--- /dev/null
+/* PSPP - a program for statistical analysis.
+ Copyright (C) 1997-9, 2000, 2007, 2009, 2010, 2011, 2012, 2013, 2014,
+ 2020 Free Software Foundation, Inc.
+
+ This program is free software: you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation, either version 3 of the License, or
+ (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program. If not, see <http://www.gnu.org/licenses/>. */
+
+#include <config.h>
+
+#include <float.h>
+#include <gsl/gsl_cdf.h>
+#include <gsl/gsl_matrix.h>
+#include <math.h>
+
+#include "data/case.h"
+#include "data/casegrouper.h"
+#include "data/casereader.h"
+#include "data/dataset.h"
+#include "data/dictionary.h"
+#include "data/format.h"
+#include "data/value.h"
+#include "language/command.h"
+#include "language/commands/split-file.h"
+#include "language/lexer/lexer.h"
+#include "language/lexer/value-parser.h"
+#include "language/lexer/variable-parser.h"
+#include "libpspp/ll.h"
+#include "libpspp/message.h"
+#include "libpspp/misc.h"
+#include "libpspp/taint.h"
+#include "linreg/sweep.h"
+#include "tukey/tukey.h"
+#include "math/categoricals.h"
+#include "math/interaction.h"
+#include "math/covariance.h"
+#include "math/levene.h"
+#include "math/moments.h"
+#include "output/pivot-table.h"
+
+#include "gettext.h"
+#define _(msgid) gettext (msgid)
+#define N_(msgid) msgid
+
+/* Workspace variable for each dependent variable */
+struct per_var_ws
+ {
+ struct interaction *iact;
+ struct categoricals *cat;
+ struct covariance *cov;
+ struct levene *nl;
+
+ double n;
+
+ double sst;
+ double sse;
+ double ssa;
+
+ int n_groups;
+
+ double mse;
+ };
+
+/* Per category data */
+struct descriptive_data
+ {
+ const struct variable *var;
+ struct moments1 *mom;
+
+ double minimum;
+ double maximum;
+ };
+
+enum missing_type
+ {
+ MISS_LISTWISE,
+ MISS_ANALYSIS,
+ };
+
+struct coeff_node
+{
+ struct ll ll;
+ double coeff;
+};
+
+
+struct contrasts_node
+{
+ struct ll ll;
+ struct ll_list coefficient_list;
+};
+
+
+struct oneway_spec;
+
+typedef double df_func (const struct per_var_ws *pvw, const struct moments1 *mom_i, const struct moments1 *mom_j);
+typedef double ts_func (int k, const struct moments1 *mom_i, const struct moments1 *mom_j, double std_err);
+typedef double p1tail_func (double ts, double df1, double df2);
+
+typedef double pinv_func (double std_err, double alpha, double df, int k, const struct moments1 *mom_i, const struct moments1 *mom_j);
+
+
+struct posthoc
+{
+ const char *syntax;
+ const char *label;
+
+ df_func *dff;
+ ts_func *tsf;
+ p1tail_func *p1f;
+
+ pinv_func *pinv;
+};
+
+struct oneway_spec
+{
+ size_t n_vars;
+ const struct variable **vars;
+
+ const struct variable *indep_var;
+
+ bool descriptive_stats;
+ bool homogeneity_stats;
+
+ enum missing_type missing_type;
+ enum mv_class exclude;
+
+ /* List of contrasts */
+ struct ll_list contrast_list;
+
+ /* The weight variable */
+ const struct variable *wv;
+ const struct fmt_spec *wfmt;
+
+ /* The confidence level for multiple comparisons */
+ double alpha;
+
+ int *posthoc;
+ int n_posthoc;
+};
+
+static double
+df_common (const struct per_var_ws *pvw, const struct moments1 *mom_i UNUSED, const struct moments1 *mom_j UNUSED)
+{
+ return pvw->n - pvw->n_groups;
+}
+
+static double
+df_individual (const struct per_var_ws *pvw UNUSED, const struct moments1 *mom_i, const struct moments1 *mom_j)
+{
+ double n_i, var_i;
+ double n_j, var_j;
+ double nom,denom;
+
+ moments1_calculate (mom_i, &n_i, NULL, &var_i, 0, 0);
+ moments1_calculate (mom_j, &n_j, NULL, &var_j, 0, 0);
+
+ if (n_i <= 1.0 || n_j <= 1.0)
+ return SYSMIS;
+
+ nom = pow2 (var_i/n_i + var_j/n_j);
+ denom = pow2 (var_i/n_i) / (n_i - 1) + pow2 (var_j/n_j) / (n_j - 1);
+
+ return nom / denom;
+}
+
+static double lsd_pinv (double std_err, double alpha, double df, int k UNUSED, const struct moments1 *mom_i UNUSED, const struct moments1 *mom_j UNUSED)
+{
+ return std_err * gsl_cdf_tdist_Pinv (1.0 - alpha / 2.0, df);
+}
+
+static double bonferroni_pinv (double std_err, double alpha, double df, int k, const struct moments1 *mom_i UNUSED, const struct moments1 *mom_j UNUSED)
+{
+ const int m = k * (k - 1) / 2;
+ return std_err * gsl_cdf_tdist_Pinv (1.0 - alpha / (2.0 * m), df);
+}
+
+static double sidak_pinv (double std_err, double alpha, double df, int k, const struct moments1 *mom_i UNUSED, const struct moments1 *mom_j UNUSED)
+{
+ const double m = k * (k - 1) / 2;
+ double lp = 1.0 - exp (log (1.0 - alpha) / m);
+ return std_err * gsl_cdf_tdist_Pinv (1.0 - lp / 2.0, df);
+}
+
