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 /* A crosstabulation of exactly 2 variables, conditional on zero
165 or more other variables having given values. */
172 int n_vars; /* Number of variables (at least 2). */
173 const struct variable **vars;
174 union value *values; /* Values of variables beyond 2. */
177 struct table_entry **entries;
180 /* Column values, number of columns. */
184 /* Row values, number of rows. */
188 /* Number of statistically interesting columns/rows
189 (columns/rows with data in them). */
190 int ns_cols, ns_rows;
192 /* Matrix contents. */
193 double *mat; /* Matrix proper. */
194 double *row_tot; /* Row totals. */
195 double *col_tot; /* Column totals. */
196 double total; /* Grand total. */
199 /* Integer mode variable info. */
202 int min; /* Minimum value. */
203 int max; /* Maximum value + 1. */
204 int count; /* max - min. */
207 static inline struct var_range *
208 get_var_range (const struct variable *v)
210 return var_get_aux (v);
213 struct crosstabs_proc
215 enum { INTEGER, GENERAL } mode;
216 enum mv_class exclude;
219 struct fmt_spec weight_format;
221 /* Variables specifies on VARIABLES. */
222 const struct variable **variables;
226 struct pivot_table *pivots;
230 int n_cells; /* Number of cells requested. */
231 unsigned int cells; /* Bit k is 1 if cell k is requested. */
232 int a_cells[CRS_CL_count]; /* 0...n_cells-1 are the requested cells. */
235 unsigned int statistics; /* Bit k is 1 if statistic k is requested. */
239 init_proc (struct crosstabs_proc *proc, struct dataset *ds)
241 const struct variable *wv = dict_get_weight (dataset_dict (ds));
242 proc->bad_warn = true;
243 proc->variables = NULL;
244 proc->n_variables = 0;
247 proc->weight_format = wv ? *var_get_print_format (wv) : F_8_0;
251 free_proc (struct crosstabs_proc *proc)
253 struct pivot_table *pt;
255 free (proc->variables);
256 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
259 free (pt->const_vars);
260 /* We must not call value_destroy on const_values because
261 it is a wild pointer; it never pointed to anything owned
264 The rest of the data was allocated and destroyed at a
265 lower level already. */
270 static int internal_cmd_crosstabs (struct lexer *lexer, struct dataset *ds,
271 struct crosstabs_proc *);
272 static bool should_tabulate_case (const struct pivot_table *,
273 const struct ccase *, enum mv_class exclude);
274 static void tabulate_general_case (struct pivot_table *, const struct ccase *,
276 static void tabulate_integer_case (struct pivot_table *, const struct ccase *,
278 static void postcalc (struct crosstabs_proc *);
279 static void submit (struct crosstabs_proc *, struct pivot_table *,
282 /* Parse and execute CROSSTABS, then clean up. */
284 cmd_crosstabs (struct lexer *lexer, struct dataset *ds)
286 struct crosstabs_proc proc;
289 init_proc (&proc, ds);
290 result = internal_cmd_crosstabs (lexer, ds, &proc);
296 /* Parses and executes the CROSSTABS procedure. */
298 internal_cmd_crosstabs (struct lexer *lexer, struct dataset *ds,
299 struct crosstabs_proc *proc)
301 struct casegrouper *grouper;
302 struct casereader *input, *group;
303 struct cmd_crosstabs cmd;
304 struct pivot_table *pt;
308 if (!parse_crosstabs (lexer, ds, &cmd, proc))
311 proc->mode = proc->n_variables ? INTEGER : GENERAL;
315 proc->cells = 1u << CRS_CL_COUNT;
316 else if (cmd.a_cells[CRS_CL_ALL])
317 proc->cells = UINT_MAX;
321 for (i = 0; i < CRS_CL_count; i++)
323 proc->cells |= 1u << i;
324 if (proc->cells == 0)
325 proc->cells = ((1u << CRS_CL_COUNT)
327 | (1u << CRS_CL_COLUMN)
328 | (1u << CRS_CL_TOTAL));
330 proc->cells &= ((1u << CRS_CL_count) - 1);
331 proc->cells &= ~((1u << CRS_CL_NONE) | (1u << CRS_CL_ALL));
333 for (i = 0; i < CRS_CL_count; i++)
334 if (proc->cells & (1u << i))
335 proc->a_cells[proc->n_cells++] = i;
338 if (cmd.a_statistics[CRS_ST_ALL])
339 proc->statistics = UINT_MAX;
340 else if (cmd.sbc_statistics)
344 proc->statistics = 0;
345 for (i = 0; i < CRS_ST_count; i++)
346 if (cmd.a_statistics[i])
347 proc->statistics |= 1u << i;
348 if (proc->statistics == 0)
349 proc->statistics |= 1u << CRS_ST_CHISQ;
352 proc->statistics = 0;
355 proc->exclude = (cmd.miss == CRS_TABLE ? MV_ANY
356 : cmd.miss == CRS_INCLUDE ? MV_SYSTEM
358 if (proc->mode == GENERAL && proc->mode == MV_NEVER)
360 msg (SE, _("Missing mode REPORT not allowed in general mode. "
361 "Assuming MISSING=TABLE."));
366 proc->pivot = cmd.pivot == CRS_PIVOT;
368 input = casereader_create_filter_weight (proc_open (ds), dataset_dict (ds),
370 grouper = casegrouper_create_splits (input, dataset_dict (ds));
371 while (casegrouper_get_next_group (grouper, &group))
375 /* Output SPLIT FILE variables. */
376 c = casereader_peek (group, 0);
379 output_split_file_values (ds, c);
384 for (; (c = casereader_read (group)) != NULL; case_unref (c))
385 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
387 double weight = dict_get_case_weight (dataset_dict (ds), c,
389 if (should_tabulate_case (pt, c, proc->exclude))
391 if (proc->mode == GENERAL)
392 tabulate_general_case (pt, c, weight);
394 tabulate_integer_case (pt, c, weight);
397 pt->missing += weight;
399 casereader_destroy (group);
404 ok = casegrouper_destroy (grouper);
405 ok = proc_commit (ds) && ok;
407 return ok ? CMD_SUCCESS : CMD_CASCADING_FAILURE;
410 /* Parses the TABLES subcommand. */
412 crs_custom_tables (struct lexer *lexer, struct dataset *ds,
413 struct cmd_crosstabs *cmd UNUSED, void *proc_)
415 struct crosstabs_proc *proc = proc_;
416 struct const_var_set *var_set;
418 const struct variable ***by = NULL;
420 size_t *by_nvar = NULL;
425 /* Ensure that this is a TABLES subcommand. */
426 if (!lex_match_id (lexer, "TABLES")
427 && (lex_token (lexer) != T_ID ||
428 dict_lookup_var (dataset_dict (ds), lex_tokid (lexer)) == NULL)
429 && lex_token (lexer) != T_ALL)
431 lex_match (lexer, '=');
433 if (proc->variables != NULL)
434 var_set = const_var_set_create_from_array (proc->variables,
437 var_set = const_var_set_create_from_dict (dataset_dict (ds));
438 assert (var_set != NULL);
442 by = xnrealloc (by, n_by + 1, sizeof *by);
443 by_nvar = xnrealloc (by_nvar, n_by + 1, sizeof *by_nvar);
444 if (!parse_const_var_set_vars (lexer, var_set, &by[n_by], &by_nvar[n_by],
445 PV_NO_DUPLICATE | PV_NO_SCRATCH))
447 if (xalloc_oversized (nx, by_nvar[n_by]))
449 msg (SE, _("Too many cross-tabulation variables or dimensions."));
455 if (!lex_match (lexer, T_BY))
459 lex_error (lexer, _("expecting BY"));
467 by_iter = xcalloc (n_by, sizeof *by_iter);
468 proc->pivots = xnrealloc (proc->pivots,
469 proc->n_pivots + nx, sizeof *proc->pivots);
470 for (i = 0; i < nx; i++)
472 struct pivot_table *pt = &proc->pivots[proc->n_pivots++];
475 pt->weight_format = proc->weight_format;
478 pt->vars = xmalloc (n_by * sizeof *pt->vars);
480 pt->const_vars = NULL;
481 pt->const_values = NULL;
482 hmap_init (&pt->data);
486 for (j = 0; j < n_by; j++)
487 pt->vars[j] = by[j][by_iter[j]];
489 for (j = n_by - 1; j >= 0; j--)
491 if (++by_iter[j] < by_nvar[j])
500 /* All return paths lead here. */
501 for (i = 0; i < n_by; i++)
506 const_var_set_destroy (var_set);
511 /* Parses the VARIABLES subcommand. */
513 crs_custom_variables (struct lexer *lexer, struct dataset *ds,
514 struct cmd_crosstabs *cmd UNUSED, void *proc_)
516 struct crosstabs_proc *proc = proc_;
519 msg (SE, _("VARIABLES must be specified before TABLES."));
523 lex_match (lexer, '=');
527 size_t orig_nv = proc->n_variables;
532 if (!parse_variables_const (lexer, dataset_dict (ds),
533 &proc->variables, &proc->n_variables,
534 (PV_APPEND | PV_NUMERIC
535 | PV_NO_DUPLICATE | PV_NO_SCRATCH)))
538 if (lex_token (lexer) != '(')
540 lex_error (lexer, "expecting `('");
545 if (!lex_force_int (lexer))
547 min = lex_integer (lexer);
550 lex_match (lexer, ',');
552 if (!lex_force_int (lexer))
554 max = lex_integer (lexer);
557 msg (SE, _("Maximum value (%ld) less than minimum value (%ld)."),
563 if (lex_token (lexer) != ')')
565 lex_error (lexer, "expecting `)'");
570 for (i = orig_nv; i < proc->n_variables; i++)
572 struct var_range *vr = xmalloc (sizeof *vr);
575 vr->count = max - min + 1;
576 var_attach_aux (proc->variables[i], vr, var_dtor_free);
579 if (lex_token (lexer) == '/')
586 free (proc->variables);
587 proc->variables = NULL;
588 proc->n_variables = 0;
592 /* Data file processing. */
595 should_tabulate_case (const struct pivot_table *pt, const struct ccase *c,
596 enum mv_class exclude)
599 for (j = 0; j < pt->n_vars; j++)
601 const struct variable *var = pt->vars[j];
602 struct var_range *range = get_var_range (var);
604 if (var_is_value_missing (var, case_data (c, var), exclude))
609 double num = case_num (c, var);
610 if (num < range->min || num > range->max)
618 tabulate_integer_case (struct pivot_table *pt, const struct ccase *c,
621 struct table_entry *te;
