i]), NULL);*/
2077 tab_next_row (direct);
2080 tab_offset (direct, 0, -1);
2083 /* Statistical calculations. */
2085 /* Returns the value of the gamma (factorial) function for an integer
2088 gamma_int (double pt)
2093 for (i = 2; i < pt; i++)
2098 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2100 static inline double
2101 Pr (int a, int b, int c, int d)
2103 return (gamma_int (a + b + 1.) / gamma_int (a + 1.)
2104 * gamma_int (c + d + 1.) / gamma_int (b + 1.)
2105 * gamma_int (a + c + 1.) / gamma_int (c + 1.)
2106 * gamma_int (b + d + 1.) / gamma_int (d + 1.)
2107 / gamma_int (a + b + c + d + 1.));
2110 /* Swap the contents of A and B. */
2112 swap (int *a, int *b)
2119 /* Calculate significance for Fisher's exact test as specified in
2120 _SPSS Statistical Algorithms_, Appendix 5. */
2122 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2126 if (MIN (c, d) < MIN (a, b))
2127 swap (&a, &c), swap (&b, &d);
2128 if (MIN (b, d) < MIN (a, c))
2129 swap (&a, &b), swap (&c, &d);
2133 swap (&a, &b), swap (&c, &d);
2135 swap (&a, &c), swap (&b, &d);
2139 for (pt = 0; pt <= a; pt++)
2140 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2142 *fisher2 = *fisher1;
2143 for (pt = 1; pt <= b; pt++)
2144 *fisher2 += Pr (a + pt, b - pt, c - pt, d + pt);
2147 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2148 columns with values COLS and N_ROWS rows with values ROWS. Values
2149 in the matrix sum to pt->total. */
2151 calc_chisq (struct pivot_table *pt,
2152 double chisq[N_CHISQ], int df[N_CHISQ],
2153 double *fisher1, double *fisher2)
2157 chisq[0] = chisq[1] = 0.;
2158 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2159 *fisher1 = *fisher2 = SYSMIS;
2161 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2163 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2165 chisq[0] = chisq[1] = SYSMIS;
2169 for (r = 0; r < pt->n_rows; r++)
2170 for (c = 0; c < pt->n_cols; c++)
2172 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2173 const double freq = pt->mat[pt->n_cols * r + c];
2174 const double residual = freq - expected;
2176 chisq[0] += residual * residual / expected;
2178 chisq[1] += freq * log (expected / freq);
2189 /* Calculate Yates and Fisher exact test. */
2190 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2192 double f11, f12, f21, f22;
2198 for (i = j = 0; i < pt->n_cols; i++)
2199 if (pt->col_tot[i] != 0.)
2208 f11 = pt->mat[nz_cols[0]];
2209 f12 = pt->mat[nz_cols[1]];
2210 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2211 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2216 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2219 chisq[3] = (pt->total * pow2 (pt_)
2220 / (f11 + f12) / (f21 + f22)
2221 / (f11 + f21) / (f12 + f22));
2229 if (f11 < 5. || f12 < 5. || f21 < 5. || f22 < 5.)
