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;
146 ds_init_empty (&reliability.scale_name);
149 lex_match (lexer, T_SLASH);
151 if (!lex_force_match_id (lexer, "VARIABLES"))
156 lex_match (lexer, T_EQUALS);
158 if (!parse_variables_const (lexer, dict, &reliability.variables, &reliability.n_variables,
159 PV_NO_DUPLICATE | PV_NUMERIC))
162 if (reliability.n_variables < 2)
163 msg (MW, _("Reliability on a single variable is not useful."));
169 /* Create a default Scale */
171 reliability.n_sc = 1;
172 reliability.sc = xzalloc (sizeof (struct cronbach) * reliability.n_sc);
174 ds_assign_cstr (&reliability.scale_name, "ANY");
176 c = &reliability.sc[0];
177 c->n_items = reliability.n_variables;
178 c->items = xzalloc (sizeof (struct variable*) * c->n_items);
180 for (i = 0 ; i < c->n_items ; ++i)
181 c->items[i] = reliability.variables[i];
186 while (lex_token (lexer) != T_ENDCMD)
188 lex_match (lexer, T_SLASH);
190 if (lex_match_id (lexer, "SCALE"))
192 struct const_var_set *vs;
193 if ( ! lex_force_match (lexer, T_LPAREN))
196 if ( ! lex_force_string (lexer) )
199 ds_assign_substring (&reliability.scale_name, lex_tokss (lexer));
203 if ( ! lex_force_match (lexer, T_RPAREN))
206 lex_match (lexer, T_EQUALS);
208 vs = const_var_set_create_from_array (reliability.variables, reliability.n_variables);
210 free (reliability.sc->items);
211 if (!parse_const_var_set_vars (lexer, vs, &reliability.sc->items, &reliability.sc->n_items, 0))
213 const_var_set_destroy (vs);
217 const_var_set_destroy (vs);
219 else if (lex_match_id (lexer, "MODEL"))
221 lex_match (lexer, T_EQUALS);
222 if (lex_match_id (lexer, "ALPHA"))
224 reliability.model = MODEL_ALPHA;
226 else if (lex_match_id (lexer, "SPLIT"))
228 reliability.model = MODEL_SPLIT;
229 reliability.split_point = -1;
231 if ( lex_match (lexer, T_LPAREN))
233 lex_force_num (lexer);
234 reliability.split_point = lex_number (lexer);
236 lex_force_match (lexer, T_RPAREN);
242 else if (lex_match_id (lexer, "SUMMARY"))
244 lex_match (lexer, T_EQUALS);
245 if (lex_match_id (lexer, "TOTAL"))
247 reliability.summary |= SUMMARY_TOTAL;
249 else if (lex_match (lexer, T_ALL))
251 reliability.summary = 0xFFFF;
256 else if (lex_match_id (lexer, "MISSING"))
258 lex_match (lexer, T_EQUALS);
259 while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
261 if (lex_match_id (lexer, "INCLUDE"))
263 reliability.exclude = MV_SYSTEM;
265 else if (lex_match_id (lexer, "EXCLUDE"))
267 reliability.exclude = MV_ANY;
271 lex_error (lexer, NULL);
278 lex_error (lexer, NULL);
283 if ( reliability.model == MODEL_SPLIT)
286 const struct cronbach *s;
288 if ( reliability.split_point >= reliability.n_variables)
290 msg (ME, _("The split point must be less than the number of variables"));
294 reliability.n_sc += 2 ;
295 reliability.sc = xrealloc (reliability.sc, sizeof (struct cronbach) * reliability.n_sc);
297 s = &reliability.sc[0];
299 reliability.sc[1].n_items =
300 (reliability.split_point == -1) ? s->n_items / 2 : reliability.split_point;
302 reliability.sc[2].n_items = s->n_items - reliability.sc[1].n_items;
303 reliability.sc[1].items = xzalloc (sizeof (struct variable *)
304 * reliability.sc[1].n_items);
306 reliability.sc[2].items = xzalloc (sizeof (struct variable *) *
307 reliability.sc[2].n_items);
309 for (i = 0; i < reliability.sc[1].n_items ; ++i)
310 reliability.sc[1].items[i] = s->items[i];
312 while (i < s->n_items)
314 reliability.sc[2].items[i - reliability.sc[1].n_items] = s->items[i];
319 if ( reliability.summary & SUMMARY_TOTAL)
322 const int base_sc = reliability.n_sc;
324 reliability.total_start = base_sc;