626 for (j = 0; j < pt->n_vars; j++)
628 /* Throw away fractional parts of values. */
629 hash = hash_int (case_num (c, pt->vars[j]), hash);
632 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
634 for (j = 0; j < pt->n_vars; j++)
635 if ((int) case_num (c, pt->vars[j]) != (int) te->values[j].f)
638 /* Found an existing entry. */
645 /* No existing entry. Create a new one. */
646 te = xmalloc (table_entry_size (pt->n_vars));
648 for (j = 0; j < pt->n_vars; j++)
649 te->values[j].f = (int) case_num (c, pt->vars[j]);
650 hmap_insert (&pt->data, &te->node, hash);
654 tabulate_general_case (struct pivot_table *pt, const struct ccase *c,
657 struct table_entry *te;
662 for (j = 0; j < pt->n_vars; j++)
664 const struct variable *var = pt->vars[j];
665 hash = value_hash (case_data (c, var), var_get_width (var), hash);
668 HMAP_FOR_EACH_WITH_HASH (te, struct table_entry, node, hash, &pt->data)
670 for (j = 0; j < pt->n_vars; j++)
672 const struct variable *var = pt->vars[j];
673 if (!value_equal (case_data (c, var), &te->values[j],
674 var_get_width (var)))
678 /* Found an existing entry. */
685 /* No existing entry. Create a new one. */
686 te = xmalloc (table_entry_size (pt->n_vars));
688 for (j = 0; j < pt->n_vars; j++)
690 const struct variable *var = pt->vars[j];
691 int width = var_get_width (var);
692 value_init (&te->values[j], width);
693 value_copy (&te->values[j], case_data (c, var), width);
695 hmap_insert (&pt->data, &te->node, hash);
698 /* Post-data reading calculations. */
700 static int compare_table_entry_vars_3way (const struct table_entry *a,
701 const struct table_entry *b,
702 const struct pivot_table *pt,
704 static int compare_table_entry_3way (const void *ap_, const void *bp_,
706 static void enum_var_values (const struct pivot_table *, int var_idx,
707 union value **valuesp, int *n_values);
708 static void output_pivot_table (struct crosstabs_proc *,
709 struct pivot_table *);
710 static void make_pivot_table_subset (struct pivot_table *pt,
711 size_t row0, size_t row1,
712 struct pivot_table *subset);
713 static void make_summary_table (struct crosstabs_proc *);
714 static bool find_crosstab (struct pivot_table *, size_t *row0p, size_t *row1p);
717 postcalc (struct crosstabs_proc *proc)
719 struct pivot_table *pt;
721 /* Convert hash tables into sorted arrays of entries. */
722 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
724 struct table_entry *e;
727 pt->n_entries = hmap_count (&pt->data);
728 pt->entries = xnmalloc (pt->n_entries, sizeof *pt->entries);
730 HMAP_FOR_EACH (e, struct table_entry, node, &pt->data)
731 pt->entries[i++] = e;
732 hmap_destroy (&pt->data);
734 sort (pt->entries, pt->n_entries, sizeof *pt->entries,
735 compare_table_entry_3way, pt);
738 make_summary_table (proc);
740 /* Output each pivot table. */
741 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
743 if (proc->pivot || pt->n_vars == 2)
744 output_pivot_table (proc, pt);
747 size_t row0 = 0, row1 = 0;
748 while (find_crosstab (pt, &row0, &row1))
750 struct pivot_table subset;
751 make_pivot_table_subset (pt, row0, row1, &subset);
752 output_pivot_table (proc, &subset);
757 /* Free output and prepare for next split file. */
758 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
764 /* Free only the members that were allocated in this
765 function. The other pointer members are either both
766 allocated and destroyed at a lower level (in
767 output_pivot_table), or both allocated and destroyed at
768 a higher level (in crs_custom_tables and free_proc,
770 for (i = 0; i < pt->n_entries; i++)
771 free (pt->entries[i]);
777 make_pivot_table_subset (struct pivot_table *pt, size_t row0, size_t row1,
778 struct pivot_table *subset)
783 assert (pt->n_consts == 0);
784 subset->missing = pt->missing;
786 subset->vars = pt->vars;
787 subset->n_consts = pt->n_vars - 2;
788 subset->const_vars = pt->vars + 2;
789 subset->const_values = &pt->entries[row0]->values[2];
791 subset->entries = &pt->entries[row0];
792 subset->n_entries = row1 - row0;
796 compare_table_entry_var_3way (const struct table_entry *a,
797 const struct table_entry *b,
798 const struct pivot_table *pt,
801 return value_compare_3way (&a->values[idx], &b->values[idx],
802 var_get_width (pt->vars[idx]));
806 compare_table_entry_vars_3way (const struct table_entry *a,
807 const struct table_entry *b,
808 const struct pivot_table *pt,
813 for (i = idx1 - 1; i >= idx0; i--)
815 int cmp = compare_table_entry_var_3way (a, b, pt, i);
822 /* Compare the struct table_entry at *AP to the one at *BP and
823 return a strcmp()-type result. */
825 compare_table_entry_3way (const void *ap_, const void *bp_, const void *pt_)
827 const struct table_entry *const *ap = ap_;
828 const struct table_entry *const *bp = bp_;
829 const struct table_entry *a = *ap;
830 const struct table_entry *b = *bp;
831 const struct pivot_table *pt = pt_;
834 cmp = compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars);
838 cmp = compare_table_entry_var_3way (a, b, pt, ROW_VAR);
842 return compare_table_entry_var_3way (a, b, pt, COL_VAR);
846 find_first_difference (const struct pivot_table *pt, size_t row)
849 return pt->n_vars - 1;
852 const struct table_entry *a = pt->entries[row];
853 const struct table_entry *b = pt->entries[row - 1];
856 for (col = pt->n_vars - 1; col >= 0; col--)
857 if (compare_table_entry_var_3way (a, b, pt, col))
863 /* Output a table summarizing the cases processed. */
865 make_summary_table (struct crosstabs_proc *proc)
867 struct tab_table *summary;
868 struct pivot_table *pt;
872 summary = tab_create (7, 3 + proc->n_pivots, 1);
873 tab_title (summary, _("Summary."));
874 tab_headers (summary, 1, 0, 3, 0);
875 tab_joint_text (summary, 1, 0, 6, 0, TAB_CENTER, _("Cases"));
876 tab_joint_text (summary, 1, 1, 2, 1, TAB_CENTER, _("Valid"));
877 tab_joint_text (summary, 3, 1, 4, 1, TAB_CENTER, _("Missing"));
878 tab_joint_text (summary, 5, 1, 6, 1, TAB_CENTER, _("Total"));
879 tab_hline (summary, TAL_1, 1, 6, 1);
880 tab_hline (summary, TAL_1, 1, 6, 2);
881 tab_vline (summary, TAL_1, 3, 1, 1);
882 tab_vline (summary, TAL_1, 5, 1, 1);
883 for (i = 0; i < 3; i++)
885 tab_text (summary, 1 + i * 2, 2, TAB_RIGHT, _("N"));
886 tab_text (summary, 2 + i * 2, 2, TAB_RIGHT, _("Percent"));
888 tab_offset (summary, 0, 3);
890 ds_init_empty (&name);
891 for (pt = &proc->pivots[0]; pt < &proc->pivots[proc->n_pivots]; pt++)
897 tab_hline (summary, TAL_1, 0, 6, 0);
900 for (i = 0; i < pt->n_vars; i++)
903 ds_put_cstr (&name, " * ");
904 ds_put_cstr (&name, var_to_string (pt->vars[i]));
906 tab_text (summary, 0, 0, TAB_LEFT, ds_cstr (&name));
909 for (i = 0; i < pt->n_entries; i++)
910 valid += pt->entries[i]->freq;
915 for (i = 0; i < 3; i++)
917 tab_double (summary, i * 2 + 1, 0, TAB_RIGHT, n[i],
918 &proc->weight_format);
919 tab_text (summary, i * 2 + 2, 0, TAB_RIGHT | TAT_PRINTF, "%.1f%%",
923 tab_next_row (summary);
927 submit (proc, NULL, summary);
932 static struct tab_table *create_crosstab_table (struct crosstabs_proc *,
933 struct pivot_table *);
934 static struct tab_table *create_chisq_table (struct pivot_table *);
935 static struct tab_table *create_sym_table (struct pivot_table *);
936 static struct tab_table *create_risk_table (struct pivot_table *);
937 static struct tab_table *create_direct_table (struct pivot_table *);
938 static void display_dimensions (struct crosstabs_proc *, struct pivot_table *,
939 struct tab_table *, int first_difference);
940 static void display_crosstabulation (struct crosstabs_proc *,
941 struct pivot_table *,
943 static void display_chisq (struct pivot_table *, struct tab_table *,
944 bool *showed_fisher);
945 static void display_symmetric (struct crosstabs_proc *, struct pivot_table *,
947 static void display_risk (struct pivot_table *, struct tab_table *);
948 static void display_directional (struct crosstabs_proc *, struct pivot_table *,
950 static void crosstabs_dim (struct tab_table *, struct outp_driver *,
952 static void table_value_missing (struct crosstabs_proc *proc,
953 struct tab_table *table, int c, int r,
954 unsigned char opt, const union value *v,
955 const struct variable *var);
956 static void delete_missing (struct pivot_table *);
957 static void build_matrix (struct pivot_table *);
959 /* Output pivot table beginning at PB and continuing until PE,
960 exclusive. For efficiency, *MATP is a pointer to a matrix that can
961 hold *MAXROWS entries. */
963 output_pivot_table (struct crosstabs_proc *proc, struct pivot_table *pt)
965 struct tab_table *table = NULL; /* Crosstabulation table. */
966 struct tab_table *chisq = NULL; /* Chi-square table. */
967 bool showed_fisher = false;
968 struct tab_table *sym = NULL; /* Symmetric measures table. */
969 struct tab_table *risk = NULL; /* Risk estimate table. */
970 struct tab_table *direct = NULL; /* Directional measures table. */