2230 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2233 /* Calculate Mantel-Haenszel. */
2234 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2236 double r, ase_0, ase_1;
2237 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2239 chisq[4] = (pt->total - 1.) * r * r;
2244 /* Calculate the value of Pearson's r. r is stored into R, ase_1 into
2245 ASE_1, and ase_0 into ASE_0. The row and column values must be
2246 passed in PT and Y. */
2248 calc_r (struct pivot_table *pt,
2249 double *PT, double *Y, double *r, double *ase_0, double *ase_1)
2251 double SX, SY, S, T;
2253 double sum_XYf, sum_X2Y2f;
2254 double sum_Xr, sum_X2r;
2255 double sum_Yc, sum_Y2c;
2258 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2259 for (j = 0; j < pt->n_cols; j++)
2261 double fij = pt->mat[j + i * pt->n_cols];
2262 double product = PT[i] * Y[j];
2263 double temp = fij * product;
2265 sum_X2Y2f += temp * product;
2268 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2270 sum_Xr += PT[i] * pt->row_tot[i];
2271 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2273 Xbar = sum_Xr / pt->total;
2275 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2277 sum_Yc += Y[i] * pt->col_tot[i];
2278 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2280 Ybar = sum_Yc / pt->total;
2282 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2283 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2284 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2287 *ase_0 = sqrt ((sum_X2Y2f - pow2 (sum_XYf) / pt->total) / (sum_X2r * sum_Y2c));
2292 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2293 for (j = 0; j < pt->n_cols; j++)
2295 double Xresid, Yresid;
2298 Xresid = PT[i] - Xbar;
2299 Yresid = Y[j] - Ybar;
2300 temp = (T * Xresid * Yresid
2302 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2303 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2308 *ase_1 = sqrt (s) / (T * T);
2312 /* Calculate symmetric statistics and their asymptotic standard
2313 errors. Returns 0 if none could be calculated. */
2315 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2316 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2317 double t[N_SYMMETRIC],
2318 double somers_d_v[3], double somers_d_ase[3],
2319 double somers_d_t[3])
2323 q = MIN (pt->ns_rows, pt->ns_cols);
2327 for (i = 0; i < N_SYMMETRIC; i++)
2328 v[i] = ase[i] = t[i] = SYSMIS;
2330 /* Phi, Cramer's V, contingency coefficient. */
2331 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2333 double Xp = 0.; /* Pearson chi-square. */
2336 for (r = 0; r < pt->n_rows; r++)
2337 for (c = 0; c < pt->n_cols; c++)
2339 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2340 const double freq = pt->mat[pt->n_cols * r + c];
2341 const double residual = freq - expected;
2343 Xp += residual * residual / expected;
2346 if (proc->statistics & (1u << CRS_ST_PHI))
2348 v[0] = sqrt (Xp / pt->total);
2349 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2351 if (proc->statistics & (1u << CRS_ST_CC))
2352 v[2] = sqrt (Xp / (Xp + pt->total));
2355 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2356 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2361 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2365 Dr = Dc = pow2 (pt->total);
2366 for (r = 0; r < pt->n_rows; r++)
2367 Dr -= pow2 (pt->row_tot[r]);
2368 for (c = 0; c < pt->n_cols; c++)
2369 Dc -= pow2 (pt->col_tot[c]);
2371 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2372 for (c = 0; c < pt->n_cols; c++)
2376 for (r = 0; r < pt->n_rows; r++)
2377 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2386 for (i = 0; i < pt->n_rows; i++)
2390 for (j = 1; j < pt->n_cols; j++)
2391 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2394 for (j = 1; j < pt->n_cols; j++)
2395 Dij += cum[j + (i - 1) * pt->n_cols];
2399 double fij = pt->mat[j + i * pt->n_cols];
2403 if (++j == pt->n_cols)
2405 assert (j < pt->n_cols);
2407 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2408 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2412 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2413 Dij -= cum[j + (i - 1) * pt->n_cols];
2419 if (proc->statistics & (1u << CRS_ST_BTAU))
2420 v[3] = (P - Q) / sqrt (Dr * Dc);
2421 if (proc->statistics & (1u << CRS_ST_CTAU))
2422 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2423 if (proc->statistics & (1u << CRS_ST_GAMMA))
2424 v[5] = (P - Q) / (P + Q);
2426 /* ASE for tau-b, tau-c, gamma. Calculations could be
2427 eliminated here, at expense of memory. */
2432 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2433 for (i = 0; i < pt->n_rows; i++)
2437 for (j = 1; j < pt->n_cols; j++)
2438 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2441 for (j = 1; j < pt->n_cols; j++)
