/* PSPP - linear regression. Copyright (C) 2005 Free Software Foundation, Inc. Written by Jason H Stover . 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 2 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, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */ #include #include #include #include #include #include "alloc.h" #include "case.h" #include "casefile.h" #include "cat.h" #include "cat-routines.h" #include "command.h" #include "design-matrix.h" #include "dictionary.h" #include "error.h" #include "file-handle.h" #include "gettext.h" #include "lexer.h" #include #include "missing-values.h" #include "tab.h" #include "var.h" #include "vfm.h" #define REG_LARGE_DATA 1000 /* (headers) */ /* (specification) "REGRESSION" (regression_): *variables=varlist; statistics[st_]=r, coeff, anova, outs, zpp, label, sha, ci, bcov, ses, xtx, collin, tol, selection, f, defaults, all; export=custom; ^dependent=varlist; ^method=enter. */ /* (declarations) */ /* (functions) */ static struct cmd_regression cmd; /* Array holding the subscripts of the independent variables. */ size_t *indep_vars; /* File where the model will be saved if the EXPORT subcommand is given. */ struct file_handle *model_file; /* Return value for the procedure. */ int pspp_reg_rc = CMD_SUCCESS; static void run_regression (const struct casefile *, void *); /* STATISTICS subcommand output functions. */ static void reg_stats_r (pspp_linreg_cache *); static void reg_stats_coeff (pspp_linreg_cache *); static void reg_stats_anova (pspp_linreg_cache *); static void reg_stats_outs (pspp_linreg_cache *); static void reg_stats_zpp (pspp_linreg_cache *); static void reg_stats_label (pspp_linreg_cache *); static void reg_stats_sha (pspp_linreg_cache *); static void reg_stats_ci (pspp_linreg_cache *); static void reg_stats_f (pspp_linreg_cache *); static void reg_stats_bcov (pspp_linreg_cache *); static void reg_stats_ses (pspp_linreg_cache *); static void reg_stats_xtx (pspp_linreg_cache *); static void reg_stats_collin (pspp_linreg_cache *); static void reg_stats_tol (pspp_linreg_cache *); static void reg_stats_selection (pspp_linreg_cache *); static void statistics_keyword_output (void (*)(pspp_linreg_cache *), int, pspp_linreg_cache *); static void reg_stats_r (pspp_linreg_cache * c) { struct tab_table *t; int n_rows = 2; int n_cols = 5; double rsq; double adjrsq; double std_error; assert (c != NULL); rsq = c->ssm / c->sst; adjrsq = 1.0 - (1.0 - rsq) * (c->n_obs - 1.0) / (c->n_obs - c->n_indeps); std_error = sqrt ((c->n_indeps - 1.0) / (c->n_obs - 1.0)); t = tab_create (n_cols, n_rows, 0); tab_dim (t, tab_natural_dimensions); tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1); tab_hline (t, TAL_2, 0, n_cols - 1, 1); tab_vline (t, TAL_2, 2, 0, n_rows - 1); tab_vline (t, TAL_0, 1, 0, 0); tab_text (t, 1, 0, TAB_CENTER | TAT_TITLE, _("R")); tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("R Square")); tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("Adjusted R Square")); tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Std. Error of the Estimate")); tab_float (t, 1, 1, TAB_RIGHT, sqrt (rsq), 10, 2); tab_float (t, 2, 1, TAB_RIGHT, rsq, 10, 2); tab_float (t, 3, 1, TAB_RIGHT, adjrsq, 10, 2); tab_float (t, 4, 1, TAB_RIGHT, std_error, 10, 2); tab_title (t, 0, _("Model Summary")); tab_submit (t); } /* Table showing estimated regression coefficients. */ static void reg_stats_coeff (pspp_linreg_cache * c) { size_t i; size_t j; int n_cols = 7; int n_rows; double t_stat; double pval; double