973 enum_var_values (pt, COL_VAR, &pt->cols, &pt->n_cols);
976 table = create_crosstab_table (proc, pt);
977 if (proc->statistics & (1u << CRS_ST_CHISQ))
978 chisq = create_chisq_table (pt);
979 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)
980 | (1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
981 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_CORR)
982 | (1u << CRS_ST_KAPPA)))
983 sym = create_sym_table (pt);
984 if (proc->statistics & (1u << CRS_ST_RISK))
985 risk = create_risk_table (pt);
986 if (proc->statistics & ((1u << CRS_ST_LAMBDA) | (1u << CRS_ST_UC)
987 | (1u << CRS_ST_D) | (1u << CRS_ST_ETA)))
988 direct = create_direct_table (pt);
991 while (find_crosstab (pt, &row0, &row1))
993 struct pivot_table x;
994 int first_difference;
996 make_pivot_table_subset (pt, row0, row1, &x);
998 /* Find all the row variable values. */
999 enum_var_values (&x, ROW_VAR, &x.rows, &x.n_rows);
1001 if (size_overflow_p (xtimes (xtimes (x.n_rows, x.n_cols),
1004 x.row_tot = xmalloc (x.n_rows * sizeof *x.row_tot);
1005 x.col_tot = xmalloc (x.n_cols * sizeof *x.col_tot);
1006 x.mat = xmalloc (x.n_rows * x.n_cols * sizeof *x.mat);
1008 /* Allocate table space for the matrix. */
1010 && tab_row (table) + (x.n_rows + 1) * proc->n_cells > tab_nr (table))
1011 tab_realloc (table, -1,
1012 MAX (tab_nr (table) + (x.n_rows + 1) * proc->n_cells,
1013 tab_nr (table) * pt->n_entries / x.n_entries));
1017 /* Find the first variable that differs from the last subtable. */
1018 first_difference = find_first_difference (pt, row0);
1021 display_dimensions (proc, &x, table, first_difference);
1022 display_crosstabulation (proc, &x, table);
1025 if (proc->exclude == MV_NEVER)
1026 delete_missing (&x);
1030 display_dimensions (proc, &x, chisq, first_difference);
1031 display_chisq (pt, chisq, &showed_fisher);
1035 display_dimensions (proc, &x, sym, first_difference);
1036 display_symmetric (proc, pt, sym);
1040 display_dimensions (proc, &x, risk, first_difference);
1041 display_risk (pt, risk);
1045 display_dimensions (proc, &x, direct, first_difference);
1046 display_directional (proc, pt, direct);
1049 /* Free the parts of x that are not owned by pt. In
1050 particular we must not free x.cols, which is the same as
1051 pt->cols, which is freed at the end of this function. */
1059 submit (proc, NULL, table);
1064 tab_resize (chisq, 4 + (pt->n_vars - 2), -1);
1065 submit (proc, pt, chisq);
1068 submit (proc, pt, sym);
1069 submit (proc, pt, risk);
1070 submit (proc, pt, direct);
1076 build_matrix (struct pivot_table *x)
1078 const int col_var_width = var_get_width (x->vars[COL_VAR]);
1079 const int row_var_width = var_get_width (x->vars[ROW_VAR]);
1082 struct table_entry **p;
1086 for (p = x->entries; p < &x->entries[x->n_entries]; p++)
1088 const struct table_entry *te = *p;
1090 while (!value_equal (&x->rows[row], &te->values[ROW_VAR], row_var_width))
1092 for (; col < x->n_cols; col++)
1098 while (!value_equal (&x->cols[col], &te->values[COL_VAR], col_var_width))
1105 if (++col >= x->n_cols)
1111 while (mp < &x->mat[x->n_cols * x->n_rows])
1113 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1115 /* Column totals, row totals, ns_rows. */
1117 for (col = 0; col < x->n_cols; col++)
1118 x->col_tot[col] = 0.0;
1119 for (row = 0; row < x->n_rows; row++)
1120 x->row_tot[row] = 0.0;
1122 for (row = 0; row < x->n_rows; row++)
1124 bool row_is_empty = true;
1125 for (col = 0; col < x->n_cols; col++)
1129 row_is_empty = false;
1130 x->col_tot[col] += *mp;
1131 x->row_tot[row] += *mp;
1138 assert (mp == &x->mat[x->n_cols * x->n_rows]);
1142 for (col = 0; col < x->n_cols; col++)
1143 for (row = 0; row < x->n_rows; row++)
1144 if (x->mat[col + row * x->n_cols] != 0.0)
1152 for (col = 0; col < x->n_cols; col++)
1153 x->total += x->col_tot[col];
1156 static struct tab_table *
1157 create_crosstab_table (struct crosstabs_proc *proc, struct pivot_table *pt)
1164 static const struct tuple names[] =
1166 {CRS_CL_COUNT, N_("count")},
1167 {CRS_CL_ROW, N_("row %")},
1168 {CRS_CL_COLUMN, N_("column %")},
1169 {CRS_CL_TOTAL, N_("total %")},
1170 {CRS_CL_EXPECTED, N_("expected")},
1171 {CRS_CL_RESIDUAL, N_("residual")},
1172 {CRS_CL_SRESIDUAL, N_("std. resid.")},
1173 {CRS_CL_ASRESIDUAL, N_("adj. resid.")},
1175 const int n_names = sizeof names / sizeof *names;
1176 const struct tuple *t;
1178 struct tab_table *table;
1179 struct string title;
1182 table = tab_create (pt->n_consts + 1 + pt->n_cols + 1,
1183 (pt->n_entries / pt->n_cols) * 3 / 2 * proc->n_cells + 10,
1185 tab_headers (table, pt->n_consts + 1, 0, 2, 0);
1187 /* First header line. */
1188 tab_joint_text (table, pt->n_consts + 1, 0,
1189 (pt->n_consts + 1) + (pt->n_cols - 1), 0,
1190 TAB_CENTER | TAT_TITLE, var_get_name (pt->vars[COL_VAR]));
1192 tab_hline (table, TAL_1, pt->n_consts + 1,
1193 pt->n_consts + 2 + pt->n_cols - 2, 1);
1195 /* Second header line. */
1196 for (i = 2; i < pt->n_consts + 2; i++)
1197 tab_joint_text (table, pt->n_consts + 2 - i - 1, 0,
1198 pt->n_consts + 2 - i - 1, 1,
1199 TAB_RIGHT | TAT_TITLE, var_to_string (pt->vars[i]));
1200 tab_text (table, pt->n_consts + 2 - 2, 1, TAB_RIGHT | TAT_TITLE,
1201 var_get_name (pt->vars[ROW_VAR]));
1202 for (i = 0; i < pt->n_cols; i++)
1203 table_value_missing (proc, table, pt->n_consts + 2 + i - 1, 1, TAB_RIGHT,
1204 &pt->cols[i], pt->vars[COL_VAR]);
1205 tab_text (table, pt->n_consts + 2 + pt->n_cols - 1, 1, TAB_CENTER, _("Total"));
1207 tab_hline (table, TAL_1, 0, pt->n_consts + 2 + pt->n_cols - 1, 2);
1208 tab_vline (table, TAL_1, pt->n_consts + 2 + pt->n_cols - 1, 0, 1);
1211 ds_init_empty (&title);
1212 for (i = 0; i < pt->n_consts + 2; i++)
1215 ds_put_cstr (&title, " * ");
1216 ds_put_cstr (&title, var_get_name (pt->vars[i]));
1218 for (i = 0; i < pt->n_consts; i++)
1220 const struct variable *var = pt->const_vars[i];
1223 ds_put_format (&title, ", %s=", var_get_name (var));
1225 /* Insert the formatted value of the variable, then trim
1226 leading spaces in what was just inserted. */
1227 ofs = ds_length (&title);
1228 data_out (&pt->const_values[i], var_get_print_format (var),
1229 ds_put_uninit (&title, var_get_width (var)));
1230 ds_remove (&title, ofs, ss_cspan (ds_substr (&title, ofs, SIZE_MAX),
1234 ds_put_cstr (&title, " [");
1236 for (t = names; t < &names[n_names]; t++)
1237 if (proc->cells & (1u << t->value))
1240 ds_put_cstr (&title, ", ");
1241 ds_put_cstr (&title, gettext (t->name));
1243 ds_put_cstr (&title, "].");
1245 tab_title (table, "%s", ds_cstr (&title));
1246 ds_destroy (&title);
1248 tab_offset (table, 0, 2);
1252 static struct tab_table *
1253 create_chisq_table (struct pivot_table *pt)
1255 struct tab_table *chisq;
1257 chisq = tab_create (6 + (pt->n_vars - 2),
1258 pt->n_entries / pt->n_cols * 3 / 2 * N_CHISQ + 10,
1260 tab_headers (chisq, 1 + (pt->n_vars - 2), 0, 1, 0);
1262 tab_title (chisq, _("Chi-square tests."));
1264 tab_offset (chisq, pt->n_vars - 2, 0);
1265 tab_text (chisq, 0, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1266 tab_text (chisq, 1, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1267 tab_text (chisq, 2, 0, TAB_RIGHT | TAT_TITLE, _("df"));
1268 tab_text (chisq, 3, 0, TAB_RIGHT | TAT_TITLE,
1269 _("Asymp. Sig. (2-sided)"));
1270 tab_text (chisq, 4, 0, TAB_RIGHT | TAT_TITLE,
1271 _("Exact. Sig. (2-sided)"));
1272 tab_text (chisq, 5, 0, TAB_RIGHT | TAT_TITLE,
1273 _("Exact. Sig. (1-sided)"));
1275 tab_offset (chisq, 0, 1);
1280 /* Symmetric measures. */
1281 static struct tab_table *
1282 create_sym_table (struct pivot_table *pt)
1284 struct tab_table *sym;
1286 sym = tab_create (6 + (pt->n_vars - 2),
1287 pt->n_entries / pt->n_cols * 7 + 10, 1);
1288 tab_headers (sym, 2 + (pt->n_vars - 2), 0, 1, 0);
1289 tab_title (sym, _("Symmetric measures."));
1291 tab_offset (sym, pt->n_vars - 2, 0);
1292 tab_text (sym, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1293 tab_text (sym, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1294 tab_text (sym, 2, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1295 tab_text (sym, 3, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1296 tab_text (sym, 4, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1297 tab_text (sym, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1298 tab_offset (sym, 0, 1);
1303 /* Risk estimate. */
1304 static struct tab_table *
1305 create_risk_table (struct pivot_table *pt)
1307 struct tab_table *risk;
1309 risk = tab_create (4 + (pt->n_vars - 2), pt->n_entries / pt->n_cols * 4 + 10,
1311 tab_headers (risk, 1 + pt->n_vars - 2, 0, 2, 0);
1312 tab_title (risk, _("Risk estimate."));
1314 tab_offset (risk, pt->n_vars - 2, 0);
1315 tab_joint_text (risk, 2, 0, 3, 0, TAB_CENTER | TAT_TITLE | TAT_PRINTF,
1316 _("95%% Confidence Interval"));
1317 tab_text (risk, 0, 1, TAB_LEFT | TAT_TITLE, _("Statistic"));