+static double tukey_pinv (double std_err, double alpha, double df, int k, const struct moments1 *mom_i UNUSED, const struct moments1 *mom_j UNUSED)
+{
+ if (k < 2 || df < 2)
+ return SYSMIS;
+
+ return std_err / sqrt (2.0) * qtukey (1 - alpha, 1.0, k, df, 1, 0);
+}
+
+static double scheffe_pinv (double std_err, double alpha, double df, int k, const struct moments1 *mom_i UNUSED, const struct moments1 *mom_j UNUSED)
+{
+ double x = (k - 1) * gsl_cdf_fdist_Pinv (1.0 - alpha, k - 1, df);
+ return std_err * sqrt (x);
+}
+
+static double gh_pinv (double std_err UNUSED, double alpha, double df, int k, const struct moments1 *mom_i, const struct moments1 *mom_j)
+{
+ double n_i, mean_i, var_i;
+ double n_j, mean_j, var_j;
+ double m;
+
+ moments1_calculate (mom_i, &n_i, &mean_i, &var_i, 0, 0);
+ moments1_calculate (mom_j, &n_j, &mean_j, &var_j, 0, 0);
+
+ m = sqrt ((var_i/n_i + var_j/n_j) / 2.0);
+
+ if (k < 2 || df < 2)
+ return SYSMIS;
+
+ return m * qtukey (1 - alpha, 1.0, k, df, 1, 0);
+}
+
+
+static double
+multiple_comparison_sig (double std_err,
+ const struct per_var_ws *pvw,
+ const struct descriptive_data *dd_i, const struct descriptive_data *dd_j,
+ const struct posthoc *ph)
+{
+ int k = pvw->n_groups;
+ double df = ph->dff (pvw, dd_i->mom, dd_j->mom);
+ double ts = ph->tsf (k, dd_i->mom, dd_j->mom, std_err);
+ if (df == SYSMIS)
+ return SYSMIS;
+ return ph->p1f (ts, k - 1, df);
+}
+
+static double
+mc_half_range (const struct oneway_spec *cmd, const struct per_var_ws *pvw, double std_err, const struct descriptive_data *dd_i, const struct descriptive_data *dd_j, const struct posthoc *ph)
+{
+ int k = pvw->n_groups;
+ double df = ph->dff (pvw, dd_i->mom, dd_j->mom);
+ if (df == SYSMIS)
+ return SYSMIS;
+
+ return ph->pinv (std_err, cmd->alpha, df, k, dd_i->mom, dd_j->mom);
+}
+
+static double tukey_1tailsig (double ts, double df1, double df2)
+{
+ double twotailedsig;
+
+ if (df2 < 2 || df1 < 1)
+ return SYSMIS;
+
+ twotailedsig = 1.0 - ptukey (ts, 1.0, df1 + 1, df2, 1, 0);
+
+ return twotailedsig / 2.0;
+}
+
+static double lsd_1tailsig (double ts, double df1 UNUSED, double df2)
+{
+ return ts < 0 ? gsl_cdf_tdist_P (ts, df2) : gsl_cdf_tdist_Q (ts, df2);
+}
+
+static double sidak_1tailsig (double ts, double df1, double df2)
+{
+ double ex = (df1 + 1.0) * df1 / 2.0;
+ double lsd_sig = 2 * lsd_1tailsig (ts, df1, df2);
+
+ return 0.5 * (1.0 - pow (1.0 - lsd_sig, ex));
+}
+
+static double bonferroni_1tailsig (double ts, double df1, double df2)
+{
+ const int m = (df1 + 1) * df1 / 2;
+
+ double p = ts < 0 ? gsl_cdf_tdist_P (ts, df2) : gsl_cdf_tdist_Q (ts, df2);
+ p *= m;
+
+ return p > 0.5 ? 0.5 : p;
+}
+
+static double scheffe_1tailsig (double ts, double df1, double df2)
+{
+ return 0.5 * gsl_cdf_fdist_Q (ts, df1, df2);
+}
+
+
+static double tukey_test_stat (int k UNUSED, const struct moments1 *mom_i, const struct moments1 *mom_j, double std_err)
+{
+ double ts;
+ double n_i, mean_i, var_i;
+ double n_j, mean_j, var_j;
+
+ moments1_calculate (mom_i, &n_i, &mean_i, &var_i, 0, 0);
+ moments1_calculate (mom_j, &n_j, &mean_j, &var_j, 0, 0);
+
+ ts = (mean_i - mean_j) / std_err;
+ ts = fabs (ts) * sqrt (2.0);
+
+ return ts;
+}
+
+static double lsd_test_stat (int k UNUSED, const struct moments1 *mom_i, const struct moments1 *mom_j, double std_err)
+{
+ double n_i, mean_i, var_i;
+ double n_j, mean_j, var_j;
+
+ moments1_calculate (mom_i, &n_i, &mean_i, &var_i, 0, 0);
+ moments1_calculate (mom_j, &n_j, &mean_j, &var_j, 0, 0);
+
+ return (mean_i - mean_j) / std_err;
+}
+
+static double scheffe_test_stat (int k, const struct moments1 *mom_i, const struct moments1 *mom_j, double std_err)
+{
+ double t;
+ double n_i, mean_i, var_i;
+ double n_j, mean_j, var_j;
+
+ moments1_calculate (mom_i, &n_i, &mean_i, &var_i, 0, 0);
+ moments1_calculate (mom_j, &n_j, &mean_j, &var_j, 0, 0);
+
+ t = (mean_i - mean_j) / std_err;
+ t = pow2 (t);
+ t /= k - 1;
+
+ return t;
+}
+
+static double gh_test_stat (int k UNUSED, const struct moments1 *mom_i, const struct moments1 *mom_j, double std_err UNUSED)
+{
+ double ts;
+ double thing;
+ double n_i, mean_i, var_i;
+ double n_j, mean_j, var_j;
+
+ moments1_calculate (mom_i, &n_i, &mean_i, &var_i, 0, 0);
+ moments1_calculate (mom_j, &n_j, &mean_j, &var_j, 0, 0);
+
+ thing = var_i / n_i + var_j / n_j;
+ thing /= 2.0;
+ thing = sqrt (thing);
+
+ ts = (mean_i - mean_j) / thing;
+
+ return fabs (ts);
+}
+
+
+
+static const struct posthoc ph_tests [] =
+ {
+ { "LSD", N_("LSD"), df_common, lsd_test_stat, lsd_1tailsig, lsd_pinv},
+ { "TUKEY", N_("Tukey HSD"), df_common, tukey_test_stat, tukey_1tailsig, tukey_pinv},
