This section applies to actions in the following action sets: phreg, quantreg, and regression.
When the method subparameter value is STEPWISE, then the stepwise method modifies the forward selection technique by allowing effects already in the model to be removed.
In the traditional implementation of stepwise selection method, the same entry and removal significance levels for the forward selection and backward elimination methods are used to assess contributions of effects as they are added to or removed from a model. If, at a step of the stepwise method, any effect in the model is not significant at the slStay level, then the least significant of these effects is removed from the model and the algorithm proceeds to the next step. This ensures that no effect can be added to a model while some effect currently in the model is not deemed significant. Another effect can be added to the model only after all necessary deletions have been accomplished. In this case the effect whose addition is the most significant is added to the model and the algorithm proceeds to the next step. The stepwise process ends when none of the effects outside the model is significant at the slEntry level and every effect in the model is significant at the slStay level. In some cases, neither of these two conditions for stopping is met and the sequence of models cycles. In this case, the stepwise method terminates at the end of the cycle.
Just as you can in forward selection and backward elimination, you can use the select subparameter to change the criterion that is used to assess effect contributions. You can also use the stop subparameter to specify a stopping criterion and use the choose subparameter to provide a criterion for selecting among the sequence of models produced. For more information, see the section Forward Selection.
For selection criteria other than the significance level, further modification to the stepwise method is supported. In the standard stepwise method, no effect can enter the model if removing any effect currently in the model would yield an improved value of the selection criterion. In the modification, you can use the competitive subparameter to specify that addition and deletion of effects should be treated competitively. The selection criterion is evaluated for all models that are produced by deleting an effect from the current model or by adding an effect to this model. The action that most improves the selection criterion is the action taken.
The following CASL language statement requests stepwise selection based on the SBC criterion:
selection={method='stepwise'}
First, if removing any effect yields a model that has a lower SBC statistic than the current model, then the effect that produces the smallest SBC statistic is removed. If removing any effect increases the SBC statistic, then provided that adding some effect lowers the SBC statistic, the effect that produces the model that has the lowest SBC is added.
The following CASL language statement requests the traditional stepwise method:
selection={method='stepwise',select='SL'}
First, if the removal of any effect in the model is not significant at the default stay level of 0.05, then the least significant effect is removed and the algorithm proceeds to the next step. Otherwise, the effect whose addition is the most significant is added, provided that it is significant at the default entry level of 0.05.
The following CASL language statement requests the traditional stepwise method, where effects enter and leave based on significance levels, but with the following extra check: if any effect to be added or removed yields a model whose SBC statistic is greater than the SBC statistic of the current model, then the stepwise method terminates at the current model.
selection={method='stepwise',select='SL',stop='SBC',stopHorizon=1}
In this case, the entry and stay significance levels still play a role because they determine whether an effect is deleted from or added to the model. This extra check might result in the selection terminating before a local minimum of the SBC criterion is found.
The following CASL language statement selects effects to enter or drop as in the previous example except that the significance level for entry is now 0.1 and the significance level to stay is 0.08. From the sequence of models produced, the selected model is chosen to yield the minimum AIC statistic:
selection={method='stepwise',select='SL',sle=0.1,sls=0.08,choose='AIC'}
The following CASL language statement requests stepwise selection that is based on the AICC criterion and treats additions and deletions competitively:
selection={method='stepwise',select='AICC',competitive=True}
Each step evaluates the AICC statistics that correspond to the removal of any effect in the current model or the addition of any effect to the current model and chooses the addition or removal that produced the minimum value, provided that this minimum is lower than the AICC statistic of the current model.
The following CASL language statement requests stepwise selection that is based on the SBC criterion, treats additions and deletions competitively, and stops based on the average square error over the validation data:
selection={method='stepwise',select='SBC',competitive=True,stop='VALIDATE'}
At any step, SBC statistics that correspond to the removal of any effect from the current model or the addition of any effect to the current model are evaluated. The addition or removal that produces the minimum SBC value is made. The average square error on the validation data for the model with this addition or removal is evaluated. The selection stops when the average square error so produced increases for three consecutive steps.