1318 tab_text (risk, 1, 1, TAB_RIGHT | TAT_TITLE, _("Value"));
1319 tab_text (risk, 2, 1, TAB_RIGHT | TAT_TITLE, _("Lower"));
1320 tab_text (risk, 3, 1, TAB_RIGHT | TAT_TITLE, _("Upper"));
1321 tab_hline (risk, TAL_1, 2, 3, 1);
1322 tab_vline (risk, TAL_1, 2, 0, 1);
1323 tab_offset (risk, 0, 2);
1328 /* Directional measures. */
1329 static struct tab_table *
1330 create_direct_table (struct pivot_table *pt)
1332 struct tab_table *direct;
1334 direct = tab_create (7 + (pt->n_vars - 2),
1335 pt->n_entries / pt->n_cols * 7 + 10, 1);
1336 tab_headers (direct, 3 + (pt->n_vars - 2), 0, 1, 0);
1337 tab_title (direct, _("Directional measures."));
1339 tab_offset (direct, pt->n_vars - 2, 0);
1340 tab_text (direct, 0, 0, TAB_LEFT | TAT_TITLE, _("Category"));
1341 tab_text (direct, 1, 0, TAB_LEFT | TAT_TITLE, _("Statistic"));
1342 tab_text (direct, 2, 0, TAB_LEFT | TAT_TITLE, _("Type"));
1343 tab_text (direct, 3, 0, TAB_RIGHT | TAT_TITLE, _("Value"));
1344 tab_text (direct, 4, 0, TAB_RIGHT | TAT_TITLE, _("Asymp. Std. Error"));
1345 tab_text (direct, 5, 0, TAB_RIGHT | TAT_TITLE, _("Approx. T"));
1346 tab_text (direct, 6, 0, TAB_RIGHT | TAT_TITLE, _("Approx. Sig."));
1347 tab_offset (direct, 0, 1);
1353 /* Delete missing rows and columns for statistical analysis when
1356 delete_missing (struct pivot_table *pt)
1360 for (r = 0; r < pt->n_rows; r++)
1361 if (var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1363 for (c = 0; c < pt->n_cols; c++)
1364 pt->mat[c + r * pt->n_cols] = 0.;
1369 for (c = 0; c < pt->n_cols; c++)
1370 if (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1372 for (r = 0; r < pt->n_rows; r++)
1373 pt->mat[c + r * pt->n_cols] = 0.;
1378 /* Prepare table T for submission, and submit it. */
1380 submit (struct crosstabs_proc *proc, struct pivot_table *pt,
1381 struct tab_table *t)
1388 tab_resize (t, -1, 0);
1389 if (tab_nr (t) == tab_t (t))
1394 tab_offset (t, 0, 0);
1396 for (i = 2; i < pt->n_vars; i++)
1397 tab_text (t, pt->n_vars - i - 1, 0, TAB_RIGHT | TAT_TITLE,
1398 var_to_string (pt->vars[i]));
1399 tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, tab_nc (t) - 1, tab_nr (t) - 1);
1400 tab_box (t, -1, -1, -1, TAL_1, tab_l (t), tab_t (t) - 1, tab_nc (t) - 1,
1402 tab_box (t, -1, -1, -1, TAL_GAP, 0, tab_t (t), tab_l (t) - 1,
1404 tab_vline (t, TAL_2, tab_l (t), 0, tab_nr (t) - 1);
1405 tab_dim (t, crosstabs_dim, proc);
1409 /* Sets the widths of all the columns and heights of all the rows in
1410 table T for driver D. */
1412 crosstabs_dim (struct tab_table *t, struct outp_driver *d, void *proc_)
1414 struct crosstabs_proc *proc = proc_;
1417 /* Width of a numerical column. */
1418 int c = outp_string_width (d, "0.000000", OUTP_PROPORTIONAL);
1419 if (proc->exclude == MV_NEVER)
1420 c += outp_string_width (d, "M", OUTP_PROPORTIONAL);
1422 /* Set width for header columns. */
1428 w = d->width - c * (t->nc - t->l);
1429 for (i = 0; i <= t->nc; i++)
1433 if (w < d->prop_em_width * 8)
1434 w = d->prop_em_width * 8;
1436 if (w > d->prop_em_width * 15)
1437 w = d->prop_em_width * 15;
1439 for (i = 0; i < t->l; i++)
1443 for (i = t->l; i < t->nc; i++)
1446 for (i = 0; i < t->nr; i++)
1447 t->h[i] = tab_natural_height (t, d, i);
1451 find_crosstab (struct pivot_table *pt, size_t *row0p, size_t *row1p)
1453 size_t row0 = *row1p;
1456 if (row0 >= pt->n_entries)
1459 for (row1 = row0 + 1; row1 < pt->n_entries; row1++)
1461 struct table_entry *a = pt->entries[row0];
1462 struct table_entry *b = pt->entries[row1];
1463 if (compare_table_entry_vars_3way (a, b, pt, 2, pt->n_vars) != 0)
1471 /* Compares `union value's A_ and B_ and returns a strcmp()-like
1472 result. WIDTH_ points to an int which is either 0 for a
1473 numeric value or a string width for a string value. */
1475 compare_value_3way (const void *a_, const void *b_, const void *width_)
1477 const union value *a = a_;
1478 const union value *b = b_;
1479 const int *width = width_;
1481 return value_compare_3way (a, b, *width);
1484 /* Given an array of ENTRY_CNT table_entry structures starting at
1485 ENTRIES, creates a sorted list of the values that the variable
1486 with index VAR_IDX takes on. The values are returned as a
1487 malloc()'d array stored in *VALUES, with the number of values
1488 stored in *VALUE_CNT.
1491 enum_var_values (const struct pivot_table *pt, int var_idx,
1492 union value **valuesp, int *n_values)
1494 const struct variable *var = pt->vars[var_idx];
1495 struct var_range *range = get_var_range (var);
1496 union value *values;
1501 values = *valuesp = xnmalloc (range->count, sizeof *values);
1502 *n_values = range->count;
1503 for (i = 0; i < range->count; i++)
1504 values[i].f = range->min + i;
1508 int width = var_get_width (var);
1509 struct hmapx_node *node;
1510 const union value *iter;
1514 for (i = 0; i < pt->n_entries; i++)
1516 const struct table_entry *te = pt->entries[i];
1517 const union value *value = &te->values[var_idx];
1518 size_t hash = value_hash (value, width, 0);
1520 HMAPX_FOR_EACH_WITH_HASH (iter, node, hash, &set)
1521 if (value_equal (iter, value, width))
1524 hmapx_insert (&set, (union value *) value, hash);
1529 *n_values = hmapx_count (&set);
1530 values = *valuesp = xnmalloc (*n_values, sizeof *values);
1532 HMAPX_FOR_EACH (iter, node, &set)
1533 values[i++] = *iter;
1534 hmapx_destroy (&set);
1536 sort (values, *n_values, sizeof *values, compare_value_3way, &width);
1540 /* Sets cell (C,R) in TABLE, with options OPT, to have a value taken
1541 from V, displayed with print format spec from variable VAR. When
1542 in REPORT missing-value mode, missing values have an M appended. */
1544 table_value_missing (struct crosstabs_proc *proc,
1545 struct tab_table *table, int c, int r, unsigned char opt,
1546 const union value *v, const struct variable *var)
1549 const struct fmt_spec *print = var_get_print_format (var);
1551 const char *label = var_lookup_value_label (var, v);
1554 tab_text (table, c, r, TAB_LEFT, label);
1558 s.string = tab_alloc (table, print->w);
1559 data_out (v, print, s.string);
1560 s.length = print->w;
1561 if (proc->exclude == MV_NEVER && var_is_num_missing (var, v->f, MV_USER))
1562 s.string[s.length++] = 'M';
1563 while (s.length && *s.string == ' ')
1568 tab_raw (table, c, r, opt, &s);
1571 /* Draws a line across TABLE at the current row to indicate the most
1572 major dimension variable with index FIRST_DIFFERENCE out of N_VARS
1573 that changed, and puts the values that changed into the table. TB
1574 and PT must be the corresponding table_entry and crosstab,
1577 display_dimensions (struct crosstabs_proc *proc, struct pivot_table *pt,
1578 struct tab_table *table, int first_difference)
1580 tab_hline (table, TAL_1, pt->n_vars - first_difference - 1, tab_nc (table) - 1, 0);
1582 for (; first_difference >= 2; first_difference--)
1583 table_value_missing (proc, table, pt->n_vars - first_difference - 1, 0,
1584 TAB_RIGHT, &pt->entries[0]->values[first_difference],
1585 pt->vars[first_difference]);
1588 /* Put VALUE into cell (C,R) of TABLE, suffixed with character
1589 SUFFIX if nonzero. If MARK_MISSING is true the entry is
1590 additionally suffixed with a letter `M'. */
1592 format_cell_entry (struct tab_table *table, int c, int r, double value,
1593 char suffix, bool mark_missing)
1595 const struct fmt_spec f = {FMT_F, 10, 1};
1600 s.string = tab_alloc (table, 16);
1602 data_out (&v, &f, s.string);
1603 while (*s.string == ' ')
1609 s.string[s.length++] = suffix;
1611 s.string[s.length++] = 'M';
1613 tab_raw (table, c, r, TAB_RIGHT, &s);
1616 /* Displays the crosstabulation table. */
1618 display_crosstabulation (struct crosstabs_proc *proc, struct pivot_table *pt,
1619 struct tab_table *table)
1625 for (r = 0; r < pt->n_rows; r++)
1626 table_value_missing (proc, table, pt->n_vars - 2, r * proc->n_cells,
1627 TAB_RIGHT, &pt->rows[r], pt->vars[ROW_VAR]);
1629 tab_text (table, pt->n_vars - 2, pt->n_rows * proc->n_cells,
1630 TAB_LEFT, _("Total"));
1632 /* Put in the actual cells. */
1634 tab_offset (table, pt->n_vars - 1, -1);
1635 for (r = 0; r < pt->n_rows; r++)
1637 if (proc->n_cells > 1)
1638 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1639 for (c = 0; c < pt->n_cols; c++)
1641 bool mark_missing = false;
1642 double expected_value = pt->row_tot[r] * pt->col_tot[c] / pt->total;
1643 if (proc->exclude == MV_NEVER
1644 && (var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER)
1645 || var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f,
1647 mark_missing = true;
1648 for (i = 0; i < proc->n_cells; i++)
1653 switch (proc->a_cells[i])
1659 v = *mp / pt->row_tot[r] * 100.;
1663 v = *mp / pt->col_tot[c] * 100.;
1667 v = *mp / pt->total * 100.;
1670 case CRS_CL_EXPECTED:
1673 case CRS_CL_RESIDUAL:
1674 v = *mp - expected_value;
1676 case CRS_CL_SRESIDUAL:
1677 v = (*mp - expected_value) / sqrt (expected_value);
