~

_ United StatesDepartment ofAgriculture

Economics andStatisticsService

StatisticalResearchDivision

ESS StaffReportNumber AGESS810S14

May 1981

One, Two, and ThreeLine Segment

"Straw Man" ModelsSoybean Yields inIowa, Illinois, and IndianaJeanne L. Sebaugh

COMPARISON OF ONE, TWO, AND THREE LINE SEGMENT "STRAW MAN" MODELS FORSOYBEAN YIELDS IN IOWA, ILLINOIS, AND INDIANA. By Jeanne L. Sebaugh;Statistical Research Division, Economics and Statistics Service, U.S.Department of Agriculture, Columbia, Missouri 65201; May 1981.ESS Staff Report No. AGESS 810514.

ABSTRACT

All of the straw man models attempt to explain differences in yields overtime by fitting trend lines to the yield data. The one line segment strawman model, simple linear regression, describes a uniform increase inyields over time. The two and three line segment straw man models allowthe rate of change in yields to vary over the time period. The performanceof the three models in predicting soybean yields in Iowa, Illinois, andIndiana is compared based on eight model characteristics. There is littledifference between the three models in relation to seven of the characteris-tics: objectivity, consistency with scientific knowledge, adequacy, timeli-ness, minimum costs, simplicity, and accurate current measures of modeledyield reliability. The one line model performs somewhat better than theother straw man models on the remaining characteristics, yield indicationreliabili ty.

Key words: Model comparison, yield modeling, linear regression.

***************************************************** *~ This paper was prepared for limited distribution ;~ to the research community outside the U.S. ;; Department of Agriculture. The views expressed ;: herein are not necessarily those of ESS or USDA. :****************************************************

ACKNOWLEDGMENTS

The author wishes to thank Wendell Wilson, other members of the YieldEvaluation Section and various AgRISTARS Yield Development Projectpersonnel for their comments and assistance, and Joan Wendt for typingthis report.

i

COMPARISON OF ONE. TWO, AND THREE LINE SEGMENT"STRAW MAN" MODELS FOR SOYBEAN YIELDS IN

IOWA, ILLINOIS, AND INDIANA

byJeanne L. Sebaugh

Mathematical Statistician

This research was conducted as part ofthe AgRISTARS Yield Model DevelopmentProject. It is part of task 3 (subtask 2)in major project element number I, asidentified in the 1980 Yield Model Develop-ment Project Implementation Plan. As aninternal project document, this report isidentified as shown below.

AgRISTARSYield Model Development

Project

YMD-1-3-2(8l-05.l)

ii

FOREWARV

Vevelopment and appUc.a;t,{.on 06 tec.hMqu~ 601t Map yield modelt~t and evaluation Me .unpoltta.nt p,aJLt6 06 the Yield ModelVevelopment Pltojec.t in AgRISTARS.l/ Pltomib-<.ngyield mode.i6avaU.a.b{e in the WeltatUlte Olt 6ltom vaJtioU6 lt~eMc.heJl.l, w.i.ll be.6ubjec.ted to pelt60ltmanc.e t~t and evaluation. In oltdelt that theltemay be a c.ommon lte6e1tenc.e 601t d~c.!tibing the c.apab~~ and-e..-<.milation.606 th~ e mode.i6, c.JtileJtia 601t doing .60 ha.ve beendeveloped and d~c.!tibed in a doc.ument e~ed CltOp Yield ModelT~t and Evaluation ClLd:eJtia (Wilion, et al., 1980 I. Th~ec.JtileJUa Me U6ed both in the evaluatio n a6 a .6ing{e model andin c.ompaJti.6on.6between mode.{.6.

The pultpO.6e 06 tMJ.> doc.ument i.6 to gMn .6ome expeJtienc.e in theapplic.ation 06 the c.JtileJtia 601t c.ompMiMn pUltpM~. PltevioU6doc.umena ha.ve U6ed the .6ame c.JtileJtia 601t model evaluation. Inaddilion, .6tat-<..6tic.a1. t~u whic.h c.ompMe the pelt60ltmanc.e 06 twomode.i6 have been developed and Me U6ed. It i.6 antiupated tha..tthe evaluation and c.ompaJti.6on 06 othelt mode.i6 w~ be done in a.6hrU..{M mannelt.

The mode.{.6 to be evaluated and c.ompalted welte c.ho.6en to be quite.6.unp{e .6inc.e the 60C.u6 06 attention i.6 on the "pilot t~t" On thepltoc.edUlt~. The mode.{.6 invo{ved Me the ".6tJtaw man" Map yieldmode.i6 developed and d-t.6c.u6.6ed by KMtie (19811. Thi.6 doc.umentc.ompaJL~ the one, two, and thttee Une .6egment mode.i6 whic.h at{lteglt~.6 yield on ye.M.

Jeanne L. SebaughMathematic.a{ Stati.6tiuanYield Evaluation SectionYield RMeMc.h Bltanc.hStafuuc.a{ R~ eMc.h V-<.vi.6ion

!.! AgRISTARS (Agltic.uUUlte and R~oUltc.~ Inventolty SUltvey.6 ThltoughAelto.6pac.e Remote Sen.6ingl i.6 a m~-agenc.y It~ealtc.h pltogltam tomeet .6ome c.u/lJl.ent and new innoltmation need6 06 the U. S. VepaJL.t-ment On AgJUc.uUUlte.

iii

Table of Contents

Page

Summary of Conclusions and Recommendations

Application Description .Exercise in Applying Procedures for Model Comparison .

Review of Models .....••..........Straw Man Models Describe Technological TrendsStraw Man Model 1 - Uniform Trend Over Time.Straw Man Model 2 - Two Trends Over Time •Straw Man Model 3 - Three Trends Over Time

Comparison Methodology ..........•Eight Model Characteristics to be ComparedQuantitative Model Comparisons Are Based on the Same Data.Models are Ranked According to Performance .•....Models are Compared Using Statistical Tests Based on d Y Y

I

I1

1I223

33347

Model Comparison ..........•...... 9Indicators of Yield Reliability Based on d = Y - Y Show All Models

Have Small Bias But the One Line Model Has the Smallest Root MeanSquare Error and Standard Deviation .•.......... 9

Indicators of Yield Reliability Based on rd = (d/Y)*lOO Show theOne Line Model Performing Best 9

Indicators of Yield Reliability Based on Y and Y Show the One LineModel Performing Somewhat Better •................ 20

Statistical Tests Based on d Y - Y Show Some Preference for theOne Line Model 20

All Models Are Objective .•.................. 40All Models Omit Consideration of Known Scientific Relationships. 40All Models Are Adequate ............•... 41All Models Are Timely 41The One Line Model is Least Expensive but None of the Models are

Costly ....................•..... 41All Models Are Simple .................•.. 41All Models Have a Poor Current Measure of Modeled Yield Reliability. 42

Conclusions.

Recommendations.

References

Appendix .Statistical FormulasBootstrap Test Results

Indiana .....•.for Soybean Yields in Iowa, Illinois, and. . . . . . . . .

iv

42

42

44

4545

48

List of Figures and Tables

PageTable 1: Average Production and Yield for Test Years 1970-79 . 5

Figure 1: Production of soybeans by CRD (1970-79 average) as apercent of the regional total •••.....• 6

Table 2: Model Comparison Based on the Bias (Quintals/Hectare)Derived From Independent Test Years ..........•• 10

Table 3: Model Comparison Based on the Root Mean Square Error(Quintals/Hectare) Derived From Independent Test Years ... 11

Figure 2: Number indicates the model with smallest root mean squareerror for soybean yields based on test years 1970-79 ...• 12

Table 4: Model Comparison Based on the Standard Deviation (Quintals/Hectare) Derived From Independent Test Years ••...... 13

Table 5: Model Comparison Based on the Percent of Years IRelativeDifference I > 10% Derived From Independent Test Years .. 14

Figure 3: Number indicates the soybean mode1(s) with smallest percentof test years (1970-1979) having absolute value of therelative difference greater than ten percent •••....• 15

Table 6: Model Comparison Based on the Largest IRe1ative DifferencelDerived From Independent Test Years ••••....... 16

Figure 4: Number indicates the soybean model with smallest value ofthe largest absolute relative difference during the testyears 1970-1979 ...••••••.••.••... 17

Table 7: Model Comparison Based on the Next Largest IRelativeDifferencel Derived From Independent Test Years .••. 18

Figure 5: Number indicates the soybean model with smallest value ofthe next largest absolute relative difference during thetest years 1970-1979 .•.••.•••.•••.•.... 19

Figure 6: Iowa State Model. Actual and Predicted Yields for theTest Years 1970-1979 .•...•...... 21

Figure 7:

Figure 8:

Illinois State Model.Test Years 1970-1979.

Indiana State Model.Test Years 1970-1979.

Actual and Predicted Yields for the

Actual and Predicted Yields for the

22

• 23

Table 8: Model Comparison Based on the Percent of Years theDirection of Change From the Previous Year is CorrectDuring Independent Test Years ••....••..•.••• 24

v

Figure 9:

Page

Number indicates the soybean model(s) with largest percentof test years (1970-1979) having agreement in direction ofchange from the previous year between predicted and actualyields ..........•....... 25

Table 9: Model Comparison Based on the Percent of Years theDirection of Change From a Three Year Base Period isCorrect During Independent Test Years . 26

Figure 10: Number indicates the soybean model(s) with largest percentof test years (1970-1979) having agreement in direction ofchange from the previous three year average between pre-dicted and actual yields •...........•...• 27

Table 10: Model Comparison Based on the Correlation Between Actualand Predicted Yields During Independent Test Years .. 28

Figure 11: Number indicates the soybean model with the largestcorrelation coefficient between actual and predictedyields over the test years (1970-1979) ...•... 29

Table 11:

Figure 12:

Figure 13:

Table 12:

Model Comparison Based on Paired-Sample Statistical Tests2 Line Model With 3 Line Model 31

Comparison of 2 line and 3 line models to predict soybeanyields based on the average of Idl = IY-Y/ for 1970-1979 32

Comparison of 2 line and 3 line models to predict soybeanyields based on the eercent of test years (1970-1979)with smaller Idl = Iy-yl .•••••....•... 33

Model Comparison Based on Paired-Sample Statistical Tests1 Line Model With 2 Line Model 34

Figure 14: Comparison of 1 line and 2 line modelsAto predict soybeanyields based on the average of Idl = Iy-yl for 1970-1979 35

Figure 15:

Table 13:

Figure 16:

Comparison of 1 line and 2 line models to predict soybeanyields based on the percent of test years (1970-1979)with smaller Id I = Iy-y I 36

Model Comparison Based on Paired-Sample Statistical Tests1 Line Model With 3 Line Model ...•.......•.. 37

Comparison of 1 line and 3 line models to predi~t soybeanyields based on the average of Idl = Iy-yl for 1970-1979 • 38

Figure 17: Comparison of 1 line and 3 line models to predict soybeanyields based on the percent of test years (1970-1979)with smaller Id I = Iy-y I 39

Table 14: Model Comparison of the Current Indication of Modeled YieldReliability Based on the Correlation Coefficient BetweenR~Re Period Predicted and Test Year Actual Accuracy .... 43

vi

Comparison of One, Two, and Three Line Segment"Straw Man" Models for Soybean Yields in

Iowa, Illinois, and Indiana

Jeanne L. Sebaugh

SUMMARY OF CONCLUSIONS AND RECOMMENDATIONS

Straw man modell, simple linear regression of yield over time, is preferredover the two and three line straw man models for predicting soybean yields.The one line model performs better than the other straw man models in termsof yield indication reliability. There is little difference between thethree models in relation to the other seven criteria. However, it cannot be concluded from this analysis that the rate of change in yields hasin fact been uniform over time. Also, other models not considered here mayoutperform straw man model 1.

APPLICATION DESCRIPTION

Exercise in Applying Proceduresfor Model Comparison

Test and evaluation of candidate crop yield models for use with particularcrops and geographic regions are major tasks within the AgRISTARS program.In order that there may be common reference for describing the capabilitiesand limitations of competing models, criteria for crop yield model test andevaluation have been developed (Wilson, et al., 1980). In addition, thecooperative agreement with the Department of Statistics at the Universityof Missouri-Columbia has produced some related documents (Bhattacharyay,1980; Moeschberger, 1980; Thompson, 1980).

This document describes the application of the criteria and statisticalprocedures to straw man models developed for soybeans in Iowa, Illinois,and Indiana (Kestle, 1981). It is hoped that this exercise will providean opportunity to see how well the criteria and statistical proceduresperform in actual use as well as establish some base lines for their im-plementation.