+ { "BONFERRONI", N_("Bonferroni"), df_common, lsd_test_stat, bonferroni_1tailsig, bonferroni_pinv},
+ { "SCHEFFE", N_("Scheffé"), df_common, scheffe_test_stat, scheffe_1tailsig, scheffe_pinv},
+ { "GH", N_("Games-Howell"), df_individual, gh_test_stat, tukey_1tailsig, gh_pinv},
+ { "SIDAK", N_("Šidák"), df_common, lsd_test_stat, sidak_1tailsig, sidak_pinv}
+ };
+
+
+struct oneway_workspace
+{
+ /* The number of distinct values of the independent variable, when all
+ missing values are disregarded */
+ int actual_number_of_groups;
+
+ struct per_var_ws *vws;
+
+ /* An array of descriptive data. One for each dependent variable */
+ struct descriptive_data **dd_total;
+};
+
+/* Routines to show the output tables */
+static void show_anova_table (const struct oneway_spec *, const struct oneway_workspace *);
+static void show_descriptives (const struct oneway_spec *, const struct oneway_workspace *);
+static void show_homogeneity (const struct oneway_spec *, const struct oneway_workspace *);
+
+static void output_oneway (const struct oneway_spec *, struct oneway_workspace *ws);
+static void run_oneway (const struct oneway_spec *cmd, struct casereader *input, const struct dataset *ds);
+
+
+static void
+destroy_coeff_list (struct contrasts_node *coeff_list)
+{
+ struct coeff_node *cn = NULL;
+ struct coeff_node *cnx = NULL;
+ struct ll_list *cl = &coeff_list->coefficient_list;
+
+ ll_for_each_safe (cn, cnx, struct coeff_node, ll, cl)
+ {
+ free (cn);
+ }
+
+ free (coeff_list);
+}
+
+static void
+oneway_cleanup (struct oneway_spec *cmd)
+{
+ struct contrasts_node *coeff_list = NULL;
+ struct contrasts_node *coeff_next = NULL;
+ ll_for_each_safe (coeff_list, coeff_next, struct contrasts_node, ll, &cmd->contrast_list)
+ {
+ destroy_coeff_list (coeff_list);
+ }
+
+ free (cmd->posthoc);
+}
+
+
+
+int
+cmd_oneway (struct lexer *lexer, struct dataset *ds)
+{
+ const struct dictionary *dict = dataset_dict (ds);
+ struct oneway_spec oneway = {
+ .missing_type = MISS_ANALYSIS,
+ .exclude = MV_ANY,
+ .wv = dict_get_weight (dict),
+ .wfmt = dict_get_weight_format (dict),
+ .alpha = 0.05,
+ };
+
+ ll_init (&oneway.contrast_list);
+ if (lex_match (lexer, T_SLASH))
+ {
+ if (!lex_force_match_id (lexer, "VARIABLES"))
+ goto error;
+ lex_match (lexer, T_EQUALS);
+ }
+
+ if (!parse_variables_const (lexer, dict,
+ &oneway.vars, &oneway.n_vars,
+ PV_NO_DUPLICATE | PV_NUMERIC))
+ goto error;
+
+ if (!lex_force_match (lexer, T_BY))
+ goto error;
+
+ oneway.indep_var = parse_variable_const (lexer, dict);
+ if (oneway.indep_var == NULL)
+ goto error;
+
+ while (lex_token (lexer) != T_ENDCMD)
+ {
+ lex_match (lexer, T_SLASH);
+
+ if (lex_match_id (lexer, "STATISTICS"))
+ {
+ lex_match (lexer, T_EQUALS);
+ while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
+ {
+ if (lex_match_id (lexer, "DESCRIPTIVES"))
+ oneway.descriptive_stats = true;
+ else if (lex_match_id (lexer, "HOMOGENEITY"))
+ oneway.homogeneity_stats = true;
+ else
+ {
+ lex_error_expecting (lexer, "DESCRIPTIVES", "HOMOGENEITY");
+ goto error;
+ }
+ }
+ }
+ else if (lex_match_id (lexer, "POSTHOC"))
+ {
+ lex_match (lexer, T_EQUALS);
+ while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
+ {
+ bool method = false;
+ for (size_t p = 0; p < sizeof ph_tests / sizeof *ph_tests; ++p)
+ if (lex_match_id (lexer, ph_tests[p].syntax))
+ {
+ oneway.n_posthoc++;
+ oneway.posthoc = xrealloc (oneway.posthoc, sizeof (*oneway.posthoc) * oneway.n_posthoc);
+ oneway.posthoc[oneway.n_posthoc - 1] = p;
+ method = true;
+ break;
+ }
+ if (method == false)
+ {
+ if (lex_match_id (lexer, "ALPHA"))
+ {
+ if (!lex_force_match (lexer, T_LPAREN)
+ || !lex_force_num (lexer))
+ goto error;
+ oneway.alpha = lex_number (lexer);
+ lex_get (lexer);
+ if (!lex_force_match (lexer, T_RPAREN))
+ goto error;
+ }
+ else
+ {
+ lex_error (lexer, _("Unknown post hoc analysis method."));
+ goto error;
+ }
+ }
+ }
+ }
+ else if (lex_match_id (lexer, "CONTRAST"))
+ {
+ struct contrasts_node *cl = XZALLOC (struct contrasts_node);
+
+ struct ll_list *coefficient_list = &cl->coefficient_list;
+ lex_match (lexer, T_EQUALS);
+
+ ll_init (coefficient_list);
+
+ while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
+ {
+ if (!lex_force_num (lexer))
+ {
+ destroy_coeff_list (cl);
+ goto error;
+ }
+
+ struct coeff_node *cc = xmalloc (sizeof *cc);
+ cc->coeff = lex_number (lexer);
+
+ ll_push_tail (coefficient_list, &cc->ll);
+ lex_get (lexer);
+ }
+
+ if (ll_count (coefficient_list) <= 0)
+ {
+ destroy_coeff_list (cl);
+ goto error;
+ }
+
+ ll_push_tail (&oneway.contrast_list, &cl->ll);
+ }
+ else if (lex_match_id (lexer, "MISSING"))
+ {