1679 case CRS_CL_ASRESIDUAL:
1680 v = ((*mp - expected_value)
1681 / sqrt (expected_value
1682 * (1. - pt->row_tot[r] / pt->total)
1683 * (1. - pt->col_tot[c] / pt->total)));
1688 format_cell_entry (table, c, i, v, suffix, mark_missing);
1694 tab_offset (table, -1, tab_row (table) + proc->n_cells);
1698 tab_offset (table, -1, tab_row (table) - proc->n_cells * pt->n_rows);
1699 for (r = 0; r < pt->n_rows; r++)
1701 bool mark_missing = false;
1703 if (proc->exclude == MV_NEVER
1704 && var_is_num_missing (pt->vars[ROW_VAR], pt->rows[r].f, MV_USER))
1705 mark_missing = true;
1707 for (i = 0; i < proc->n_cells; i++)
1712 switch (proc->a_cells[i])
1722 v = pt->row_tot[r] / pt->total * 100.;
1726 v = pt->row_tot[r] / pt->total * 100.;
1729 case CRS_CL_EXPECTED:
1730 case CRS_CL_RESIDUAL:
1731 case CRS_CL_SRESIDUAL:
1732 case CRS_CL_ASRESIDUAL:
1739 format_cell_entry (table, pt->n_cols, 0, v, suffix, mark_missing);
1740 tab_next_row (table);
1744 /* Column totals, grand total. */
1746 if (proc->n_cells > 1)
1747 tab_hline (table, TAL_1, -1, pt->n_cols, 0);
1748 for (c = 0; c <= pt->n_cols; c++)
1750 double ct = c < pt->n_cols ? pt->col_tot[c] : pt->total;
1751 bool mark_missing = false;
1754 if (proc->exclude == MV_NEVER && c < pt->n_cols
1755 && var_is_num_missing (pt->vars[COL_VAR], pt->cols[c].f, MV_USER))
1756 mark_missing = true;
1758 for (i = 0; i < proc->n_cells; i++)
1763 switch (proc->a_cells[i])
1769 v = ct / pt->total * 100.;
1777 v = ct / pt->total * 100.;
1780 case CRS_CL_EXPECTED:
1781 case CRS_CL_RESIDUAL:
1782 case CRS_CL_SRESIDUAL:
1783 case CRS_CL_ASRESIDUAL:
1789 format_cell_entry (table, c, i, v, suffix, mark_missing);
1794 tab_offset (table, -1, tab_row (table) + last_row);
1795 tab_offset (table, 0, -1);
1798 static void calc_r (struct pivot_table *,
1799 double *PT, double *Y, double *, double *, double *);
1800 static void calc_chisq (struct pivot_table *,
1801 double[N_CHISQ], int[N_CHISQ], double *, double *);
1803 /* Display chi-square statistics. */
1805 display_chisq (struct pivot_table *pt, struct tab_table *chisq,
1806 bool *showed_fisher)
1808 static const char *chisq_stats[N_CHISQ] =
1810 N_("Pearson Chi-Square"),
1811 N_("Likelihood Ratio"),
1812 N_("Fisher's Exact Test"),
1813 N_("Continuity Correction"),
1814 N_("Linear-by-Linear Association"),
1816 double chisq_v[N_CHISQ];
1817 double fisher1, fisher2;
1823 calc_chisq (pt, chisq_v, df, &fisher1, &fisher2);
1825 tab_offset (chisq, pt->n_vars - 2, -1);
1827 for (i = 0; i < N_CHISQ; i++)
1829 if ((i != 2 && chisq_v[i] == SYSMIS)
1830 || (i == 2 && fisher1 == SYSMIS))
1834 tab_text (chisq, 0, 0, TAB_LEFT, gettext (chisq_stats[i]));
1837 tab_double (chisq, 1, 0, TAB_RIGHT, chisq_v[i], NULL);
1838 tab_double (chisq, 2, 0, TAB_RIGHT, df[i], &pt->weight_format);
1839 tab_double (chisq, 3, 0, TAB_RIGHT,
1840 gsl_cdf_chisq_Q (chisq_v[i], df[i]), NULL);
1844 *showed_fisher = true;
1845 tab_double (chisq, 4, 0, TAB_RIGHT, fisher2, NULL);
1846 tab_double (chisq, 5, 0, TAB_RIGHT, fisher1, NULL);
1848 tab_next_row (chisq);
1851 tab_text (chisq, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1852 tab_double (chisq, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1853 tab_next_row (chisq);
1855 tab_offset (chisq, 0, -1);
1858 static int calc_symmetric (struct crosstabs_proc *, struct pivot_table *,
1859 double[N_SYMMETRIC], double[N_SYMMETRIC],
1860 double[N_SYMMETRIC],
1861 double[3], double[3], double[3]);
1863 /* Display symmetric measures. */
1865 display_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
1866 struct tab_table *sym)
1868 static const char *categories[] =
1870 N_("Nominal by Nominal"),
1871 N_("Ordinal by Ordinal"),
1872 N_("Interval by Interval"),
1873 N_("Measure of Agreement"),
1876 static const char *stats[N_SYMMETRIC] =
1880 N_("Contingency Coefficient"),
1881 N_("Kendall's tau-b"),
1882 N_("Kendall's tau-c"),
1884 N_("Spearman Correlation"),
1889 static const int stats_categories[N_SYMMETRIC] =
1891 0, 0, 0, 1, 1, 1, 1, 2, 3,
1895 double sym_v[N_SYMMETRIC], sym_ase[N_SYMMETRIC], sym_t[N_SYMMETRIC];
1896 double somers_d_v[3], somers_d_ase[3], somers_d_t[3];
1899 if (!calc_symmetric (proc, pt, sym_v, sym_ase, sym_t,
1900 somers_d_v, somers_d_ase, somers_d_t))
1903 tab_offset (sym, pt->n_vars - 2, -1);
1905 for (i = 0; i < N_SYMMETRIC; i++)
1907 if (sym_v[i] == SYSMIS)
1910 if (stats_categories[i] != last_cat)
1912 last_cat = stats_categories[i];
1913 tab_text (sym, 0, 0, TAB_LEFT, gettext (categories[last_cat]));
1916 tab_text (sym, 1, 0, TAB_LEFT, gettext (stats[i]));
1917 tab_double (sym, 2, 0, TAB_RIGHT, sym_v[i], NULL);
1918 if (sym_ase[i] != SYSMIS)
1919 tab_double (sym, 3, 0, TAB_RIGHT, sym_ase[i], NULL);
1920 if (sym_t[i] != SYSMIS)
1921 tab_double (sym, 4, 0, TAB_RIGHT, sym_t[i], NULL);
1922 /*tab_double (sym, 5, 0, TAB_RIGHT, normal_sig (sym_v[i]), NULL);*/
1926 tab_text (sym, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1927 tab_double (sym, 2, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1930 tab_offset (sym, 0, -1);
1933 static int calc_risk (struct pivot_table *,
1934 double[], double[], double[], union value *);
1936 /* Display risk estimate. */
1938 display_risk (struct pivot_table *pt, struct tab_table *risk)
1941 double risk_v[3], lower[3], upper[3];
1945 if (!calc_risk (pt, risk_v, upper, lower, c))
1948 tab_offset (risk, pt->n_vars - 2, -1);
1950 for (i = 0; i < 3; i++)
1952 const struct variable *cv = pt->vars[COL_VAR];
1953 const struct variable *rv = pt->vars[ROW_VAR];
1954 int cvw = var_get_width (cv);
1955 int rvw = var_get_width (rv);
1957 if (risk_v[i] == SYSMIS)
1963 if (var_is_numeric (cv))
1964 sprintf (buf, _("Odds Ratio for %s (%g / %g)"),
1965 var_get_name (cv), c[0].f, c[1].f);
1967 sprintf (buf, _("Odds Ratio for %s (%.*s / %.*s)"),
1969 cvw, value_str (&c[0], cvw),
1970 cvw, value_str (&c[1], cvw));
1974 if (var_is_numeric (rv))
1975 sprintf (buf, _("For cohort %s = %g"),
1976 var_get_name (rv), pt->rows[i - 1].f);
1978 sprintf (buf, _("For cohort %s = %.*s"),
1980 rvw, value_str (&pt->rows[i - 1], rvw));
1984 tab_text (risk, 0, 0, TAB_LEFT, buf);
1985 tab_double (risk, 1, 0, TAB_RIGHT, risk_v[i], NULL);
1986 tab_double (risk, 2, 0, TAB_RIGHT, lower[i], NULL);
1987 tab_double (risk, 3, 0, TAB_RIGHT, upper[i], NULL);
1988 tab_next_row (risk);
1991 tab_text (risk, 0, 0, TAB_LEFT, _("N of Valid Cases"));
1992 tab_double (risk, 1, 0, TAB_RIGHT, pt->total, &pt->weight_format);
1993 tab_next_row (risk);
1995 tab_offset (risk, 0, -1);
1998 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
1999 double[N_DIRECTIONAL], double[N_DIRECTIONAL],
2000 double[N_DIRECTIONAL]);
2002 /* Display directional measures. */
2004 display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2005 struct tab_table *direct)
2007 static const char *categories[] =
2009 N_("Nominal by Nominal"),
2010 N_("Ordinal by Ordinal"),
2011 N_("Nominal by Interval"),
2014 static const char *stats[] =
2017 N_("Goodman and Kruskal tau"),
2018 N_("Uncertainty Coefficient"),
2023 static const char *types[] =
2030 static const int stats_categories[N_DIRECTIONAL] =
2032 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2,
2035 static const int stats_stats[N_DIRECTIONAL] =
2037 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4,
2040 static const int stats_types[N_DIRECTIONAL] =
2042 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2,
2045 static const int *stats_lookup[] =
2052 static const char **stats_names[] =
2064 double direct_v[N_DIRECTIONAL];
2065 double direct_ase[N_DIRECTIONAL];
2066 double direct_t[N_DIRECTIONAL];
2070 if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t))
2073 tab_offset (direct, pt->n_vars - 2, -1);
2075 for (i = 0; i < N_DIRECTIONAL; i++)
2077 if (direct_v[i] == SYSMIS)
2083 for (j = 0; j < 3; j++)
2084 if (last[j] != stats_lookup[j][i])
2087 tab_hline (direct, TAL_1, j, 6, 0);
2092 int k = last[j] = stats_lookup[j][i];
2097 string = var_get_name (pt->vars[0]);
2099 string = var_get_name (pt->vars[1]);
2101 tab_text (direct, j, 0, TAB_LEFT | TAT_PRINTF,
2102 gettext (stats_names[j][k]), string);
2107 tab_double (direct, 3, 0, TAB_RIGHT, direct_v[i], NULL);
2108 if (direct_ase[i] != SYSMIS)
2109 tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL);
2110 if (direct_t[i] != SYSMIS)
2111 tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL);
2112 /*tab_double (direct, 6, 0, TAB_RIGHT, normal_sig (direct_v[i]), NULL);*/
2113 tab_next_row (direct);
2116 tab_offset (direct, 0, -1);
2119 /* Statistical calculations. */
2121 /* Returns the value of the gamma (factorial) function for an integer
2124 gamma_int (double pt)
2129 for (i = 2; i < pt; i++)
2134 /* Calculate P_r as specified in _SPSS Statistical Algorithms_,
2136 static inline double
2137 Pr (int a, int b, int c, int d)
2139 return (gamma_int (a + b + 1.) / gamma_int (a + 1.)