coeff; double std_err; double beta; const char *label; struct tab_table *t; assert (c != NULL); n_rows = c->n_coeffs + 2; t = tab_create (n_cols, n_rows, 0); tab_headers (t, 2, 0, 1, 0); tab_dim (t, tab_natural_dimensions); tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1); tab_hline (t, TAL_2, 0, n_cols - 1, 1); tab_vline (t, TAL_2, 2, 0, n_rows - 1); tab_vline (t, TAL_0, 1, 0, 0); tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("B")); tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("Std. Error")); tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Beta")); tab_text (t, 5, 0, TAB_CENTER | TAT_TITLE, _("t")); tab_text (t, 6, 0, TAB_CENTER | TAT_TITLE, _("Significance")); tab_text (t, 1, 1, TAB_LEFT | TAT_TITLE, _("(Constant)")); coeff = c->coeff[0].estimate; tab_float (t, 2, 1, 0, coeff, 10, 2); std_err = sqrt (gsl_matrix_get (c->cov, 0, 0)); tab_float (t, 3, 1, 0, std_err, 10, 2); beta = coeff / c->depvar_std; tab_float (t, 4, 1, 0, beta, 10, 2); t_stat = coeff / std_err; tab_float (t, 5, 1, 0, t_stat, 10, 2); pval = 2 * gsl_cdf_tdist_Q (fabs (t_stat), 1.0); tab_float (t, 6, 1, 0, pval, 10, 2); for (j = 1; j <= c->n_indeps; j++) { i = indep_vars[j]; label = var_to_string (c->coeff[j].v); tab_text (t, 1, j + 1, TAB_CENTER, label); /* Regression coefficients. */ coeff = c->coeff[j].estimate; tab_float (t, 2, j + 1, 0, coeff, 10, 2); /* Standard error of the coefficients. */ std_err = sqrt (gsl_matrix_get (c->cov, j, j)); tab_float (t, 3, j + 1, 0, std_err, 10, 2); /* 'Standardized' coefficient, i.e., regression coefficient if all variables had unit variance. */ beta = gsl_vector_get (c->indep_std, j); beta *= coeff / c->depvar_std; tab_float (t, 4, j + 1, 0, beta, 10, 2); /* Test statistic for H0: coefficient is 0. */ t_stat = coeff / std_err; tab_float (t, 5, j + 1, 0, t_stat, 10, 2); /* P values for the test statistic above. */ pval = 2 * gsl_cdf_tdist_Q (fabs (t_stat), 1.0); tab_float (t, 6, j + 1, 0, pval, 10, 2); } tab_title (t, 0, _("Coefficients")); tab_submit (t); } /* Display the ANOVA table. */ static void reg_stats_anova (pspp_linreg_cache * c) { int n_cols = 7; int n_rows = 4; const double msm = c->ssm / c->dfm; const double mse = c->sse / c->dfe; const double F = msm / mse; const double pval = gsl_cdf_fdist_Q (F, c->dfm, c->dfe); struct tab_table *t; assert (c != NULL); t = tab_create (n_cols, n_rows, 0); tab_headers (t, 2, 0, 1, 0); tab_dim (t, tab_natural_dimensions); tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1); tab_hline (t, TAL_2, 0, n_cols - 1, 1); tab_vline (t, TAL_2, 2, 0, n_rows - 1); tab_vline (t, TAL_0, 1, 0, 0); tab_text (t, 2, 0, TAB_CENTER | TAT_TITLE, _("Sum of Squares")); tab_text (t, 3, 0, TAB_CENTER | TAT_TITLE, _("df")); tab_text (t, 4, 0, TAB_CENTER | TAT_TITLE, _("Mean Square")); tab_text (t, 5, 0, TAB_CENTER | TAT_TITLE, _("F")); tab_text (t, 6, 0, TAB_CENTER | TAT_TITLE, _("Significance")); tab_text (t, 1, 1, TAB_LEFT | TAT_TITLE, _("Regression")); tab_text (t, 1, 2, TAB_LEFT | TAT_TITLE, _("Residual")); tab_text (t, 1, 3, TAB_LEFT | TAT_TITLE, _("Total")); /* Sums of Squares */ tab_float (t, 2, 1, 0, c->ssm, 10, 2); tab_float (t, 2, 3, 0, c->sst, 10, 2); tab_float (t, 2, 2, 0, c->sse, 10, 2); /* Degrees of freedom */ tab_float (t, 3, 1, 0, c->dfm, 4, 0); tab_float (t, 3, 2, 0, c->dfe, 4, 0); tab_float (t, 3, 3, 0, c->dft, 4, 0); /* Mean Squares */ tab_float (t, 4, 1, TAB_RIGHT, msm, 8, 3); tab_float (t, 4, 2, TAB_RIGHT, mse, 8, 3); tab_float (t, 5, 1, 0, F, 8, 3); tab_float (t, 6, 1, 0, pval, 