REVIEW OF MODELS

Straw Man Models Describe Technological Trends

All of the straw man models attempt to explain differences in crop yieldsover time by simply fitting trend lines to the yield data. Improvements intechnology, including varieties, hybrids, fertilizers, insecticides, herbicides,farming practices, equipment, etc., have resulted in.steady improvements inyields. There are occasional set backs, primarily due to weather, but theoverall trend has been towards increasing yields. By using year as the only

1

independent variable, the straw man models demonstrate how much of theyear-to-year differences in yield can be explained by this analogue totechnological trend.

Straw Man Model 1 - Uniform Trend Over Time

Straw man model 1 is a simple linear regression over time. The statisticalmodel is

where Y is the yield in quintals per hectare and X is the corresponding yearnumber (1950 0).

The inherent assumption in a simple linear regression model is that the rateof change in the Y variable is constant over the entire range of the X values.In our case, this means that the year-to-year increases in yield are assumedto be the same throughout the entire time period. More information aboutstraw man model 1 may be found in Evaluation of "Straw Man" Modell. theSimple Linear Model. For Soybean Yields in Iowa, Illinois, and Indiana(Sebaugh, 1981).

Straw Man Model 2 - Two Trends Over Time

Straw man model 2 consists of two intersecting line segments. The statisticalmodel is

E(Y)

E(Y)

where Y is the yield in quintals per hectare, X is the corresponding yearnumber (1950 = 0), and T is the join point where the two lines intersect.T is unknown but is objectively estimated using a FORTRAN program based onHudson's (1966) least squares algorithm. Following Kestle's (1981) suggestion,the slopes of the two lines, S11 and S21 are constrained to be positive andthe last line segment is constrained to cover at least five years. The lengthof the first line segment is not so constrained since the beginning point isarbitrary.

This model assumes that Y increases in a continuous fashion but that therate of change in Y is not the same over the entire range of X values. Twodifferent rates of change are allowed, Sll and 821' So year-to-year in-creases in yield may occur at a faster (or slower) rate later on in thetime period than they did earlier in the time period. More informationabout straw man model 2 may be found in Evaluation of "Straw Man" Model2, Two Trends Over Time, For Soybean Yields in Iowa, Illinois, and Indiana(Sebaugh, 1981).

2

Straw Man Model 3 - Three Trends Over Time

Straw man model 3 consists of three intersecting line segments. The statis-tical model is

where Y is the yield in quintals per hectare~ X is the corresponding yearnumber (1950 = O)~ Tl is the join point where the first two lines intersect~and T2 is the join point where the last two lines intersect. Tl and T2 areunknown but are objectively estimated using a FORTRAN program based onHudson's (1966) least squares algorithm. Again~ following Kestle's (1981)suggestions, the slopes of the three lines~ 811~ 821~ and 831~ are constrainedto be positive and the last two line segments are constrained to cover atleast five years each. The length of the first line segment is not soconstrained since the beginning point is arbitrary.

This model assumes that Y increases in a continuous fashion but that therate of change in Y is not the same over the entire range of X values. Threedifferent rates of change are allowed, 811, 821~ and 831' So year-to-yearincreases in yield may occur at different rates at different intervals overthe time period. More information about straw man model 3 may be found inEvaluation of "Straw Man" Model 3, Three Trends Over Time~ For Soybean Yieldsin Iowa, Illinois~ and Indiana (Sebaugh, 1981).

COMPARISON METHODOLOGY

Eight Model Characteristics to be Compared

The document, Crop Yield Model Test and Evaluation Criteria, (Wilson, et al.,1980), states:

"The model characteristics to be emphasized in theevaluation process are: yield indication reliability,objectivity, consistency with scientific knowledge,adequacy, timeliness, minimum costs, simplicity, andaccurate current measures of modeled yield reliability."

The models will be compared using these characteristics. Each characteristicis discussed individually without regard to the other characteristics. Thepresent discussion makes no presumption as to the relative importance of thecharacteristics.

Quantitative Model ComparisonsAre Based on the Same Data

Direct quantitative comparisons between models will be made for two of thepreviously mentioned criteria: (1) yield indication reliability and(2) accurate current measures of modeled yield reliability. The quantities

3

involved are derived from the observed yields and the model predictedyields and standard errors of prediction obtained from independent boot-strap tests for each of ten years (1970-1979). The same base period isused for all models in computing model related values for a particularyear.

The average production and yield over the ten year test period are listedin Table 1 for each geographic area. Also shown is the percent productioneach crop reporting district (CRD) contributes to its state and the threestate region and the percent production each state contributes to the region.The percentage of regional production for each CRD is shown graphically inFigure 1. Darker shades indicate higher productivity.

Separate models are derived for each CRD, state, and the region. Modelrelated values (predictions and standard errors of prediction) at the statelevel are also obtained by using a weighted average of that state's CRD modelvalues. Model related values for the region are also obtained using a weight-ed average of the values from the CRD models and from the state models. Theweighting factor used is harvested acreage. Results obtained by aggregatingfrom the CRD models are identified as "CRD aggr." Results obtained by aggre-gating from the state models are identified as "states aggr."

Models Are Ranked According to Performance

Models are ranked for each of the following indicators of yield reliability(order does not imply relative importance):

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

the bias,

the root mean square error (RMSE),

the standard deviation (SD).

the percent of years the absolute value of the relative differenceexceeds ten percent,

the largest absolute value of the relative difference,

the next largest absolute value of the relative difference,

the percent of years in which the direction of change from theprevious year in the Y's agrees with the Y's.

the percent of years in which the direction of change from theaverage of the previous three years in the Y's agrees with theY's, and

the Pearson correlation coefficient between the actual and pre-dicted yields during the independent test years.

Models are also ranked according to the value of the Spearman correlationcoefficient which indicates the utility of the model's current measure ofmodeled yield reliahility. For most of the indicators (1-6), the model withthe smallest numeric value exhibits the best performance in terms of yield

4

TABLE 1AVfQAGE PRODUCTION AND YIEl)p~q TEST YEARS 1970-79

SOYBEANC;IOWA. ILLINOIS. INDIANAPRODUCTION (1.000) PERCfNT O~ YIFLOSTATE CRC> QUINTALC; BUC;l-iELSSTATE RE3IO'J I Q~Tl/HA BU/ACRE

--- ..-------- ----------------------------------t----------------IOWA 10 10.714 39.439 16.9 6.2 23.4 3~.8

20 10.992 40.389 17.3 6.e. ??7 33.830 3.929 14.435 6.2 2.3 21.7 32.340 8 •189 30.090 12.9 4.8 22.] 33.150 11.207 41.177 17.7 6.5 23.7 35.360 4.996 18.358 7.9 2.9 24.5 36.470 5.016 18.430 7.9 2.9 22.1 32.980 3.107 11.415 4.9 1.9 20.4 30.490 5.187 19.060 8.2 3.0 23.1 34.3

STATE 63.357 232.793 36.8 22.9 34.0

ILLINOIC; 10 5.670 20.834 7.5 3.3 24.0 35.620 6.960 2'5.575 9.2 4.0 22.2 33.030 6.331 23.263 A.4 3.7 23.5 35.040 10.855 39.885 14.4 6.3 25.0 37.250 12.870 47.2A8 17.1 7.5 24.2 36.060 11.412 41.931 15.~ 6.6 23.2 34.670 11.739 43.133 15. 6.8 20.8 30.980 't.800 17.637 6.4 2.8 19.2 2Q.690 4.694 17.2't8 6.2 2.7 17.4 25.8

STATE 75.333 276.795 43.7 22.4 33.3

INDIANA 10 5.258 19.320 15.6 3.1 22.2 33.020 3.717 13.659 11.1 2.2 21.5 32.030 3.A97 14.319 11.6 2.3 20.8 :31.040 4.443 16.326 13.2 2.6 22.5 33.550 8.100 29.761 24.1 4.7 23.6 35.160 3.142 11.544 9.3 1.8 21.0 31.270 3.304 12.139 9.8 1.9 21.0 31.380 709 2.604 2.1 O.~ 18.3 27.390 1.042 3.827 3.1 0.6 1~.8 27.9

STATE 33.612 123.500 19.5 21.9 32.5

RFGION 172.301 633.088 22.5 33.4

5

1.8

IOWA,ILLINOIS AND INDIANACROP REPORTING DISTRICTS

Figure 1. production of soybeans by CRD (1970-79 average) as a percent of theregional total. Darker shades indicate CRDs with higher production.

reliability and is given a rank of 1. For the remaining quantities, themodel with the largest value exhibits the most desirable performance. Ifmodels are tied for the same level of performance, they are all assignedthe lowest rank for which they are tied. For example, if two models aretied for best performance, they are both assigned a rank of 1, the lower ofranks 1 and 2.

It should be remembered that the models are ranked only in relation to eachother and not to an absolute standard. Therefore, saying that a particularmodel performs best or is superior to or more desirable than another modeldoes not necessarily imply that the model is the best of all possible models.It is the best of only those with which it is currently being compared.

Models are Compared Using StatisticalTests Based on d = Y - y

It is desirable to run a statistical test comparing the reliabilitypeting models. A formal statistical test considers the variabilityperformance over time and allows the user to specify an upper limitprobability of incorrectly declaring one model better than another.probability is known as a, the level of significance, or the Type I

of com-of modelon the

Thiserror.

However, because of the manner in which models are chosen for testing andhow they are evaluated, it is challenging to construct a meaningful statis-tical test. Only yield models which have been presented in the literatureor developed by known experts are considered. Therefore, a priori, greatdifferences between the reliability of the models are not expected. Apowerful statistical procedure is needed which is able to detect small,although important, differences in reliability. Also, the test should beable to function well with relatively small samples of data for each model,say ten years.The test should also perform well when only two models are being compared.Often only two models of a particular type, for example, two monthly weatherdata models or two daily weather data models, are competitive and availablefor testing. When models of different types are to be compared, it is un-likely that all possible model comparisons will be made. It is more likelythat the best models of each type will be compared.

It would appear that an F test could be useful in comparing the mean squareerrors of two models. However, if the mean square errors are based on tenyears of test data and a = .05, then one model's mean square error must befour times larger than anothers before the models can be declared different.This is an unreasonable requirement since models which are in the evaluationprocess will almost always be more competitive than this.

A test may be constructed by considering that one mod~l is considered morereliable than another model if its predicted yields, Y's, are closer to theactual yields, Y's. No difference in the reliability of two models for aparticular year means that the absolute value of the difference betweentheir predicted yields and the actual yield is the same. The absolute valueof the difference is used because it does not matter whether one model over-estimates and the other underestimates or whether they both over or under-estimate. The reliability of a model for that year is related to the amount

7

o~ the discrepancy, not its direction. We may define Idll = IYl - YI, Idzl =!Yz - YI, and D = Idll - IdZI. Then the models are equally reliable in ayear for which D equals zero. If D is not equal to zero, one model is morereliable than the other for that year. In formal terms, we want to test thenull hypothesis that there is no difference in the reliability of the modelsover all years. To do so the values of D from the ten test years may be usedto compute a test statistic and a decision made whether or not to reject thenull hypothesis. Since the results for the models are paired each year,paired-sample statistical tests are used.

Two types of paired-sample statistical tests are used: a parametric testusing the student "t" test statistic and a nonparametric test using theWilcoxon signed rank test statistic. One reason for applying both testsis that they require different assumptions. The parametric t-test assumesthe D values are normally distributed while the nonparametric test does not.The d values may be considered to be approximately normally distributed. TheIdl values would then be folded normals rather than normally distributed.Although both models are folded at Idl = 0, their means may be different andthe distribution of D has a possibility of not being normally distributed.The t-test is robust with respect to the normality assumption; however, thispossible violation of the assumption is one reason for also running the non-parametric test.

The other reason for running both tests concerns the conditions under whichthe null hypothesis is rejected by each test. Using the parametric test,the basis for rejecting the null hypothesis is the average size of the Dvalues as compared to their variability. The t-test statistic is the averageof the sample D's divided by the sample standard error of the D's. Thehypothesis will be rejected and the model with the smaller Idl values de-clared more reliable if t is large (either positive or negative). However,it is possible that one model could have a smaller Idl value for each of thetest years, in other words, be very consistent in outperforming the othermodel, and still the null hypothesis may not be rejected by the parametrictest unless the average value of D is large enough. The parametric testimplicitly requires that one model have more years with smaller Idl valuesthan the other model and explicitly requires that, on the average, the Idlvalues be smaller by a sufficient amount before that model may be declaredmore reliable.