2140 * gamma_int (c + d + 1.) / gamma_int (b + 1.)
2141 * gamma_int (a + c + 1.) / gamma_int (c + 1.)
2142 * gamma_int (b + d + 1.) / gamma_int (d + 1.)
2143 / gamma_int (a + b + c + d + 1.));
2146 /* Swap the contents of A and B. */
2148 swap (int *a, int *b)
2155 /* Calculate significance for Fisher's exact test as specified in
2156 _SPSS Statistical Algorithms_, Appendix 5. */
2158 calc_fisher (int a, int b, int c, int d, double *fisher1, double *fisher2)
2162 if (MIN (c, d) < MIN (a, b))
2163 swap (&a, &c), swap (&b, &d);
2164 if (MIN (b, d) < MIN (a, c))
2165 swap (&a, &b), swap (&c, &d);
2169 swap (&a, &b), swap (&c, &d);
2171 swap (&a, &c), swap (&b, &d);
2175 for (pt = 0; pt <= a; pt++)
2176 *fisher1 += Pr (a - pt, b + pt, c + pt, d - pt);
2178 *fisher2 = *fisher1;
2179 for (pt = 1; pt <= b; pt++)
2180 *fisher2 += Pr (a + pt, b - pt, c - pt, d + pt);
2183 /* Calculates chi-squares into CHISQ. MAT is a matrix with N_COLS
2184 columns with values COLS and N_ROWS rows with values ROWS. Values
2185 in the matrix sum to pt->total. */
2187 calc_chisq (struct pivot_table *pt,
2188 double chisq[N_CHISQ], int df[N_CHISQ],
2189 double *fisher1, double *fisher2)
2193 chisq[0] = chisq[1] = 0.;
2194 chisq[2] = chisq[3] = chisq[4] = SYSMIS;
2195 *fisher1 = *fisher2 = SYSMIS;
2197 df[0] = df[1] = (pt->ns_cols - 1) * (pt->ns_rows - 1);
2199 if (pt->ns_rows <= 1 || pt->ns_cols <= 1)
2201 chisq[0] = chisq[1] = SYSMIS;
2205 for (r = 0; r < pt->n_rows; r++)
2206 for (c = 0; c < pt->n_cols; c++)
2208 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2209 const double freq = pt->mat[pt->n_cols * r + c];
2210 const double residual = freq - expected;
2212 chisq[0] += residual * residual / expected;
2214 chisq[1] += freq * log (expected / freq);
2225 /* Calculate Yates and Fisher exact test. */
2226 if (pt->ns_cols == 2 && pt->ns_rows == 2)
2228 double f11, f12, f21, f22;
2234 for (i = j = 0; i < pt->n_cols; i++)
2235 if (pt->col_tot[i] != 0.)
2244 f11 = pt->mat[nz_cols[0]];
2245 f12 = pt->mat[nz_cols[1]];
2246 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2247 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2252 const double pt_ = fabs (f11 * f22 - f12 * f21) - 0.5 * pt->total;
2255 chisq[3] = (pt->total * pow2 (pt_)
2256 / (f11 + f12) / (f21 + f22)
2257 / (f11 + f21) / (f12 + f22));
2265 if (f11 < 5. || f12 < 5. || f21 < 5. || f22 < 5.)
2266 calc_fisher (f11 + .5, f12 + .5, f21 + .5, f22 + .5, fisher1, fisher2);
2269 /* Calculate Mantel-Haenszel. */
2270 if (var_is_numeric (pt->vars[ROW_VAR]) && var_is_numeric (pt->vars[COL_VAR]))
2272 double r, ase_0, ase_1;
2273 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &r, &ase_0, &ase_1);
2275 chisq[4] = (pt->total - 1.) * r * r;
2280 /* Calculate the value of Pearson's r. r is stored into R, ase_1 into
2281 ASE_1, and ase_0 into ASE_0. The row and column values must be
2282 passed in PT and Y. */
2284 calc_r (struct pivot_table *pt,
2285 double *PT, double *Y, double *r, double *ase_0, double *ase_1)
2287 double SX, SY, S, T;
2289 double sum_XYf, sum_X2Y2f;
2290 double sum_Xr, sum_X2r;
2291 double sum_Yc, sum_Y2c;
2294 for (sum_X2Y2f = sum_XYf = 0., i = 0; i < pt->n_rows; i++)
2295 for (j = 0; j < pt->n_cols; j++)
2297 double fij = pt->mat[j + i * pt->n_cols];
2298 double product = PT[i] * Y[j];
2299 double temp = fij * product;
2301 sum_X2Y2f += temp * product;
2304 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
2306 sum_Xr += PT[i] * pt->row_tot[i];
2307 sum_X2r += pow2 (PT[i]) * pt->row_tot[i];
2309 Xbar = sum_Xr / pt->total;
2311 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
2313 sum_Yc += Y[i] * pt->col_tot[i];
2314 sum_Y2c += Y[i] * Y[i] * pt->col_tot[i];
2316 Ybar = sum_Yc / pt->total;
2318 S = sum_XYf - sum_Xr * sum_Yc / pt->total;
2319 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
2320 SY = sum_Y2c - pow2 (sum_Yc) / pt->total;
2323 *ase_0 = sqrt ((sum_X2Y2f - pow2 (sum_XYf) / pt->total) / (sum_X2r * sum_Y2c));
2328 for (s = c = 0., i = 0; i < pt->n_rows; i++)
2329 for (j = 0; j < pt->n_cols; j++)
2331 double Xresid, Yresid;
2334 Xresid = PT[i] - Xbar;
2335 Yresid = Y[j] - Ybar;
2336 temp = (T * Xresid * Yresid
2338 * (Xresid * Xresid * SY + Yresid * Yresid * SX)));
2339 y = pt->mat[j + i * pt->n_cols] * temp * temp - c;
2344 *ase_1 = sqrt (s) / (T * T);
2348 /* Calculate symmetric statistics and their asymptotic standard
2349 errors. Returns 0 if none could be calculated. */
2351 calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
2352 double v[N_SYMMETRIC], double ase[N_SYMMETRIC],
2353 double t[N_SYMMETRIC],
2354 double somers_d_v[3], double somers_d_ase[3],
2355 double somers_d_t[3])
2359 q = MIN (pt->ns_rows, pt->ns_cols);
2363 for (i = 0; i < N_SYMMETRIC; i++)
2364 v[i] = ase[i] = t[i] = SYSMIS;
2366 /* Phi, Cramer's V, contingency coefficient. */
2367 if (proc->statistics & ((1u << CRS_ST_PHI) | (1u << CRS_ST_CC)))
2369 double Xp = 0.; /* Pearson chi-square. */
2372 for (r = 0; r < pt->n_rows; r++)
2373 for (c = 0; c < pt->n_cols; c++)
2375 const double expected = pt->row_tot[r] * pt->col_tot[c] / pt->total;
2376 const double freq = pt->mat[pt->n_cols * r + c];
2377 const double residual = freq - expected;
2379 Xp += residual * residual / expected;
2382 if (proc->statistics & (1u << CRS_ST_PHI))
2384 v[0] = sqrt (Xp / pt->total);
2385 v[1] = sqrt (Xp / (pt->total * (q - 1)));
2387 if (proc->statistics & (1u << CRS_ST_CC))
2388 v[2] = sqrt (Xp / (Xp + pt->total));
2391 if (proc->statistics & ((1u << CRS_ST_BTAU) | (1u << CRS_ST_CTAU)
2392 | (1u << CRS_ST_GAMMA) | (1u << CRS_ST_D)))
2397 double btau_cum, ctau_cum, gamma_cum, d_yx_cum, d_xy_cum;
2401 Dr = Dc = pow2 (pt->total);
2402 for (r = 0; r < pt->n_rows; r++)
2403 Dr -= pow2 (pt->row_tot[r]);
2404 for (c = 0; c < pt->n_cols; c++)
2405 Dc -= pow2 (pt->col_tot[c]);
2407 cum = xnmalloc (pt->n_cols * pt->n_rows, sizeof *cum);
2408 for (c = 0; c < pt->n_cols; c++)