2442 Dij += cum[j + (i - 1) * pt->n_cols];
2446 double fij = pt->mat[j + i * pt->n_cols];
2448 if (proc->statistics & (1u << CRS_ST_BTAU))
2450 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2451 + v[3] * (pt->row_tot[i] * Dc
2452 + pt->col_tot[j] * Dr));
2453 btau_cum += fij * temp * temp;
2457 const double temp = Cij - Dij;
2458 ctau_cum += fij * temp * temp;
2461 if (proc->statistics & (1u << CRS_ST_GAMMA))
2463 const double temp = Q * Cij - P * Dij;
2464 gamma_cum += fij * temp * temp;
2467 if (proc->statistics & (1u << CRS_ST_D))
2469 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2470 - (P - Q) * (pt->total - pt->row_tot[i]));
2471 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2472 - (Q - P) * (pt->total - pt->col_tot[j]));
2475 if (++j == pt->n_cols)
2477 assert (j < pt->n_cols);
2479 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2480 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2484 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2485 Dij -= cum[j + (i - 1) * pt->n_cols];
2491 btau_var = ((btau_cum
2492 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2494 if (proc->statistics & (1u << CRS_ST_BTAU))
2496 ase[3] = sqrt (btau_var);
2497 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2500 if (proc->statistics & (1u << CRS_ST_CTAU))
2502 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2503 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2504 t[4] = v[4] / ase[4];
2506 if (proc->statistics & (1u << CRS_ST_GAMMA))
2508 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2509 t[5] = v[5] / (2. / (P + Q)
2510 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2512 if (proc->statistics & (1u << CRS_ST_D))
2514 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2515 somers_d_ase[0] = 2. * btau_var / (Dr + Dc) * sqrt (Dr * Dc);
2516 somers_d_t[0] = (somers_d_v[0]
2518 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2519 somers_d_v[1] = (P - Q) / Dc;
2520 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2521 somers_d_t[1] = (somers_d_v[1]
2523 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2524 somers_d_v[2] = (P - Q) / Dr;
2525 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2526 somers_d_t[2] = (somers_d_v[2]
2528 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2534 /* Spearman correlation, Pearson's r. */
2535 if (proc->statistics & (1u << CRS_ST_CORR))
2537 double *R = xmalloc (sizeof *R * pt->n_rows);
2538 double *C = xmalloc (sizeof *C * pt->n_cols);
2541 double y, t, c = 0., s = 0.;
2546 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2547 y = pt->row_tot[i] - c;
2551 if (++i == pt->n_rows)
2553 assert (i < pt->n_rows);
2558 double y, t, c = 0., s = 0.;
2563 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2564 y = pt->col_tot[j] - c;
2568 if (++j == pt->n_cols)
2570 assert (j < pt->n_cols);
2574 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2580 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2584 /* Cohen's kappa. */
2585 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2587 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2590 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2591 i < pt->ns_rows; i++, j++)
2595 while (pt->col_tot[j] == 0.)
2598 prod = pt->row_tot[i] * pt->col_tot[j];
2599 sum = pt->row_tot[i] + pt->col_tot[j];
2601 sum_fii += pt->mat[j + i * pt->n_cols];
2603 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2604 sum_riciri_ci += prod * sum;
2606 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2607 for (j = 0; j < pt->ns_cols; j++)
2609 double sum = pt->row_tot[i] + pt->col_tot[j];
2610 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2613 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2615 ase[8] = sqrt ((pow2 (pt->total) * sum_rici
2616 + sum_rici * sum_rici
2617 - pt->total * sum_riciri_ci)
2618 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2620 t[8] = v[8] / sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2621 / pow2 (pow2 (pt->total) - sum_rici))
2622 + ((2. * (pt->total - sum_fii)
2623 * (2. * sum_fii * sum_rici
2624 - pt->total * sum_fiiri_ci))
2625 / cube (pow2 (pt->total) - sum_rici))
2626 + (pow2 (pt->total - sum_fii)
2627 * (pt->total * sum_fijri_ci2 - 4.
2628 * sum_rici * sum_rici)
2629 / pow4 (pow2 (pt->total) - sum_rici))));
2631 t[8] = v[8] / ase[8];
2638 /* Calculate risk estimate. */
2640 calc_risk (struct pivot_table *pt,
2641 double *value, double *upper, double *lower, union value *c)
2643 double f11, f12, f21, f22;
2649 for (i = 0; i < 3; i++)
2650 value[i] = upper[i] = lower[i] = SYSMIS;
2653 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2660 for (i = j = 0; i < pt->n_cols; i++)
2661 if (pt->col_tot[i] != 0.)
