topic Non Standard Regression in Statistical Procedures

Non Standard Regression

BillJones — Mon, 06 Apr 2015 22:19:43 GMT

Hello Everyone,

I want to estimate z1-z9 of the function below:

y=w1[(x1-1)z1+1] + w2[(x2-1)z2+1] + *** + w9[(x9-1)z9+1]

where

y=dependent variable

w1-w9 are weights (between 0 and 1) that have already been selected

x1-x9 are the independent variables

What is the best way to do this? Exponential regression? If so, then how to separate out the zs?

Thanks very much for any suggestions.

-Bill

sample code:

data input;

input y x1 x2 x3 x4 x5 x6 x7 x8 x9;

datalines;

0.433009378 0.260269441 1.092278706 0.425360662 0.164029628 0.429880491 0.950489941 0.047595925 0.531987245 0.336139451

0.386133454 0.184529366 0.033661616 0.245561093 0.105340609 0.882803079 0.981167833 1.07619815 0.781841268 0.233372548

0.258993942 1.119821022 0.109476847 0.000812581 0.419804897 0.391490911 0.769809934 0.659436672 0.144127286 0.746489656

0.359816223 1.046465239 0.268638572 0.137649556 1.059282484 0.142724361 0.902195762 0.073187585 1.044987784 0.080340265

0.41451314 0.07467261 1.142594057 0.097833794 0.6281817 0.804104506 0.953123478 0.877716887 0.986232903 0.413012511

0.499895162 0.388482105 0.769424554 0.449226135 0.864276043 0.093162782 0.735842414 0.729262551 0.021170317 0.946582289

0.554731409 0.059169663 0.671669625 0.573134236 0.059555794 0.688838956 1.112734086 0.082975813 0.985157911 0.954789222

0.933065823 1.09077688 0.937373275 0.961720206 1.137356787 0.912617055 0.414739423 1.179989148 0.793556015 0.527731975

0.449350652 0.889961987 0.448923153 0.16477621 1.039273537 1.101642002 0.417949375 0.892596492 0.107396261 0.300592589

0.436482177 0.218474064 0.817187061 0.444305392 0.010617679 0.316182089 0.871165126 0.396994326 0.274244319 1.054925185

0.844492128 1.199795926 0.562302873 1.087265891 0.857350825 0.717381217 0.361552016 0.188030616 0.078408845 0.477629287

0.986259829 1.11546778 0.67784779 1.076318082 0.711326509 1.147214979 0.949628603 1.159315584 0.683949937 0.658723083

0.536026142 0.03874538 0.603083965 0.615275769 1.199564925 0.097081463 1.116060342 0.025003849 0.125264809 0.066314023

0.478861694 0.623029236 1.118083449 0.343243377 0.445421704 0.990867977 0.074432208 0.093372058 0.301435613 1.061868184

0.755038738 0.917477552 0.568455848 0.653801794 1.11512354 1.167247795 0.78977679 0.620451789 0.21932299 0.882529179

0.870345527 0.278402165 0.645632762 1.04345974 1.192690633 0.317710531 0.946307396 0.799783639 0.66667504 0.614709813

0.653262402 1.077775155 0.181791546 0.669990623 0.776631367 0.513769454 0.39812198 0.078470159 0.870051912 1.178329425

0.577799576 0.545255692 0.898698641 0.635702755 0.768766323 0.60748745 0.478514258 0.208562345 0.057506345 0.257919144

0.640086114 0.347670625 0.760234063 0.733585918 0.638387923 0.510148474 0.07436439 0.352510307 0.593989168 1.040021751

0.823371633 0.638037368 1.01259897 1.097597318 0.644682512 0.266643423 0.344110563 0.450192716 0.383177214 0.840690779

0.62449019 0.282835785 1.007170731 0.610136182 1.029590947 0.074149805 1.116463349 0.503368539 1.007803905 0.263318173

0.444804746 0.017693426 0.526388959 0.187740591 1.129412956 0.915406787 1.073308894 0.619777948 0.146676128 0.54520417

0.484480172 0.497735344 0.104527198 0.500746335 0.985787824 0.199781266 0.065829102 0.202553479 0.626455295 0.813901488

0.317012256 1.192924294 0.251183508 0.093961339 0.174368642 0.477715786 0.657812327 1.031320803 0.245768093 0.717453859

0.588034285 0.489578192 0.207186181 0.699312378 0.4967007 0.891018763 0.097971171 0.532467973 0.37236279 0.292556691

0.598541777 0.331222229 1.194910587 0.566202209 1.181182139 0.344148387 1.135667393 0.369079141 0.224891936 0.002381108

