High-performance statistical procedures that support model selection use the SELECTION statement to control details about the model selection process. This statement is supported in different degrees by the HPGENSELECT, HPREG, and HPLOGISTIC procedures. The HPREG procedure supports the most complete set of options.
You can specify the following options in the SELECTION statement:
specifies the method used to select the model. You can also specify method-options that apply to the specified method by enclosing them in parentheses after the method. The default selection method (when the METHOD= option is not specified) is METHOD=STEPWISE.
The following methods are available and are explained in detail in the section Methods.
specifies no model selection.
specifies forward selection. This method starts with no effects in the model and adds effects.
specifies backward elimination. This method starts with all effects in the model and deletes effects.
specifies stepwise regression. This method is similar to the FORWARD method except that effects already in the model do not necessarily stay there.
specifies forward-swap selection, which is an extension of the forward selection method. Before any addition step, all pairwise swaps of one effect in the model and one effect out of the current model that improve the selection criterion are made. When the selection criterion is R square, this method is the same as the MAXR method in the REG procedure in SAS/STAT software. The high-performance statistical procedure that supports this method is the HPREG procedure.
specifies least angle regression. Like forward selection, this method starts by adding effects to an empty model. The parameter estimates at any step are "shrunk" when they are compared to the corresponding least squares estimates. If the model contains classification variables, then these classification variables are split. See the SPLIT option in the CLASS statement for details. The only high-performance statistical procedure that supports this method is the HPREG procedure.
adds and deletes parameters by using a version of ordinary least squares in which the sum of the absolute regression coefficients is constrained. If the model contains classification variables, then these classification variables are split. For more information, see the SPLIT option in the CLASS statement. The only high-performance statistical procedure that supports this method is the HPREG procedure.
Table 4.1 lists the applicable method-options for each of these methods.
Table 4.1: Applicable method-options by method
|
method-option |
FORWARD |
BACKWARD |
STEPWISE |
FORWARDSWAP |
LAR |
LASSO |
|---|---|---|---|---|---|---|
|
ADAPTIVE |
x |
|||||
|
CHOOSE = |
x |
x |
x |
x |
x |
|
|
COMPETITIVE |
x |
|||||
|
CRITERION = |
x |
x |
x |
x |
||
|
FAST |
x |
|||||
|
LSCOEFFS |
x |
x |
||||
|
MAXEFFECTS = |
x |
x |
x |
x |
x |
|
|
MAXSTEPS = |
x |
x |
x |
x |
x |
x |
|
MINEFFECTS = |
x |
x |
||||
|
SELECT = |
x |
x |
x |
x |
||
|
SLENTRY = |
x |
x |
x |
x |
||
|
SLSTAY = |
x |
x |
x |
|||
|
STOP = |
x |
x |
x |
x |
x |
x |
The syntax of the method-options that you can specify in parentheses after the SELECTION= option method follows. As described in Table 4.1, not all selection method-options are applicable to every SELECTION= method.
requests that adaptive weights be applied to each of the coefficients when METHOD=LASSO. Ordinary least squares estimates of the model parameters are used to form the adaptive weights. You use the GAMMA= option to specify the power transformation that is applied to the parameters in forming the adaptive weights. The default value is GAMMA=1.
chooses from the list of models (at each step of the selection process) the model that yields the best value of the specified criterion. If the optimal value of the specified criterion occurs for models at more than one step, then the model that has the smallest number of parameters is chosen. If you do not specify the CHOOSE= option, then the selected model is the model at the final step in the selection process. The criteria that are supported depend on the type of model that is being fit. For the supported criteria, see the chapters for the relevant high-performance statistical procedures.
is applicable only as a method-option when METHOD=STEPWISE and the SELECT criterion is not SL. If you specify the COMPETITIVE option, then the SELECT= criterion is evaluated for all models in which an effect currently in the model is dropped or an effect not yet in the model is added. The effect whose removal from or addition to the model yields the maximum improvement to the SELECT= criterion is dropped or added.
is an alias for the SELECT option.
implements the computational algorithm of Lawless and Singhal (1978) to compute a first-order approximation to the remaining slope estimates for each subsequent elimination of a variable from the model. When applied in backward selection, this option essentially leads to approximating the selection process as the selection process of a linear regression model in which the crossproducts matrix equals the Hessian matrix in the full model under consideration. The FAST option is available only when METHOD=BACKWARD in the HPLOGISTIC procedure. It is computationally efficient in logistic regression models because the model is not fit after removal of each effect.
requests a hybrid version of the LAR and LASSO methods, in which the sequence of models is determined by the LAR or LASSO algorithm but the coefficients of the parameters for the model at any step are determined by using ordinary least squares.
specifies the maximum number of effects in any model that is considered during the selection process. This option is ignored with METHOD=BACKWARD. If at some step of the selection process the model contains the specified maximum number of effects, then no candidates for addition are considered.
specifies the maximum number of selection steps that are performed. The default value of n is the number of effects in the MODEL statement when METHOD=FORWARD, METHOD=BACKWARD, or METHOD=LAR. The default is three times the number of effects when METHOD=STEPWISE or METHOD=LASSO.
specifies the minimum number of effects in any model that is considered during backward selection. This option is ignored unless METHOD=BACKWARD is specified. The backward selection process terminates if, at some step of the selection process, the model contains the specified minimum number of effects.
specifies the criterion that the procedure uses to determine the order in which effects enter or leave at each step of the selection method. The criteria that are supported depend on type of model that is being fit. See the chapter for the relevant high-performance statistical procedure for the supported criteria.
