Logistic Regression: Added the Classification Table

Added a table to logistic regression to show how the predicted values
would be classified by the calculated coefficients.

diff --git a/doc/statistics.texi b/doc/statistics.texi
index 5723323337559ec4076be50b300d9b8152e1a1c2..a4f03ca6dd52fcce3a1b6b8babd747c263a4633b 100644 (file)
--- a/doc/statistics.texi
+++ b/doc/statistics.texi
@@ -741,7 +741,8 @@ LOGISTIC REGRESSION [VARIABLES =] @var{dependent_var} WITH @var{predictors}
      [/PRINT = [SUMMARY] [DEFAULT] [CI(@var{confidence})] [ALL]]
 
      [/CRITERIA = [BCON(@var{min_delta})] [ITERATE(@var{max_interations})]
-                  [LCON(@var{min_likelihood_delta})] [EPS(@var{min_epsilon})]]
+                  [LCON(@var{min_likelihood_delta})] [EPS(@var{min_epsilon})]
+                  [CUT(@var{cut_point})]]
 
      [/MISSING = @{INCLUDE|EXCLUDE@}]
 @end display
@@ -773,10 +774,14 @@ If you want a model without the constant term @math{b_0}, use the keyword @subcm
 @subcmd{/NOCONST} is a synonym for @subcmd{/ORIGIN}.
 
 An iterative Newton-Raphson procedure is used to fit the model.
-The @subcmd{/CRITERIA} subcommand is used to specify the stopping criteria of the procedure.
+The @subcmd{/CRITERIA} subcommand is used to specify the stopping criteria of the procedure,
+and other parameters.
+The value of @var{cut_point} is used in the classification table.  It is the 
+threshold above which predicted values are considered to be 1.  Values
+of @var{cut_point} must lie in the range [0,1].
 During iterations, if any one of the stopping criteria are satisfied, the procedure is
 considered complete.
-The criteria are:
+The stopping criteria are:
 @itemize
 @item The number of iterations exceeds @var{max_iterations}.  
       The default value of @var{max_iterations} is 20.
@@ -790,6 +795,7 @@ In other words, the probabilities are close to zero or one.
 The default value of @var{min_epsilon} is 0.00000001.
 @end itemize
 
+
 The @subcmd{PRINT} subcommand controls the display of optional statistics.
 Currently there is one such option, @subcmd{CI}, which indicates that the 
 confidence interval of the odds ratio should be displayed as well as its value.

diff --git a/src/language/stats/logistic.c b/src/language/stats/logistic.c
index 7171563032e396b37ec2a83df8bf94fd6c15a347..cdd31c268d8f41cfb53c3bcef1b9804690b62b9e 100644 (file)
--- a/src/language/stats/logistic.c
+++ b/src/language/stats/logistic.c
@@ -172,6 +172,10 @@ struct lr_result
 
   /* The estimates of the predictor coefficients */
   gsl_vector *beta_hat;
+
+  /* The predicted classifications: 
+     True Negative, True Positive, False Negative, False Positive */
+  double tn, tp, fn, fp;
 };
 
 
@@ -197,6 +201,7 @@ map_dependent_var (const struct lr_spec *cmd, const struct lr_result *res, const
   return SYSMIS;
 }
 
+static void output_classification_table (const struct lr_spec *cmd, const struct lr_result *res);
 
 static void output_categories (const struct lr_spec *cmd, const struct lr_result *res);
 
@@ -328,7 +333,9 @@ hessian (const struct lr_spec *cmd,
    y is the vector of observed independent variables
    pi is the vector of estimates for y
 
-   As a side effect, the likelihood is stored in LIKELIHOOD
+   Side effects:
+     the likelihood is stored in LIKELIHOOD;
+     the predicted values are placed in the respective tn, fn, tp fp values in RES
 */
 static gsl_vector *
 xt_times_y_pi (const struct lr_spec *cmd,
@@ -343,9 +350,11 @@ xt_times_y_pi (const struct lr_spec *cmd,
   gsl_vector *output = gsl_vector_calloc (res->beta_hat->size);
 