Using the nonparametric test, the null hypothesis will always be rejected ifone model has smaller Idl values for each of the test years, regardless ofthe magnitude of the D values. Therefore, if the models are very competitivein terms of the Idl values each year, but one model consistently, althoughslightly, outperforms the other model, the nonparametric test will stilldeclare the consistent model to be more reliable.

The hypothesis of equal model performance will only be rejected by the non-parametric test if one model has more years with smaller Idl values than theother model. The model with more smaller Idl values is considered the morereliable model in terms of consistency of performance. However, to rejectthe null hypothesis and declare one model clearly better than another, con-sistency of performance is not a sufficient requirement (although it isnecessary). Consider the situation in which one model is more consistent

8

than the other but the largest D values occur when the less consistent modelperforms better. In the few years the less consistent model performs better,it performs much better. A dilemma exists since one model is more consistentthan the other but the biggest differences between the models occur when theconsistent model performs worse. The null hypothesis will not be rejectedand the consistent model will not be declared better if this situation occurs.The null hypothesis will be rejected only if one model is more consistent andthe biggest differences between the models occur when the consistent modelperforms better.

MODEL COMPARISON

Indicators of Yield Reliability Based ond = ~ - Y Show All Models Have Small Bias

But the One Line Model Has the Smallest RootMean Square Error and Standard Deviation

The model values and comparative ranks for the bias, the root mean squareerror (RMSE), and the standard deviation (SD) are given in Tables 2, 3 and4. There is no clear cut best model in terms of bias. At the CRD level,the three line model has the smallest bias more often than either ot~ermodel (12 out of 27 times). However, it is not ranked 1 for bias at eitherthe state or region levels. This inconsistency in performance is symptomaticof the small amount of bias produced by each of the models.

The one line model is clearly the most accurate model. In 24 of the 27 CRDs(89%), the one line model has the smallest root mean square error and standarddeviation. The best performing model in each CRD according to the root meansquare error is shown in Figure 2. The one line model also has the bestperformance at the state and region levels.

The three line model has the worst accuracy. It has the largest RMSE in 15(56%) and the largest SD in 16 (59%) out of 27 CRDs. The state and regionresults are also poorest for the three line model.

Indicators of Yield Reliability Based onrd = (d/Y)*lOO Show the One Line Model Performing Best

The model values and comparative ranks for the indicators of yield reliabilitybased on the relative difference, rd, are given in Tables 5, 6 and 7. Theseindicators are valuable for demonstrating the worst performance of a model.Therefore, the best performing model will have the smallest values for thepercent of years the absolute value of the relative difference exceeds tenpercent and for the largest and the next largest absolute value of therelative difference.

In 20 of 27 CRDs (74%), the one line model has the smallest (or is tied forthe smallest) percent of years in which the absolute value of rd exceeds tenpercent (Figure 3). Except for the Iowa state model, the one line model alsoperforms best at the state and region levels. There is little differencebetween the performance of the two and three line models.

9

TA8U: ?\.4rH)[L((),,\PARISOr-J HASEr) O~ Tl-i~HIAC) (QUINTAlS/~ECTARE)DFRIVF:D FQO,,\ INnEpE~DENT TEST Y~A~S<;T~Aw MA~~ "'10DELS - SOYdEANSIOWA. ILLINOIS. I~DIANA

"-1f)[)ELI 1 I_I~JF: I 2 l II\JES 3 LINE,STATE Cp) I RIAS QA"!K I i·HAS ~AI\JK I dIAS PA~'K------------1---------------1---------------1-------------I IIOWA 10 I -0.79 ( J) -0.21 (2 ) I 0.05 <1\20 I o.1/j ( 2) 1).10 (1) , 0.20 (3)30 I -O.bG ( 3) -0.45 (2) I -0.27 (1\4U I 0.06 (1) -0.26 (2) , -0.61 (3 )SO I ().37 (3) 0.30 ( 2) , 0.21 <1,

60 I I1.S1 (3 ) 0.1~ ( 2) -0.06 (1)70 I 1.06 (3) 0.41 (? ) -0.30 <1\80 I o.ll+ (1) 0.3h (3) 0.31 (2)GO I -0.35 ( 3) 0.00 (1) 0.01 ( 2)

ISTATE "1'10£ '_ I 0.00 (I) -0.10 (2) -0.32 ()CRr)C) AG(,~. I n.v1 (1) 0.03 (3) -0.02 (2)IIILLINOIS 10 I -0.29 (3 ) 0.13 (? ) 0.09 <1\20 I -0.13 (3) -0.04 (1) 0.33 (2)30 I -0.24 (3 ) -0.1 c:; (2) 0.02 (1)40 I 0.01+ (1) 0.19 (?) 0.38 (3\SO , -().3~ (3 ) 0.32 (2) 0.24 <1\60 I O.:;~ (1) 0.19 P) -0.01 el\70 I -0.14 (1) 0.37 (? ) 0.39 (3)

80 I 0.0c.; el) -O.l~ () -O.OA (2\90 I -0.00 (1) -0.60 (3) -0.3h (?,ISTATE M')OEL I - 0 • () S el) 0.29 (3) 0.20 (2)CPOS AC,Gq. I -0.12 ( 2) o • 11 (1) O.17 (3\II

P.,IO IAI\JA lU I -O.=Jq (J) -0.01 (I) 0.30 (2,20 I -0.'10 (3 ) 0.11 (1) 0.19 (2)30 I -1.11 ( :; ) -0.11 el) -0.12 (2)40 I -0.13 (1) 0.44 (2) 0.49 (3)50 I -0.'11 ( 3) 0.23 el) 0.63 ( 2 \60 I -0.68 (1) 0.76 (2) 0.80 ()70 I 0.63 (3) 0.41 (? ) 0.02 (1)AO I 1. 74 ( '3) 0.91 ( 2) 0.55 (1)90 I 1.~2 (3) 0.66 ( ?) 0.58 el)

ISTATE MODEL I -().::'1 (3) 0.24 (1) 0.39 (2)CRDS AGG~. I -0.1+2 (3) O.2R (1) 0.39 (2)I,

REGIOl\J ~ODELI -0.07 (1) 0.1f> ( 1) 0.13 (2)CRr)S Ar,G~. I -0.11 (1) O.lf> ( 2) 0.18 <3\STATES Ar,Gi-? I -0.07 (1) 0.19 ( 3) O.O~ (2)

10

TABLE 3'-1nOEL r.a~PARISO~ ~ASEO O~ TH::RO:)T ~EAN SQIJAQE ERf.lO~ (QUINTALS/H::CTARE)DERIVED FQO"1 INDEPEf\JDENT TE<;T Y::A~SSTRAW ~AN MODELS - SOYBEANStO~A. ILLINOIS. INOIANA

~()"lfLI 1 l I~JE 2 L It-.JE<; 3 LINE<;STATE CRD I KMSE RANK RMSF: RANK RMSE RA'JK--~----~--~-,~----------------------------~I-------------IIOIAIA 10 I 2.70 (1) 3.35 (2 ) 3.41 (3120 I 1•'+9 (1) 1.68 (2 ) 1.~2 (3)30 I 2.13 (1) 2.6q ( 3) 2.54 (2140 I 2.bO (1) 2.QO (3) 2.8A (2150 I 2.60 (1) 2.74 (2) 3.02 ( 3)60 I 2.19 (1) 2.65 () 2.48 (2)70 2.18 (]) 2.00 (2) 1.90 (1)80 2.87 (1) 3.34 (2) 3.61 (3)90 2.66 (1) 3.22 ( 2) 3.3'+ (3\

STATE t.10f)EL 1.95 (1) 2.29 (?) 2.51 (31CROS AGGR. 1.95 (1) 2.21 P) 2.32 (3)

IlLINOlc; 10 2.93 (1) 3.41 ( ~) 3.4h (3)20 2.71 el) 2.81 (2) 2.9f, (3)30 2.80 (1) 3.32 (3) 3.19 (2)40 3.21 (1) 3.12 (2) 3.93 (3)50 2.74 (1) 3.31 (2) 3.3~ (3)60 2.'+9 (1) 2.7S (3) 2.b6 (2)70 2.47 (1) 2.67 ( ~) 2.94 (3)80 2.39 (1) 2.40 (2) 2.46 (3190 2.44 (1) 2.45 (2) 2.95 (3)STATE t.1f)DEL 2.51 (1) 2.6Q (2) 3.0A (3)CRDS AGGR. 2.:>3 (1) 2.80 (2) 2.90 (3)

INDIANA 10 2.23 (1l 2.62 (2) 2.85 (3)20 2.65 (ll 3.10 (3) 2.99 (2)30 2.34 (ll 2.4F, (2) 2.56 (3)40 2.67 ell 3.44 (3) 3.40 (2150 I 2.51 (1) 3.03 (3) 2.94 (2)~o I 1.79 (1) 2.17 (2) 2.36 (3)70 I 1.93 (1) 2.04 (3) 1.97 (2)80 I 2.74 (3) 2.39 (2) 2.19 <1,90 I 2.74 (3) 2.34 (\) 2 •3-f (2)I 2.51STATE Mf')OEL I 2.05 (1) 2.44 (2) (3)CROS AGGR. I 2.03 (1) 2.47 (2) 2.50 (3)IIREGION MODELl 1.96 (ll 2.39 (2) 2.51 (3)CROS AGGR. I 1.99 (1) 2.30 (2) 2.33 (3)STATES AGGR. I 7.00 (1) 2.29 (2) 2.44 (3,

11

root1970-1979.

error forindicate

Figure 2. Number indicates the model with smallestsoybean yields based on test yearsCRDs with higher production.

mean squareDarker shades

TABLE 4I.4f)OELCO~PARISON dASEO O~ THESTANDARD DEVIATION (QUINT~lS/YECTA~E)DERIvED FDO~ INOEPE~DENT TEST YEA~SSTRA~ MAN M0DELS - SOYAE~NSIOwA. ILLINOIS. INDIANA

1-10l)EL1 1_ INE 2 L PJF:S 3 LINEC:STATE CRD I SO qANK I SD QIP·JK I <;D QA'IK------------,---------------I-----~---------,-------------IIOWA 10 2.58 (1) I 3.3t5 (2 ) 3.41 (3)20 1.48 (1) , 1.67 (? ) 1.91 (3>30 2.01 (1) 2 •6'+ (] ) 2.53 (2>40 2.60 (1) 2.89 (3) 2.82 (2)50 2.57 (1) 2.73 (2) 3.01 (3>60 2.13 (1) 2.65 (3) 2.48 ( 2)70 1.91 (2) 1.95 Ll) 1.88 (1)80 2.86 (1) 3.32 (2) 3.60 (3)90 2.64 (1) 3.22 ( 2) 3.34 (3)STATE ,",ODEL 1.~S (1) 2.29 (? ) 2.49 (3)CRDS ~GGq. 1.95 (1) 2.27 (2) 2.32 (3)

ILLINOIS 10 2.91 (1) 3.41 (2) 3.46 (3>20 2.61 (1) 2.83 (2) 2.84 (3>30 2.19 (1) 3.31 (1) 3.19 (2)40 3.21 (1) 3.71 (2) 3.91 (3)50 2.72 (1) 3.29 (2) 3.37 (3)60 ~.46 (1) 2.74 () 2.66 (2)70 2.47 (1) 2.65 (2) 2.91 (3)80 2.39 (1) 2.39 (2) 2.46 (3>90 2.44 ( 2) 2.3~ (1) 2.82 (3)STATE M()DEL 2.51 (1) 2.67 (2) 3.08 (3)CRDS Ar,G~. 2.52 (1) 2.80 (2) 2.90 (3)

INOI A~JA 10 2.15 (1) 2.62 (2) 2.84 (3)20 2.'+9 (1) 3.09 (3) 2.98 (2)30 2.06 (1) 2.45 (2) 2.56 (3)40 2.67 (1) 3.41 (3) 3.36 (2)SO 2.34 (1) 3.02 (3) 2.87 (2)60 1.66 (1) 2.03 (2) 2.22 (3)70 1.83 (1) 2.00 (3) 1.97 (2)~O ?.12 (2) 2.21 (3) 2.12 (1)90 2.21 (1) 2.25 (2) 2.30 (3)STATE MODEL , 2.01 (1) 2.43 (2) 2.48 (3)CRDS AGGR. , 1.99 (1) 2.46 (2) 2.47 (3)I

I2.50REGION 1-10DELI 1.96 (1) 2.38 (2) (3)CRDS AGG~. , 1.'i9 (1) 2.29 (2) 2.33 (3)STATES AGGR. I 2.00 (1) 2.28 (2) 2.44 (3)

