1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 2009, 2010, 2011, 2013 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/>. */
21 #include "data/casegrouper.h"
22 #include "data/casereader.h"
23 #include "data/dataset.h"
24 #include "data/dictionary.h"
25 #include "data/format.h"
26 #include "data/missing-values.h"
27 #include "language/command.h"
28 #include "language/lexer/lexer.h"
29 #include "language/lexer/variable-parser.h"
30 #include "libpspp/message.h"
31 #include "libpspp/misc.h"
32 #include "libpspp/str.h"
33 #include "math/moments.h"
34 #include "output/tab.h"
35 #include "output/text-item.h"
38 #define _(msgid) gettext (msgid)
39 #define N_(msgid) msgid
43 const struct variable **items;
46 double sum_of_variances;
47 double variance_of_sums;
48 int totals_idx; /* Casereader index into the totals */
50 struct moments1 **m ; /* Moments of the items */
51 struct moments1 *total ; /* Moments of the totals */
56 dump_cronbach (const struct cronbach *s)
59 printf ("N items %d\n", s->n_items);
60 for (i = 0 ; i < s->n_items; ++i)
62 printf ("%s\n", var_get_name (s->items[i]));
65 printf ("Totals idx %d\n", s->totals_idx);
67 printf ("scale variance %g\n", s->variance_of_sums);
68 printf ("alpha %g\n", s->alpha);
82 SUMMARY_TOTAL = 0x0001,
88 const struct variable **variables;
90 enum mv_class exclude;
97 struct string scale_name;
103 enum summary_opts summary;
105 const struct variable *wv;
109 static bool run_reliability (struct dataset *ds, const struct reliability *reliability);
112 reliability_destroy (struct reliability *rel)
115 ds_destroy (&rel->scale_name);
117 for (j = 0; j < rel->n_sc ; ++j)
120 free (rel->sc[j].items);
121 moments1_destroy (rel->sc[j].total);
122 for (x = 0; x < rel->sc[j].n_items; ++x)
123 free (rel->sc[j].m[x]);
128 free (rel->variables);
132 cmd_reliability (struct lexer *lexer, struct dataset *ds)
134 const struct dictionary *dict = dataset_dict (ds);
136 struct reliability reliability;
137 reliability.n_variables = 0;
138 reliability.variables = NULL;
139 reliability.model = MODEL_ALPHA;
140 reliability.exclude = MV_ANY;
141 reliability.summary = 0;
142 reliability.n_sc = 0;
143 reliability.sc = NULL;
144 reliability.wv = dict_get_weight (dict);
145 reliability.total_start = 0;
147 lex_match (lexer, T_SLASH);
149 if (!lex_force_match_id (lexer, "VARIABLES"))
154 lex_match (lexer, T_EQUALS);
156 if (!parse_variables_const (lexer, dict, &reliability.variables, &reliability.n_variables,
157 PV_NO_DUPLICATE | PV_NUMERIC))
160 if (reliability.n_variables < 2)
161 msg (MW, _("Reliability on a single variable is not useful."));
167 /* Create a default Scale */
169 reliability.n_sc = 1;
170 reliability.sc = xzalloc (sizeof (struct cronbach) * reliability.n_sc);
172 ds_init_cstr (&reliability.scale_name, "ANY");
174 c = &reliability.sc[0];
175 c->n_items = reliability.n_variables;
176 c->items = xzalloc (sizeof (struct variable*) * c->n_items);
178 for (i = 0 ; i < c->n_items ; ++i)
179 c->items[i] = reliability.variables[i];
184 while (lex_token (lexer) != T_ENDCMD)
186 lex_match (lexer, T_SLASH);
188 if (lex_match_id (lexer, "SCALE"))
190 struct const_var_set *vs;
191 if ( ! lex_force_match (lexer, T_LPAREN))
194 if ( ! lex_force_string (lexer) )
197 ds_assign_substring (&reliability.scale_name, lex_tokss (lexer));
