÷H(Wed Mar 25 17:14:02 1998) From Theil.vmfdle, h¼hähähïhäh"¡7L¿ÌÌÈ ¼"('&)$%-.4+*,YdQT;:<:d    €? ([î€ö€ö&¼ Sä€ö€ö¼ >m€ö€öc$¼ 3dø€ö€ö ¼$ €ö€ö¼Š$M€ö€ö(¼('€ö€ö¼ ‡*#S9€ö€ö*¼(-,[a€ö€ö"¼*17ci€ö€öF!¼*5Bk€ö€öf(¼*7Ms€ö€öp*¼*@9X q€ö€ö?¼$;$ ?€ö€ö¼ ‡Ds˜Š€ö€öh)¼$F‚¡•€ö€ös+¼$H‘³  €ö€ö¼(KB€ö€ö ¼$M¦¿§€ö€öQ¼(P¹Ì®€ö€öU¼(SÐÙµ€ö€öS¼(Vãæ¼€ö€öY ¼(YúôÀö€öW¼(\ Ç€ö€ö¼(_6 Ï€ö€öM¼(b d{T fU5 Ø€ö€öO¼(i‚Lã€ö€ö,¼$k•Wé€ö€ö0¼$m¦bï€ö€ö9¼$o·nö€ö€ö=¼$qÈzý€ö€ö;¼$sÙˆ€ö€ö["¼$uHC wð•1€ö€ö_#¼$y¥ ^€ö€öC¼${&½w€ö€ö ¼$~CË€ö€ö ¼$^Ú†€ö€ö ¼$„{玀ö€ö4¼$†Žû€ö€ö¼$‰€ö€ö¼ ‹Ž£ ¦€ö€ö¼$´®€ö€ö¼$’Á µ€ö€ö&¼$”Ò& ½€ö€ö'¼$–ã1 Æ€ö€ö%¼$˜ô: Ï€ö€ö¼$š€ö€ö¼ ‡žKØ€ö€ö¼$¢ÛÌ€ö¼Š\œܼ¼,ŒüÜ윌üL|ÌìL\< lŒ|<<ÌŒ¬L¬ ¬, <¬ü̼ìÜœ¼lœ|\l\Ll,|,C¡7L¿ÍÍÈ¥SUMPRODVMINVMAXTimeINITIAL TIMEFINAL TIMETIME STEP SAVEPER.Theil m input 1 -Units input 2historicalsimulatedXYpickIF THEN ELSE-DimensionlessXiYi countdt Sum Xi SumX2 Sum Yi SumY2 SumXY Sum XmY2 Sum APEABSZIDZ Sum SPEM XM YMX2MY2MxySxSQRTSyr dif mea dif var dif covmse RMSPE:SUPPLEMENTARYmapermseumusucr2-Time Unitsresiduals .Control˜Ì¡7L¿ ‡¡7L¿ÈÜ\ ÜÜœ¡7L¿È¡7L¿‰‰d L\<lŒ| | \ l Œ <¬ü̼ìÜ,<lü ÜÌœÜ̼L|\lœÌ¼Œl|üŒLœ¼<L\lŒ|üìÌüìÌœ¬l¬ <¬ü¼ì<|¬ <üÌìÜ L\<lŒ|Ì <|\l    RPÿÿÿÿÿÿÿÿHelvetica dView 1 %BIP[flH¡7L¿ÍÍÈrni ­ã‚Rename the inputs to the series you want to test and supply them in a .vdf file.rn ªYsEnsure that time bounds cover the whole range of data availability; + 1 dt on the end ü_¡#ÿ ¡%ÿ*( Ì«¢(ÿÿÿÿÿ€€*( ì¡Ÿ(ÿÿÿÿÿ€€¡_ŸdÌV ,"Ì"Ì$ÌCÌ6ÌHIÌFÌ\ÌaÌfÌÌhÌmÌpÌsÌC…ÌG˜ÌžÌÌ ì£ì¦ìC¸ìGÌìÒììÔüÛüÞüçüüé ï ò û  ý,,,,</"<#,<1<)=<8L<<Nl RlUl(`llb| f|i|)u||wŒ~Œ…ŒŠŒ’ŒŒ”¬›¬ž¬¦¬¬¨¼°¼µ¼½¼¼¿ÌÆÌÉÌÑÌÌÓÜÛÜàÜèÜÜêìòì÷ì üììþüü&üüüü )* / !9  ;<5J<O<+[<<]L,iLpLsLzLL|\ƒ\†\\\l–l›l£ll¥|¬|±|¹||»ŒÂŒÇŒÏŒŒÑœØœÛœLïœNœ œœ¼¼¼L,¼NA¼I¼¼KÌTÌYÌGlÌtÌÌvÜ(ÜŠÜܘÜÜšì¢ì§ì¯ìì±ü¸ü½üÅüüÇ !Ñ Ö :æ  èî!øû!  <<<#<)<<+L0L3L;LALLC\J\O\X\^\\`lglll!vl|ll~|…|Š|#”|š||œŒŸŒ¤Œ"®Œ´ŒŒ¶œ»œ ÀœœÃ¬É¬Ì¬ Ь¬Ò¼8á¼ ç¼9÷¼¼¼ŒŒ Œ%ŒŒ|| $|'/||1¬ 5¬;¬ @¬-M¬¬OœTœ Yœ$cœœeBwA‰Œ7›%¦P»$ÅUÜ-é,õI I,),C¡7L¿’’È5FC:\Fid\Model Library\Theil\"Theil.vmfdl{FModule to Calculate Summary Statistics for Historical Fit based on:JSterman, J.D., (1984) Appropriate Summary Statistics for Evaluating the JHistorical Fit of System Dynamics Models. Dynamica, 10 (Winter), 51-66Rogelio Oliva.September, 1995.