2670 f11 = pt->mat[nz_cols[0]];
2671 f12 = pt->mat[nz_cols[1]];
2672 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2673 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2675 c[0] = pt->cols[nz_cols[0]];
2676 c[1] = pt->cols[nz_cols[1]];
2679 value[0] = (f11 * f22) / (f12 * f21);
2680 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2681 lower[0] = value[0] * exp (-1.960 * v);
2682 upper[0] = value[0] * exp (1.960 * v);
2684 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2685 v = sqrt ((f12 / (f11 * (f11 + f12)))
2686 + (f22 / (f21 * (f21 + f22))));
2687 lower[1] = value[1] * exp (-1.960 * v);
2688 upper[1] = value[1] * exp (1.960 * v);
2690 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2691 v = sqrt ((f11 / (f12 * (f11 + f12)))
2692 + (f21 / (f22 * (f21 + f22))));
2693 lower[2] = value[2] * exp (-1.960 * v);
2694 upper[2] = value[2] * exp (1.960 * v);
2699 /* Calculate directional measures. */
2701 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2702 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2703 double t[N_DIRECTIONAL])
2708 for (i = 0; i < N_DIRECTIONAL; i++)
2709 v[i] = ase[i] = t[i] = SYSMIS;
2713 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2715 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2716 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2717 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2718 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2719 double sum_fim, sum_fmj;
2721 int rm_index, cm_index;
2724 /* Find maximum for each row and their sum. */
2725 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2727 double max = pt->mat[i * pt->n_cols];
2730 for (j = 1; j < pt->n_cols; j++)
2731 if (pt->mat[j + i * pt->n_cols] > max)
2733 max = pt->mat[j + i * pt->n_cols];
2737 sum_fim += fim[i] = max;
2738 fim_index[i] = index;
2741 /* Find maximum for each column. */
2742 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2744 double max = pt->mat[j];
2747 for (i = 1; i < pt->n_rows; i++)
2748 if (pt->mat[j + i * pt->n_cols] > max)
2750 max = pt->mat[j + i * pt->n_cols];
2754 sum_fmj += fmj[j] = max;
2755 fmj_index[j] = index;
2758 /* Find maximum row total. */
2759 rm = pt->row_tot[0];
2761 for (i = 1; i < pt->n_rows; i++)
2762 if (pt->row_tot[i] > rm)
2764 rm = pt->row_tot[i];
2768 /* Find maximum column total. */
2769 cm = pt->col_tot[0];
2771 for (j = 1; j < pt->n_cols; j++)
2772 if (pt->col_tot[j] > cm)
2774 cm = pt->col_tot[j];
2778 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2779 v[1] = (sum_fmj - rm) / (pt->total - rm);
2780 v[2] = (sum_fim - cm) / (pt->total - cm);
2782 /* ASE1 for Y given PT. */
2786 for (accum = 0., i = 0; i < pt->n_rows; i++)
2787 for (j = 0; j < pt->n_cols; j++)
2789 const int deltaj = j == cm_index;
2790 accum += (pt->mat[j + i * pt->n_cols]
2791 * pow2 ((j == fim_index[i])
2796 ase[2] = sqrt (accum - pt->total * v[0]) / (pt->total - cm);
2799 /* ASE0 for Y given PT. */
2803 for (accum = 0., i = 0; i < pt->n_rows; i++)
2804 if (cm_index != fim_index[i])
2805 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2806 + pt->mat[i * pt->n_cols + cm_index]);
2807 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2810 /* ASE1 for PT given Y. */
2814 for (accum = 0., i = 0; i < pt->n_rows; i++)
2815 for (j = 0; j < pt->n_cols; j++)
2817 const int deltaj = i == rm_index;
2818 accum += (pt->mat[j + i * pt->n_cols]
2819 * pow2 ((i == fmj_index[j])
2824 ase[1] = sqrt (accum - pt->total * v[0]) / (pt->total - rm);
2827 /* ASE0 for PT given Y. */
2831 for (accum = 0., j = 0; j < pt->n_cols; j++)
2832 if (rm_index != fmj_index[j])
2833 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2834 + pt->mat[j + pt->n_cols * rm_index]);
2835 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2838 /* Symmetric ASE0 and ASE1. */
2843 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2844 for (j = 0; j < pt->n_cols; j++)
2846 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2847 int temp1 = (i == rm_index) + (j == cm_index);
2848 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2849 accum1 += (pt->mat[j + i * pt->n_cols]