201 if ( ! lex_force_match (lexer, T_RPAREN))
204 lex_match (lexer, T_EQUALS);
206 vs = const_var_set_create_from_array (reliability.variables, reliability.n_variables);
208 free (reliability.sc->items);
209 if (!parse_const_var_set_vars (lexer, vs, &reliability.sc->items, &reliability.sc->n_items, 0))
211 const_var_set_destroy (vs);
215 const_var_set_destroy (vs);
217 else if (lex_match_id (lexer, "MODEL"))
219 lex_match (lexer, T_EQUALS);
220 if (lex_match_id (lexer, "ALPHA"))
222 reliability.model = MODEL_ALPHA;
224 else if (lex_match_id (lexer, "SPLIT"))
226 reliability.model = MODEL_SPLIT;
227 reliability.split_point = -1;
229 if ( lex_match (lexer, T_LPAREN))
231 lex_force_num (lexer);
232 reliability.split_point = lex_number (lexer);
234 lex_force_match (lexer, T_RPAREN);
240 else if (lex_match_id (lexer, "SUMMARY"))
242 lex_match (lexer, T_EQUALS);
243 if (lex_match_id (lexer, "TOTAL"))
245 reliability.summary |= SUMMARY_TOTAL;
247 else if (lex_match (lexer, T_ALL))
249 reliability.summary = 0xFFFF;
254 else if (lex_match_id (lexer, "MISSING"))
256 lex_match (lexer, T_EQUALS);
257 while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
259 if (lex_match_id (lexer, "INCLUDE"))
261 reliability.exclude = MV_SYSTEM;
263 else if (lex_match_id (lexer, "EXCLUDE"))
265 reliability.exclude = MV_ANY;
269 lex_error (lexer, NULL);
276 lex_error (lexer, NULL);
281 if ( reliability.model == MODEL_SPLIT)
284 const struct cronbach *s;
286 if ( reliability.split_point >= reliability.n_variables)
288 msg (ME, _("The split point must be less than the number of variables"));
292 reliability.n_sc += 2 ;
293 reliability.sc = xrealloc (reliability.sc, sizeof (struct cronbach) * reliability.n_sc);
295 s = &reliability.sc[0];
297 reliability.sc[1].n_items =
298 (reliability.split_point == -1) ? s->n_items / 2 : reliability.split_point;
300 reliability.sc[2].n_items = s->n_items - reliability.sc[1].n_items;
301 reliability.sc[1].items = xzalloc (sizeof (struct variable *)
302 * reliability.sc[1].n_items);
304 reliability.sc[2].items = xzalloc (sizeof (struct variable *) *
305 reliability.sc[2].n_items);
307 for (i = 0; i < reliability.sc[1].n_items ; ++i)
308 reliability.sc[1].items[i] = s->items[i];
310 while (i < s->n_items)
312 reliability.sc[2].items[i - reliability.sc[1].n_items] = s->items[i];
317 if ( reliability.summary & SUMMARY_TOTAL)
320 const int base_sc = reliability.n_sc;
322 reliability.total_start = base_sc;
324 reliability.n_sc += reliability.sc[0].n_items ;
325 reliability.sc = xrealloc (reliability.sc, sizeof (struct cronbach) * reliability.n_sc);
328 for (i = 0 ; i < reliability.sc[0].n_items; ++i )
332 struct cronbach *s = &reliability.sc[i + base_sc];
334 s->n_items = reliability.sc[0].n_items - 1;
335 s->items = xzalloc (sizeof (struct variable *) * s->n_items);
336 for (v_src = 0 ; v_src < reliability.sc[0].n_items ; ++v_src)
339 s->items[v_dest++] = reliability.sc[0].items[v_src];
345 if ( ! run_reliability (ds, &reliability))
348 reliability_destroy (&reliability);
352 reliability_destroy (&reliability);
358 do_reliability (struct casereader *group, struct dataset *ds,
359 const struct reliability *rel);
362 static void reliability_summary_total (const struct reliability *rel);
364 static void reliability_statistics (const struct reliability *rel);