13

TABLE 5~ODEL CO~PARISON ~ASEn ON TH~PERCENT Of YEAR~ IRE~ATIVE DIfFEqENCEI > 10,*,DERIVED FRO~ IND_PE~DENT TE~T Y~A~S

~TRAW MAN MODELS - SOyBEANSIOWA. ILLINOIS. INDIANA

~Oi1ELSTATE CRD 1 LINE 2 LINES 3 LINEe:% qANK 'Kl RANK I 3; QANK~ ...~ .._------- ...•------------- ~--------------,-------------IOWA 10 60 (3) 50 (1) 50 (1)

20 10 el) 20 (2) 20 (2)30 40 (1) 50 (1) 40 (1l40 40 el) 50 ( 3 ) 40 (1)50 40 (3) 20 (1) 30 (2)60 20 (1) 40 ( 2) 50 ( 3)70 30 (3) 20 (1) 20 (1)80 20 (1) 40 (2 ) 50 (3 )90 20 (1) 40 (2) '+0 (2 )

STATE W)f)F.:L ?O (2) 10 (1) 20 (2)CROS AGGR. 20 el) 20 (1) 20 (1)

ILLINOIS 10 40 (2) 30 (1) 40 (2)20 40 (2) 40 ( ?) 30 (1,30 20 (1) 50 (2 ) 50 (2)40 10 (1) 30 (?) 40 (3)SO 40 el) 40 (1) 40 (1)60 20 (1) 40 ( 3) 30 (2,70 40 (1) 40 (1) 60 (3)80 '50 (1) 50 (1) 50 (1,90 SO (1) 70 (2) 70 <2,

STATE ~ODE~ 20 (1) 40 (2) 60 (])c!:ms AGG • 30 (1) 40 (? ) 40 (2)

INDIANA 10 40 (ll 40 (ll 40 (1)20 40 (1) 50 <2) ~o (2)30 30 (3) 20 (1) 20 (1)40 20 (1'> SO (3) 40 (2)SO 30 (2) 50 (3) 20 (1)60 20 (1) 20 (1) 30 ()70 20 (1) 50 ( 3) 30 (2)80 40 el) 50 (f!) 50 (2 )90 40 (1) 50 (3) 40 (1)

STATE MODEL 20 el) 30 (2) 30 (2)CRDS AGGR. 20 (1) 30 (?) 30 (2)

REGION ~OOEL 10 (1) 20 (2 ) 20 (2)CRDS ~GGR. 10 (1) 20 (2) 20 (2)

STATES ~GGR. 10 (1) 20 (? ) 20 (2)

14

Figure 3. Number indicates the soybean model(s) with smallest percent of testyears (1970-1979) having absolute value of the relative differencegreater than ten percent. Darker shades indicate CRDs with higherproduction.

80 90IOWA, ILLINOIS AND INDIANA

CROP REPORTING DISTRICTS

TABLE I.,

"'()i)ELCOMPAP ISO'''''H~SEn 0,..., TH~LA~GEST I~ELATIvE JIFFERE~CEI[)f~TVED FROM I~OEPE~DENT TEST Y::A~SC;T~AW "1~N MODELS - SOYtjEANSIOWA. ILLINOIS. INOIANA

MonEL1 L I~'JE 2 LI'JES 3 LINEc:STATE C~D RO qA~IK RO RA''.jK I RD R A 'I I(------------t--------------- ---------------1-------------II()~A 1U I -17.4 (1) 30.~ ( 2) 33.8 (3120 I 19.6 (2) 18.0 (1) 24.2 (3110 I 15.~ el) 22.4 ( 2) 23.0 (3)40 I 25.4 (3) 20.S (1) 23.R (2)50 I 2S.!) el) 33.7 (31 33.2 (21~o I 27.1 (2) 28.6 (3) 23.1 (1)70 I ?6.5 (3) 20.6 (2) 19.0 (1)80 I 57.4 ( 1 ) 65.4 (2 ) 68.4 (3190 I 313.1 el) 43.5 (2) 45.8 (3),

C:;TATE Mf)r)EL I 23.9 (ll 29.8 (2) 29.R (21CROS AGG~. I 23.9 el) 28.2 ( 2) 29.3 (3)I

IL L I"J') IS 10 41.2 (1) 46.5 (2) 47.1 (3)20 26.5 el) 32.9 ( 2) 33.5 (3)10 42.M el) 49.4 (3) 4').8 (2140 52.7 el) '59.9 () 59.3 ( 2)50 36.9 el) 43.2 ( 2) 43.7 (3)60 34.3 (2) 36.0 (3) 32.0 (1)70 36.~ (2) 13.6 <I) 38.8 (3)80 26.6 (3) 22.1 (1) 25.3 (2 )90 26.6 (2 ) 18.7 (1) 30.5 (3)

STATE "'1f)f)EL 37.6 (ll 40.0 (2) 41.2 ( 3)CROS ~GGq. 37.0 el) 3"1.4 (2) 40.0 (3)t

INOIA"lA 10 25.4 (1) JO.6 (2) 31.8 (3 )20 31.0 el) '+0.5 (2) 40.5 (2)30 24.5 (ll 33.3 (2) 33.3 (2)40 48.1 (1) 56.5 ( 2) 57.8 (3)50 28.2 el) 37.9 (2) 39.0 (3)60 lii.6 (1) 27.9 ( 2) 30.2 (3)7U 22.6 (3) 16.4 (1) -16.9 (2)80 31.B (3) 21.2 ( 2) 20.5 (1)90 33.1 (3) 26.1 (2) 23.6 (1)STATE MODEL 211.0 el) 32.1 (2) 33.9 (3)CROS AGGQ. 2H.O el) 33.9 (2) 34.5 (3)

REGJ')~ "10n::L 2~.9 (1) 33.9 ( 2) 35.1 (3)CROS AGG~. 29.9 el) 33.9 (2) 34.5 (3)STAH::S AGGQ. ]0.5 (1) 34.5 (2) 35.1 (3)

16

smallestyears

Figure 4. Number indicates the soybean model withabsolute relative difference during the testshades indicate CRDs with higher production.

value of the1970-1979.

largestDarker

80 90

IOWA, ILLINOIS AND INDIANACROP REPORTING DISTRICTS

T ~BLf:: 7'1()DEL CaMPARIsn~ gASEO ON THENtXT LAqGE~T IRELATIVE OIFFERE~CEIDERIVEu FPO'1 INOEP(NJE~T TEST YEA~S<;TPt\vl"'AN 1'-10DELS- SOyBEANSIO~A, ILLINOtc;, I~OIANA

MOr)EL1 '.I~JE 2 LINfS 3 LINE~STATE CRD P.D RA~K RD R A I"K RD RA~IK------------- --------------- --------------- - .._-------- ..-

InwA 10 17.0 (1) 23.0 (2) 24.5 (J)20 7.4 (1) -11.0 (1) -10.2 (2\'30 -14.4 (1) -20.0 (2) -20.0 (2)40 10.5 (1) -18.3 (2 ) -19.4 (]\50 16.2 (2) -13.h (1) -16.8 (3\60 11.9 (1) -12.7 (2) -13.0 (3)70 13.1 (3) 10.£' (1) -10.8 (2)80 -12.7 (1) 17.5 ( 2) 19.0 ()\90 -12.4 (1) 19.1 (3) 18.6 (2\

STATE "'1()OELI 12.5 (2) -9.7 (1) -13.9 ()\CROS AGG~. 12.5 (3) -10.8 (1) -11.6 (2)

ILLINnIS 10 -12.A (1) -16.8 (J) -16.1 (2)20 -1£'.6 (2) -17.2 () -16.0 (1)30 -10.3 (1) 14.5 (2) 16.8 (J)40 -9.6 (1) -14.4 (2) 17•2 ()\50 -12.5 (}) 15.4 (2) - 5.5 ()\60 -10.3 (1) -ll.0 (2) -15.8 ()70 -12.4 (1) 18.0 (2) lA.8 ()80 -13.9 (}) -17.7 () -16.0 (2)90 19.9 ( 2 ) 17.9 (1) 23.7 ()

STATE "'1nDfL -10.9 (11 12.3 (2) -15.6 (J)CROe; AGGq. -11.7 (1) -14.5 (2) -14.5 (2)

INOJA"'JA 10 -13.4 ( 1 ) 17.'3 (2) 20.8 ()\20 -15.5 (1) -18.9 (1) -15.9 (2)30 -18.9 (2) -17.3 (1) -19.7 ()40 -12.9 (1) 16.2 (3) 13.4 (2)50 -13.0 (}) 20.3 ( ?) 21.3 ()60 -10.8 (1) 22.7 () 22.2 (2)70 16.7 (3) -13.5 (1) 14.7 (2)80 27.6 (3) 20.9 (2) 20.2 (1)90 30.4 (3) 22.3 (1) 22.9 (2)

STATE MOOEl -12.0 (ll 16.2 (2) 19.7 (3)CROe; AGGR. -11.6 (ll 1£'.7 () 16.2 (2)

REGION ~ODEl -8.1 (1) -13.3 (2) -13.3 (2)CROS ~GG~. -8.5 (1) -11.1 (2) -11.7 (2)

STATfS AGGR. -8.1 (ll -10.9 (2) -12.1 ()

18

value of the nextyears 1970-1979.

Figure 5. Number indicates the soybean model with smallestlargest absolute relative difference during the testDarker shades indicate CRDs with higher production.

8090IOWA, ILLINOIS AND INDIANA

CROP REPORTING DISTRICTS

In 16 of 27 CRDs (59%), the one line model has the smallest value of thelargest absolute relative difference (Figure 4). It also has the smallestvalue at the state and region levels. The three line model performs worst.

In 19 of 27 CRDs (70%), the one line model has the smallest value of thenext largest absolute relative difference (Figure 5). Except for Iowa, theone line model also ranks first at the state and region levels. The threeline model performs worst at the CRD level and is somewhat worse than thetwo line model at the state and region levels.

Indicators of Yield Reliability Based on Y and Y Showthe One Line Model Performing Somewhat Better

Plots of the actual and predicted yields over the ten-year test period foreach state model are displayed in Figures 6-8. The model values and thecomparative ranks for the indicators of yield reliability based on Y and Yare given in Tables 8, 9 and 10. These indicators demonstrate the correspon-dence between actual and predicted yields. The best performing model willhave the largest value for the percent of years in which the direction ofchange from the previous year and from the average of the previous threeyears in the Y's agrees with the Y's and for the correlation coefficientbetween the actual and predicted yields.

In terms of correctness in direction of change from the previous year, thereis little difference in model performance at any level. Figure 9 shows thehighest ranking model(s) for each CRD.

When considering correctness of change from the average of the three previousyears, the three line model does worst at the CRD level with little differencebetween the one and two line models (Figure 10). However, the one line modelranks highest at the state and region levels.

In 21 of 27 CRDs (78%), the Pearson correlation coefficient is closest to +1for the one line model (Figure 11). The one line model also ranks first atthe state and region levels. The three line model performs worst at alllevels.

Statistical Tests Based on d = Y - YShow Some Preference for the One Line Model

The results of the parametric and nonparametric paired-sample statisticaltest are given in Tables 11, 12 and 13. The results for the comparison ofthe two multi-line models are given in Table 11. There is little evidenceof statistically significant differences between the models.

In only one CRD do the parametric test results show a significant differencebetween the 2 and 3 line models. The 3 line model performs better in that CRD.However, the 2 line model performs significantly better in the Iowa and Illinoisstate models and the regional results aggregated from the state models.