   *likelihood = 1.0;
+  res->tn = res->tp = res->fn = res->fp = 0;
   for (reader = casereader_clone (input);
        (c = casereader_read (reader)) != NULL; case_unref (c))
     {
+      double pred_y = 0;
       int v0;
       double pi = pi_hat (cmd, res, x, n_x, c);
       double weight = dict_get_case_weight (cmd->dict, c, &res->warn_bad_weight);
@@ -360,6 +369,26 @@ xt_times_y_pi (const struct lr_spec *cmd,
          double in0 = predictor_value (c, x, n_x, res->cats, v0);
          double *o = gsl_vector_ptr (output, v0);
          *o += in0 * (y - pi) * weight;
+         pred_y += gsl_vector_get (res->beta_hat, v0) * in0;
+       }
+
+      pred_y = 1 / (1.0 + exp(-pred_y));
+      assert (pred_y >= 0);
+      assert (pred_y <= 1);
+
+      if (pred_y <= cmd->cut_point)
+       {
+         if (y == 0)
+           res->tn += weight;
+         else
+           res->fn += weight;
+       }
+      else
+       {
+         if (y == 0)
+           res->fp += weight;
+         else
+           res->tp += weight;
        }
     }
 
@@ -665,6 +694,7 @@ run_lr (const struct lr_spec *cmd, struct casereader *input,
   if (work.cats)
     output_categories (cmd, &work);
 
+  output_classification_table (cmd, &work);
   output_variables (cmd, &work);
 
   gsl_matrix_free (work.hessian);
@@ -928,6 +958,29 @@ cmd_logistic (struct lexer *lexer, struct dataset *ds)
                        }
                    }
                }
+             else if (lex_match_id (lexer, "CUT"))
+               {
+                 if (lex_force_match (lexer, T_LPAREN))
+                   {
+                     if (! lex_force_num (lexer))
+                       {
+                         lex_error (lexer, NULL);
+                         goto error;
+                       }
+                     lr.cut_point = lex_number (lexer);
+                     if (lr.cut_point < 0 || lr.cut_point > 1.0)
+                       {
+                         msg (ME, _("Cut point value must be in the range [0,1]"));
+                         goto error;
+                       }
+                     lex_get (lexer);
+                     if ( ! lex_force_match (lexer, T_RPAREN))
+                       {
+                         lex_error (lexer, NULL);
+                         goto error;
+                       }
+                   }
+               }
              else
                {
                  lex_error (lexer, NULL);
@@ -1436,3 +1489,86 @@ output_categories (const struct lr_spec *cmd, const struct lr_result *res)
   tab_submit (t);
 
 }
+
+
+static void 
+output_classification_table (const struct lr_spec *cmd, const struct lr_result *res)
+{
+  const struct fmt_spec *wfmt =
+    cmd->wv ? var_get_print_format (cmd->wv) : &F_8_0;
+
+  const int heading_columns = 3;
+  const int heading_rows = 3;
+
+  struct string sv0, sv1;
+
+  const int nc = heading_columns + 3;
+  const int nr = heading_rows + 3;
+
+  struct tab_table *t = tab_create (nc, nr);
+
+  ds_init_empty (&sv0);
+  ds_init_empty (&sv1);
+
+  tab_title (t, _("Classification Table"));
+
+  tab_headers (t, heading_columns, 0, heading_rows, 0);
+
+  tab_box (t, TAL_2, TAL_2, -1, -1, 0, 0, nc - 1, nr - 1);
+  tab_box (t, -1, -1, -1, TAL_1, heading_columns, 0, nc - 1, nr - 1);
+
+  tab_hline (t, TAL_2, 0, nc - 1, heading_rows);
+  tab_vline (t, TAL_2, heading_columns, 0, nr - 1);
+
+  tab_text (t,  0, heading_rows, TAB_CENTER | TAT_TITLE, _("Step 1"));
+
+
+  tab_joint_text (t, heading_columns, 0, nc - 1, 0,
+                 TAB_CENTER | TAT_TITLE, _("Predicted"));
+
+  tab_joint_text (t, heading_columns, 1, heading_columns + 1, 1, 
+                 0, var_to_string (cmd->dep_var) );
+
+  tab_joint_text (t, 1, 2, 2, 2,
+                 TAB_LEFT | TAT_TITLE, _("Observed"));
+
+  tab_text (t, 1, 3, TAB_LEFT, var_to_string (cmd->dep_var) );
+
+
+  tab_joint_text (t, nc - 1, 1, nc - 1, 2,
+                 TAB_CENTER | TAT_TITLE, _("Percentage\nCorrect"));
+
+
+  tab_joint_text (t, 1, nr - 1, 2, nr - 1,
+                 TAB_LEFT | TAT_TITLE, _("Overall Percentage"));
+
+
+  tab_hline (t, TAL_1, 1, nc - 1, nr - 1);
+
+  var_append_value_name (cmd->dep_var, &res->y0, &sv0);
+  var_append_value_name (cmd->dep_var, &res->y1, &sv1);
+
+  tab_text (t, 2, heading_rows,     TAB_LEFT,  ds_cstr (&sv0));
+  tab_text (t, 2, heading_rows + 1, TAB_LEFT,  ds_cstr (&sv1));
+
+  tab_text (t, heading_columns,     2, 0,  ds_cstr (&sv0));
+  tab_text (t, heading_columns + 1, 2, 0,  ds_cstr (&sv1));
+
+  ds_destroy (&sv0);
+  ds_destroy (&sv1);
+
+  tab_double (t, heading_columns, 3,     0, res->tn, wfmt);
+  tab_double (t, heading_columns + 1, 4, 0, res->tp, wfmt);
+
+  tab_double (t, heading_columns + 1, 3, 0, res->fp, wfmt);
+  tab_double (t, heading_columns,     4, 0, res->fn, wfmt);
+
+  tab_double (t, heading_columns + 2, 3, 0, 100 * res->tn / (res->tn + res->fp), 0);
+  tab_double (t, heading_columns + 2, 4, 0, 100 * res->tp / (res->tp + res->fn), 0);
+
+  tab_double (t, heading_columns + 2, 5, 0, 
+             100 * (res->tp + res->tn) / (res->tp  + res->tn + res->fp + res->fn), 0);
+
+
+  tab_submit (t);
+}