368 run_reliability (struct dataset *ds, const struct reliability *reliability)
370 struct dictionary *dict = dataset_dict (ds);
372 struct casereader *group;
374 struct casegrouper *grouper = casegrouper_create_splits (proc_open (ds), dict);
376 while (casegrouper_get_next_group (grouper, &group))
378 do_reliability (group, ds, reliability);
380 reliability_statistics (reliability);
382 if (reliability->summary & SUMMARY_TOTAL )
383 reliability_summary_total (reliability);
386 ok = casegrouper_destroy (grouper);
387 ok = proc_commit (ds) && ok;
396 /* Return the sum of all the item variables in S */
398 append_sum (const struct ccase *c, casenumber n UNUSED, void *aux)
401 const struct cronbach *s = aux;
404 for (v = 0 ; v < s->n_items; ++v)
406 sum += case_data (c, s->items[v])->f;
413 case_processing_summary (casenumber n_valid, casenumber n_missing,
414 const struct dictionary *dict);
418 alpha (int k, double sum_of_variances, double variance_of_sums)
420 return k / ( k - 1.0) * ( 1 - sum_of_variances / variance_of_sums);
424 do_reliability (struct casereader *input, struct dataset *ds,
425 const struct reliability *rel)
430 casenumber n_missing ;
431 casenumber n_valid = 0;
434 for (si = 0 ; si < rel->n_sc; ++si)
436 struct cronbach *s = &rel->sc[si];
438 s->m = xzalloc (sizeof (s->m) * s->n_items);
439 s->total = moments1_create (MOMENT_VARIANCE);
441 for (i = 0 ; i < s->n_items ; ++i )
442 s->m[i] = moments1_create (MOMENT_VARIANCE);
445 input = casereader_create_filter_missing (input,
452 for (si = 0 ; si < rel->n_sc; ++si)
454 struct cronbach *s = &rel->sc[si];
457 s->totals_idx = caseproto_get_n_widths (casereader_get_proto (input));
459 casereader_create_append_numeric (input, append_sum,
463 for (; (c = casereader_read (input)) != NULL; case_unref (c))
468 for (si = 0; si < rel->n_sc; ++si)
470 struct cronbach *s = &rel->sc[si];
472 for (i = 0 ; i < s->n_items ; ++i )
473 moments1_add (s->m[i], case_data (c, s->items[i])->f, weight);
475 moments1_add (s->total, case_data_idx (c, s->totals_idx)->f, weight);
478 casereader_destroy (input);
480 for (si = 0; si < rel->n_sc; ++si)
482 struct cronbach *s = &rel->sc[si];
484 s->sum_of_variances = 0;
485 for (i = 0 ; i < s->n_items ; ++i )
487 double weight, mean, variance;
488 moments1_calculate (s->m[i], &weight, &mean, &variance, NULL, NULL);
490 s->sum_of_variances += variance;
493 moments1_calculate (s->total, NULL, NULL, &s->variance_of_sums,
497 alpha (s->n_items, s->sum_of_variances, s->variance_of_sums);
500 text_item_submit (text_item_create_format (TEXT_ITEM_PARAGRAPH, _("Scale: %s"),
501 ds_cstr (&rel->scale_name)));
503 case_processing_summary (n_valid, n_missing, dataset_dict (ds));
511 case_processing_summary (casenumber n_valid, casenumber n_missing,
512 const struct dictionary *dict)
514 const struct variable *wv = dict_get_weight (dict);
515 const struct fmt_spec *wfmt = wv ? var_get_print_format (wv) : & F_8_0;
520 int heading_columns = 2;
521 int heading_rows = 1;
522 struct tab_table *tbl;
523 tbl = tab_create (n_cols, n_rows);
524 tab_headers (tbl, heading_columns, 0, heading_rows, 0);
526 tab_title (tbl, _("Case Processing Summary"));
528 /* Vertical lines for the data only */
533 n_cols - 1, n_rows - 1);
535 /* Box around table */
540 n_cols - 1, n_rows - 1);
543 tab_hline (tbl, TAL_2, 0, n_cols - 1, heading_rows);