The more reliable model in each CRD according to the average value of Idl ispresented in Figure 12. The 2 line model performs better in 15 of 27 CRDs(56%), while the 3 line model performs better in 11 of 27 CRDs (41%), and the

20

FIGURE 6IOWA

State ModelActual and Predicted Yields for

~he Test Years 1970-1979

STQAWMAN MODELSSOY8EA\jSA = ACTUAL YIELD1 = ~REDTCTED YIELD rOP 1 LINE MODEL2 = ~REDTCTE~ YIELD rop. 2 LINE MODEL3 = ~REDTCTED YIELD rop 3 LINE MODEL

YIELD II27 +II

26 +II25 +II24 +

I23 +

II 3

22 +I aI

21 +II20 +II

19 +II

18 +II

17 +II

16 +II

15 +I--~+----.--~-.----.----.---~+---_.---_.----+----+-~1~10 1971 1972 1973 1974 1975 1976 1977 1978 1979

YEAR

32 a

1

12

J2

21

FIGURE 7

ILLINOISState Model

Actual and Predicted Yields forthe Test Years 1970-1979

A =1 = ~REDTCTE,)2 = PREDTCTE')3 = PREDTCTED

ST~AW'4AN MODELSSOytiEA\jSACTUAL YIELDYIELD FOR 1 LINEYIELD FOR 2 LI~EYIELD FOR 3 LINE

~ODEl.~OOELMODEL

,I+,,+I,+II+,,+ 3,I+,,+,,+,,+,,+,I+,,+,,+,---+----+----+~---+----.~---+----+----.--~-+~---.--1970 1971 1972 1973 1974 1975 1976 1977 1978 }979

YEAR

2j

3

f

I12

3

I{

3211

32

,\

11

2

15

18

16

17

21

20

23

22

24

25

YIELD27

26

22

FIGURE 8INDIANA

State ModelActual and Predicted Yields for

the Test Years 1970-1979

A =1 = PREDTCTED2 = PREDTCTED3 = PREDICTED

STRAW~AN MODELSSOYBEA~SACTUAL YIELDYIELD fOR 1 LI~EYIELD fOR 2 LI~EYIELD fOR 3 LINE

~ODELMODELMODELYIELD21

26

2S

24

23

22

21

20

19

18

11

16

15

II•II•II•II•I 1I• ?I 3 1123• 1I J 2I• 2II•II•II•II•II•II•I---+----.----.----.----.---~+----+----+----.----.--1910 1911 1912 1913 1914 1915 1916 1911 1918 1919

YEAR

23

TA9LE R~0~Er CO~P~RISO~ BASED ON THEPERCE~T 0 YE~RS THE DIRECTION Of C~A~GEfR~~ T~f PQEVIOUS YEAR IS CORRECT,)UPI'\JGI~DEPENDf.~T TEST YEARSSTRAW ~A~ MODEl S - SOYBEANSIO~A, ILLI~ofs. INDIANA

MO')EL1 '_ T \j E 2 LINES 3 LINF.:~STATE CR~ ~ ~ANK % RANK % RA~IK------------ --------------- --------------- -------------

InWA 10 22 (1I 22 (1) 22 (]l20 ?2 (2I 33 (11 0 (3)30 33 (ll 22 (2) 22 (2 )40 22 ell 11 01 22 (ll50 22 (ll 22 (II 22 (}l60 13 (ll 33 (ll 33 (})70 ?2 (3) 44 (? ) 56 (})80 56 (1) 44 (2) 33 (3)90 44 (2) 56 (}) 44 (21

STATE MnOEL I 22 (21 22 (2) 33 (1)CROS AGGQ. I 22 (I) 22 (1) 22 (1lIIILLINOIS 10 I 22 (ll 22 (}) 22 (1)20 I 11 (31 22 (}) 22 (1)30 I 33 (3) 44 (2) 56 (})

40 I 33 (2) 44 (1) 33 (2)50 I 33 (3) 44 (2) 56 (1 )60 11 (3) 33 (2) 44 (1)70 44 (2) 56 (}) 44 (2 )80 11 (2) 33 (1) 11 (2190 22 (3) 44 (}) 33 (2)

STATE MOOEl 11 (3) 44 (ll 33 (2)CRDS ~GGR. 11 (3) 44 (1) 44 (1)

INDIANA 10 44 (ll 44 (1) 33 (3)20 33 el) 22 (2) 11 (3)30 56 (ll 56 (}) 44 (3)40 56 (1) 33 ( "3) 56 (1)50 44 (ll 33 (2 ) 33 (2 )60 33 (1) 22 (2) 11 (3)70 33 () 67 (}) 44 (2)80 22 (2) 22 (2) 33 (1190 33 (2) S6 (}) 33 (2 )

STA.TE MODEL S6 (1) 44 (2) 44 (2 )CRDS A.GGR. 56 (1) 44 (2) 44 (2 )

REGION MODEL 44 (1) 44 (1) 44 (})CRDS AGGR. 33 (3) 44 (}) 44 (1)STATES AGGR. 33 (3 I 56 (1) 56 (1)

24

Figure 9. Number indicates the soybean(1970-1979) having agreementbetween predicted and actualhigher production.

mode1(s) with largest percent of test yearsin direction of change from the previous yearyields. Darker shades indicate CRDs with

80 90IOWA I ILLINOIS AND INDIANA

CROP REPORTING DISTRICTS

TABLE 9~ODE~ COMPARISO~ BASED ON TH~pERCc~T 0 YEARS THE JIRECTION Of C~A~GEF~OM A T~REE YEAR BASE PERIOD IS CO~~ECTI)URI~G INOEPENDENT TEST YEARSSTRAW ~A~ MODELS - SOYBEANSIOWA, ILLINOIS, INDIA~A

MOnEL "I 1 LINE 2 LINES 3 LINEc;STATE CRD I % PANK % RA~~K I ~ RA"!K

~.._-_ ...•_---- -----------~---,----~----------I-----------~-, I-IOWA 10 71 (1) , 71 (1) I 71 (1)20 71 (1) I 71 (1) 57 <3>30 57 (3) I 71 (1) 71 (1)40 57 (1) I 57 (1) 57 (I>50 43 (3) I 71 (1) 57 (2)60 43 (1) I 43 (1) 41 (1)70 43 (? ) , 57 (1) 29 (3)80 29 (1) I 29 (1) 14 (3)90 57 (1) I 43 ( 2) 43 (2>

ISTATE MODEL 71 (1) I 57 (2) 57 (21CROe:;AGGR. 71 (1) I 57 ( 2) '57 (~)IIILLINOIS 10 29 (1) I 29 (1) 14 (3120 43 (2) I 57 (}) 43 (2)

30 43 (1) I 14 (3) 29 (2)40 43 (1) I 14 (2) 14 ( 2 )SO 43 (1) , 29 (2) 29 (2)60 43 (1) 29 (2) 14 (3170 43 (1) 43 (1) 29 (3)~o 29 (2) 43 (1) 29 ( 2)qO 29 (2) 43 (1) 29 (2)

STATE MODEL 43 (1) 43 (ll 14 <3>CRDS "GG~. 43 (1) 14 (1) 29 (2)

It..JOIA~A 10 43 (1) 43 (1) 43 (1)20 57 (1) '57 (ll 43 (3)30 57 (1) 43 ( 2) 43 (2)40 57 (1) 29 ( 2) 29 (2)SO 57 (1) 43 (? ) 43 (2)"0 71 (1) 57 (2) 29 (3)70 29 ( 2) 43 (1) 29 (2)80 29 (3) 57 (1) 57 (1)90 0 (3) 29 (1) 29 (l>

STATE MODEL S7 (1) 57 (1 ) 57 (1)CRoe; AGGR. 57 (1) 43 ( 2) 43 (2)

REGION t.10DEL 57 (1) 29 (2) 29 (2)CROS AGGR. 57 (1) 29 (2) 29 (2)STATES Ar,GR. 57 (1) 29 (2) 29 (2)

26

Number indicates the(1970-1979) havingthree year averageindicate CRDs with

Figure 10.

10 20

80 90

IOWA, ILLINOIS AND INDIANACROP REPORTING DISTRICTS

soybean model(s) with largest percent of test yearsagreement in direction of change from the previousbetween predicted and actual yields. Darker shadeshigher production.

TAt3LE 10~ODE~ CO~DAQI50~ ~ASEO O~ TH~COQQELATIO~ 8 TWEE~ ACTU~L AND PREOICTE) VI EL::>C;uU~H:\JG P-IOEPENDE"JT TEST YF ARS

STQAI,oI~AN ~OOELS - SOyBEANSIOWA. ILLINOIS. INI)IM·IA

MonF.LI LI"lE 2 LI\lF.S 3 LIN~c:.

STATE CR::> R qAI\IK R KA\JK I R RAt-.lK--~--_.._---- --------------- ---------------1-------------I0WA 10 0.'+6 (1) 0.10 ( 3 ) O.~5 (~ )

20 0.37 (ll 0.17 (2 ) -O.~8 (3)30 0.51 (1) 0.10 ( 3) 0.~1 ( 2140 O.3~ 11) O.O? ( 3) u.23 (? I50 -i).12 (2) -(J.I? (}) -0.24 (3)60 1).~5 11) -0.32 ()} -0.08 (2170 -f).43 ( 3) -f).IS (l) -0.24 ( 2)80 -1).,+9 ( j) -fJ.3A ( 1 ) -0.'+3 (2)90 f).13 (ll -0.21 (? ) -0•34 ( 11

STATE ~nDEL f).34 (}) 0.f)4 P) -O.Oh ()ICROC; AGGR. n.33 11) -O.OS (? ) -O.OA ()I

ILLINOIS 10 0.14 (1) -0.27 ( ?) -0.44 (3)20 0.28 (1) O.OA (2) -0.03 ()I30 0.04 (1) -1).37 (1) -0.32 (2140 0.05 (ll -0.27 (2 ) -0.54 (3)50 0.08 (I) -().23 (2) -0.41 (3160 0.23 ( 1 ) -0.1? <3} 0.01 PI70 1).'+11( 1 ) 0.30 p} 0.1? <3180 0.30 (1) 0.29 ( ?) 0.21 (3190 0.07 (2 ) 0.21 <I) -0.05 (31

STATE ~OOEL 0.20 (11 0.02 (" ) -0.42 (3)CPOC; AGG~. 0.19 11) -0.10 (2 ) -O.2~ (3)

I"JOIANA 10 0.36 ( 1 ) -v.OO (2) -0.19 ()}20 0.30 (1) -0.011 ( 2 ) -0.15 (3130 1).48 11) 0.27 (2 ) 0.16 (3)40 0.lf3 (1) -0.33 ( "3) -0.25 ( 2)50 fl.47 () 0.1? ( 3 ) 0.16 ( 2)60 0.44 (1) -O.'.>? (? ) -0.20 (3)70 0.53 ( 1 ) 0.34 (3 ) 0.45 (2)80 -0.74 ( 3) -fl.l] ( 1) -0.27 ( 2)90 -0.77 ( "3) -0.'>4 (? ) -0.03 (l)

STATE "'100EL 0.44 (ll fl.If, (2 ) 0.04 <3}CROC; AGG~. 0.45 (1) 0.')9 P} 0.07 (3)

REGION ~ODEL O. 3~ (ll -0.14 (?) -0.21 (3)CROC; AGGR. , 0.35 (1) D.01 ( ~ ) -0.05 <3}

STATE~ AGGR. I 0.33 Il) I).OS (?) -O.IS (3)

28

Number indicatescoefficient(1970-1979) •

Figure 11. the soybean model with the largest correlationbetween actual and predicted yields over the test years

Darker shades indicate eRDs with higher production.

80 90IOWA, ILLINOIS AND INDIANA

CROP REPORTING DISTRICTS

models are tied in 1 CRD. The 2 line model performs better in more of thehigh producing CRDs.

The nonparametric test results show somewhat more statistical differencebetween the two models. Significant differences between the models areobserved in four CRDs. Three of these favor the 2 line model. The 2 linemodel performs significantly better in the Iowa and Illinois state modelsand in the regional results aggregated from the state models. The 2 linemodel also performs significantly better in the Illinois results aggregatedfrom the CRDs and in the region model.

The better model in each CRD according to the percent of years with smallerIdl is presented in Figure 13. The 2 line model performs better in 12 of 27CRDs (44%), the 3 line model performs better in 10 of 27 CRDs (37%) and themodels are tied in 5 CRDs. The 2 line model performs better in more of thehigh producing CRDs.

In summary, the results of the statistical tests for yield reliability in-dicate that the 2 line state model performs better than the 3 line model inIowa and Illinois. No conclusion can be drawn for Indiana.

The results for the comparison of the 1 line model with the 2 line model aregiven in Table 12. Again, there is little evidence of statistically sig-nificant differences between the models.

The parametric test results show a significant difference in three CRDs,favoring the 1 line model over the 2 line model in each case. There are nosignificant differences between the models at the state or region level.

The better model in each CRD according to the average value of Idl ispresented in Figure 14. The 1 line model performs better than the 2 linemodel in 24 of 27 CRDs (89%). including the high producing CRDs.

The nonparametric test results again show somewhat more statistical differencebetween the two models. Seven CRDs show significant differences between themodels, all favoring the 1 line model. The 1 line model also performs sig-nificantly better in the Iowa results aggregated from the CRDs.

The better model in each CRD according to the percent of years with smallerIdl is presented in Figure 15. The 1 line model performs better in 19 of 27CRDs (70%), the 2 line model performs better in 3 of 27 CRDs (11%) and themodels are tied in 5 CRDs. The 1 line model performs better in more of thehigh producing CRDs.

