School of Population Health 13. Strategy

The Strategy dialog box is used to set restrictions on a search and the way a search is to be carried out. When you OK the strategy dialog box you may be presented with other dialog boxes and menus to give details of the selected options.

13.1 Constrain X space

You can restrict the analysis to a subgroup, defined in terms of an attribute, with this option. For example, if a variable x has cutpoints specified in the control file as, say, 20, 30 and 50, you could carry out the analysis only on subjects with x £ 30.

Restrictions of this kind can only be done in terms of attributes that have been defined, either in the attribute creating lines of the control file or from added attributes created during the analysis. These will be listed in a Select attributes dialog box:

The attributes listed tagged with a + are positive attributes with respect to the dependent Y variable(s). Note that this option will essentially do an analysis in one specific data sub-group. The Y:By-group option (see 10.8) will achieve the same for data split into a number of groups.

10.8

13.2 Force in attribute

This option allows you to force attributes into a partition. Suppose you have an attribute X. Then for a given partition A you can "force" in X by either forming X ÇA- or XÇA. Each partition, A, for given size p1,...,pq that is generated will have X forced into it. It is the forced partitions that are assessed by the chosen criterion, not A itself.

When OK of the Strategy dialog box is pressed, a dialog of all the attributes will be presented for you to choose a forcing attribute:

The attributes listed that are tagged with a + are positive attributes with respect to the dependent Y variable(s). Selecting a tagged positive attribute, X say, will force the intersection XÇA which is equivalent to forcing the union X-ÈA-. Selecting a non-tagged negative attribute, X- say, will force the intersection X-ÇA- , which is equivalent to forcing the union XÈA. SPAN will automatically implement the Boolean expansion and simplification of the forced union or intersection during the search and, if the variable dependent reduction option is set, may make further simplifications (see 17.3)

13.3 Iterative mode

With this option SPAN enters the iterative procedure to search for an optimal partition, described in reference 2. A search is first done for the best partition with parameters set in the Search Extent menu. The best partition will then become an added attribute which is added to the attribute set for the next iteration. New searches are then automatically generated until "convergence" is achieved. Convergence is deemed to occur when the optimal partition on the current iteration is identical to that on the previous iteration. (Convergence also occurs if the best partition on the first iteration is a single single attribute, that is, p_1 ... p_q=1, since subsequent iterations cannot improve the partition.)

The sequence of added attributes that are created in this process are denoted +a_1 , +a_2 , etc. If iterative searches have previously been implemented they are distinguished by alphabetical sequence; +b_1 , +b_2 , etc on the new iterative search, +c_1 , +c_2 , etc on the next and so on until +A_1, +A_2 etc. Once capitals are used up, SPAN goes back to lower case.

13.4 Tree

SPAN has a facility for tree-structured partitioning. With this option SPAN will enter "tree mode" and, when Search is invoked, will carry out a series of by-group analyses to create a tree. (Note that this effectively precludes the ability to do a by-group analysis in tree mode or cross-validate trees).

The tree is generated down to 5 levels, creating maximum 2**5=32 terminal nodes. This full tree is then pruned once the search is completed, A Tree Auto Stopping rule dialog box is presented (see 15.8) to establish the tree. Usually a tree search is made with q=1 and p1=1 which means splits are done on a single risk factor. You can change this to allow "Boolean" splits in the Extent dialog. Also for trees it sensible to allow floating cut levels in the Extent dialog to 3.

13.5 Top m

This gives the number attributes to be used in the search. It forms the attribute set Tm from the m best attributes. Generally this should be <15 (see (see Appendix A2.1).

13.6 Decide positivity

With this checked (which is always recommended) SPAN will decide the direction of an attribute and Y according to the correlation and fix the attributes deemed to be positive with respect to Y.