8, 3); tab_title (t, 0, _("ANOVA")); tab_submit (t); } static void reg_stats_outs (pspp_linreg_cache * c) { assert (c != NULL); } static void reg_stats_zpp (pspp_linreg_cache * c) { assert (c != NULL); } static void reg_stats_label (pspp_linreg_cache * c) { assert (c != NULL); } static void reg_stats_sha (pspp_linreg_cache * c) { assert (c != NULL); } static void reg_stats_ci (pspp_linreg_cache * c) { assert (c != NULL); } static void reg_stats_f (pspp_linreg_cache * c) { assert (c != NULL); } static void reg_stats_bcov (pspp_linreg_cache * c) { int n_cols; int n_rows; int i; int j; int k; int row; int col; const char *label; struct tab_table *t; assert (c != NULL); n_cols = c->n_indeps + 1 + 2; n_rows = 2 * (c->n_indeps + 1); t = tab_create (n_cols, n_rows, 0); tab_headers (t, 2, 0, 1, 0); tab_dim (t, tab_natural_dimensions); tab_box (t, TAL_2, TAL_2, -1, TAL_1, 0, 0, n_cols - 1, n_rows - 1); tab_hline (t, TAL_2, 0, n_cols - 1, 1); tab_vline (t, TAL_2, 2, 0, n_rows - 1); tab_vline (t, TAL_0, 1, 0, 0); tab_text (t, 0, 0, TAB_CENTER | TAT_TITLE, _("Model")); tab_text (t, 1, 1, TAB_CENTER | TAT_TITLE, _("Covariances")); for (i = 1; i < c->n_indeps + 1; i++) { j = indep_vars[(i - 1)]; struct variable *v = cmd.v_variables[j]; label = var_to_string (v); tab_text (t, 2, i, TAB_CENTER, label); tab_text (t, i + 2, 0, TAB_CENTER, label); for (k = 1; k < c->n_indeps + 1; k++) { col = (i <= k) ? k : i; row = (i <= k) ? i : k; tab_float (t, k + 2, i, TAB_CENTER, gsl_matrix_get (c->cov, row, col), 8, 3); } } tab_title (t, 0, _("Coefficient Correlations")); tab_submit (t); } static void reg_stats_ses (pspp_linreg_cache * c) { assert (c != NULL); } static void reg_stats_xtx (pspp_linreg_cache * c) { assert (c != NULL); } static void reg_stats_collin (pspp_linreg_cache * c) { assert (c != NULL); } static void reg_stats_tol (pspp_linreg_cache * c) { assert (c != NULL); } static void reg_stats_selection (pspp_linreg_cache * c) { assert (c != NULL); } static void statistics_keyword_output (void (*function) (pspp_linreg_cache *), int keyword, pspp_linreg_cache * c) { if (keyword) { (*function) (c); } } static void subcommand_statistics (int *keywords, pspp_linreg_cache * c) { /* The order here must match the order in which the STATISTICS keywords appear in the specification section above. */ enum { r, coeff, anova, outs, zpp, label, sha, ci, bcov, ses, xtx, collin, tol, selection, f, defaults, all }; int i; int d = 1; if (keywords[all]) { /* Set everything but F. */ for (i = 0; i < f; i++) { keywords[i] = 1; } } else { for (i = 0; i < all; i++) { if (keywords[i]) { d = 0; } } /* Default output: ANOVA table, parameter estimates, and statistics for variables not entered into model, if appropriate. */ if (keywords[defaults] | d) { keywords[anova] = 1; keywords[outs] = 1; keywords[coeff] = 1; keywords[r] = 1; } } statistics_keyword_output (reg_stats_r, keywords[r], c); statistics_keyword_output (reg_stats_anova, keywords[anova], c); statistics_keyword_output (reg_stats_coeff, keywords[coeff], c); statistics_keyword_output (reg_stats_outs, keywords[outs], c); statistics_keyword_output (reg_stats_zpp, keywords[zpp], c); statistics_keyword_output (reg_stats_label, keywords[label], c); statistics_keyword_output (reg_stats_sha, keywords[sha], c); statistics_keyword_output (reg_stats_ci, keywords[ci], c); statistics_keyword_output (reg_stats_f, keywords[f], c); statistics_keyword_output (reg_stats_bcov, keywords[bcov], c); statistics_keyword_output (reg_stats_ses, keywords[ses], c); statistics_keyword_output (reg_stats_xtx, keywords[xtx], c); statistics_keyword_output (reg_stats_collin, keywords[collin], c); statistics_keyword_output (reg_stats_tol, keywords[tol], c); statistics_keyword_output (reg_stats_selection, keywords[selection], c); } static void subcommand_export (int export, pspp_linreg_cache *c) { FILE *fp; size_t i; struct pspp_linreg_coeff coeff; if (export) { assert (c != NULL); assert (model_file != NULL); assert (fp != NULL); fp = fopen (handle_get_filename (model_file), "w"); fprintf (fp, "/* PSPP-generated linear regression model.\n Copyright (C) 2005 Free Software Foundation, Inc.\n Generated by the GNU PSPP regression procedure.\n\n This program is free software; you can redistribute it and/or\n modify it under the terms of the GNU General Public License as\n published by the Free Software Foundation; either version 2 of the\n License, or (at your option) any later version.\n\n This program is distributed in the hope that it will be useful, but\n WITHOUT ANY WARRANTY; without even the implied warranty of\n MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU\n General Public License for more details.\n\n You should have received a copy of the GNU General Public License\n along with GNU PSPP; if not, write to the Free Software\n Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA\n 02110-1301, USA. */\n\n"); fprintf (fp, "#include \n\n"); fprintf (fp, "double\npspp_reg_estimate (const double *var_vals, conts char *[] var_names)\n{\n\tchar *model_depvars[%d] = {", c->n_indeps); for (i = 1; i < c->n_indeps; i++) { coeff = c->coeff[i]; fprintf (fp, "%s,\n\t\t", coeff.v->name); } coeff = c->coeff[i]; fprintf (fp, "%s};\n\t", coeff.v->name); fprintf (fp, "double model_coeffs[%d] = {", c->n_indeps); for (i = 1; i < c->n_indeps; i++) { coeff = c->coeff[i]; fprintf (fp, "%.15e,\n\t\t", coeff.estimate); } coeff = c->coeff[i]; fprintf (fp, "%.15e};\n\t", coeff.estimate); coeff = c->coeff[0]; fprintf (fp, "double estimate = %.15e\n\t", coeff.estimate); fprintf (fp, "int i;\n\tint j;\n\n\t"); fprintf (fp, "for (i = 0; i < %d; i++)\n\t", c->n_indeps); fprintf (fp, "{\n\t\tfor (j = 0; j < %d; j++)\n\t\t", c->n_indeps); fprintf (fp, "{\n\t\t\tif (strcmp (var_names[i], model_names[j]) == 0)\n"); fprintf (fp, "\t\t\t{\n\t\t\t\testimate += var_vals[i] * model_coeffs[j];\n"); fprintf (fp, "\t\t\t}\n\t\t}\n\t}\n\treturn estimate;\n}\n"); fclose (fp); } } static int regression_custom_export (struct cmd_regression *cmd) { /* 0 on failure, 1 on success, 2 on failure that should result in syntax error */ if (!lex_force_match ('(')) return 0; if (lex_match ('*')) model_file = NULL; else { model_file = fh_parse (); if (model_file == NULL) return 0; } if (!lex_force_match (')')) return 0; return 1; } int cmd_regression (void) { if (!parse_regression (&cmd)) { return CMD_FAILURE; } multipass_procedure_with_splits (run_regression, &cmd); return pspp_reg_rc; } /* Is variable k one of the dependent variables? */ static int is_depvar (size_t k) { size_t j = 0; for (j = 0; j < cmd.n_dependent; j++) { /* compare_var_names returns 0 if the variable names match. */ if (!compare_var_names (cmd.v_dependent[j], cmd.v_variables[k], NULL)) return 1; } return 0; } static void run_regression (const struct casefile *cf, void *cmd_ UNUSED) { size_t i; size_t n_data = 0; size_t row; size_t case_num; int n_indep; int j = 0; /* Keep track of the missing cases. */ int *is_missing_case; const union value *val; struct casereader *r; struct casereader *r2; struct ccase