+ lex_match (lexer, T_EQUALS);
+ while (lex_token (lexer) != T_ENDCMD && lex_token (lexer) != T_SLASH)
+ {
+ if (lex_match_id (lexer, "INCLUDE"))
+ oneway.exclude = MV_SYSTEM;
+ else if (lex_match_id (lexer, "EXCLUDE"))
+ oneway.exclude = MV_ANY;
+ else if (lex_match_id (lexer, "LISTWISE"))
+ oneway.missing_type = MISS_LISTWISE;
+ else if (lex_match_id (lexer, "ANALYSIS"))
+ oneway.missing_type = MISS_ANALYSIS;
+ else
+ {
+ lex_error_expecting (lexer, "INCLUDE", "EXCLUDE",
+ "LISTWISE", "ANALYSIS");
+ goto error;
+ }
+ }
+ }
+ else
+ {
+ lex_error_expecting (lexer, "STATISTICS", "POSTHOC", "CONTRAST",
+ "MISSING");
+ goto error;
+ }
+ }
+
+ struct casegrouper *grouper = casegrouper_create_splits (proc_open (ds), dict);
+ struct casereader *group;
+ while (casegrouper_get_next_group (grouper, &group))
+ run_oneway (&oneway, group, ds);
+ bool ok = casegrouper_destroy (grouper);
+ ok = proc_commit (ds) && ok;
+
+ oneway_cleanup (&oneway);
+ free (oneway.vars);
+ return CMD_SUCCESS;
+
+ error:
+ oneway_cleanup (&oneway);
+ free (oneway.vars);
+ return CMD_FAILURE;
+}
+\f
+static struct descriptive_data *
+dd_create (const struct variable *var)
+{
+ struct descriptive_data *dd = xmalloc (sizeof *dd);
+
+ dd->mom = moments1_create (MOMENT_VARIANCE);
+ dd->minimum = DBL_MAX;
+ dd->maximum = -DBL_MAX;
+ dd->var = var;
+
+ return dd;
+}
+
+static void
+dd_destroy (struct descriptive_data *dd)
+{
+ moments1_destroy (dd->mom);
+ free (dd);
+}
+
+static void *
+makeit (const void *aux1, void *aux2 UNUSED)
+{
+ const struct variable *var = aux1;
+
+ struct descriptive_data *dd = dd_create (var);
+
+ return dd;
+}
+
+static void
+killit (const void *aux1 UNUSED, void *aux2 UNUSED, void *user_data)
+{
+ struct descriptive_data *dd = user_data;
+
+ dd_destroy (dd);
+}
+
+
+static void
+updateit (const void *aux1, void *aux2, void *user_data,
+ const struct ccase *c, double weight)
+{
+ struct descriptive_data *dd = user_data;
+
+ const struct variable *varp = aux1;
+
+ const union value *valx = case_data (c, varp);
+
+ struct descriptive_data *dd_total = aux2;
+
+ moments1_add (dd->mom, valx->f, weight);
+ if (valx->f < dd->minimum)
+ dd->minimum = valx->f;
+
+ if (valx->f > dd->maximum)
+ dd->maximum = valx->f;
+
+ {
+ const struct variable *var = dd_total->var;
+ const union value *val = case_data (c, var);
+
+ moments1_add (dd_total->mom,
+ val->f,
+ weight);
+
+ if (val->f < dd_total->minimum)
+ dd_total->minimum = val->f;
+
+ if (val->f > dd_total->maximum)
+ dd_total->maximum = val->f;
+ }
+}
+
+static void
+run_oneway (const struct oneway_spec *cmd, struct casereader *input,
+ const struct dataset *ds)
+{
+ struct dictionary *dict = dataset_dict (ds);
+ struct oneway_workspace ws = {
+ .vws = xcalloc (cmd->n_vars, sizeof *ws.vws),
+ .dd_total = XCALLOC (cmd->n_vars, struct descriptive_data *),
+ };
+
+ for (size_t v = 0; v < cmd->n_vars; ++v)
+ ws.dd_total[v] = dd_create (cmd->vars[v]);
+
+ for (size_t v = 0; v < cmd->n_vars; ++v)
+ {
+ static const struct payload payload =
+ {
+ .create = makeit,
+ .update = updateit,
+ .destroy = killit,
+ };
+
+ ws.vws[v].iact = interaction_create (cmd->indep_var);
+ ws.vws[v].cat = categoricals_create (&ws.vws[v].iact, 1, cmd->wv,
+ cmd->exclude);
+
+ categoricals_set_payload (ws.vws[v].cat, &payload,
+ CONST_CAST (struct variable *, cmd->vars[v]),
+ ws.dd_total[v]);
+
+
+ ws.vws[v].cov = covariance_2pass_create (1, &cmd->vars[v],
+ ws.vws[v].cat,
+ cmd->wv, cmd->exclude, true);
+ ws.vws[v].nl = levene_create (var_get_width (cmd->indep_var), NULL);
+ }
+
+ output_split_file_values_peek (ds, input);
+
+ struct taint *taint = taint_clone (casereader_get_taint (input));
+ input = casereader_create_filter_missing (input, &cmd->indep_var, 1,
+ cmd->exclude, NULL, NULL);
+ if (cmd->missing_type == MISS_LISTWISE)
+ input = casereader_create_filter_missing (input, cmd->vars, cmd->n_vars,
+ cmd->exclude, NULL, NULL);
+ input = casereader_create_filter_weight (input, dict, NULL, NULL);
+
+ struct casereader *reader = casereader_clone (input);
+ struct ccase *c;
+ for (; (c = casereader_read (reader)) != NULL; case_unref (c))
+ {
+ double w = dict_get_case_weight (dict, c, NULL);
+
+ for (size_t i = 0; i < cmd->n_vars; ++i)
+ {
+ struct per_var_ws *pvw = &ws.vws[i];
+ const struct variable *v = cmd->vars[i];
+ const union value *val = case_data (c, v);
+
+ if (MISS_ANALYSIS == cmd->missing_type)
+ {
+ if (var_is_value_missing (v, val) & cmd->exclude)
+ continue;
+ }
+
+ covariance_accumulate_pass1 (pvw->cov, c);
+ levene_pass_one (pvw->nl, val->f, w, case_data (c, cmd->indep_var));
+ }
+ }