}{Input Series} input 1 ~ UnitsF ~ Rename this variable to the test data available in the .vdf fileJ The series has no value (no '=' sign) to indicate that it will be  exogenous data. | input 2 ~ UnitsF ~ Rename this variable to the test data available in the .vdf fileL The series has no value (no '=' sign) to indicate that it will be  exogenous data. |historical := input 1 ~ Units" ~ Dummy variable to id series |simulated := input 2 ~ Units" ~ Dummy variable to id series |X := simulated ~ Units ~ |Y :RAW: := historical ~ Units ~ |2{Selection of points through the PICK function}&pick = IF THEN ELSE(Y = :NA:, 0, 1) ~ Dimensionless. ~ Flag to id historical value available.: Takes a value of one for every data point available |Xi = pick*X ~ Units* ~ Simulated point entering calculations |Yi = pick*Y ~ Units. ~ Historical point entering calculations |{Basic Accumulations}count = INTEG(pick/dt,0) ~ Dimensionless ~ Counter for # of points |Sum Xi = INTEG(Xi/dt,0) ~ Units ~ Sum of x's (simulated) |SumX2 = INTEG(Xi*Xi/dt,0) ~ Units*Units ~ Sum of x^2 (simulated) |Sum Yi = INTEG(Yi/dt,0) ~ Units ~ Sum of y's (historical) |SumY2 = INTEG(Yi*Yi/dt,0) ~ Units*Units ~ Sum of y^2 (historical) |SumXY = INTEG(Xi*Yi/dt,0) ~ Units*Units ~ Sum of x*y |{Sum of Errors}*Sum XmY2 = INTEG((Xi-Yi)*(Xi-Yi)/dt,0) ~ Units*Units" ~ Sum of Square Errors (x-y)^2 |.Sum APE = INTEG(ABS(ZIDZ(Xi-Yi,Yi))/dt,0) ~ Dimensionless& ~ Sum of Absolute Percent Errors |:Sum SPE = INTEG((ZIDZ(Xi-Yi,Yi)*ZIDZ(Xi-Yi,Yi))/dt,0) ~ Dimensionless. ~ Sum of Square Percent Errors ((x-y)/y)^2 |.{Calculation of Mean and Standard Deviation}M X = ZIDZ(Sum Xi,count) ~ Units ~ Mean of x (sum x)/n |M Y = ZIDZ(Sum Yi,count) ~ Units ~ Mean of y (sum y)/n |MX2 = ZIDZ(SumX2,count) ~ Units*Units ~ Mean of x^2 (sum x^2)/n |MY2 = ZIDZ(SumY2,count) ~ Units*Units ~ Mean of y^2 (sum y^2)/n |Mxy = ZIDZ(SumXY,count) ~ Units*Units ~ Mean of x*y (sum x*y)/n |Sx = SQRT(MX2-(M X*M X)) ~ UnitsN ~ Standard Deviation of x. Calculated using the 'hand computation' formula R to calculate the standard deviation without prior knowledge of the mean.  