In summary, the 1 line model consistently performs slightly better than the2 line model at the CRD level. Consequently, the state and region resultsaggregated from the CRDs favor the 1 line model, although usually not byenough to be declared statistically significant. The Iowa and Indiana statemodels and the region model favor the 1 line model, but again, the differenceis not statistically significant.

The results for the comparison of the 1 line model with the 3 line model aregiven in Table 13. Again, there is little evidence of statistically sig-nificant differences between the models.

30

TI\9LE 11~ODEL COMPARISON 8~~ED O~PAIREn-SA~PLE STATISTICAL TESTS2 LINE MOOEL ~ITH 3 LINE ~OJEL(0=p<.10. 00=p<.05. ooo=P<.OI)STRA~ ~AN MOOELS - SOYBEA~SI~~A. ILLI~OIS. I~DIA~A

STATE CRD

PAR~M~TqIC T-TEST~-------------------------~VERAGE IUI IDIfFERENCEMOnEL I OF~M 2 SM 3 I ~VERAGES

NONPARAMETRIC RANK TEST-------------------------% S~ALLEP. I~I IDTFFERENCE1010DEL I OFSM 2 SM 3 IPfRCE~TAGE------------ ------------------~------- -------------------------

IOWA 102030405060708090

STATE MODELCRDS AGGR.ILLINOIS 102030

405060708090

STATE MODELCRoe; ~C;GR.INDIANA 1020304050

60708090STATE MODELC~OC; AGGR.REGION MODELCROS AGGR.STATES AGGR.

2.671.362.292.562.162.141.832.162.441.7~1.817.592.282.432.412.522.052.312.102.261.912.012.152.491.912.642.451.461.832.191.1361.921.84l.b~1.501.49

;;>.591.421.932.292.392.061.582.372.472.041.862.592.412.26".842.582.152.512.222.502.422.21;;>.242.311.942.47?211.681.681.931.921.831.1371.811.541.66

0.080.060.36 0-'.271).230.080.250.210.030.26 000.050.000.130.170.430.060.100.200.120.2'+o • 51 000.200.090.180.0]0.110.240.220.11)0.260.060.090.030.130.04().11 00

31

504()20506040404030705040704050505070506080605020504040604040404050603070

406060502030603040105060204020205030403020105060405060306050406040302020

102040 00o40 01020101060 000

o2050o30 0030o40103060 0050 00

o4010102030 02010o201030 010SO 00

Figure 12. Comparison of 2 line and 3 line models to predict soybean yields basedon the average of Idl = IY-YI for 1970-1979. Number indicates model withsmaller average Id Blank denotes tie. Stars indicate the level ofsignificance, none (P>0.10). *(0.05<P<0.10), **(O.Ol<P<O.OS) ***{P<O.Ol).Darker shades indicate CRDs with higher production.

80 90IOWA, ILLINOIS AND INDIANA

CROP REPORTING DISTRICTS

VJN

Figure 13. Comparison of 2 line and 3 line models to predict soybean yie~ds basedon the percent of test years (1970-1979) with smaller Idl = IY-yl. Numberindicates model with larger percent. Blank denotes tie. Stars indicatethe level of significance, none (P>O.lO), *(0.05<P<0.10), **(0.01<P<0.05),***(P<O.Ol). Darker shades indicate CRDs with higher production.

STATE

TARLE 1~~n~El CO~PA~tSO~ 8~~EO O~PAIREO-SAMPLE ~TATI~Tlr.AL T~STSI LT~~ MonEL ~ITH 2 LINE ~O)El(0=P<.10. oo=P<.O~. 0*0=p<.v1)

ST~A~ MA~ ~0DElS - SOYB~A~SIOWA. IlLPIiHS. INOIA~A

PARA4FTRIC T-Tf~T NO~~QRA~ETRTC RANK TF'ST------------~------------- ---~---------------------AVERAG!=.: IDI IOIF'FEPENCE % S~ALLEp 1')1 1o Tf'-fERENCE~onEL 1 Of ~OOEL 1 OFSM 1 SM 2 1 AVERAGES SM 1 5~ 2 IP~RCE~TAGE------------ -------------------------- .---------------.--------IOWA

ILLI~OIC; 10203040506070BO90

STATE MODELCRD'i AGGR.

INDIANA 102030 140 I50 I60 I70 I80 I90 1

ISTATE MODEL ICR~e; AGGR.IIwEGION t.100EllCRne; AGGR.ISTATES AGGR.I

2.411.081.83~.Oij?091.571.741.981.9~1.42] .41

2.112.012.1~2.1H2.061.981.942.11?08

1.931.94

1.7'-J2.221.891.6'52.1q1.501. S 1c.o,+2.22I.S~1.5131.391.431.,+3

1.7~1.~1?592.28::>.43?.41?52?052.31?10?26

1.91?Ol?11"::>2.491.91?b42.,+51.461.83~.191.861.921.84

1. 6~1.501.49

O.?h'1.28:1.46!).4~ 00

0.07.).57:).09').18O.~5'1.36i).40

0.48 00.27i).25!).230.460.070.37.').01O.lH0.020.0T

o.Y,f).?71).02f).99 000.260.100.320.1'50.360.3)0.26'I. 2~f).OT0.06

34

606080905080705070

6070

70bO705071)507040504060605050906040706CJ408050605040

'+0'+02010502030'+0301.+03030'+030::;030503060'+060'+0'+0505010'+0602040602050405040

202060 0~o 00o60 04010402040 0

40 02040o40 a-

o40 02010202020oo80 ***202050202060o20oo

Figure 14. Comparison of 1 line and 2 line models to predict soybean yields basedon the average of Idl = IY-YI for 1970-1979. Number indicates modelwith smaller average Idl Blank denotes tie. Stars indicate the levelof significance, none (P>0.10), *(0.05<P<0.10), **(O.Ol<P<O.OS), ***(P<O.Ol).Darker shades indicate CRDs with higher production.

80 90IOWA, ILLINOIS AND INDIANA

CROP REPORTING DISTRICTS

Figure 15. Comparison of 1 line and 2 line models to predict soybean yields basedon the percent of test years (1970-1979) with smaller Idl = IY-YI· Numberindicates model with larger percent. Blank denotes tie. stars indicatethe level of significance, none (P>O.lO), *(0.05<P<0.10) **(0.01<P<0.05)***(P<O.Ol). Darker shades indicate CRDs with higher production.

80 90IOWA ,ILLINOIS AND INDIANA

CROP REPORTING DISTRICTS

TARLE 13 BASEDMOnEL COMPARISOt\J O'IJPAIRED-SA~PLE STATISTICAL T~STS1 LINE MODEL ~IT~ 3 LINE "10)EL(*=P<.10. ~~=P<.05, ~~~=P<.01)

STRAW MAN ~ODEIS - SOYB~A'lJSIOWA, ILLI~n s. I~nTA'lJAI PARAMETRIC T-TF.:ST I N'JNPl\~~~ETRIC RANK T~ST1--------------------------1-------------------------I AVERAGE 101 IDIFFERENCE I % S"1ALLER I~I 10TFFE~ENCEI MOOEL 1 OF I "100EL I OF"STATE CRD I SM 1 SM 3 I AVERAGES I SM 1 SM 3 IPERCE~TAGE------------1--------------------------1-------------------------t IIOWA 10 t 2.41 ?59 O.IA I 50 so. 020 1 1.0~ 1.42 0.34 I 60 40 2030 t 1.83 1.93 0.10 I 40 60 2040 I 2.08 2.29 0.21 I 50 50 050 I 2.09 2.39 0.30 I 60 40 2060 t 1.57 2.06 0.49 70 30 4070 I 1.74 1.513 f).lo 40 60 2080 t 1.98 2.37 0.39 60 30 1090 I 1.99 2.47 0.48 70 30 40I 1.42 90STATE M()OEL I 2.04 fl.62 * 10 RO *~CRDS AGGR. I 1.41 1.86 0.45 * 80 20 60 ~~IILLINOIS 10 2.11 2.59 !).48 80 20 60 *20 2.01 2.41 0.40 60 40 2030 2.18 2.26 1).08 60 40 2040 2.18 ::>.84 0.66 70 20 5050 2.06 2.58 0.52 ~o 20 60 *60 1.98 2.15 1).11 30 60 3070 1.94 2.51 1).57 70 20 50 ~

80 2.11 2.22 I) • 11 60 40 2090 2.08 2.50 0.42 60 30 30STATE MODEL 1.93 ?42 0.49 80 20 60 *CRDS AGGR. 1.94 2.21 0.27 70 30 40INDIANA 10 1.79 2.24 0.45 60 40 2020 2.22 2.31 :).09 40 60 2030 1.A9 1.94 1).05 60 40 2040 1.65 2.47 0.82 * 70 30 40 *50 2.19 2.21 1).02 30 70 4060 1.56 1.68 J.12 50 50 070 1.51 1.68 0.17 50 50 080 2.04 1.93 I) • 11 30 70 4090 2.22 1.92 1).30 40 60 20STATE MODEL 1.59 1.83 0.24 50 50 0CRDS AGGR. 1.58 1.87 0.29 70 30 40REGION MODEL 1.39 1.81 0.'+2 60 30 30 *CRDS AGGR. 1.43 1.54 0.11 60 '+0 20STATES AGGR. 1.43 1.66 0.23 70 30 40

37

Figure 16. Comparison of 1 line and 3 line models to predict soybean yields basedon the average of Idl = Iy-yl for 1970-1979. Number indicates model withsmaller average Id Blank denotes tie. Stars indicate the level ofsignificance, none (P>O.lO), *(O.OS<P<O.lO), **(O.Ol<P<O.OS), ***(P<O.Ol).Darker shades indicate CRDs with higher production.

8090IOWA,ILLINOIS AND INDIANA

CROP REPORTING DISTRICTS

w00

Figure 17: Comparison of 1 line and 3 line models to predict soybean yields based onthe percent of test years (1970-1979) with smaller Idl = It-YI. Numberindicates model with larger percent. Blank denotes tie. Stars indicatelevel of significance, none (P>0.10), *(0.OS<P<0.10), **(O.Ol<P<O.OS),***(P<O.Ol). Darker shades indicate CRDs with higher production.

IOWA, ILLINOIS AND INDIANACROP REPORTING DISTRICTS

The parametric test results show a significant difference in only one CRO.It favors the 1 line model over the 3 line model. The 1 line model per-forms significantly better in the Iowa state model and the Iowa resultsaggregated from the CROs.

The better model in each CRO according to the average value of Idl ispresented in Figure 16. The 1 line model performs better than the 3 linemodel in 24 of 27 CROs (89%), including the high producing CROs.

The nonparametric test results again show somewhat more statistical dif-ference between the models. Four CRDs show significant differences betweenthe two models, all favoring the 1 line model. The 1 line model also per-forms significantly better in the Iowa and Illinois state models, the Iowaresults aggregated from the CROs, and the region model.

The better model in each CRO according to the percent of years with sma~lerIdl is presented in Figure 17. The 1 line model performs better in 16 of27 CRDs (59%), the 3 line model performs better in 7 of 27 CRDs (26%) andthe models are tied in 4 CROs. The 1 line model performs better in more ofthe high producing CROs.

In summary, the 1 line model often performs slightly better than the 3 linemodel at the CRD level. Consequently, the state and region results aggre-gated from the CRDs favor the 1 line model, although usually not by enoughto be declared statistically significant. The Iowa and Illinois statemodels and the region model favor the 1 line model, significantly so forboth the parametric and nonparametric tests in Iowa. The nonparametricresults were significant for the Illinois state model and the region model.The Indiana parametric results favor the 1 line model, but the nonparametricresults show no difference between the models.

All Models Are Objective

No subjective inputs are required to run any of these models. In all threecases, the single independent variable is objectively defined as year minus1950. The join point(s) for the multi-line models as well as the parameterestimates for all models are objectively determined using least squaresalgorithms.

All Models Omit Considerationof Known Scientific Relationships

The straw man models do not consider factors which have a recognized causalrelationship with crop yields. For example, it is well known that year-to-yearvariations in weather have an important effect on yield. Therefore, ifweather data were available, it would be consistent with scientific knowledgeto include weather variables in a model predicting crop yields. Weathervariables are excluded from the straw man models yet nothing is done to accountfor the fact that the yields have been influenced by weather. The yields mayalso have been influenced by other non-technology factors. However, since noadjustment is made to the yields for these non-technology factors and sincethese factors are not included as independent variables in the model, thestraw man model results will be affected by non-technology influences.