+ casereader_destroy (reader);
+
+ reader = casereader_clone (input);
+ for (; (c = casereader_read (reader)); case_unref (c))
+ {
+ double w = dict_get_case_weight (dict, c, NULL);
+ for (size_t i = 0; i < cmd->n_vars; ++i)
+ {
+ struct per_var_ws *pvw = &ws.vws[i];
+ const struct variable *v = cmd->vars[i];
+ const union value *val = case_data (c, v);
+
+ if (MISS_ANALYSIS == cmd->missing_type)
+ {
+ if (var_is_value_missing (v, val) & cmd->exclude)
+ continue;
+ }
+
+ covariance_accumulate_pass2 (pvw->cov, c);
+ levene_pass_two (pvw->nl, val->f, w, case_data (c, cmd->indep_var));
+ }
+ }
+ casereader_destroy (reader);
+
+ reader = casereader_clone (input);
+ for (; (c = casereader_read (reader)); case_unref (c))
+ {
+ double w = dict_get_case_weight (dict, c, NULL);
+
+ for (size_t i = 0; i < cmd->n_vars; ++i)
+ {
+ struct per_var_ws *pvw = &ws.vws[i];
+ const struct variable *v = cmd->vars[i];
+ const union value *val = case_data (c, v);
+
+ if (MISS_ANALYSIS == cmd->missing_type)
+ {
+ if (var_is_value_missing (v, val) & cmd->exclude)
+ continue;
+ }
+
+ levene_pass_three (pvw->nl, val->f, w, case_data (c, cmd->indep_var));
+ }
+ }
+ casereader_destroy (reader);
+
+ for (size_t v = 0; v < cmd->n_vars; ++v)
+ {
+ struct per_var_ws *pvw = &ws.vws[v];
+
+ const struct categoricals *cats = covariance_get_categoricals (pvw->cov);
+ if (!categoricals_sane (cats))
+ {
+ msg (MW, _("Dependent variable %s has no non-missing values. "
+ "No analysis for this variable will be done."),
+ var_get_name (cmd->vars[v]));
+ continue;
+ }
+
+ const gsl_matrix *ucm = covariance_calculate_unnormalized (pvw->cov);
+
+ gsl_matrix *cm = gsl_matrix_alloc (ucm->size1, ucm->size2);
+ gsl_matrix_memcpy (cm, ucm);
+
+ moments1_calculate (ws.dd_total[v]->mom, &pvw->n, NULL, NULL, NULL, NULL);
+
+ pvw->sst = gsl_matrix_get (cm, 0, 0);
+
+ reg_sweep (cm, 0);
+
+ pvw->sse = gsl_matrix_get (cm, 0, 0);
+ gsl_matrix_free (cm);
+
+ pvw->ssa = pvw->sst - pvw->sse;
+
+ pvw->n_groups = categoricals_n_total (cats);
+
+ pvw->mse = (pvw->sst - pvw->ssa) / (pvw->n - pvw->n_groups);
+ }
+
+ for (size_t v = 0; v < cmd->n_vars; ++v)
+ {
+ const struct categoricals *cats = covariance_get_categoricals (ws.vws[v].cov);
+ if (categoricals_is_complete (cats))
+ {
+ if (categoricals_n_total (cats) > ws.actual_number_of_groups)
+ ws.actual_number_of_groups = categoricals_n_total (cats);
+ }
+ }
+ casereader_destroy (input);
+
+ if (!taint_has_tainted_successor (taint))
+ output_oneway (cmd, &ws);
+
+ taint_destroy (taint);
+
+ for (size_t v = 0; v < cmd->n_vars; ++v)
+ {
+ covariance_destroy (ws.vws[v].cov);
+ levene_destroy (ws.vws[v].nl);
+ dd_destroy (ws.dd_total[v]);
+ interaction_destroy (ws.vws[v].iact);
+ }
+
+ free (ws.vws);
+ free (ws.dd_total);
+}
+
+static void show_contrast_coeffs (const struct oneway_spec *, const struct oneway_workspace *);
+static void show_contrast_tests (const struct oneway_spec *, const struct oneway_workspace *);
+static void show_comparisons (const struct oneway_spec *, const struct oneway_workspace *, int depvar);
+
+static void
+output_oneway (const struct oneway_spec *cmd, struct oneway_workspace *ws)
+{
+ size_t list_idx = 0;
+
+ /* Check the sanity of the given contrast values */
+ struct contrasts_node *coeff_list = NULL;
+ struct contrasts_node *coeff_next = NULL;
+ ll_for_each_safe (coeff_list, coeff_next, struct contrasts_node, ll, &cmd->contrast_list)
+ {
+ struct coeff_node *cn = NULL;
+ double sum = 0;
+ struct ll_list *cl = &coeff_list->coefficient_list;
+ ++list_idx;
+
+ if (ll_count (cl) != ws->actual_number_of_groups)
+ {
+ msg (SW,
+ _("In contrast list %zu, the number of coefficients (%zu) does not equal the number of groups (%d). This contrast list will be ignored."),
+ list_idx, ll_count (cl), ws->actual_number_of_groups);
+
+ ll_remove (&coeff_list->ll);
+ destroy_coeff_list (coeff_list);
+ continue;
+ }
+
+ ll_for_each (cn, struct coeff_node, ll, cl)
+ sum += cn->coeff;
+
+ if (sum != 0.0)
+ msg (SW, _("Coefficients for contrast %zu do not total zero"),
+ list_idx);
+ }
+
+ if (cmd->descriptive_stats)
+ show_descriptives (cmd, ws);
+
+ if (cmd->homogeneity_stats)
+ show_homogeneity (cmd, ws);
+
+ show_anova_table (cmd, ws);
+
+ if (ll_count (&cmd->contrast_list) > 0)
+ {
+ show_contrast_coeffs (cmd, ws);
+ show_contrast_tests (cmd, ws);
+ }
+
+ if (cmd->posthoc)
+ for (size_t v = 0; v < cmd->n_vars; ++v)
+ {
+ const struct categoricals *cats = covariance_get_categoricals (ws->vws[v].cov);
+
+ if (categoricals_is_complete (cats))
+ show_comparisons (cmd, ws, v);
+ }
+}
+
+
+/* Show the ANOVA table */
+static void