326 reliability.n_sc += reliability.sc[0].n_items ;
327 reliability.sc = xrealloc (reliability.sc, sizeof (struct cronbach) * reliability.n_sc);
330 for (i = 0 ; i < reliability.sc[0].n_items; ++i )
334 struct cronbach *s = &reliability.sc[i + base_sc];
336 s->n_items = reliability.sc[0].n_items - 1;
337 s->items = xzalloc (sizeof (struct variable *) * s->n_items);
338 for (v_src = 0 ; v_src < reliability.sc[0].n_items ; ++v_src)
341 s->items[v_dest++] = reliability.sc[0].items[v_src];
347 if ( ! run_reliability (ds, &reliability))
350 reliability_destroy (&reliability);
354 reliability_destroy (&reliability);
360 do_reliability (struct casereader *group, struct dataset *ds,
361 const struct reliability *rel);
364 static void reliability_summary_total (const struct reliability *rel);
366 static void reliability_statistics (const struct reliability *rel);
370 run_reliability (struct dataset *ds, const struct reliability *reliability)
372 struct dictionary *dict = dataset_dict (ds);
374 struct casereader *group;
376 struct casegrouper *grouper = casegrouper_create_splits (proc_open (ds), dict);
378 while (casegrouper_get_next_group (grouper, &group))
380 do_reliability (group, ds, reliability);
382 reliability_statistics (reliability);
384 if (reliability->summary & SUMMARY_TOTAL )
385 reliability_summary_total (reliability);
388 ok = casegrouper_destroy (grouper);
389 ok = proc_commit (ds) && ok;
398 /* Return the sum of all the item variables in S */
400 append_sum (const struct ccase *c, casenumber n UNUSED, void *aux)
403 const struct cronbach *s = aux;
406 for (v = 0 ; v < s->n_items; ++v)
408 sum += case_data (c, s->items[v])->f;
415 case_processing_summary (casenumber n_valid, casenumber n_missing,
416 const struct dictionary *dict);
420 alpha (int k, double sum_of_variances, double variance_of_sums)
422 return k / ( k - 1.0) * ( 1 - sum_of_variances / variance_of_sums);
426 do_reliability (struct casereader *input, struct dataset *ds,
427 const struct reliability *rel)
432 casenumber n_missing ;
433 casenumber n_valid = 0;
436 for (si = 0 ; si < rel->n_sc; ++si)
438 struct cronbach *s = &rel->sc[si];
440 s->m = xzalloc (sizeof (s->m) * s->n_items);
441 s->total = moments1_create (MOMENT_VARIANCE);
443 for (i = 0 ; i < s->n_items ; ++i )
444 s->m[i] = moments1_create (MOMENT_VARIANCE);
447 input = casereader_create_filter_missing (input,
454 for (si = 0 ; si < rel->n_sc; ++si)
456 struct cronbach *s = &rel->sc[si];
459 s->totals_idx = caseproto_get_n_widths (casereader_get_proto (input));
461 casereader_create_append_numeric (input, append_sum,
465 for (; (c = casereader_read (input)) != NULL; case_unref (c))
470 for (si = 0; si < rel->n_sc; ++si)
472 struct cronbach *s = &rel->sc[si];
474 for (i = 0 ; i < s->n_items ; ++i )
475 moments1_add (s->m[i], case_data (c, s->items[i])->f, weight);
477 moments1_add (s->total, case_data_idx (c, s->totals_idx)->f, weight);
480 casereader_destroy (input);
482 for (si = 0; si < rel->n_sc; ++si)
484 struct cronbach *s = &rel->sc[si];
486 s->sum_of_variances = 0;
487 for (i = 0 ; i < s->n_items ; ++i )
489 double weight, mean, variance;
490 moments1_calculate (s->m[i], &weight, &mean, &variance, NULL, NULL);
492 s->sum_of_variances += variance;
495 moments1_calculate (s->total, NULL, NULL, &s->variance_of_sums,
499 alpha (s->n_items, s->sum_of_variances, s->variance_of_sums);
502 text_item_submit (text_item_create_format (TEXT_ITEM_PARAGRAPH, _("Scale: %s"),
503 ds_cstr (&rel->scale_name)));
505 case_processing_summary (n_valid, n_missing, dataset_dict (ds));
513 case_processing_summary (casenumber n_valid, casenumber n_missing,