40

The assumption of straw man modell, the simple linear model, is that therate of change in yields has stayed constant over the model developmentbase period. An attempt was made to investigate the validity of thatassumption by fitting multi-line models which allow more than one timetrend. However, if the multi-line models do not perform as well as thesingle line model. one should not necessarily conclude that the assumptionof the single line model has been confirmed. Rather the method of account-ing for variation in time trends by the multi-line straw man models may notbe adequate.

All Models Are Adequate

The three straw man models require the same input data, year and yield.Therefore, they are equally adequate. They can be developed for any cropgrowing region or subdivisions thereof and for any special application,such as irrigated yield, as long as the basic inputs of year and yieldare available. Likewise they can be developed for areas for which acreageestimates are available in order that production estimates may be obtained.

All Models Are Timely

As soon as reliable figures are available for the current year's yield,each of the models can be developed and used to produce an estimate of thefollowing year's yield. In this respect, they are all, equally, very timely.

The One Line Model is Least Expensivebut None of the Models Are Costly

The only data required by any of the straw man models are the year and actualyield. These data are readily available at no additional cost.

The one line model can be fit using any standard statistical packaged programor statistical calculator. The multi-line models require the use of a specialFORTRAN program which contains the least squares algorithm for objectivelyestimating the join point(s). Objectively determining two join points takesmore computer time than determining a single join point. In summary, the costof fitting the model parameters is least expensive for the one line model andmost expensive for the three line model. However, the cost of fitting any ofthese models is very low.

All Models Are Simple

The philosophy behind the straw man models, describing technological trend,is simple. Users can clearly understand the basis for predicted yields.They can also understand the limitations of the models. What a user is todo in interpreting these limitations may not be so simple. The calculationof predicted yields is easy. The X values in the model are simply the yearminus 1950. Thus to estimate the yield for 1980, multiply the slope by 30and add the intercept. In the case of the multi-line models, the slope andintercept corresponding to the most recent line segment is used.

41

One cautionary note needs to be made, however. Although the philosophy be-hind the model is simple, the implementation of the idea may not have beensuccessful. The data has not been adjusted for the effects of weather. Anunusually low or high yield related to weather conditions will have an impact,particularly on the multi-line models. This is because their line segmentparameters are estimated from shorter time periods and will be influencedmore by variations from an overall trend due to an individual year's weatheror other non-persistent factors.

All Models Have a Poor CurrentMeasure of Modeled Yield Reliability

The Spearman correlation coefficient between the estimate of the standarderror of a predicted yield from the base period model, Sy, and the absolutevalue of the difference between the predicted and actual yield, Idl, indicateswhether the model provides a useful current measure of modeled yield reliability.An r value close to +1 is desirable since it indicates that a smaller standarderror of prediction (and therefore a narrower confidence interval about thepredicted value) is associated with smaller discrepancies between predictedand actual yields. If this were the case, one would have confidence in sy as(at least) a relative indicator of the accuracy of Y. Any model which isprimarily a function of trend, such as the straw man models, is not expectedto perform well on this criteria using the test described.From examining Table 14, one can see that most of the correlations are negativefor all three models. The results for all three models are so poor that thereis no value in making detailed model comparison for this characteristic.

CONCLUSIONS

All of the straw man models attempt to explain differences in soybean yieldsover time by fitting trend lines to the yield data. Straw man model 1.simple linear regression, describes a uniform increase in yield over time.Straw man models 2 and 3 allow the rate of change in yields to vary over thetime period. There is little difference between the three models in relationto seven of the eight criteria for model comparison: objectivity, consistencywith scientific knowledge, adequacy, timeliness, minimum costs, simplicity,and accurate current measures of modeled yield reliability. Straw man model 1is somewhat less consistent with scientific knowledge, less costly, and simpler.It performs best in terms of the remaining criteria, yield indication reliability.However, the superior performance is often by a small margin and is often notstatistically significant.

RECOMMENDATIONS

Since the largest difference between models is in relation to yield indicationreliability and the one line model performs best in regard to that criteria,straw man model 1 is recommended for predicting soybean yields over straw manmodels 2 and 3. However, this does not necessarily substantiate that the rateof change in yields is uniform over time. More sophisticated trend modelsstill might be able to demonstrate the validity of different rates of changeover different portions of the time period considered.

42

TAALf 1~MOQ[L COMPA~~SON OF THEClJ~RE 'H l~DICATJO~ Of MO. ELEO YIE~D R~LIABI~ITY~ASED O~ THE COo.RELATI0~ COEFFI tENT 3~TW E~~AC;E Pf~lOI) PREDICTED AND 1EC;T YEAR ACTJA,- ACCURACYSTRA~ ~AN MODE~S - SOyBEANSIO~~, ILLINO S. I~DIANA

MODEL1 '-I~E 2 LI~ES I 3 LINEC;STATE ern P PANI< R RA~K I R RA""K-_ ..- ....------ --------------- ---------------1-------------

101,IA 10 -0.15 ( 2) O.OR (1) -0.31 (3'20 0.16 (1) 0.08 ( 2) -0.21 (),30 -0.U8 (1) -0.33 (?) -0.60 ()40 -0.32 ( 2) -0.23 (}) -0.61 (3)5U ().31 (1) -0.34 (2) -0.~2 ()6U -0.05 (2) -().30 () -0.02 (1)70 -0.59 (2) -0.1'3 (l) -0.62 ()80 -0.70 (3) -0.53 (1) -0.66 (2)90 -0.62 (3) -0.20 (2) -0.16 (1)

STATE '>1f)OEL -0.28 ( 3) -0.2S (2) 0.09 (1,CROS AGGR. - r) • 2 1 (2) -0.16 (1) -0.56 ()

ILL I'~O1S 10 -0.04 (2) 0.19 (1) -0.32 ()20 0.12 (1) 0.02 (2 ) -0.20 ()30 -0.'+8 (3) -0.07 ( 2) 0.14 (1)40 -0.36 (3) 0.13 (1) -0.09 (2)50 -O.6b ( 3) 0.01 (1) -0.34 (2'60 -n.b2 (2) -0.27 (1) -0.75 ()70 -0.11 (2) 0.07 (1) -0.2A (3,~o -0.62 (3) -0.43 (1) -0.47 (2)90 -0. 11 (3) -0.46 (2) -0.02 (1)

STATE MOOEL -0.30 ( 3) -0.02 (2) 0.07 (1)CRO~ AGGR. -0.15 (2) O.2~ (1) -0.18 (3)

I~DIA~A 10 -f).]3 (2 ) 0.27 (l) -0.33 ()20 0.09 (2) 0.11) (1) -0.09 (),)0 -0.16 (2) -0.41 () 0.10 (\)40 -0.10 (2) -().29 (3 ) 0.01 (1)50 -0.06 (\) -0.30 ( ) -0.18 (2)60 -0.78 (3) -1).55 (2 ) -0.41 (1,70 -f).11 (1) -0.25 () -0.11 (2)~u -0.30 (1) -0.43 () -0.36 (2)90 0.05 (1) -0.60 (3) -0.14 (2'

STATE wlOEL -0.21 (1) -0.48 ('3) -0.27 (2)CPOS AGGR. O.Oc (1) -0.43 (3) -0.30 (2)

RF.GtOf\J'-100EL -O.ld (,) 0.19 (1) -0.15 (2)c~o<; AGG~. 0.1 7 (2) 0.53 (1) 0.07 (3)STATES AGGR. 0.02 (3) 0.35 (1) 0.18 (2)

43

REFERENCES

BHATTACHARYAY, B. N., 1980. Crop Yield Model Test and Evaluation, a Statis-tical Approach. Department of Statistics. University of Missouri-Columbia.

HUDSON, DEREK J., 1966. Fitting Segmented Curves Whose Join Points Have tobe Estimated. Journal of the American Statistical Association, 61:1097-1129.

KESTLE, RICHARD A., 1981. Analysis of Crop Yield Trends and Development ofSimple Corn and Soybean "Straw Man" Models for Indiana, Illinois, and Iowa.AgRISTARS Yield Model Development Project, Document YMD-2-ll-l(80-ll.l).

MOESCHBERGER, MELVIN D., 1980. Model Testing and Evaluation. Department ofStatistics, University of Missouri-Columbia.

SEBAUGH, JEANNE L., 1981. Evaluation of "Straw Man" Modell. The SimpleLinear Model, for Soybean Yields in Iowa, Illinois, and Indiana. AgRISTARSYield Model Development Project, Document YMD-1-3-2(8l-02.1).

SEBAUGH, JEANNE L., 1981. Evaluation of "Straw Man" Model 2, Two Trends OverTime, for Soybean Yields in Iowa, Illinois, and Indiana. [File Report].

SEBAUGH, JEANNE L., 1981. Evaluation of "Straw Man" Model 3, Three TrendsOver Time, for Soybean Yields in Iowa, Illinois, and Indiana. [File Report].

THOMPSON, W. A., 1980. On Model Testing and Evaluation. Department ofStatistics, University of Missouri-Columbia.

WILSON, WENDELL W., BARNETT, THOMAS L., LeDUC, SHARON K., WARREN, FRED B.,1980. Crop Yield Model Test and Eva1ution Criteria. AgRISTARS Yield ModelDevelopment Project, Document YMD-1-1-2(80-2.l).

44

APPENDIX - STATISTICAL FORMULAS

Measures of Model Performance

Definition of Terms:

Y, = Yield as reported by U.S.D.A. for year i ("true" or "actual" vield).]. .

Yi Yield as predicted by a model for year i.

Yi = difference between predicted and actual yield for year i.

rd,].

100 dt/Yi = relative difference for year i.

Standard error of regression = (Residual or Error Mean Square from Model

Development Base Period)~ for year i.

s~Y,

].

Standard error of a predicted value for

where X is the regression design matrix

-1 ~year i = By (1 + ~'(~'10 ~) ,i

of independent variable values and

~ is the vector of independent variable values for the year the prediction

is being made.

i = 1, ..., n = number of test years and L

Y = l/nnL

i=ly,

].average actual yield.

nL

i=lsummation over the test years.

Measures:

Bias = B = l/n L d. = d.].

Relative Bias = RB = 100 B/Y.

2Mean Square Error = MSE = l/n L d, .].

1Root Mean Square Error = RMSE = (MSE)~.

Relative Root Mean Square Error = RRMSE = 100 RMSE/Y.

- 2Variance = Var = l/n L (di - d) .

Standard Deviation = SD = (Var)~.

45

Relative Standard Deviation = RSD - 100 SD/(Y + d).2Mean Square Error = Variance + (Bias) ,

or2Accuracy = Precision + (Bias) •

r = EYtYi - n I;Yi - --n- EYi - n

Spearman r between Idil and Sy :i

Let R(ldil) = the rank of Idil, R(Bf ) = the rank of BY ' andi i

fi = R(ldil) - R(sy ), i = 1, ••• , n. Then,i

r = 1 -6Lf 2

i3n -n

Paired-Sample Statistical Tests Comparingthe Performance of Two Crop Yield Models.

Definition of Terms:

Yl - Yield as predicted by model 1 for year i.i

'"Y2 - Yield is predicted by model 2 for year i.i

Idl I - lil - Yil = Absolute value of the difference between model 1 predictedi i

and actual yield for year i.

Id2 I - IY2 - Yil = Absolute value of the difference between model 2 predictedi i

~nd actual yield for year i.

46

Rank (IDil) = Ranks of the absolute values of Di assigned in ascending order

(smallest value of ID. I = rank 1, •••, largest value of ID I =1 i

rank n). If two or more years have the same value for IDil,

assign each year the average of the ranks.

Parametric Test - Student t:

Test Statistic

D = l/n m.,1

Dt = - wheres-'

D

2 ~sj)= (sD In) •2 2sD = [IDi

and

2l/n(LD.) ]/(n-l).1

Reject HO if ItI > to. (n-l)'

Nonparametric Test - Wilcoxon Signed Rank:

HO: There is no difference in the performance of the models.