545 tab_vline (tbl, TAL_2, heading_columns, 0, n_rows - 1);
548 tab_text (tbl, 0, heading_rows, TAB_LEFT | TAT_TITLE,
551 tab_text (tbl, 1, heading_rows, TAB_LEFT | TAT_TITLE,
554 tab_text (tbl, 1, heading_rows + 1, TAB_LEFT | TAT_TITLE,
557 tab_text (tbl, 1, heading_rows + 2, TAB_LEFT | TAT_TITLE,
560 tab_text (tbl, heading_columns, 0, TAB_CENTER | TAT_TITLE,
563 tab_text (tbl, heading_columns + 1, 0, TAB_CENTER | TAT_TITLE, _("%"));
565 total = n_missing + n_valid;
567 tab_double (tbl, 2, heading_rows, TAB_RIGHT,
571 tab_double (tbl, 2, heading_rows + 1, TAB_RIGHT,
575 tab_double (tbl, 2, heading_rows + 2, TAB_RIGHT,
579 tab_double (tbl, 3, heading_rows, TAB_RIGHT,
580 100 * n_valid / (double) total, NULL);
583 tab_double (tbl, 3, heading_rows + 1, TAB_RIGHT,
584 100 * n_missing / (double) total, NULL);
587 tab_double (tbl, 3, heading_rows + 2, TAB_RIGHT,
588 100 * total / (double) total, NULL);
597 reliability_summary_total (const struct reliability *rel)
600 const int n_cols = 5;
601 const int heading_columns = 1;
602 const int heading_rows = 1;
603 const int n_rows = rel->sc[0].n_items + heading_rows ;
605 struct tab_table *tbl = tab_create (n_cols, n_rows);
606 tab_headers (tbl, heading_columns, 0, heading_rows, 0);
608 tab_title (tbl, _("Item-Total Statistics"));
610 /* Vertical lines for the data only */
615 n_cols - 1, n_rows - 1);
617 /* Box around table */
622 n_cols - 1, n_rows - 1);
625 tab_hline (tbl, TAL_2, 0, n_cols - 1, heading_rows);
627 tab_vline (tbl, TAL_2, heading_columns, 0, n_rows - 1);
629 tab_text (tbl, 1, 0, TAB_CENTER | TAT_TITLE,
630 _("Scale Mean if Item Deleted"));
632 tab_text (tbl, 2, 0, TAB_CENTER | TAT_TITLE,
633 _("Scale Variance if Item Deleted"));
635 tab_text (tbl, 3, 0, TAB_CENTER | TAT_TITLE,
636 _("Corrected Item-Total Correlation"));
638 tab_text (tbl, 4, 0, TAB_CENTER | TAT_TITLE,
639 _("Cronbach's Alpha if Item Deleted"));
642 for (i = 0 ; i < rel->sc[0].n_items; ++i)
644 double cov, item_to_total_r;
645 double mean, weight, var;
647 const struct cronbach *s = &rel->sc[rel->total_start + i];
648 tab_text (tbl, 0, heading_rows + i, TAB_LEFT| TAT_TITLE,
649 var_to_string (rel->sc[0].items[i]));
651 moments1_calculate (s->total, &weight, &mean, &var, 0, 0);
653 tab_double (tbl, 1, heading_rows + i, TAB_RIGHT,
656 tab_double (tbl, 2, heading_rows + i, TAB_RIGHT,
657 s->variance_of_sums, NULL);
659 tab_double (tbl, 4, heading_rows + i, TAB_RIGHT,
663 moments1_calculate (rel->sc[0].m[i], &weight, &mean, &var, 0,0);
664 cov = rel->sc[0].variance_of_sums + var - s->variance_of_sums;
667 item_to_total_r = (cov - var) / (sqrt(var) * sqrt (s->variance_of_sums));
670 tab_double (tbl, 3, heading_rows + i, TAB_RIGHT,
671 item_to_total_r, NULL);
679 static void reliability_statistics_model_alpha (struct tab_table *tbl,
680 const struct reliability *rel);
682 static void reliability_statistics_model_split (struct tab_table *tbl,
683 const struct reliability *rel);
686 struct reliability_output_table
692 void (*populate) (struct tab_table *, const struct reliability *);
696 static struct reliability_output_table rol[2] =
698 { 2, 2, 1, 1, reliability_statistics_model_alpha},
699 { 4, 9, 3, 0, reliability_statistics_model_split}
703 reliability_statistics (const struct reliability *rel)
705 int n_cols = rol[rel->model].n_cols;