diff --git a/tests/language/stats/logistic.at b/tests/language/stats/logistic.at
index 9ab04f8cec0045192eba5d1368a8909fb5a6de10..5f6232f7ca3fbd2b2c2a71f3f51224f0ac8c77c5 100644 (file)
--- a/tests/language/stats/logistic.at
+++ b/tests/language/stats/logistic.at
@@ -112,6 +112,15 @@ Table: Model Summary
 Step 1,-2 Log likelihood,Cox & Snell R Square,Nagelkerke R Square
 ,37.323,.455,.659
 
+Table: Classification Table
+,,,Predicted,,
+,,,outcome,,"Percentage
+Correct"
+,Observed,,1.000,2.000,
+Step 1,outcome,1.000,43,5,89.583
+,,2.000,4,14,77.778
+,Overall Percentage,,,,86.364
+
 Table: Variables in the Equation
 ,,B,S.E.,Wald,df,Sig.,Exp(B)
 Step 1,survrate,-.081,.019,17.756,1,.000,.922
@@ -213,6 +222,12 @@ AT_CHECK([diff unweighted-result weighted-result], [1], [dnl
 < Total,66,100.000
 ---
 > Total,63,100.000
+23,24c23,24
+< Step 1,outcome,1.000,43,5,89.583
+< ,,2.000,4,14,77.778
+---
+> Step 1,outcome,1.000,43.000,5.000,89.583
+> ,,2.000,4.000,14.000,77.778
 ])
 
 
@@ -259,6 +274,15 @@ Table: Model Summary
 Step 1,-2 Log likelihood,Cox & Snell R Square,Nagelkerke R Square
 ,275.637,.008,.011
 
+Table: Classification Table
+,,,Predicted,,
+,,,female,,"Percentage
+Correct"
+,Observed,,.00,1.00,
+Step 1,female,.00,0,91,.000
+,,1.00,0,109,100.000
+,Overall Percentage,,,,54.500
+
 Table: Variables in the Equation
 ,,B,S.E.,Wald,df,Sig.,Exp(B)
 Step 1,constant,.180,.142,1.616,1,.204,1.198
@@ -738,6 +762,15 @@ bcat,1.000,61,1,0,0
 ,3.000,121,0,0,1
 ,4.000,67,0,0,0
 
+Table: Classification Table
+,,,Predicted,,
+,,,y,,"Percentage
+Correct"
+,Observed,,4.000,9.000,
+Step 1,y,4.000,254,19,93.040
+,,9.000,97,30,23.622
+,Overall Percentage,,,,71.000
+
 Table: Variables in the Equation
 ,,B,S.E.,Wald,df,Sig.,Exp(B)
 Step 1,b1,.002,.001,4.284,1,.038,1.002
@@ -997,6 +1030,15 @@ ses,a,47,1,0
 ,b,95,0,1
 ,c,58,0,0
 
+Table: Classification Table
+,,,Predicted,,
+,,,honcomp,,"Percentage
+Correct"
+,Observed,,.000,1.000,
+Step 1,honcomp,.000,132,15,89.796
+,,1.000,26,27,50.943
+,Overall Percentage,,,,79.500
+
 Table: Variables in the Equation
 ,,B,S.E.,Wald,df,Sig.,Exp(B)
 Step 1,read,.098,.025,15.199,1,.000,1.103