0.789085218 0.561051456 0.430842595 1.05544095 0.176816812 0.475019069 0.669435603 0.443071061 0.681417633 1.137804746

0.487889626 0.634337348 1.155309283 0.341090334 0.523437654 1.041496843 0.658849627 0.407481423 0.212381753 0.148660757

0.500437513 1.003388064 0.028107549 0.408941718 1.140653445 0.546878092 0.312132981 0.164647159 0.896599531 0.139394726

0.648913057 0.23470331 0.708473294 0.715658801 0.503438628 0.778258155 0.824497121 1.003766639 0.281078622 0.205760578

0.47675595 0.226090918 0.267337491 0.207966394 0.959121283 1.097665676 0.222061633 0.836446043 0.960294339 0.82965073

0.709378295 0.009130251 0.192221036 0.993585371 0.209080202 0.157499618 1.190016415 0.748792229 0.836817845 0.541574774

0.696826726 0.879948846 1.125725147 0.744493446 0.740876159 0.219321144 1.089204287 0.920192756 0.351082149 0.205052275

0.260997361 0.00973165 0.176036305 0.059693106 0.111782576 1.025158879 0.136361192 0.918763623 0.595752643 0.512487841

0.570310745 0.632237184 0.304292779 0.526779408 0.822717014 1.004175775 0.548448316 0.063847267 0.41276116 0.523048535

0.736222587 0.24588289 0.14861863 0.844209142 0.629919526 0.941650487 0.532280328 0.696269823 0.870934505 0.645234111

0.434171719 0.948062641 0.696583303 0.254165508 0.674046478 0.242673335 1.188268109 0.934818027 0.506338586 0.034269001

0.705494851 0.68325986 0.106653146 0.811958384 0.269531941 0.696427753 1.081084338 1.057956238 0.729979889 0.399460328

0.280503587 0.416168159 0.409217298 0.05717669 0.130358799 0.904330781 0.486648621 0.915596266 0.580948113 0.160347238

0.458996388 1.029620307 0.152837123 0.460200554 0.306766207 0.638229727 0.323942705 0.470856463 0.595152795 0.115520964

0.740670108 0.829959193 0.801371222 0.700047998 1.02184578 1.130850744 0.500220331 0.29845238 1.054722256 0.022803759

0.628111577 0.775435333 0.899677969 0.809379813 0.630802294 0.346100793 0.296477882 0.378814672 0.117778822 0.04644256

0.616620558 1.195580632 0.66884203 0.629953026 0.580271276 0.452977027 0.748081499 0.103261188 0.903194269 0.347424679

0.485100919 0.640793811 0.984983366 0.174869342 0.568463983 1.075565391 0.768921803 1.017558465 0.700763394 0.552245365

0.380522255 1.026669851 0.023575147 0.181301495 0.678121679 0.126734702 0.498002422 1.116297938 0.781122541 0.742049492

0.386310145 0.489322502 0.928953839 0.108098712 0.887426928 0.61118902 0.460495358 0.892752621 0.013579578 0.862879983

0.644081655 0.791733164 0.807384987 0.832247035 0.041075155 0.063473692 0.424127906 0.853328728 0.293989069 1.179501191

0.664011771 0.235924253 0.284018069 0.772072735 0.303979747 0.781867879 0.345935375 0.990578377 0.83253673 0.698820026

0.695065576 0.263981518 0.911212968 0.780187919 0.956728666 0.033297408 0.486447384 1.160349181 0.697104382 0.600284743

0.742614249 0.389088378 0.856478819 0.855145861 0.507586603 0.737463437 0.021562337 1.154630872 0.806242913 0.582722966

;

run;

data input;

set input;

w1=0.23; w2=0.07; w3=0.21; w4=0.09; w5=0.05; w6=0.15; w7=0.10; w8=0.04; w9=0.06;

run;

Re: Non Standard Regression

BillJones — Tue, 07 Apr 2015 10:40:16 GMT

It appears that I need to use proc nlin. I drafted some code, see below. It runs but I'm a bit perplexed by the output. I try to limit z1-z9 from 0.25 to 1, but there are estimates for z over 2? Additionally, I tried to set z1-z9 from 0 to 1 by 0.01 and got an "insufficient memory" error. Is there a way to have sas search for the best fit by 0.01? Perhaps employ some logic that would reduce the possible number of combinations? Also, I got a warning stating that DER.z1 to DER.z9 are missing and sas will compute them automatically. Should I specify DER.z1 to DER.z9?

Thanks for any suggestions.

-Bill

dm 'clear log';