double detR; /* The determinant of the correlation matrix */
+ gsl_matrix *ai_cov; /* The anti-image covariance matrix */
+ gsl_matrix *ai_cor; /* The anti-image correlation matrix */
struct covariance *cvm;
};
gsl_vector_free (id->msr);
gsl_vector_free (id->eval);
gsl_matrix_free (id->evec);
+ gsl_matrix_free (id->ai_cov);
+ gsl_matrix_free (id->ai_cor);
free (id);
}
-
-static gsl_matrix *
-anti_image (const gsl_matrix *m)
+/* Return the sum of squares of all the elements in row J excluding column J */
+static double
+ssq_row_od_n (const gsl_matrix *m, int j)
{
- int i, j;
- gsl_matrix *a;
+ int i;
+ double ss = 0;
assert (m->size1 == m->size2);
- a = gsl_matrix_alloc (m->size1, m->size2);
+ assert (j < m->size1);
for (i = 0; i < m->size1; ++i)
{
- for (j = 0; j < m->size2; ++j)
- {
- double *p = gsl_matrix_ptr (a, i, j);
- *p = gsl_matrix_get (m, i, j);
- *p /= gsl_matrix_get (m, i, i);
- *p /= gsl_matrix_get (m, j, j);
- }
+ if (i == j ) continue;
+ ss += pow2 (gsl_matrix_get (m, i, j));
}
- return a;
+ return ss;
}
-
/* Return the sum of all the elements excluding row N */
static double
ssq_od_n (const gsl_matrix *m, int n)
}
+static gsl_matrix *
+anti_image_corr (const gsl_matrix *m, const struct idata *idata)
+{
+ int i, j;
+ gsl_matrix *a;
+ assert (m->size1 == m->size2);
+
+ a = gsl_matrix_alloc (m->size1, m->size2);
+
+ for (i = 0; i < m->size1; ++i)
+ {
+ for (j = 0; j < m->size2; ++j)
+ {
+ double *p = gsl_matrix_ptr (a, i, j);
+ *p = gsl_matrix_get (m, i, j);
+ *p /= sqrt (gsl_matrix_get (m, i, i) *
+ gsl_matrix_get (m, j, j));
+ }
+ }
+
+ for (i = 0; i < m->size1; ++i)
+ {
+ double r = ssq_row_od_n (idata->mm.corr, i);
+ double u = ssq_row_od_n (a, i);
+ gsl_matrix_set (a, i, i, r / (r + u));
+ }
+
+ return a;
+}
+
+static gsl_matrix *
+anti_image_cov (const gsl_matrix *m)
+{
+ int i, j;
+ gsl_matrix *a;
+ assert (m->size1 == m->size2);
+
+ a = gsl_matrix_alloc (m->size1, m->size2);
+
+ for (i = 0; i < m->size1; ++i)
+ {
+ for (j = 0; j < m->size2; ++j)
+ {
+ double *p = gsl_matrix_ptr (a, i, j);
+ *p = gsl_matrix_get (m, i, j);
+ *p /= gsl_matrix_get (m, i, i);
+ *p /= gsl_matrix_get (m, j, j);
+ }
+ }
+
+ return a;
+}
#if 0
static void
else if (lex_match_id (lexer, "INV"))
{
}
+#endif
else if (lex_match_id (lexer, "AIC"))
{
+ factor.print |= PRINT_AIC;
}
-#endif
else if (lex_match_id (lexer, "SIG"))
{
factor.print |= PRINT_SIG;
tab_submit (t);
}
+static void
+show_aic (const struct cmd_factor *factor, const struct idata *idata)
+{
+ struct tab_table *t ;
+ size_t i;
+
+ const int heading_rows = 1;
+ const int heading_columns = 2;
+
+ const int nc = heading_columns + factor->n_vars;
+ const int nr = heading_rows + 2 * factor->n_vars;
+
+ if ((factor->print & PRINT_AIC) == 0)
+ return;
+
+ t = tab_create (nc, nr);
+
+ tab_title (t, _("Anti-Image Matrices"));
+
+ tab_hline (t, TAL_1, 0, nc - 1, heading_rows);
+