2412 for (r = 0; r < pt->n_rows; r++)
2413 cum[c + r * pt->n_cols] = ct += pt->mat[c + r * pt->n_cols];
2422 for (i = 0; i < pt->n_rows; i++)
2426 for (j = 1; j < pt->n_cols; j++)
2427 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2430 for (j = 1; j < pt->n_cols; j++)
2431 Dij += cum[j + (i - 1) * pt->n_cols];
2435 double fij = pt->mat[j + i * pt->n_cols];
2439 if (++j == pt->n_cols)
2441 assert (j < pt->n_cols);
2443 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2444 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2448 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2449 Dij -= cum[j + (i - 1) * pt->n_cols];
2455 if (proc->statistics & (1u << CRS_ST_BTAU))
2456 v[3] = (P - Q) / sqrt (Dr * Dc);
2457 if (proc->statistics & (1u << CRS_ST_CTAU))
2458 v[4] = (q * (P - Q)) / (pow2 (pt->total) * (q - 1));
2459 if (proc->statistics & (1u << CRS_ST_GAMMA))
2460 v[5] = (P - Q) / (P + Q);
2462 /* ASE for tau-b, tau-c, gamma. Calculations could be
2463 eliminated here, at expense of memory. */
2468 btau_cum = ctau_cum = gamma_cum = d_yx_cum = d_xy_cum = 0.;
2469 for (i = 0; i < pt->n_rows; i++)
2473 for (j = 1; j < pt->n_cols; j++)
2474 Cij += pt->col_tot[j] - cum[j + i * pt->n_cols];
2477 for (j = 1; j < pt->n_cols; j++)
2478 Dij += cum[j + (i - 1) * pt->n_cols];
2482 double fij = pt->mat[j + i * pt->n_cols];
2484 if (proc->statistics & (1u << CRS_ST_BTAU))
2486 const double temp = (2. * sqrt (Dr * Dc) * (Cij - Dij)
2487 + v[3] * (pt->row_tot[i] * Dc
2488 + pt->col_tot[j] * Dr));
2489 btau_cum += fij * temp * temp;
2493 const double temp = Cij - Dij;
2494 ctau_cum += fij * temp * temp;
2497 if (proc->statistics & (1u << CRS_ST_GAMMA))
2499 const double temp = Q * Cij - P * Dij;
2500 gamma_cum += fij * temp * temp;
2503 if (proc->statistics & (1u << CRS_ST_D))
2505 d_yx_cum += fij * pow2 (Dr * (Cij - Dij)
2506 - (P - Q) * (pt->total - pt->row_tot[i]));
2507 d_xy_cum += fij * pow2 (Dc * (Dij - Cij)
2508 - (Q - P) * (pt->total - pt->col_tot[j]));
2511 if (++j == pt->n_cols)
2513 assert (j < pt->n_cols);
2515 Cij -= pt->col_tot[j] - cum[j + i * pt->n_cols];
2516 Dij += pt->col_tot[j - 1] - cum[j - 1 + i * pt->n_cols];
2520 Cij += cum[j - 1 + (i - 1) * pt->n_cols];
2521 Dij -= cum[j + (i - 1) * pt->n_cols];
2527 btau_var = ((btau_cum
2528 - (pt->total * pow2 (pt->total * (P - Q) / sqrt (Dr * Dc) * (Dr + Dc))))
2530 if (proc->statistics & (1u << CRS_ST_BTAU))
2532 ase[3] = sqrt (btau_var);
2533 t[3] = v[3] / (2 * sqrt ((ctau_cum - (P - Q) * (P - Q) / pt->total)
2536 if (proc->statistics & (1u << CRS_ST_CTAU))
2538 ase[4] = ((2 * q / ((q - 1) * pow2 (pt->total)))
2539 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2540 t[4] = v[4] / ase[4];
2542 if (proc->statistics & (1u << CRS_ST_GAMMA))
2544 ase[5] = ((4. / ((P + Q) * (P + Q))) * sqrt (gamma_cum));
2545 t[5] = v[5] / (2. / (P + Q)
2546 * sqrt (ctau_cum - (P - Q) * (P - Q) / pt->total));
2548 if (proc->statistics & (1u << CRS_ST_D))
2550 somers_d_v[0] = (P - Q) / (.5 * (Dc + Dr));
2551 somers_d_ase[0] = 2. * btau_var / (Dr + Dc) * sqrt (Dr * Dc);
2552 somers_d_t[0] = (somers_d_v[0]
2554 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2555 somers_d_v[1] = (P - Q) / Dc;
2556 somers_d_ase[1] = 2. / pow2 (Dc) * sqrt (d_xy_cum);
2557 somers_d_t[1] = (somers_d_v[1]
2559 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2560 somers_d_v[2] = (P - Q) / Dr;
2561 somers_d_ase[2] = 2. / pow2 (Dr) * sqrt (d_yx_cum);
2562 somers_d_t[2] = (somers_d_v[2]
2564 * sqrt (ctau_cum - pow2 (P - Q) / pt->total)));
2570 /* Spearman correlation, Pearson's r. */
2571 if (proc->statistics & (1u << CRS_ST_CORR))
2573 double *R = xmalloc (sizeof *R * pt->n_rows);
2574 double *C = xmalloc (sizeof *C * pt->n_cols);
2577 double y, t, c = 0., s = 0.;
2582 R[i] = s + (pt->row_tot[i] + 1.) / 2.;
2583 y = pt->row_tot[i] - c;
2587 if (++i == pt->n_rows)
2589 assert (i < pt->n_rows);
2594 double y, t, c = 0., s = 0.;
2599 C[j] = s + (pt->col_tot[j] + 1.) / 2;
2600 y = pt->col_tot[j] - c;
2604 if (++j == pt->n_cols)
2606 assert (j < pt->n_cols);
2610 calc_r (pt, R, C, &v[6], &t[6], &ase[6]);
2616 calc_r (pt, (double *) pt->rows, (double *) pt->cols, &v[7], &t[7], &ase[7]);
2620 /* Cohen's kappa. */
2621 if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
2623 double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
2626 for (sum_fii = sum_rici = sum_fiiri_ci = sum_riciri_ci = 0., i = j = 0;
2627 i < pt->ns_rows; i++, j++)
2631 while (pt->col_tot[j] == 0.)
2634 prod = pt->row_tot[i] * pt->col_tot[j];
2635 sum = pt->row_tot[i] + pt->col_tot[j];
2637 sum_fii += pt->mat[j + i * pt->n_cols];
2639 sum_fiiri_ci += pt->mat[j + i * pt->n_cols] * sum;
2640 sum_riciri_ci += prod * sum;
2642 for (sum_fijri_ci2 = 0., i = 0; i < pt->ns_rows; i++)
2643 for (j = 0; j < pt->ns_cols; j++)
2645 double sum = pt->row_tot[i] + pt->col_tot[j];
2646 sum_fijri_ci2 += pt->mat[j + i * pt->n_cols] * sum * sum;
2649 v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
2651 ase[8] = sqrt ((pow2 (pt->total) * sum_rici
2652 + sum_rici * sum_rici
2653 - pt->total * sum_riciri_ci)
2654 / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
2656 t[8] = v[8] / sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
2657 / pow2 (pow2 (pt->total) - sum_rici))
2658 + ((2. * (pt->total - sum_fii)
2659 * (2. * sum_fii * sum_rici
2660 - pt->total * sum_fiiri_ci))
2661 / cube (pow2 (pt->total) - sum_rici))
2662 + (pow2 (pt->total - sum_fii)
2663 * (pt->total * sum_fijri_ci2 - 4.
2664 * sum_rici * sum_rici)
2665 / pow4 (pow2 (pt->total) - sum_rici))));
2667 t[8] = v[8] / ase[8];
2674 /* Calculate risk estimate. */
2676 calc_risk (struct pivot_table *pt,
2677 double *value, double *upper, double *lower, union value *c)
2679 double f11, f12, f21, f22;
2685 for (i = 0; i < 3; i++)
2686 value[i] = upper[i] = lower[i] = SYSMIS;
2689 if (pt->ns_rows != 2 || pt->ns_cols != 2)
2696 for (i = j = 0; i < pt->n_cols; i++)
2697 if (pt->col_tot[i] != 0.)