+show_anova_table (const struct oneway_spec *cmd, const struct oneway_workspace *ws)
+{
+ struct pivot_table *table = pivot_table_create (N_("ANOVA"));
+
+ pivot_dimension_create (table, PIVOT_AXIS_COLUMN, N_("Statistics"),
+ N_("Sum of Squares"), PIVOT_RC_OTHER,
+ N_("df"), PIVOT_RC_INTEGER,
+ N_("Mean Square"), PIVOT_RC_OTHER,
+ N_("F"), PIVOT_RC_OTHER,
+ N_("Sig."), PIVOT_RC_SIGNIFICANCE);
+
+ pivot_dimension_create (table, PIVOT_AXIS_ROW, N_("Type"),
+ N_("Between Groups"), N_("Within Groups"),
+ N_("Total"));
+
+ struct pivot_dimension *variables = pivot_dimension_create (
+ table, PIVOT_AXIS_ROW, N_("Variables"));
+
+ for (size_t i = 0; i < cmd->n_vars; ++i)
+ {
+ int var_idx = pivot_category_create_leaf (
+ variables->root, pivot_value_new_variable (cmd->vars[i]));
+
+ const struct per_var_ws *pvw = &ws->vws[i];
+
+ double n;
+ moments1_calculate (ws->dd_total[i]->mom, &n, NULL, NULL, NULL, NULL);
+
+ double df1 = pvw->n_groups - 1;
+ double df2 = n - pvw->n_groups;
+ double msa = pvw->ssa / df1;
+ double F = msa / pvw->mse;
+
+ struct entry
+ {
+ int stat_idx;
+ int type_idx;
+ double x;
+ }
+ entries[] = {
+ /* Sums of Squares. */
+ { 0, 0, pvw->ssa },
+ { 0, 1, pvw->sse },
+ { 0, 2, pvw->sst },
+ /* Degrees of Freedom. */
+ { 1, 0, df1 },
+ { 1, 1, df2 },
+ { 1, 2, n - 1 },
+ /* Mean Squares. */
+ { 2, 0, msa },
+ { 2, 1, pvw->mse },
+ /* F. */
+ { 3, 0, F },
+ /* Significance. */
+ { 4, 0, gsl_cdf_fdist_Q (F, df1, df2) },
+ };
+ for (size_t j = 0; j < sizeof entries / sizeof *entries; j++)
+ {
+ const struct entry *e = &entries[j];
+ pivot_table_put3 (table, e->stat_idx, e->type_idx, var_idx,
+ pivot_value_new_number (e->x));
+ }
+ }
+
+ pivot_table_submit (table);
+}
+
+/* Show the descriptives table */
+static void
+show_descriptives (const struct oneway_spec *cmd, const struct oneway_workspace *ws)
+{
+ if (!cmd->n_vars)
+ return;
+ const struct categoricals *cats = covariance_get_categoricals (
+ ws->vws[0].cov);
+
+ struct pivot_table *table = pivot_table_create (N_("Descriptives"));
+ pivot_table_set_weight_format (table, cmd->wfmt);
+
+ const double confidence = 0.95;
+
+ struct pivot_dimension *statistics = pivot_dimension_create (
+ table, PIVOT_AXIS_COLUMN, N_("Statistics"),
+ N_("N"), PIVOT_RC_COUNT, N_("Mean"), N_("Std. Deviation"),
+ N_("Std. Error"));
+ struct pivot_category *interval = pivot_category_create_group__ (
+ statistics->root,
+ pivot_value_new_text_format (N_("%g%% Confidence Interval for Mean"),
+ confidence * 100.0));
+ pivot_category_create_leaves (interval, N_("Lower Bound"),
+ N_("Upper Bound"));
+ pivot_category_create_leaves (statistics->root,
+ N_("Minimum"), N_("Maximum"));
+
+ struct pivot_dimension *indep_var = pivot_dimension_create__ (
+ table, PIVOT_AXIS_ROW, pivot_value_new_variable (cmd->indep_var));
+ indep_var->root->show_label = true;
+ size_t n;
+ union value *values = categoricals_get_var_values (cats, cmd->indep_var, &n);
+ for (size_t j = 0; j < n; j++)
+ pivot_category_create_leaf (
+ indep_var->root, pivot_value_new_var_value (cmd->indep_var, &values[j]));
+ pivot_category_create_leaf (
+ indep_var->root, pivot_value_new_text_format (N_("Total")));
+
+ struct pivot_dimension *dep_var = pivot_dimension_create (
+ table, PIVOT_AXIS_ROW, N_("Dependent Variable"));
+
+ const double q = (1.0 - confidence) / 2.0;
+ for (int v = 0; v < cmd->n_vars; ++v)
+ {
+ int dep_var_idx = pivot_category_create_leaf (
+ dep_var->root, pivot_value_new_variable (cmd->vars[v]));
+
+ struct per_var_ws *pvw = &ws->vws[v];
+ const struct categoricals *cats = covariance_get_categoricals (pvw->cov);
+
+ int count;
+ for (count = 0; count < categoricals_n_total (cats); ++count)
+ {
+ const struct descriptive_data *dd
+ = categoricals_get_user_data_by_category (cats, count);
+
+ double n, mean, variance;
+ moments1_calculate (dd->mom, &n, &mean, &variance, NULL, NULL);
+
+ double std_dev = sqrt (variance);
+ double std_error = std_dev / sqrt (n);
+ double T = gsl_cdf_tdist_Qinv (q, n - 1);
+
+ double entries[] = {
+ n,
+ mean,
+ std_dev,
+ std_error,
+ mean - T * std_error,
+ mean + T * std_error,
+ dd->minimum,
+ dd->maximum,
+ };
+ for (size_t i = 0; i < sizeof entries / sizeof *entries; i++)
+ pivot_table_put3 (table, i, count, dep_var_idx,
+ pivot_value_new_number (entries[i]));
+ }
+
+ if (categoricals_is_complete (cats))
+ {
+ double n, mean, variance;
+ moments1_calculate (ws->dd_total[v]->mom, &n, &mean, &variance,
+ NULL, NULL);
+
+ double std_dev = sqrt (variance);
+ double std_error = std_dev / sqrt (n);
+ double T = gsl_cdf_tdist_Qinv (q, n - 1);
+
+ double entries[] = {