514 const struct dictionary *dict)
516 const struct variable *wv = dict_get_weight (dict);
517 const struct fmt_spec *wfmt = wv ? var_get_print_format (wv) : & F_8_0;
522 int heading_columns = 2;
523 int heading_rows = 1;
524 struct tab_table *tbl;
525 tbl = tab_create (n_cols, n_rows);
526 tab_headers (tbl, heading_columns, 0, heading_rows, 0);
528 tab_title (tbl, _("Case Processing Summary"));
530 /* Vertical lines for the data only */
535 n_cols - 1, n_rows - 1);
537 /* Box around table */
542 n_cols - 1, n_rows - 1);
545 tab_hline (tbl, TAL_2, 0, n_cols - 1, heading_rows);
547 tab_vline (tbl, TAL_2, heading_columns, 0, n_rows - 1);
550 tab_text (tbl, 0, heading_rows, TAB_LEFT | TAT_TITLE,
553 tab_text (tbl, 1, heading_rows, TAB_LEFT | TAT_TITLE,
556 tab_text (tbl, 1, heading_rows + 1, TAB_LEFT | TAT_TITLE,
559 tab_text (tbl, 1, heading_rows + 2, TAB_LEFT | TAT_TITLE,
562 tab_text (tbl, heading_columns, 0, TAB_CENTER | TAT_TITLE,
565 tab_text (tbl, heading_columns + 1, 0, TAB_CENTER | TAT_TITLE, _("%"));
567 total = n_missing + n_valid;
569 tab_double (tbl, 2, heading_rows, TAB_RIGHT,
573 tab_double (tbl, 2, heading_rows + 1, TAB_RIGHT,
577 tab_double (tbl, 2, heading_rows + 2, TAB_RIGHT,
581 tab_double (tbl, 3, heading_rows, TAB_RIGHT,
582 100 * n_valid / (double) total, NULL);
585 tab_double (tbl, 3, heading_rows + 1, TAB_RIGHT,
586 100 * n_missing / (double) total, NULL);
589 tab_double (tbl, 3, heading_rows + 2, TAB_RIGHT,
590 100 * total / (double) total, NULL);
599 reliability_summary_total (const struct reliability *rel)
602 const int n_cols = 5;
603 const int heading_columns = 1;
604 const int heading_rows = 1;
605 const int n_rows = rel->sc[0].n_items + heading_rows ;
607 struct tab_table *tbl = tab_create (n_cols, n_rows);
608 tab_headers (tbl, heading_columns, 0, heading_rows, 0);
610 tab_title (tbl, _("Item-Total Statistics"));
612 /* Vertical lines for the data only */
617 n_cols - 1, n_rows - 1);
619 /* Box around table */
624 n_cols - 1, n_rows - 1);
627 tab_hline (tbl, TAL_2, 0, n_cols - 1, heading_rows);
629 tab_vline (tbl, TAL_2, heading_columns, 0, n_rows - 1);
631 tab_text (tbl, 1, 0, TAB_CENTER | TAT_TITLE,
632 _("Scale Mean if Item Deleted"));
634 tab_text (tbl, 2, 0, TAB_CENTER | TAT_TITLE,
635 _("Scale Variance if Item Deleted"));
637 tab_text (tbl, 3, 0, TAB_CENTER | TAT_TITLE,
638 _("Corrected Item-Total Correlation"));
640 tab_text (tbl, 4, 0, TAB_CENTER | TAT_TITLE,
641 _("Cronbach's Alpha if Item Deleted"));
644 for (i = 0 ; i < rel->sc[0].n_items; ++i)
646 double cov, item_to_total_r;
647 double mean, weight, var;
649 const struct cronbach *s = &rel->sc[rel->total_start + i];
650 tab_text (tbl, 0, heading_rows + i, TAB_LEFT| TAT_TITLE,
651 var_to_string (rel->sc[0].items[i]));
653 moments1_calculate (s->total, &weight, &mean, &var, 0, 0);
655 tab_double (tbl, 1, heading_rows + i, TAB_RIGHT,
658 tab_double (tbl, 2, heading_rows + i, TAB_RIGHT,
659 s->variance_of_sums, NULL);
661 tab_double (tbl, 4, heading_rows + i, TAB_RIGHT,
665 moments1_calculate (rel->sc[0].m[i], &weight, &mean, &var, 0,0);
666 cov = rel->sc[0].variance_of_sums + var - s->variance_of_sums;
669 item_to_total_r = (cov - var) / (sqrt(var) * sqrt (s->variance_of_sums));
672 tab_double (tbl, 3, heading_rows + i, TAB_RIGHT,
673 item_to_total_r, NULL);
681 static void reliability_statistics_model_alpha (struct tab_table *tbl,
682 const struct reliability *rel);
684 static void reliability_statistics_model_split (struct tab_table *tbl,
685 const struct reliability *rel);
688 struct reliability_output_table
694 void (*populate) (struct tab_table *, const struct reliability *);
