Next: Stepwise selection Up: Automatic variable selection procedures Previous: Forward selection

### Backward selection

Forward selection has drawbacks, including the fact that each addition of a new variable may render one or more of the already included variables non-significant. An alternate approach which avoids this is backward selection. Under this approach, one starts with fitting a model with all the variables of interest (following the initial screen). Then the least significant variable is dropped, so long as it is not significant at our chosen critical level. We continue by successively re-fitting reduced models and applying the same rule until all remaining variables are statistically significant. Applying this to the same data as before:

```. sw reg  wtpct12 ventdays blish gest bw bl conv, pr(.10)
begin with full model
p = 0.9705 >= 0.1000  removing bl
p = 0.3065 >= 0.1000  removing conv

Source |       SS       df       MS              Number of obs =     150
-------------+------------------------------           F(  4,   145) =    8.65
Model |  21074.0503     4  5268.51257           Prob > F      =  0.0000
Residual |  88363.3897   145  609.402688           R-squared     =  0.1926
Total |   109437.44   149  734.479463           Root MSE      =  24.686

------------------------------------------------------------------------------
wtpct12 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
ventdays |  -.2031126   .0946998    -2.14   0.034     -.390283   -.0159423
blish |  -.2658678   .1301217    -2.04   0.043    -.5230482   -.0086874
gest |  -3.601116    1.10194    -3.27   0.001    -5.779057   -1.423175
bw |   .0247148   .0054799     4.51   0.000     .0138839    .0355456
_cons |   113.7379   29.14385     3.90   0.000     56.13626    171.3396
------------------------------------------------------------------------------
```

Though we have started from the "other end", in this case we wind up with the same model. There is no guarantee that this will always happen. Backward selection has it's own drawbacks, as well. Sometimes variables are dropped that would be significant when added to the final reduced models. This suggests that some compromise between forward and backward selection methods should be considered.

Next: Stepwise selection Up: Automatic variable selection procedures Previous: Forward selection
Rollin Brant 2004-03-24