2850 * pow2 (temp0 + (v[0] - 1.) * temp1));
2852 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2853 t[0] = v[0] / (sqrt (accum0 - pow2 ((sum_fim + sum_fmj - cm - rm) / pt->total))
2854 / (2. * pt->total - rm - cm));
2863 double sum_fij2_ri, sum_fij2_ci;
2864 double sum_ri2, sum_cj2;
2866 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2867 for (j = 0; j < pt->n_cols; j++)
2869 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2870 sum_fij2_ri += temp / pt->row_tot[i];
2871 sum_fij2_ci += temp / pt->col_tot[j];
2874 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2875 sum_ri2 += pow2 (pt->row_tot[i]);
2877 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2878 sum_cj2 += pow2 (pt->col_tot[j]);
2880 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2881 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2885 if (proc->statistics & (1u << CRS_ST_UC))
2887 double UX, UY, UXY, P;
2888 double ase1_yx, ase1_xy, ase1_sym;
2891 for (UX = 0., i = 0; i < pt->n_rows; i++)
2892 if (pt->row_tot[i] > 0.)
2893 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2895 for (UY = 0., j = 0; j < pt->n_cols; j++)
2896 if (pt->col_tot[j] > 0.)
2897 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2899 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2900 for (j = 0; j < pt->n_cols; j++)
2902 double entry = pt->mat[j + i * pt->n_cols];
2907 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2908 UXY -= entry / pt->total * log (entry / pt->total);
2911 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2912 for (j = 0; j < pt->n_cols; j++)
2914 double entry = pt->mat[j + i * pt->n_cols];
2919 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2920 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2921 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2922 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2923 ase1_sym += entry * pow2 ((UXY
2924 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2925 - (UX + UY) * log (entry / pt->total));
2928 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2929 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2930 t[5] = v[5] / ((2. / (pt->total * (UX + UY)))
2931 * sqrt (P - pow2 (UX + UY - UXY) / pt->total));
2933 v[6] = (UX + UY - UXY) / UX;
2934 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2935 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2937 v[7] = (UX + UY - UXY) / UY;
2938 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2939 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2943 if (proc->statistics & (1u << CRS_ST_D))
2945 double v_dummy[N_SYMMETRIC];
2946 double ase_dummy[N_SYMMETRIC];
2947 double t_dummy[N_SYMMETRIC];
2948 double somers_d_v[3];
2949 double somers_d_ase[3];
2950 double somers_d_t[3];
2952 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2953 somers_d_v, somers_d_ase, somers_d_t))
2956 for (i = 0; i < 3; i++)
2958 v[8 + i] = somers_d_v[i];
2959 ase[8 + i] = somers_d_ase[i];
2960 t[8 + i] = somers_d_t[i];
2966 if (proc->statistics & (1u << CRS_ST_ETA))
2969 double sum_Xr, sum_X2r;
2973 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2975 sum_Xr += pt->rows[i].f * pt->row_tot[i];
2976 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
2978 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2980 for (SXW = 0., j = 0; j < pt->n_cols; j++)
2984 for (cum = 0., i = 0; i < pt->n_rows; i++)
2986 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
2987 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
2990 SXW -= cum * cum / pt->col_tot[j];
2992 v[11] = sqrt (1. - SXW / SX);
2996 double sum_Yc, sum_Y2c;
3000 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
3002 sum_Yc += pt->cols[i].f * pt->col_tot[i];
3003 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
3005 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
3007 for (SYW = 0., i = 0; i < pt->n_rows; i++)
3011 for (cum = 0., j = 0; j < pt->n_cols; j++)
3013 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
3014 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
3017 SYW -= cum * cum / pt->row_tot[i];
3019 v[12] = sqrt (1. - SYW / SY);