The SELECT option is not valid when METHOD=LAR or METHOD=LASSO. You can use SELECT=SL to request the traditional approach, where effects enter and leave the model based on the significance level. When the value of the SELECT= option is not SL, the effect that is selected to enter or leave at any step of the selection process is the effect whose addition to or removal from the current model yields the maximum improvement in the specified criterion.
specifies the significance level for entry when STOP= SL or SELECT= SL. The default is 0.05.
specifies the significance level for staying in the model when STOP= SL or SELECT= SL. The default is 0.05.
specifies a criterion that is used to stop the selection process. The criteria that are supported depend on the type of model that is being fit. For information about the supported criteria, see the chapter about the relevant high-performance statistical procedure.
If you do not specify the STOP= option but do specify the SELECT= option, then the criterion specified in the SELECT= option is also used as the STOP= criterion.
If you specify STOP=NONE, then the selection process stops if no suitable add or drop candidates can be found or if a size-based limit is reached. For example, if you specify STOP=NONE MAXEFFECTS=5, then the selection process stops at the first step that produces a model with five effects.
When STOP=SL, selection stops at the step where the significance level of the candidate for entry is greater than the SLENTRY= value for addition steps when METHOD=FORWARD or METHOD=STEPWISE and where the significance level of the candidate for removal is greater than the SLSTAY= value when METHOD=BACKWARD or METHOD=STEPWISE.
If you specify a criterion other than SL for the STOP= option, then the selection process stops if the selection process produces a local extremum of this criterion or if a size-based limit is reached. For example, if you specify STOP=AIC MAXSTEPS=5, then the selection process stops before step 5 if the sequence of models has a local minimum of the AIC criterion before step 5. The determination of whether a local minimum is reached is made on the basis of a stop horizon. The default stop horizon is 3, but you can change it by using the STOPHORIZON= option. If the stop horizon is n and the STOP= criterion at any step is better than the stop criterion at the next n steps, then the selection process terminates.
specifies the level of detail to be produced about the selection process. The default is DETAILS=SUMMARY.
The DETAILS=ALL and DETAILS=STEPS options produce the following output:
tables that provide information about the model that is selected at each step of the selection process.
entry and removal statistics for inclusion or exclusion candidates at each step. By default, only the top 10 candidates at each step are shown. If you specify STEPS(CANDIDATES(n)), then the best n candidates are shown. If you specify STEPS(CANDIDATES(ALL)), then all candidates are shown.
a selection summary table that shows by step the effect that is added to or removed from the model in addition to the values of the SELECT, STOP, and CHOOSE criteria for the resulting model.
a stop reason table that describes why the selection process stopped.
a selection reason table that describes why the selected model was chosen.
a selected effects table that lists the effects that are in the selected model.
The DETAILS=SUMMARY option produces only the selection summary, stop reason, selection reason, and selected effects tables.
specifies whether and how the model hierarchy requirement is applied. This option also controls whether a single effect or multiple effects are allowed to enter or leave the model in one step. You can specify that only classification effects, or both classification and continuous effects, be subject to the hierarchy requirement. The HIERARCHY= option is ignored unless you also specify one of the following options: METHOD= FORWARD, METHOD= BACKWARD, or METHOD= STEPWISE.
Model hierarchy refers to the requirement that, for any term to be in the model, all model effects that are contained in the term must be present in the model. For example, in order for the interaction A*B to enter the model, the main effects A and B must be in the model. Likewise, neither effect A nor effect B can leave the model while the interaction A*B is in the model.
You can specify the following values:
specifies that model hierarchy not be maintained. Any single effect can enter or leave the model at any given step of the selection process.
specifies that only one effect enter or leave the model at one time, subject to the model hierarchy requirement. For example, suppose that the model contains the main effects A and B and the interaction A*B. In the first step of the selection process, either A or B can enter the model. In the second step, the other main effect can enter the model. The interaction effect can enter the model only when both main effects have already entered. Also, before A or B can be removed from the model, the A*B interaction must first be removed. All effects (CLASS and interval) are subject to the hierarchy requirement.
is the same as HIERARCHY=SINGLE except that only CLASS effects are subject to the hierarchy requirement.
The default value is HIERARCHY=NONE.
requests that a subset of the effects specified in the MODEL statement be chosen as candidate effects for model selection. You use the global-screen-options and screen-options to specify how such a subset is chosen and to control the detail level of the associated output. The SCREEN option is fully documented in the section SELECTION Statement in Chapter 14: The HPREG Procedure, which is the only high-performance statistical procedure that supports the SCREEN option.
is an alias for the METHOD= option.
specifies the number of consecutive steps at which the STOP= criterion must worsen in order for a local extremum to be detected. The default value is STOPHORIZON=3. The stop horizon value is ignored if you also specify STOP=NONE or STOP=SL. For example, suppose that STOP=AIC and the sequence of AIC values at steps 1 to 6 of a selection are 10, 7, 4, 6, 5, 2. If STOPHORIZON=2, then the AIC criterion is deemed to have a local minimum at step 3 because the AIC value at the next two steps are greater than the value 4 that occurs at step 3. However, if STOPHORIZON=3, then the value at step 3 is not deemed to be a local minimum because the AIC value at step 6 is lower than the AIC value at step 3.