+ tab_headers (t, heading_columns, 0, heading_rows, 0);
+
+ tab_vline (t, TAL_2, 2, 0, nr - 1);
+
+ /* Outline the box */
+ tab_box (t,
+ TAL_2, TAL_2,
+ -1, -1,
+ 0, 0,
+ nc - 1, nr - 1);
+
+ /* Vertical lines */
+ tab_box (t,
+ -1, -1,
+ -1, TAL_1,
+ heading_columns, 0,
+ nc - 1, nr - 1);
+
+
+ for (i = 0; i < factor->n_vars; ++i)
+ tab_text (t, heading_columns + i, 0, TAT_TITLE, var_to_string (factor->vars[i]));
+
+ tab_text (t, 0, heading_rows, TAT_TITLE, _("Anti-image Covariance"));
+ tab_hline (t, TAL_1, 0, nc - 1, heading_rows + factor->n_vars);
+ tab_text (t, 0, heading_rows + factor->n_vars, TAT_TITLE, _("Anti-image Correlation"));
+
+ for (i = 0; i < factor->n_vars; ++i)
+ {
+ tab_text (t, 1, i + heading_rows, TAT_TITLE,
+ var_to_string (factor->vars[i]));
+
+ tab_text (t, 1, factor->n_vars + i + heading_rows, TAT_TITLE,
+ var_to_string (factor->vars[i]));
+ }
+
+ for (i = 0; i < factor->n_vars; ++i)
+ {
+ int j;
+ for (j = 0; j < factor->n_vars; ++j)
+ {
+ tab_double (t, heading_columns + i, heading_rows + j, 0,
+ gsl_matrix_get (idata->ai_cov, i, j), NULL, RC_OTHER);
+ }
+
+
+ for (j = 0; j < factor->n_vars; ++j)
+ {
+ tab_double (t, heading_columns + i, factor->n_vars + heading_rows + j, 0,
+ gsl_matrix_get (idata->ai_cor, i, j), NULL, RC_OTHER);
+ }
+ }
+
+ tab_submit (t);
+}
static void
show_correlation_matrix (const struct cmd_factor *factor, const struct idata *idata)
else
idata->analysis_matrix = idata->mm.cov;
+ gsl_matrix *r_inv;
+ r_inv = clone_matrix (idata->mm.corr);
+ gsl_linalg_cholesky_decomp (r_inv);
+ gsl_linalg_cholesky_invert (r_inv);
+
+ idata->ai_cov = anti_image_cov (r_inv);
+ idata->ai_cor = anti_image_corr (r_inv, idata);
+
+ int i;
+ double sum_ssq_r = 0;
+ double sum_ssq_a = 0;
+ for (i = 0; i < r_inv->size1; ++i)
+ {
+ sum_ssq_r += ssq_od_n (r_inv, i);
+ sum_ssq_a += ssq_od_n (idata->ai_cov, i);
+ }
+
+ gsl_matrix_free (r_inv);
+
if (factor->print & PRINT_DETERMINANT
|| factor->print & PRINT_KMO)
{
if (factor->print & PRINT_KMO)
{
int i;
- double sum_ssq_r = 0;
- double sum_ssq_a = 0;
-
double df = factor->n_vars * (factor->n_vars - 1) / 2;
double w = 0;
const int nr = heading_rows + 4;
const int nc = heading_columns + 1;
- gsl_matrix *a, *x;
+
struct tab_table *t = tab_create (nc, nr);
tab_title (t, _("KMO and Bartlett's Test"));
- x = clone_matrix (idata->mm.corr);
- gsl_linalg_cholesky_decomp (x);
- gsl_linalg_cholesky_invert (x);
-
- a = anti_image (x);
-
- for (i = 0; i < x->size1; ++i)
- {
- sum_ssq_r += ssq_od_n (x, i);
- sum_ssq_a += ssq_od_n (a, i);
- }
-
- gsl_matrix_free (a);
- gsl_matrix_free (x);
tab_headers (t, heading_columns, 0, heading_rows, 0);
}
+ show_aic (factor, idata);
show_communalities (factor, initial_communalities, extracted_communalities);
-
if ( factor->rotation != ROT_NONE)
{
rotated_factors = gsl_matrix_calloc (factor_matrix->size1, factor_matrix->size2);
projects / pspp / blobdiff