698 static struct reliability_output_table rol[2] =
700 { 2, 2, 1, 1, reliability_statistics_model_alpha},
701 { 4, 9, 3, 0, reliability_statistics_model_split}
705 reliability_statistics (const struct reliability *rel)
707 int n_cols = rol[rel->model].n_cols;
708 int n_rows = rol[rel->model].n_rows;
709 int heading_columns = rol[rel->model].heading_cols;
710 int heading_rows = rol[rel->model].heading_rows;
712 struct tab_table *tbl = tab_create (n_cols, n_rows);
713 tab_headers (tbl, heading_columns, 0, heading_rows, 0);
715 tab_title (tbl, _("Reliability Statistics"));
717 /* Vertical lines for the data only */
722 n_cols - 1, n_rows - 1);
724 /* Box around table */
729 n_cols - 1, n_rows - 1);
732 tab_hline (tbl, TAL_2, 0, n_cols - 1, heading_rows);
734 tab_vline (tbl, TAL_2, heading_columns, 0, n_rows - 1);
736 if ( rel->model == MODEL_ALPHA )
737 reliability_statistics_model_alpha (tbl, rel);
738 else if (rel->model == MODEL_SPLIT )
739 reliability_statistics_model_split (tbl, rel);
746 reliability_statistics_model_alpha (struct tab_table *tbl,
747 const struct reliability *rel)
749 const struct variable *wv = rel->wv;
750 const struct fmt_spec *wfmt = wv ? var_get_print_format (wv) : & F_8_0;
752 const struct cronbach *s = &rel->sc[0];
754 tab_text (tbl, 0, 0, TAB_CENTER | TAT_TITLE,
755 _("Cronbach's Alpha"));
757 tab_text (tbl, 1, 0, TAB_CENTER | TAT_TITLE,
760 tab_double (tbl, 0, 1, TAB_RIGHT, s->alpha, NULL);
762 tab_double (tbl, 1, 1, TAB_RIGHT, s->n_items, wfmt);
767 reliability_statistics_model_split (struct tab_table *tbl,
768 const struct reliability *rel)
770 const struct variable *wv = rel->wv;
771 const struct fmt_spec *wfmt = wv ? var_get_print_format (wv) : & F_8_0;
773 tab_text (tbl, 0, 0, TAB_LEFT,
774 _("Cronbach's Alpha"));
776 tab_text (tbl, 1, 0, TAB_LEFT,
779 tab_text (tbl, 2, 0, TAB_LEFT,
782 tab_text (tbl, 2, 1, TAB_LEFT,
787 tab_text (tbl, 1, 2, TAB_LEFT,
790 tab_text (tbl, 2, 2, TAB_LEFT,
793 tab_text (tbl, 2, 3, TAB_LEFT,
798 tab_text (tbl, 1, 4, TAB_LEFT,
799 _("Total N of Items"));
801 tab_text (tbl, 0, 5, TAB_LEFT,
802 _("Correlation Between Forms"));
805 tab_text (tbl, 0, 6, TAB_LEFT,
806 _("Spearman-Brown Coefficient"));
808 tab_text (tbl, 1, 6, TAB_LEFT,
811 tab_text (tbl, 1, 7, TAB_LEFT,
812 _("Unequal Length"));
815 tab_text (tbl, 0, 8, TAB_LEFT,
816 _("Guttman Split-Half Coefficient"));
820 tab_double (tbl, 3, 0, TAB_RIGHT, rel->sc[1].alpha, NULL);
821 tab_double (tbl, 3, 2, TAB_RIGHT, rel->sc[2].alpha, NULL);
823 tab_double (tbl, 3, 1, TAB_RIGHT, rel->sc[1].n_items, wfmt);
824 tab_double (tbl, 3, 3, TAB_RIGHT, rel->sc[2].n_items, wfmt);
826 tab_double (tbl, 3, 4, TAB_RIGHT,
827 rel->sc[1].n_items + rel->sc[2].n_items, wfmt);
830 /* R is the correlation between the two parts */
831 double r = rel->sc[0].variance_of_sums -
832 rel->sc[1].variance_of_sums -
833 rel->sc[2].variance_of_sums ;
835 /* Guttman Split Half Coefficient */
836 double g = 2 * r / rel->sc[0].variance_of_sums;
838 /* Unequal Length Spearman Brown Coefficient, and
839 intermediate value used in the computation thereof */
842 r /= sqrt (rel->sc[1].variance_of_sums);
843 r /= sqrt (rel->sc[2].variance_of_sums);
846 tab_double (tbl, 3, 5, TAB_RIGHT, r, NULL);
848 /* Equal length Spearman-Brown Coefficient */
849 tab_double (tbl, 3, 6, TAB_RIGHT, 2 * r / (1.0 + r), NULL);
851 tab_double (tbl, 3, 8, TAB_RIGHT, g, NULL);
853 tmp = (1.0 - r*r) * rel->sc[1].n_items * rel->sc[2].n_items /
854 pow2 (rel->sc[0].n_items);
856 uly = sqrt( pow4 (r) + 4 * pow2 (r) * tmp);
860 tab_double (tbl, 3, 7, TAB_RIGHT, uly, NULL);