Sterman (1984), pg. 64 |Sy = SQRT(MY2-(M Y*M Y)) ~ UnitsN ~ Standard Deviation of y. Calculated using the 'hand computation' formula R to calculate the standard deviation without prior knowledge of the mean.  Sterman (1984), pg. 64 |"r = ZIDZ(Mxy-(M X*M Y),Sx*Sy) ~ DimensionlessJ ~ Correlation coefficient. Calculated through the 'hand computation'.  Sterman (1984) pg. 63 |*{Decomposition of the Mean Square Error}"dif mea = (M X-M Y)*(M X-M Y) ~ Units*Units" ~ Difference of Means (bias) |dif var = (Sx-Sy)*(Sx-Sy) ~ Units*Units ~ Difference of variances |dif cov = 2*Sx*Sy*(1-r) ~ Units*Units ~ Difference of covariances |&mse = dif mea + dif var + dif cov ~ Units*Units> ~ Mean Square Error. The addition of the three components |{Summary Statistics}&RMSPE = SQRT(ZIDZ(Sum SPE,count)) ~ Units& ~ Root Mean Square Percent Error ~ :SUPPLEMENTARY  |mape = ZIDZ(Sum APE,count) ~ Dimensionless" ~ Mean Absolute Percent Error ~ :SUPPLEMENTARY  |rmse = SQRT(mse) ~ Units ~ Root Mean Square Error ~ :SUPPLEMENTARY  |um = ZIDZ(dif mea,mse) ~ Dimensionless" ~ Bias inequality proportion ~ :SUPPLEMENTARY  |us = ZIDZ(dif var,mse) ~ Dimensionless& ~ Variance inequality proportion ~ :SUPPLEMENTARY  |uc = ZIDZ(dif cov,mse) ~ Dimensionless& ~ Covariance inequality proportion ~ :SUPPLEMENTARY  | r2 = r*r ~ Dimensionless& ~ Correlation coefficient squared ~ :SUPPLEMENTARY  |dt = TIME STEP ~ Time Units ~ |residuals = Xi-Yi ~ Units ~ Errors |:******************************************************** .Control>********************************************************~" Simulation Control Parameters |FINAL TIME = 55 ~ Time Units* ~ The final time for the simulation. |INITIAL TIME = 0 ~ Time Units* ~ The initial time for the simulation. |SAVEPER =  TIME STEP ~ Time Units2 ~ The frequency with which output is stored. |TIME STEP = 1 ~ Time Units& ~ The time step for the simulation. |F\\\---/// Sketch information - do not modify anything except namesFV300 Do not put anything below this section - it will be ignored *View 1:$0,0,Helvetica|14|B|0-0-0|0-0-0|0-0-0|-1--1--1|-1--1--1*12,1,0,429,227,130,23,8,4,0,0,0,0,0,0RRename the inputs to the series you want to test and supply them in a .vdf file.