Table 2.
Selection Model Identification by Sample Size and Selection Model, Simulation A
| Covariate flagged as significant (rejection rate)
|
Covariate used in tree
|
|||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
t tests
|
Logistic
|
CART
|
CART + Prune
|
|||||||||
| v | z | w | v | z | w | v | z | w | v | z | w | |
| N = 100 | ||||||||||||
| Linear | .612 | .041 | .052 | .611 | .054 | .042 | .914 | .710 | .698 | .876 | .396 | .387 |
| One split | .944 | .052 | .058 | .943 | .049 | .047 | .997 | .428 | .408 | .989 | .065 | .063 |
| Two splits | .892 | .539 | .056 | .926 | .049 | .620 | .991 | .903 | .219 | .964 | .699 | .055 |
| Three splits | .044 | .371 | .593 | .046 | .616 | .393 | .848 | .796 | .943 | .576 | .597 | .828 |
| N = 250 | ||||||||||||
| Linear | .786 | .050 | .054 | .783 | .064 | .053 | .996 | .924 | .912 | .97 | .482 | .483 |
| One split | .999 | .051 | .048 | .999 | .047 | .041 | 1.000 | .545 | .539 | 1.000 | .033 | .034 |
| Two splits | 1.000 | .922 | .044 | 1.000 | .052 | .958 | 1.000 | .997 | .518 | .993 | .838 | .081 |
| Three splits | .048 | .734 | .884 | .054 | .896 | .777 | .999 | .996 | 1.000 | .902 | .804 | .964 |
| N = 500 | ||||||||||||
| Linear | .929 | .053 | .052 | .928 | .048 | .054 | .978 | .811 | .816 | .966 | .477 | .482 |
| One split | 1.000 | .053 | .060 | 1.000 | .054 | .042 | 1.000 | .306 | .316 | 1.000 | .018 | .018 |
| Two splits | 1.000 | .996 | .044 | 1.000 | .044 | .999 | 1.000 | 1.000 | .484 | .999 | .911 | .070 |
| Three splits | .076 | .959 | .989 | .078 | .991 | .972 | 1.000 | 1.000 | 1.000 | .993 | .901 | .998 |
Note. CART = classification and regression trees; Prune = pruned CART analysis. Table entries indicate the percentage of simulated iterations that each variable was either flagged as statistically significant (t-tests, logistic regression) or included as a split variable (CART, CART + Prune).