706 int n_rows = rol[rel->model].n_rows;
707 int heading_columns = rol[rel->model].heading_cols;
708 int heading_rows = rol[rel->model].heading_rows;
710 struct tab_table *tbl = tab_create (n_cols, n_rows);
711 tab_headers (tbl, heading_columns, 0, heading_rows, 0);
713 tab_title (tbl, _("Reliability Statistics"));
715 /* Vertical lines for the data only */
720 n_cols - 1, n_rows - 1);
722 /* Box around table */
727 n_cols - 1, n_rows - 1);
730 tab_hline (tbl, TAL_2, 0, n_cols - 1, heading_rows);
732 tab_vline (tbl, TAL_2, heading_columns, 0, n_rows - 1);
734 if ( rel->model == MODEL_ALPHA )
735 reliability_statistics_model_alpha (tbl, rel);
736 else if (rel->model == MODEL_SPLIT )
737 reliability_statistics_model_split (tbl, rel);
744 reliability_statistics_model_alpha (struct tab_table *tbl,
745 const struct reliability *rel)
747 const struct variable *wv = rel->wv;
748 const struct fmt_spec *wfmt = wv ? var_get_print_format (wv) : & F_8_0;
750 const struct cronbach *s = &rel->sc[0];
752 tab_text (tbl, 0, 0, TAB_CENTER | TAT_TITLE,
753 _("Cronbach's Alpha"));
755 tab_text (tbl, 1, 0, TAB_CENTER | TAT_TITLE,
758 tab_double (tbl, 0, 1, TAB_RIGHT, s->alpha, NULL);
760 tab_double (tbl, 1, 1, TAB_RIGHT, s->n_items, wfmt);
765 reliability_statistics_model_split (struct tab_table *tbl,
766 const struct reliability *rel)
768 const struct variable *wv = rel->wv;
769 const struct fmt_spec *wfmt = wv ? var_get_print_format (wv) : & F_8_0;
771 tab_text (tbl, 0, 0, TAB_LEFT,
772 _("Cronbach's Alpha"));
774 tab_text (tbl, 1, 0, TAB_LEFT,
777 tab_text (tbl, 2, 0, TAB_LEFT,
780 tab_text (tbl, 2, 1, TAB_LEFT,
785 tab_text (tbl, 1, 2, TAB_LEFT,
788 tab_text (tbl, 2, 2, TAB_LEFT,
791 tab_text (tbl, 2, 3, TAB_LEFT,
796 tab_text (tbl, 1, 4, TAB_LEFT,
797 _("Total N of Items"));
799 tab_text (tbl, 0, 5, TAB_LEFT,
800 _("Correlation Between Forms"));
803 tab_text (tbl, 0, 6, TAB_LEFT,
804 _("Spearman-Brown Coefficient"));
806 tab_text (tbl, 1, 6, TAB_LEFT,
809 tab_text (tbl, 1, 7, TAB_LEFT,
810 _("Unequal Length"));
813 tab_text (tbl, 0, 8, TAB_LEFT,
814 _("Guttman Split-Half Coefficient"));
818 tab_double (tbl, 3, 0, TAB_RIGHT, rel->sc[1].alpha, NULL);
819 tab_double (tbl, 3, 2, TAB_RIGHT, rel->sc[2].alpha, NULL);
821 tab_double (tbl, 3, 1, TAB_RIGHT, rel->sc[1].n_items, wfmt);
822 tab_double (tbl, 3, 3, TAB_RIGHT, rel->sc[2].n_items, wfmt);
824 tab_double (tbl, 3, 4, TAB_RIGHT,
825 rel->sc[1].n_items + rel->sc[2].n_items, wfmt);
828 /* R is the correlation between the two parts */
829 double r = rel->sc[0].variance_of_sums -
830 rel->sc[1].variance_of_sums -
831 rel->sc[2].variance_of_sums ;
833 /* Guttman Split Half Coefficient */
834 double g = 2 * r / rel->sc[0].variance_of_sums;
836 /* Unequal Length Spearman Brown Coefficient, and
837 intermediate value used in the computation thereof */
840 r /= sqrt (rel->sc[1].variance_of_sums);
841 r /= sqrt (rel->sc[2].variance_of_sums);
844 tab_double (tbl, 3, 5, TAB_RIGHT, r, NULL);
846 /* Equal length Spearman-Brown Coefficient */
847 tab_double (tbl, 3, 6, TAB_RIGHT, 2 * r / (1.0 + r), NULL);
849 tab_double (tbl, 3, 8, TAB_RIGHT, g, NULL);
851 tmp = (1.0 - r*r) * rel->sc[1].n_items * rel->sc[2].n_items /
852 pow2 (rel->sc[0].n_items);
854 uly = sqrt( pow4 (r) + 4 * pow2 (r) * tmp);
858 tab_double (tbl, 3, 7, TAB_RIGHT, uly, NULL);