&12,2,0,426,89,115,31,8,4,0,0,0,0,0,0ZEnsure that time bounds cover the whole range of data availability; + 1 dt on the end210,3,historical,351,161,35,8,0,3,0,0,-1,0,0,0.10,4,simulated,531,161,37,8,0,3,0,0,-1,0,0,0N10,5,input 1,171,162,40,20,8,3,0,2,0,0,0,0,-1--1--1,0-0-0,|0||255-128-128N10,6,input 2,673,159,40,20,8,3,0,2,0,0,0,0,-1--1--1,0-0-0,|0||255-128-128.1,7,5,3,0,0,0,0,0,0,0,-1--1--1,,1|(256,161)|.1,8,6,4,0,0,0,0,0,0,0,-1--1--1,,1|(607,159)|l‘H¡7L¿``ÈI:•lG¦€?•|2©©þ•Ì"P•ì*V •ü•Ì*^ • •ì*f" •• *n& •,•üjv*©•<L00&•,¦€ö¦¦€?:’1•l%•<•:›5•|%•<•,R¤9©•ŒG'•<•œ¦J¶>•¬G'•l•œ¦ZÂB•¼G'%•l•l•œ¦JÐF•ÌG'•|•œ¦ZÜJ•ÜG'%•|•|•œ¦ZêN•ìG'%•l•|•œ¦’øR©•üG ' %$•l•|$•l•|•œ¦zW• G ',0$•l•|•|•œ¦²![•<G'%,0$•l•|•|,0$•l•|•|•œ¦J8_©•L,0•¬•ŒBOd•\,0•Ì•ŒBZh•l,0•¼•ŒBfl•|,0•Ü•ŒBrp•Œ,0•ì•ŒZ~t•œ¬$•l%•L•LZ‹z•¼¬$•|%•\•\z˜€•Ì,0$•Œ%•L•\%•œ•¼r¨†©•Ü%$•L•\$•L•\jÁ‹•ì%$•œ•¼$•œ•¼rÏ•ü%%%¦@•œ•¼$¦€?•ÌJÞ“• ##•Ü•ì•üR똩•¬,0•<•ŒBþŸ•<,0• •Œ2 ¥•L¬• B«•\,0•Ü• B±•l,0•ì• B)·•|,0•ü• :4¾•Œ%•Ì•Ì*=Ä•œ•œ:EÈ•¬$•l•|*NÒ•Œ¦\B*Vו|¦*^Ü•¬•œ*gâ•œ¦€?T_H¡7L¿99Èp©{ Module to Calculate Summary Statistics for Historical Fit based on: Sterman, J.D., (1984) Appropriate Summary Statistics for Evaluating the Historical Fit of System Dynamics Models. Dynamica, 10 (Winter), 51-66 Rogelio Oliva. September, 1995. }¸®®©{Input Series}¸®•Ì ‡Ü •ì ‡Ü•ü¸ ¸•Ì ‡Ü• ¸ ¸•ì ‡Ü•¹ ¸•  ‡Ü•,¸@¸ ¸•ü ‡Üb©{Selection of points through the PICK function}¸®•<¸&¸•L•,¸&¸»:NA:±¸¦±¸¦€? ‡\•l¸&¸•<%• ‡Ü•|¸&¸•<%•, ‡Ü:©{Basic Accumulations}¸®•Œ¸&¸G•<'•œ±¦ ‡\"•¬¸&¸G•l'•œ±¦ ‡Ü$•¼¸&¸G•l%•l'•œ±¦‡Ü%‡Ü"•Ì¸&¸G•|'•œ±¦ ‡Ü&•Ü¸&¸G•|%•|'•œ±¦‡Ü%‡Ü&•ì¸&¸G•l%•|'•œ±¦‡Ü%‡ÜJ©{Sum of Errors}¸®•ü¸&¸G•l$•|%•l$•|'•œ±¦‡Ü%‡Ü:• ¸&¸G••,•l$•|±•|'•œ±¦ ‡\N•<¸&¸G•,•l$•|±•|%•,•l$•|±•|'•œ±¦ ‡\N©{Calculation of Mean and Standard Deviation}¸®•L¸&¸•,•¬±•Œ ‡Ü•\¸&¸•,•Ì±•Œ ‡Ü•l¸&¸•,•¼±•Œ‡Ü%‡Ü•|¸&¸•,•Ü±•Œ‡Ü%‡Ü•Œ¸&¸•,•ì±•Œ‡Ü%‡Ü&•œ¸&¸•¬•l$•L%•L ‡Ü&•¼¸&¸•¬•|$•\%•\‡Ü2•Ì¸&¸•,•Œ$•L%•\±•œ%•¼ ‡\R©{Decomposition of the Mean Square Error}¸®•Ü¸&¸•L$•\%•L$•\‡Ü%‡Ü&•ì¸&¸•œ$•¼%•œ$•¼‡Ü%‡Ü*•ü¸&¸¦@%•œ%•¼%¦€?