c; struct variable *v; struct variable **indep_vars; struct design_matrix *X; gsl_vector *Y; pspp_linreg_cache *lcache; pspp_linreg_opts lopts; n_data = casefile_get_case_cnt (cf); is_missing_case = xnmalloc (n_data, sizeof (*is_missing_case)); for (i = 0; i < n_data; i++) is_missing_case[i] = 0; n_indep = cmd.n_variables - cmd.n_dependent; indep_vars = xnmalloc (n_indep, sizeof *indep_vars); lopts.get_depvar_mean_std = 1; lopts.get_indep_mean_std = xnmalloc (n_indep, sizeof (int)); /* Read from the active file. The first pass encodes categorical variables and drops cases with missing values. */ j = 0; for (i = 0; i < cmd.n_variables; i++) { if (!is_depvar (i)) { v = cmd.v_variables[i]; indep_vars[j] = v; j++; if (v->type == ALPHA) { /* Make a place to hold the binary vectors corresponding to this variable's values. */ cat_stored_values_create (v); } for (r = casefile_get_reader (cf); casereader_read (r, &c); case_destroy (&c)) { row = casereader_cnum (r) - 1; val = case_data (&c, v->fv); cat_value_update (v, val); if (mv_is_value_missing (&v->miss, val)) { if (!is_missing_case[row]) { /* Now it is missing. */ n_data--; is_missing_case[row] = 1; } } } } } Y = gsl_vector_alloc (n_data); X = design_matrix_create (n_indep, (const struct variable **) indep_vars, n_data); lcache = pspp_linreg_cache_alloc (X->m->size1, X->m->size2); lcache->indep_means = gsl_vector_alloc (X->m->size2); lcache->indep_std = gsl_vector_alloc (X->m->size2); /* The second pass creates the design matrix. */ row = 0; for (r2 = casefile_get_reader (cf); casereader_read (r2, &c); case_destroy (&c)) /* Iterate over the cases. */ { case_num = casereader_cnum (r2) - 1; if (!is_missing_case[case_num]) { for (i = 0; i < cmd.n_variables; ++i) /* Iterate over the variables for the current case. */ { v = cmd.v_variables[i]; val = case_data (&c, v->fv); /* Independent/dependent variable separation. The 'variables' subcommand specifies a varlist which contains both dependent and independent variables. The dependent variables are specified with the 'dependent' subcommand. We need to separate the two. */ if (is_depvar (i)) { if (v->type != NUMERIC) { msg (SE, gettext ("Dependent variable must be numeric.")); pspp_reg_rc = CMD_FAILURE; return; } lcache->depvar = (const struct variable *) v; gsl_vector_set (Y, row, val->f); } else { if (v->type == ALPHA) { design_matrix_set_categorical (X, row, v, val); } else if (v->type == NUMERIC) { design_matrix_set_numeric (X, row, v, val); } lopts.get_indep_mean_std[i] = 1; } } row++; } } /* Now that we know the number of coefficients, allocate space and store pointers to the variables that correspond to the coefficients. */ lcache->coeff = xnmalloc (X->m->size2 + 1, sizeof (*lcache->coeff)); for (i = 0; i < X->m->size2; i++) { j = i + 1; /* The first coeff is the intercept. */ lcache->coeff[j].v = (const struct variable *) design_matrix_col_to_var (X, i); assert (lcache->coeff[j].v != NULL); } /* For large data sets, use QR decomposition. */ if (n_data > sqrt (n_indep) && n_data > REG_LARGE_DATA) { lcache->method = PSPP_LINREG_SVD; } /* Find the least-squares estimates and other statistics. */ pspp_linreg ((const gsl_vector *) Y, X->m, &lopts, lcache); subcommand_statistics (cmd.a_statistics, lcache); subcommand_export (cmd.sbc_export, lcache); gsl_vector_free (Y); design_matrix_destroy (X); pspp_linreg_cache_free (lcache); free (lopts.get_indep_mean_std); free (indep_vars); free (is_missing_case); casereader_destroy (r); return; } /* Local Variables: mode: c End: */