+ n,
+ mean,
+ std_dev,
+ std_error,
+ mean - T * std_error,
+ mean + T * std_error,
+ ws->dd_total[v]->minimum,
+ ws->dd_total[v]->maximum,
+ };
+ for (size_t i = 0; i < sizeof entries / sizeof *entries; i++)
+ pivot_table_put3 (table, i, count, dep_var_idx,
+ pivot_value_new_number (entries[i]));
+ }
+ }
+
+ pivot_table_submit (table);
+}
+
+/* Show the homogeneity table */
+static void
+show_homogeneity (const struct oneway_spec *cmd, const struct oneway_workspace *ws)
+{
+ struct pivot_table *table = pivot_table_create (
+ N_("Test of Homogeneity of Variances"));
+
+ pivot_dimension_create (table, PIVOT_AXIS_COLUMN, N_("Statistics"),
+ N_("Levene Statistic"), PIVOT_RC_OTHER,
+ N_("df1"), PIVOT_RC_INTEGER,
+ N_("df2"), PIVOT_RC_INTEGER,
+ N_("Sig."), PIVOT_RC_SIGNIFICANCE);
+
+ struct pivot_dimension *variables = pivot_dimension_create (
+ table, PIVOT_AXIS_ROW, N_("Variables"));
+
+ for (int v = 0; v < cmd->n_vars; ++v)
+ {
+ int var_idx = pivot_category_create_leaf (
+ variables->root, pivot_value_new_variable (cmd->vars[v]));
+
+ double n;
+ moments1_calculate (ws->dd_total[v]->mom, &n, NULL, NULL, NULL, NULL);
+
+ const struct per_var_ws *pvw = &ws->vws[v];
+ double df1 = pvw->n_groups - 1;
+ double df2 = n - pvw->n_groups;
+ double F = levene_calculate (pvw->nl);
+
+ double entries[] =
+ {
+ F,
+ df1,
+ df2,
+ gsl_cdf_fdist_Q (F, df1, df2),
+ };
+ for (size_t i = 0; i < sizeof entries / sizeof *entries; i++)
+ pivot_table_put2 (table, i, var_idx,
+ pivot_value_new_number (entries[i]));
+ }
+
+ pivot_table_submit (table);
+}
+
+
+/* Show the contrast coefficients table */
+static void
+show_contrast_coeffs (const struct oneway_spec *cmd, const struct oneway_workspace *ws)
+{
+ struct pivot_table *table = pivot_table_create (N_("Contrast Coefficients"));
+
+ struct pivot_dimension *indep_var = pivot_dimension_create__ (
+ table, PIVOT_AXIS_COLUMN, pivot_value_new_variable (cmd->indep_var));
+ indep_var->root->show_label = true;
+
+ struct pivot_dimension *contrast = pivot_dimension_create (
+ table, PIVOT_AXIS_ROW, N_("Contrast"));
+ contrast->root->show_label = true;
+
+ const struct covariance *cov = ws->vws[0].cov;
+
+ const struct contrasts_node *cn;
+ int c_num = 1;
+ ll_for_each (cn, struct contrasts_node, ll, &cmd->contrast_list)
+ {
+ int contrast_idx = pivot_category_create_leaf (
+ contrast->root, pivot_value_new_integer (c_num++));
+
+ const struct coeff_node *coeffn;
+ int indep_idx = 0;
+ ll_for_each (coeffn, struct coeff_node, ll, &cn->coefficient_list)
+ {
+ const struct categoricals *cats = covariance_get_categoricals (cov);
+ const struct ccase *gcc = categoricals_get_case_by_category (
+ cats, indep_idx);
+
+ if (!contrast_idx)
+ pivot_category_create_leaf (
+ indep_var->root, pivot_value_new_var_value (
+ cmd->indep_var, case_data (gcc, cmd->indep_var)));
+
+ pivot_table_put2 (table, indep_idx++, contrast_idx,
+ pivot_value_new_integer (coeffn->coeff));
+ }
+ }
+
+ pivot_table_submit (table);
+}
+
+/* Show the results of the contrast tests */
+static void
+show_contrast_tests (const struct oneway_spec *cmd, const struct oneway_workspace *ws)
+{
+ struct pivot_table *table = pivot_table_create (N_("Contrast Tests"));
+
+ pivot_dimension_create (table, PIVOT_AXIS_COLUMN, N_("Statistics"),
+ N_("Value of Contrast"), PIVOT_RC_OTHER,
+ N_("Std. Error"), PIVOT_RC_OTHER,
+ N_("t"), PIVOT_RC_OTHER,
+ N_("df"), PIVOT_RC_OTHER,
+ N_("Sig. (2-tailed)"), PIVOT_RC_SIGNIFICANCE);
+
+ struct pivot_dimension *contrasts = pivot_dimension_create (
+ table, PIVOT_AXIS_ROW, N_("Contrast"));
+ contrasts->root->show_label = true;
+ int n_contrasts = ll_count (&cmd->contrast_list);
+ for (int i = 1; i <= n_contrasts; i++)
+ pivot_category_create_leaf (contrasts->root, pivot_value_new_integer (i));
+
+ pivot_dimension_create (table, PIVOT_AXIS_ROW, N_("Assumption"),
+ N_("Assume equal variances"),
+ N_("Does not assume equal variances"));
+
+ struct pivot_dimension *variables = pivot_dimension_create (
+ table, PIVOT_AXIS_ROW, N_("Dependent Variable"));
+
+ for (int v = 0; v < cmd->n_vars; ++v)
+ {
+ const struct per_var_ws *pvw = &ws->vws[v];
+ const struct categoricals *cats = covariance_get_categoricals (pvw->cov);
+ if (!categoricals_is_complete (cats))
+ continue;
+
+ int var_idx = pivot_category_create_leaf (
+ variables->root, pivot_value_new_variable (cmd->vars[v]));
+
+ struct contrasts_node *cn;
+ int contrast_idx = 0;
+ ll_for_each (cn, struct contrasts_node, ll, &cmd->contrast_list)
+ {
+
+ /* Note: The calculation of the degrees of freedom in the
+ "variances not equal" case is painfull!!