$•Ì‡Ü%‡Ü"• ¸&¸•Ü¸#¸•ì¸#¸•ü‡Ü%‡Ü>©{Summary Statistics}¸®•¸&¸•¬•,•<±•Œ ‡Ü•<¸&¸•,• ±•Œ ‡\•L¸&¸•¬•  ‡Ü•\¸&¸•,•Ü±•  ‡\•l¸&¸•,•ì±•  ‡\•|¸&¸•,•ü±•  ‡\•Œ¸&¸•Ì%•Ì ‡\•œ¸&¸•œ ‡œ•¬¸&¸•l$•| ‡Ü•Œ¹&¸¦\B ‡œ•|¹&¸¦ ‡œ•¬¹&¸®¹•œ ‡œ•œ¹&¸¦€? ‡œ8H¡7L¿ttÈ&Internally defined simulation time.žRename this variable to the test data available in the .vdf file The series has no value (no '=' sign) to indicate that it will be exogenous data.žRename this variable to the test data available in the .vdf file The series has no value (no '=' sign) to indicate that it will be exogenous data.Dummy variable to id seriesDummy variable to id seriesbFlag to id historical value available. Takes a value of one for every data point available*Simulated point entering calculations*Historical point entering calculationsCounter for # of pointsSum of x's (simulated)Sum of x^2 (simulated)Sum of y's (historical)Sum of y^2 (historical)Sum of x*ySum of Square Errors (x-y)^2"Sum of Absolute Percent Errors*Sum of Square Percent Errors ((x-y)/y)^2Mean of x (sum x)/nMean of y (sum y)/nMean of x^2 (sum x^2)/nMean of y^2 (sum y^2)/nMean of x*y (sum x*y)/n²Standard Deviation of x. Calculated using the 'hand computation' formula to calculate the standard deviation without prior knowledge of the mean. Sterman (1984), pg. 64²Standard Deviation of y. Calculated using the 'hand computation' formula to calculate the standard deviation without prior knowledge of the mean. Sterman (1984), pg. 64bCorrelation coefficient. Calculated through the 'hand computation'. Sterman (1984) pg. 63Difference of Means (bias)Difference of variancesDifference of covariances:Mean Square Error. The addition of the three components"Root Mean Square Percent ErrorMean Absolute Percent ErrorRoot Mean Square ErrorBias inequality proportion"Variance inequality proportion"Covariance inequality proportion"Correlation coefficient squared Errors" Simulation Control Parameters&The final time for the simulation.&The initial time for the simulation..The frequency with which output is stored.&The time step for the simulation.s€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö\B€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€ö€?€ö€ö€ö€ö€ö€ö€ö¡7L¿ È///---\\\ :L<%^E!@ 15:0,0,0,0 19:100,0 5:count