MR-2010I %MktBSize Macro 989. %MktBSize Macro

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1 MR-2010I %MktBSize Macro 989 %MktBSize Macro The %MktBSize autocall macro suggests sizes for balaced icomplete block desigs (BIBDs). The sizes that it reports are sizes that meet ecessary but ot sufficiet coditios for the existece of a BIBD, so a BIBD might ot exist for every size reported. I the followig example, a list of desigs with 12 treatmets, betwee 4 ad 8 treatmets per block, ad betwee 12 ad 30 blocks are requested: %mktbsize(t=12, k=4 to 8, b=12 to 30) The results are as follows: You ca use this iformatio to create a BIBD with the %MktBIBD macro as follows: %mktbibd(t=12, k=6, b=22, seed=104) There is o guaratee that %MktBIBD will fid a BIBD for ay specificatio, but i this case it does, ad it fids the followig desig: Balaced Icomplete Block Desig x1 x2 x3 x4 x5 x

2 990 MR-2010I Experimetal Desig ad Choice Modelig Macros The desig has b=22 blocks (rows), k=6 treatmets per block (colums), ad t=12 treatmets (the etries are the itegers 1 to 12). Each of the t=12 treatmets occurs r=11 times, ad each treatmet occurs i a block with every other treatmet λ=5 times. The followig step creates a list of over 50 desigs: %mktbsize(t=5 to 20, k=3 to t - 1, b=t to 30) Some of the results are as follows: Note that by default, maxreps=1 (the maximum umber of replicatios is 1), so for example, the desig t=5, k=3, b=20 is ot listed sice it cosists of two replicatios of t=5, k=3, b=10, which is listed. Also ote that b, the umber of blocks, was specified so that it is ever less tha the umber of treatmets. Furthermore, k, the block size (umber of treatmets per block), is set to always be less tha the umber of treatmets. Eve more complicated expressios are permitted. For example, to limit the umber of treatmets per block to o more tha half of the umber of treatmets, you could specify the followig: %mktbsize(t=2 to 10, k=2 to 0.5 * t, b=t to 10) The results are as follows:

3 MR-2010I %MktBSize Macro To limit the umber of blocks as a fuctio of the umber of treatmets, you could specify the followig: %mktbsize(t=2 to 10, k=2 to t - 1, b=t to 2 * t) However, if you wat to limit the umber of treatmets as a fuctio of the umber of blocks, you eed to use the order= optio to esure that the umber of blocks loop comes first, for example, as follows: %mktbsize(b=2 to 10, t=2 to 0.5 * b, k=2 to t - 1, order=btk) The macro reports sizes i which r = b k/t ad l = r (k 1)/(t 1) are itegers, 2 k < t, ad b t. Whe r = b k/t ad l = r (k 1)/(t 1) are itegers, ad k = t ad b t, the a complete block desig might be possible. This is a ecessary but ot sufficiet coditio for the existece of a complete block desig. Whe r = b k/t ad l = r (k 1)/(t 1) are itegers, ad k < t ad b t, the a balaced icomplete block desig might be possible. This is a ecessary but ot sufficiet coditio for the existece of a BIBD. Whe you specify optios=ubd ad r = b k/t is a iteger, the ubalaced block desig sizes are reported as well. For example, if you wat a desig with t=20 treatmets ad a block size of 6, you ca ru the followig to fid out how may blocks you eed: %mktbsize(t=20, k=6, optios=ubd) The results are as follows: The the %MktBIBD macro ca be used to fid a desig where each treatmet occurs 3 times, but the treatmets do ot appear together a equal umber of times, for example, as follows: %mktbibd(t=20, k=6, b=10, seed=104)

4 992 MR-2010I Experimetal Desig ad Choice Modelig Macros Some of the results are as follows: Treatmet by Treatmet Frequecies %MktBSize Macro Optios The followig optios ca be used with the %MktBIBD macro: Optio help b=do-list k=do-list maxreps= attrs=do-list sets=do-list order=order-list optios=ocheck optios=ubd out=sas-data-set setsize=do-list t=do-list Descriptio (positioal) help or? displays sytax summary umber of blocks (alias for sets=) block size (alias for setsize=) maximum umber of replicatios umber of attributes (alias for t=) umber of sets (alias for b=) order of the loops suppress checkig b, t, ad k lifts the balace restrictio o the desig output data set desig list set size (alias for k=) umber of treatmets (alias for attrs=)

5 MR-2010I %MktBSize Macro 993 You ca specify either of the followig to display the optio ames ad simple examples of the macro sytax: %mktbsize(help) %mktbsize(?) The k= or setsize=, ad the t= or attrs= optios must be specified. b= do-list sets= do-list specifies the umber of blocks. I a partial-profile desig, this is the umber of profiles. I a MaxDiff desig, this is the umber of sets. Specify either a iteger or a list of itegers i the SAS do-list sytax. The default is b=2 to 500. The sets= ad b= optios are aliases. k= do-list setsize= do-list specifies the block size, or the umber of treatmets i each block. I a partial-profile or MaxDiff desig, this is the umber of attributes or messages show at oe time i each set. Specify either a iteger or a list of itegers i the SAS do-list sytax. The setsize= ad k= optios are aliases. This optio (i oe of its two forms) must be specified. maxreps= specifies the maximum umber of replicatios. The default is maxreps=1. By default, this optio prevets the %MktBSize macro from reportig desigs of size 2b, 3b, ad so o after it has foud a size with b blocks. optios= optios-list specifies biary optios. By default, oe of these optios are specified. Specify oe or more of the followig values after optios=. ocheck by default, certai checks are performed o b, t, ad k. Specify optios=ocheck to tur them off. This lets you make some creative expressios that otherwise would ot be permitted. ubd lifts the balace restrictio o the desig. Results are reported whe r = b k/t is i iteger but l = r (k 1)/(t 1) might or might ot be a iteger. Use this optio whe you wat to see sizes where every treatmet ca occur equally ofte, but the pairwise frequecies ca be uequal. The listig ca cotai both sizes where a BIBD might be possible (λ, the expected pairwise frequecy, is a iteger) ad sizes where a BIBD is ot possible (λ is ot a iteger). You might use this optio, for example, whe the block desig is beig used to make a partial-profile desig.

6 994 MR-2010I Experimetal Desig ad Choice Modelig Macros order= tkb tbk btk bkt kbt ktb specifies the order of the loops, the default is tkb, t the k the b. If you specify expressios i t=, b=, or k=, you might eed some other orderig. For example, if you specify somethig like t = 2 to 0.5 * b, the you must specify order=bkt or ay other orderig that defies b before t. Alteratively, you ca specify this optio just to chage the default orderig of the results. out= SAS-data-set specifies the output data set with the list of potetial desig sizes. The default is out=bibd. t= do-list attrs= do-list specifies the umber of treatmets. I a partial-profile or MaxDiff desig, this is the total umber of attributes or messages. Specify either a iteger or a list of itegers i the SAS do-list sytax. The attrs= ad t= optios are aliases. This optio (i oe of its two forms) must be specified. Whe the attrs= optio is specified, the output will use the word Attribute rather tha Treatmet ad Set rather tha Block. %MktBSize Macro Notes This macro specifies optios ootes throughout most of its executio. If you wat to see all of the otes, submit the statemet %let mktopts = otes; before ruig the macro. To see the macro versio, submit the statemet %let mktopts = versio; before ruig the macro.