2706 f11 = pt->mat[nz_cols[0]];
2707 f12 = pt->mat[nz_cols[1]];
2708 f21 = pt->mat[nz_cols[0] + pt->n_cols];
2709 f22 = pt->mat[nz_cols[1] + pt->n_cols];
2711 c[0] = pt->cols[nz_cols[0]];
2712 c[1] = pt->cols[nz_cols[1]];
2715 value[0] = (f11 * f22) / (f12 * f21);
2716 v = sqrt (1. / f11 + 1. / f12 + 1. / f21 + 1. / f22);
2717 lower[0] = value[0] * exp (-1.960 * v);
2718 upper[0] = value[0] * exp (1.960 * v);
2720 value[1] = (f11 * (f21 + f22)) / (f21 * (f11 + f12));
2721 v = sqrt ((f12 / (f11 * (f11 + f12)))
2722 + (f22 / (f21 * (f21 + f22))));
2723 lower[1] = value[1] * exp (-1.960 * v);
2724 upper[1] = value[1] * exp (1.960 * v);
2726 value[2] = (f12 * (f21 + f22)) / (f22 * (f11 + f12));
2727 v = sqrt ((f11 / (f12 * (f11 + f12)))
2728 + (f21 / (f22 * (f21 + f22))));
2729 lower[2] = value[2] * exp (-1.960 * v);
2730 upper[2] = value[2] * exp (1.960 * v);
2735 /* Calculate directional measures. */
2737 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
2738 double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
2739 double t[N_DIRECTIONAL])
2744 for (i = 0; i < N_DIRECTIONAL; i++)
2745 v[i] = ase[i] = t[i] = SYSMIS;
2749 if (proc->statistics & (1u << CRS_ST_LAMBDA))
2751 double *fim = xnmalloc (pt->n_rows, sizeof *fim);
2752 int *fim_index = xnmalloc (pt->n_rows, sizeof *fim_index);
2753 double *fmj = xnmalloc (pt->n_cols, sizeof *fmj);
2754 int *fmj_index = xnmalloc (pt->n_cols, sizeof *fmj_index);
2755 double sum_fim, sum_fmj;
2757 int rm_index, cm_index;
2760 /* Find maximum for each row and their sum. */
2761 for (sum_fim = 0., i = 0; i < pt->n_rows; i++)
2763 double max = pt->mat[i * pt->n_cols];
2766 for (j = 1; j < pt->n_cols; j++)
2767 if (pt->mat[j + i * pt->n_cols] > max)
2769 max = pt->mat[j + i * pt->n_cols];
2773 sum_fim += fim[i] = max;
2774 fim_index[i] = index;
2777 /* Find maximum for each column. */
2778 for (sum_fmj = 0., j = 0; j < pt->n_cols; j++)
2780 double max = pt->mat[j];
2783 for (i = 1; i < pt->n_rows; i++)
2784 if (pt->mat[j + i * pt->n_cols] > max)
2786 max = pt->mat[j + i * pt->n_cols];
2790 sum_fmj += fmj[j] = max;
2791 fmj_index[j] = index;
2794 /* Find maximum row total. */
2795 rm = pt->row_tot[0];
2797 for (i = 1; i < pt->n_rows; i++)
2798 if (pt->row_tot[i] > rm)
2800 rm = pt->row_tot[i];
2804 /* Find maximum column total. */
2805 cm = pt->col_tot[0];
2807 for (j = 1; j < pt->n_cols; j++)
2808 if (pt->col_tot[j] > cm)
2810 cm = pt->col_tot[j];
2814 v[0] = (sum_fim + sum_fmj - cm - rm) / (2. * pt->total - rm - cm);
2815 v[1] = (sum_fmj - rm) / (pt->total - rm);
2816 v[2] = (sum_fim - cm) / (pt->total - cm);
2818 /* ASE1 for Y given PT. */
2822 for (accum = 0., i = 0; i < pt->n_rows; i++)
2823 for (j = 0; j < pt->n_cols; j++)
2825 const int deltaj = j == cm_index;
2826 accum += (pt->mat[j + i * pt->n_cols]
2827 * pow2 ((j == fim_index[i])
2832 ase[2] = sqrt (accum - pt->total * v[0]) / (pt->total - cm);
2835 /* ASE0 for Y given PT. */
2839 for (accum = 0., i = 0; i < pt->n_rows; i++)
2840 if (cm_index != fim_index[i])
2841 accum += (pt->mat[i * pt->n_cols + fim_index[i]]
2842 + pt->mat[i * pt->n_cols + cm_index]);
2843 t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
2846 /* ASE1 for PT given Y. */
2850 for (accum = 0., i = 0; i < pt->n_rows; i++)
2851 for (j = 0; j < pt->n_cols; j++)
2853 const int deltaj = i == rm_index;
2854 accum += (pt->mat[j + i * pt->n_cols]
2855 * pow2 ((i == fmj_index[j])
2860 ase[1] = sqrt (accum - pt->total * v[0]) / (pt->total - rm);
2863 /* ASE0 for PT given Y. */
2867 for (accum = 0., j = 0; j < pt->n_cols; j++)
2868 if (rm_index != fmj_index[j])
2869 accum += (pt->mat[j + pt->n_cols * fmj_index[j]]
2870 + pt->mat[j + pt->n_cols * rm_index]);
2871 t[1] = v[1] / (sqrt (accum - pow2 (sum_fmj - rm) / pt->total) / (pt->total - rm));
2874 /* Symmetric ASE0 and ASE1. */
2879 for (accum0 = accum1 = 0., i = 0; i < pt->n_rows; i++)
2880 for (j = 0; j < pt->n_cols; j++)
2882 int temp0 = (fmj_index[j] == i) + (fim_index[i] == j);
2883 int temp1 = (i == rm_index) + (j == cm_index);
2884 accum0 += pt->mat[j + i * pt->n_cols] * pow2 (temp0 - temp1);
2885 accum1 += (pt->mat[j + i * pt->n_cols]
2886 * pow2 (temp0 + (v[0] - 1.) * temp1));
2888 ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
2889 t[0] = v[0] / (sqrt (accum0 - pow2 ((sum_fim + sum_fmj - cm - rm) / pt->total))
2890 / (2. * pt->total - rm - cm));
2899 double sum_fij2_ri, sum_fij2_ci;
2900 double sum_ri2, sum_cj2;
2902 for (sum_fij2_ri = sum_fij2_ci = 0., i = 0; i < pt->n_rows; i++)
2903 for (j = 0; j < pt->n_cols; j++)
2905 double temp = pow2 (pt->mat[j + i * pt->n_cols]);
2906 sum_fij2_ri += temp / pt->row_tot[i];
2907 sum_fij2_ci += temp / pt->col_tot[j];
2910 for (sum_ri2 = 0., i = 0; i < pt->n_rows; i++)
2911 sum_ri2 += pow2 (pt->row_tot[i]);
2913 for (sum_cj2 = 0., j = 0; j < pt->n_cols; j++)
2914 sum_cj2 += pow2 (pt->col_tot[j]);
2916 v[3] = (pt->total * sum_fij2_ci - sum_ri2) / (pow2 (pt->total) - sum_ri2);
2917 v[4] = (pt->total * sum_fij2_ri - sum_cj2) / (pow2 (pt->total) - sum_cj2);
2921 if (proc->statistics & (1u << CRS_ST_UC))
2923 double UX, UY, UXY, P;
2924 double ase1_yx, ase1_xy, ase1_sym;
2927 for (UX = 0., i = 0; i < pt->n_rows; i++)
2928 if (pt->row_tot[i] > 0.)
2929 UX -= pt->row_tot[i] / pt->total * log (pt->row_tot[i] / pt->total);
2931 for (UY = 0., j = 0; j < pt->n_cols; j++)
2932 if (pt->col_tot[j] > 0.)
2933 UY -= pt->col_tot[j] / pt->total * log (pt->col_tot[j] / pt->total);
2935 for (UXY = P = 0., i = 0; i < pt->n_rows; i++)
2936 for (j = 0; j < pt->n_cols; j++)
2938 double entry = pt->mat[j + i * pt->n_cols];
2943 P += entry * pow2 (log (pt->col_tot[j] * pt->row_tot[i] / (pt->total * entry)));
2944 UXY -= entry / pt->total * log (entry / pt->total);
2947 for (ase1_yx = ase1_xy = ase1_sym = 0., i = 0; i < pt->n_rows; i++)
2948 for (j = 0; j < pt->n_cols; j++)
2950 double entry = pt->mat[j + i * pt->n_cols];
2955 ase1_yx += entry * pow2 (UY * log (entry / pt->row_tot[i])
2956 + (UX - UXY) * log (pt->col_tot[j] / pt->total));
2957 ase1_xy += entry * pow2 (UX * log (entry / pt->col_tot[j])
2958 + (UY - UXY) * log (pt->row_tot[i] / pt->total));
2959 ase1_sym += entry * pow2 ((UXY
2960 * log (pt->row_tot[i] * pt->col_tot[j] / pow2 (pt->total)))
2961 - (UX + UY) * log (entry / pt->total));
2964 v[5] = 2. * ((UX + UY - UXY) / (UX + UY));
2965 ase[5] = (2. / (pt->total * pow2 (UX + UY))) * sqrt (ase1_sym);
2966 t[5] = v[5] / ((2. / (pt->total * (UX + UY)))
2967 * sqrt (P - pow2 (UX + UY - UXY) / pt->total));
2969 v[6] = (UX + UY - UXY) / UX;
2970 ase[6] = sqrt (ase1_xy) / (pt->total * UX * UX);
2971 t[6] = v[6] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UX));
2973 v[7] = (UX + UY - UXY) / UY;
2974 ase[7] = sqrt (ase1_yx) / (pt->total * UY * UY);
2975 t[7] = v[7] / (sqrt (P - pt->total * pow2 (UX + UY - UXY)) / (pt->total * UY));
2979 if (proc->statistics & (1u << CRS_ST_D))
2981 double v_dummy[N_SYMMETRIC];
2982 double ase_dummy[N_SYMMETRIC];
2983 double t_dummy[N_SYMMETRIC];
2984 double somers_d_v[3];
2985 double somers_d_ase[3];
2986 double somers_d_t[3];
2988 if (calc_symmetric (proc, pt, v_dummy, ase_dummy, t_dummy,
2989 somers_d_v, somers_d_ase, somers_d_t))
2992 for (i = 0; i < 3; i++)
2994 v[8 + i] = somers_d_v[i];
2995 ase[8 + i] = somers_d_ase[i];
2996 t[8 + i] = somers_d_t[i];
3002 if (proc->statistics & (1u << CRS_ST_ETA))
3005 double sum_Xr, sum_X2r;
3009 for (sum_Xr = sum_X2r = 0., i = 0; i < pt->n_rows; i++)
3011 sum_Xr += pt->rows[i].f * pt->row_tot[i];
3012 sum_X2r += pow2 (pt->rows[i].f) * pt->row_tot[i];
3014 SX = sum_X2r - pow2 (sum_Xr) / pt->total;
3016 for (SXW = 0., j = 0; j < pt->n_cols; j++)
3020 for (cum = 0., i = 0; i < pt->n_rows; i++)
3022 SXW += pow2 (pt->rows[i].f) * pt->mat[j + i * pt->n_cols];
3023 cum += pt->rows[i].f * pt->mat[j + i * pt->n_cols];
3026 SXW -= cum * cum / pt->col_tot[j];
3028 v[11] = sqrt (1. - SXW / SX);
3032 double sum_Yc, sum_Y2c;
3036 for (sum_Yc = sum_Y2c = 0., i = 0; i < pt->n_cols; i++)
3038 sum_Yc += pt->cols[i].f * pt->col_tot[i];
3039 sum_Y2c += pow2 (pt->cols[i].f) * pt->col_tot[i];
3041 SY = sum_Y2c - sum_Yc * sum_Yc / pt->total;
3043 for (SYW = 0., i = 0; i < pt->n_rows; i++)
3047 for (cum = 0., j = 0; j < pt->n_cols; j++)
3049 SYW += pow2 (pt->cols[j].f) * pt->mat[j + i * pt->n_cols];
3050 cum += pt->cols[j].f * pt->mat[j + i * pt->n_cols];
3053 SYW -= cum * cum / pt->row_tot[i];
3055 v[12] = sqrt (1. - SYW / SY);