+ The following formula may help to understand it:
+ \frac{\left (\sum_{i=1}^k{c_i^2\frac{s_i^2}{n_i}}\right)^2}
+ {
+ \sum_{i=1}^k\left (
+ \frac{\left (c_i^2\frac{s_i^2}{n_i}\right)^2} {n_i-1}
+ \right)
+ }
+ */
+
+ double grand_n;
+ moments1_calculate (ws->dd_total[v]->mom, &grand_n, NULL, NULL,
+ NULL, NULL);
+ double df = grand_n - pvw->n_groups;
+
+ double contrast_value = 0.0;
+ double coef_msq = 0.0;
+ double sec_vneq = 0.0;
+ double df_denominator = 0.0;
+ double df_numerator = 0.0;
+ struct coeff_node *coeffn;
+ int ci = 0;
+ ll_for_each (coeffn, struct coeff_node, ll, &cn->coefficient_list)
+ {
+ const struct descriptive_data *dd
+ = categoricals_get_user_data_by_category (cats, ci);
+ const double coef = coeffn->coeff;
+
+ double n, mean, variance;
+ moments1_calculate (dd->mom, &n, &mean, &variance, NULL, NULL);
+
+ double winv = variance / n;
+ contrast_value += coef * mean;
+ coef_msq += pow2 (coef) / n;
+ sec_vneq += pow2 (coef) * variance / n;
+ df_numerator += pow2 (coef) * winv;
+ df_denominator += pow2(pow2 (coef) * winv) / (n - 1);
+
+ ci++;
+ }
+ sec_vneq = sqrt (sec_vneq);
+ df_numerator = pow2 (df_numerator);
+
+ double std_error_contrast = sqrt (pvw->mse * coef_msq);
+ double T = contrast_value / std_error_contrast;
+ double T_ne = contrast_value / sec_vneq;
+ double df_ne = df_numerator / df_denominator;
+
+ struct entry
+ {
+ int stat_idx;
+ int assumption_idx;
+ double x;
+ }
+ entries[] =
+ {
+ /* Assume equal. */
+ { 0, 0, contrast_value },
+ { 1, 0, std_error_contrast },
+ { 2, 0, T },
+ { 3, 0, df },
+ { 4, 0, 2 * gsl_cdf_tdist_Q (fabs(T), df) },
+ /* Do not assume equal. */
+ { 0, 1, contrast_value },
+ { 1, 1, sec_vneq },
+ { 2, 1, T_ne },
+ { 3, 1, df_ne },
+ { 4, 1, 2 * gsl_cdf_tdist_Q (fabs(T_ne), df_ne) },
+ };
+
+ for (size_t i = 0; i < sizeof entries / sizeof *entries; i++)
+ {
+ const struct entry *e = &entries[i];
+ pivot_table_put4 (
+ table, e->stat_idx, contrast_idx, e->assumption_idx, var_idx,
+ pivot_value_new_number (e->x));
+ }
+
+ contrast_idx++;
+ }
+ }
+
+ pivot_table_submit (table);
+}
+
+static void
+show_comparisons (const struct oneway_spec *cmd, const struct oneway_workspace *ws, int v)
+{
+ struct pivot_table *table = pivot_table_create__ (
+ pivot_value_new_user_text_nocopy (xasprintf (
+ _("Multiple Comparisons (%s)"),
+ var_to_string (cmd->vars[v]))),
+ "Multiple Comparisons");
+
+ struct pivot_dimension *statistics = pivot_dimension_create (
+ table, PIVOT_AXIS_COLUMN, N_("Statistics"),
+ N_("Mean Difference (I - J)"), PIVOT_RC_OTHER,
+ N_("Std. Error"), PIVOT_RC_OTHER,
+ N_("Sig."), PIVOT_RC_SIGNIFICANCE);
+ struct pivot_category *interval = pivot_category_create_group__ (
+ statistics->root,
+ pivot_value_new_text_format (N_("%g%% Confidence Interval"),
+ (1 - cmd->alpha) * 100.0));
+ pivot_category_create_leaves (interval,
+ N_("Lower Bound"), PIVOT_RC_OTHER,
+ N_("Upper Bound"), PIVOT_RC_OTHER);
+
+ struct pivot_dimension *j_family = pivot_dimension_create (
+ table, PIVOT_AXIS_ROW, N_("(J) Family"));
+ j_family->root->show_label = true;
+
+ struct pivot_dimension *i_family = pivot_dimension_create (
+ table, PIVOT_AXIS_ROW, N_("(J) Family"));
+ i_family->root->show_label = true;
+
+ const struct per_var_ws *pvw = &ws->vws[v];
+ const struct categoricals *cat = pvw->cat;
+ for (int i = 0; i < pvw->n_groups; i++)
+ {
+ const struct ccase *gcc = categoricals_get_case_by_category (cat, i);
+ for (int j = 0; j < 2; j++)
+ pivot_category_create_leaf (
+ j ? j_family->root : i_family->root,
+ pivot_value_new_var_value (cmd->indep_var,
+ case_data (gcc, cmd->indep_var)));
+ }
+
+ struct pivot_dimension *test = pivot_dimension_create (
+ table, PIVOT_AXIS_ROW, N_("Test"));
+
+ for (int p = 0; p < cmd->n_posthoc; ++p)
+ {
+ const struct posthoc *ph = &ph_tests[cmd->posthoc[p]];
+
+ int test_idx = pivot_category_create_leaf (
+ test->root, pivot_value_new_text (ph->label));
+
+ for (int i = 0; i < pvw->n_groups; ++i)
+ {
+ struct descriptive_data *dd_i
+ = categoricals_get_user_data_by_category (cat, i);
+ double weight_i, mean_i, var_i;
+ moments1_calculate (dd_i->mom, &weight_i, &mean_i, &var_i, 0, 0);
+
+ for (int j = 0; j < pvw->n_groups; ++j)
+ {
+ if (j == i)
+ continue;
+
+ struct descriptive_data *dd_j
+ = categoricals_get_user_data_by_category (cat, j);
+ double weight_j, mean_j, var_j;
+ moments1_calculate (dd_j->mom, &weight_j, &mean_j, &var_j, 0, 0);
+
+ double std_err = pvw->mse;
+ std_err *= weight_i + weight_j;
+ std_err /= weight_i * weight_j;
+ std_err = sqrt (std_err);
+
+ double sig = 2 * multiple_comparison_sig (std_err, pvw,
+ dd_i, dd_j, ph);
+ double half_range = mc_half_range (cmd, pvw, std_err,
+ dd_i, dd_j, ph);
+ double entries[] = {
+ mean_i - mean_j,
+ std_err,
+ sig,
+ (mean_i - mean_j) - half_range,
+ (mean_i - mean_j) + half_range,
+ };
+ for (size_t k = 0; k < sizeof entries / sizeof *entries; k++)
+ pivot_table_put4 (table, k, j, i, test_idx,
+ pivot_value_new_number (entries[k]));
+ }
+ }
+ }
+
+ pivot_table_submit (table);
+}