H: There is a difference in the performance of the models.a

Procedure to compute test statistic, T:

1. Compute the D ..1

2. Assign ranks to ID .1·1

3. Assign signs to Rank (IDil) corresponding to the signs of Di.

4. Let T = the absolute value of the sum of the ranks with the less frequent sign.

Reject HO if T ~ To(l tailed), n'

47

i"lPi->E"'ID T XBOOTSTRAP TEST RESUlT~FOR SOYdEA~ YIELQ~ I~I0\'fA.ILLII\JOI;. ANI) IN;)TA I\J A

COMPARING <; TRA \.j "'1 AI\J MOnELSSM 1=S TPA',o}'-1MJ 1 s~ 2=ST~Aw MA"J 2 5"1 3=c;TRAw I.1AN3

ACTIIAL DhltDICTEU D=Y IFLl) YI[LD (()/H) ~~EDICTf0-ACTUAL

STATE CRD YEAR (CJ/H) S;-11 5"'1 2 <;"'1 j SI.1 1 <;\.12 SM 3-------------------------------------------------------------IOwA 10 1970 19.1 20.4 20.7 19.3 1.3 1.6 0.:>

1971 21.6 2f1.4 19.6 19.2 -1.2 -2.0 -2.,+1972 2c;.3 20.Q 21.2 ?o.2 -4.4 -'+.1 -5.11973 24.7 22.0 24.3 24.7 -?7 -0.'+ 0.01974 19.~ 2c.9 25.9 2h.:; 3.1 S.l 6.71975 24.1 22.7 24.G ~4.;'> -1.'+ -0.1 U.l1976 20.0 23.4 24.6 24.'-1 '3.4 4.6 4.91977 2h.3 23.3 22.1 23.9 -3.0 -'+.U -2.41978 27.9 24.6 24.1 25.1 -3.3 -3.~ -2.A1974 25.1 25.4 25.1 26.4 0.3 0.0 1.3

20 1970 2?2 21 .1 2·).9 21.~ - 1•1 -1.3 -0.41971 21.'+ 21.7 22.9 23.? 0.3 1•5 1•Q1972 23.4 22.1 21. q ~3.u -1.3 -1. S -0.41973 2?~ 22.1 23.9 ?1." -0.1 1•1 1•(\1974 14.4 23.2 22.9 24.1 3.d 3.S 4.71975 23.2 22.7 23.0 ?1.~ -0.5 -0.2 -1.41976 21.7 23.3 22.4 22.3 1.6 0.7 0.61977 ~4.6 23.'+ 21.9 ~2.i -1.2 -2.7 -2.;1978 24.5 24.2 23.9 23.;:> -0.3 -O.h -1.31979 21.9 24.5 24.4 ?3.~ 0.6 D."'> -0.1

30 1970 21.i3 18.9 18.7 19.0 -2.~ -3.1 -2.R1971 19.1 19.~ 21.1 21.=) 0.7 2.0 2.'+1972 22.0 20.1 19.9 21.2 -1.9 -2.1 -O.~1973 21.0 20.11 22.4 22.4 -0.2 1.4 1.41974 1B.3 21.2 22.4 22.5 2.9 4.1 4.21975 2').4 21.0 21.5 ?0.4 U.6 1•1 0.01976 19.i3 21.1 20.4 20.1 1.':5 0.6 0.31977 2S.0 21.4 20.0 :>o.() -j.6 -:;.() -').01978 2S.1 22.S 22.3 ?2.7 -2.6 -2."3 -2.41979 24.6 23.2 23.9 24.6 -1.4 -0.7 0.0

40 1970 19.3 21.1 21.7 211.b 1. H 2.4 1.31971 20.1 21.1 21.S ?0.1I 1.0 1.'+ -0.11972 24.':> 21.2 .?O.S 7().1 -3.3 -4.0 -4.41973 2?1 22.1 22.h 21.~ 0.0 O.s -o.?197'+ lq.4 2i?b 22.1-\ 22.1 3.2 3.4 2.71975 23.2 22.1.) ?1.7 21.:; -0.7 -1.5 -1.71976 lR.S 23.2 22.3 ?2.~ 4.7 3.R 4.41977 2?9 22.(-, 21.6 21.0 -0.3 -1.3 -1.91978 27.3 23.2 22.3 22.0 -4.1 -5.0 -5.3197~ 25.6 2J.q 23.3 74.7 -1.7 -2.3 -0.9

48

APPE'\JOIl(BOOTSTRAP TEST RESULTSFOQ SOYBEA~ YIELDS INIOil/A.tLLI~OIC:;.AND INDIANACOMPA~ING STRAWMAN MODELS

SM 1=5TRA'~ MAN 1 5M 2=STPAW MAN 2 S"1 3=5TRAW "1AN 3ACTUAL PREDICTED D=YIELD YIELD CQ/H) P~EDICTE~-ACTUAL

STATE CRD YEAR CQ/H) St..,1 SM 2 $M 3 5M 1 s~ 2 SM 3~-~-------~--~-----------------------------------------------I()wA 50 1q70 24.4 22.6 23.0 22.3 -1.8 -1.4 -2.11971 23.2 23.3 24.8 25.3 0.1 1.6 2.11972 215.1 23.7 24.0 25.1 -1.4 -1.1 0.01973 24.5 24.3 25.6 25.9 -O.~ 1•1 1.41974 1Q.3 24.7 25.8 ~5.7 5.4 6.5 6.41975 23.5 24.2 23.1 22 •.} 0.7 -0.4 -0.6lQ76 21.9 24.6 23.2 23.2 2.7 1.3 1.31977 21.0 24.4 22.8 22.8 3.4 1.8 1.A1978 27.3 24.3 23.6 22.7 -3.0 -3.7 -4.61979 27.1 24.9 24.4 23.5 -2.2 -2.7 -3.6

60 1970 24.5 23.6 24.5 24.~ -0.9 0.0 0.01971 24.3 24.2 25.8 25.7 -0.1 1.5 1.41972 24.6 24.7 25.5 25.5 0.1 0.9 0.91973 23.4 25.1 25.8 25.8 1.7 2.4 2.41Q74 19.9 25.3 25.6 24.5 5.4 5.7 4.61975 24.3 24.8 23.4 23.1 0.5 -0.9 -1.21976 22.6 25.3 23.7 23.3 2.7 1•1 0.71977 2h.O 25.1 23.5 23.3 -0.9 -2.5 -2.71978 26.7 25.7 23.9 23.7 -1.0 -2.8 -3.01979 2R.4 26.0 24.8 24.7 -2.4 -3.6 -3.7

70 1970 21.8 22.6 23.0 21.3 0.8 1.2 -0.51971 21.6 22.~ 23.2 21.6 1.2 1.6 0.01972 23.9 23.0 22.2 21.7 -0.9 -1.7 -2.21973 21.6 23.6 23.9 22.S 2.0 2.3 1.01974 1R.9 23.9 22.8 22.5 5.0 3.9 3.61975 20.9 23.2 21.9 21.7 2.3 1.0 0.81976 20.6 23.3 21.A 21.~ 2.7 1.2 1.0lQ77 23.3 23.0 21.6 21.5 -(}.3 -1.7 -1.81978 23.B 23.3 22.3 21.6 -0.5 -1.5 -2.21Q79 24.9 23.2 22.7 22.2 -1.7 -2.2 -2.7

80 1970 22.1 1~.3 19.6 18.5 -2.8 -2.5 -3.61971 21.0 20.0 21.2 21.1 -1.0 0.2 0.11972 22.4 20.5 22.1 22.5 -1.9 -0.3 0.11973 20.0 21.1 23.5 ~3.':\ 1•1 3.5 3.81974 13.6 21.4 22.5 22.9 7.8 8.9 9.31975 19.4 20.3 19.2 19.5 0.9 -0.2 0.11976 20.2 20.6 19.5 19.5 0.4 -0.7 -0.71977 20.2 20.6 19.8 19.~ 0.4 -0.4 -0.41978 22.1 20.8 20.3 19.5 -1.3 -1.8 -2.51979 23.1 20.9 20.0 20.0 -2.2 -3.1 -3.1

49

APP~\Ir)IX~OOTSTRAP TEST RESULTSfOq SOYBEA~ YIELDS I~rOWA. ILLINOIS. AND rN0TA~ACOMP6QING STRA~MAN MOOELSSM 1=STRAW MAN 1 SM 2=STRA~ MAN 2 S~ACTI JAL ORE!)! ClED

YI~LD fIELO CO/H)STATE CRO YEAR (Q/H) s~ 1 SM? SM 3

3=STRA\~ "1AN ~

0=D ~F.O I C TE I)-ACTUAL

5 '-1 1 c; ~ 2 SM 3--~--~--~--------~-------------------------------------------IOWA 90

STATE W)OEL

CROS AGGR.

lCHO1971197219731974197519761977197H1979

19701971197219731974197519761977197~1979

19701971197219731974197~1976197719781979

21.123.724.321.51~.B22.622.624.824.027.521.921.924.22?9lA.822.920.823.925.925.621.921.924.222.918.82?920.823.92S.925.6

20.921.622.322.923.222.523.023.123.824.121 .221.722.122.823.122.>323.423.223.924.421.321.72?122.B23.322.923.421.223.924.3

50

21.923.~2:;.025.624.121.221.721.1322.523.121.522.'122.424.42.4.421.822.021.823.424.1

21.622.622.S24.32'+.122.522.621.923.123.9

21.~23.7?5.025.524.521.3;;>1.g?l.tl22.422.':1;;>1.0?1.~?2.n24.1~4.'+21.022.021.7?2.324.321.122.~22.724.224.322.222.722.122.924.U

-2.2-2.1-2.01.46.4-f).10.4

-1. 7-\l.2-3.4-0.7-0.2-2.1-}.14.5-1).1

2.6-0.7-2.0-1.2-0.6-0.2-2.1-U.l4.5

0.02.6-0.7-2.0-1.3

-1.2f).10.74. 17.3

-1.4-0.9-3.0-1.5-4.?-0.4

[). 1-l.A1.55.6-1.11.2-2.1-2.5-1.5-0 • .3

0.7-1.71.45.3-0.41.8-2.n-2.11

-1.7

-1.20.00.74.07.7

-1.1-0.8-3.0-1.6-4.6-o.y-0.3-2.21 • B5.6-1.31.2-2.2-3.'"-1.3-O.P.

O.?-1.51.35.5-0.71.9-1.~-3.0-1.6

l\PPF:\lDI(BOOTSTRAP TEST RESULTSFOQ S0Y8EA~ YIELDS INIQ~A. tLLINOIS. ~ND INDIANACOMPARING STRA~MAN MOnELS

S"'11=5TRAW ""AN 1 SM 2=STQAW ~AN ~ S~ 3=STRAW "'AN "3

ACTIJAL PREDICTEO 0=YI~LD YIELD lO/rO ~~EOICTE1-l\CTUALSTATE CRD YEAR (Q/H) 5'" 1 5'''?' SM .3 S"1 1 S'" ? SM 3-~~----------~---~--------------------------------------.----IL LINOIS 10 1910 21.4 22.6 22.4 ;;>4.3 -0.8 -1.0 0.9

1911 23.0 22.R 24.9 24.'3 -0.2 1.9 I.R1912 24.4 23.1 24.9 24.1 -1.3 0.5 0.41973 23.5 23.8 25.2 25.1 0.3 1.7 1.61914 11.0 24.0 24.9 ?5.11 7.0 7.Y 8.01915 2~.4 23.2 22.4 22.2 -3.2 -4.0 -4.2191h 2'.3 24.1 23.9 23.0 1.13 1.6 0.11911 27.3 23.8 22.7 22.~ -3.5 -4.6 -4.41978 24.H 24.1 24.fl 24.2 -0.1 -0.2 -0.61979 21.8 24.9 25.3 ?4.5 -2.9 -2.5 -3.'3

20 1910 21.0 20.7 20.4 ?1.~ -0.3 -O.fl 0.91971 20.6 20.1 22.2 ~2.? 0.1 1.6 1.91912 22.0 20.8 22.3 22.5 -1.2 0.3 0.51913 21.4 21.4 22.6 22.~ 0.0 1.2 1.41914 11.0 21.5 22.6 t!2.7 4.5 5.6 5.7191~ 25.0 20.9 20.7 21.0 -4.1 -4.3 -4.01916 20.5 21.8 21.6 22.3 1.3 1.1 1.81911 2c;.9 21.6 22.1 ?2.1 -4.3 -3.8 -3.81978 22.1 22.6 23.5 23.b 0.5 1.4 1.51919 26.4 22.6 23.5 ;:13.8 -3.M -2.~ -2.6

30 1970 23.1 21.8 21.3 23.2 -1.3 -l.A 0.11911 24.3 21.8 23.1 23.7 -2.5 -0.6 -0.61912 21).0 22.5 24.6 ?5.0 -2.5 -0.4 0.01973 2;;>.0 23.4 25.2 25.7 1.4 3.2 3.11914 16.6 23.1 24.8 24.2 7.1 8.2 1.61975 21).0 23.0 21.8 21.~ -2.0 -3.2 -3.11976 21.3 23.8 22.6 22.4 0.5 -0.7 -0.91917 25.6 23.9 22.6 22.6 -1.7 -3.0 -3.01918 23.8 24.5 23.6 23.4 0.7 -0.2 -0.41979 26.8 24.7 23.A 23.S -2.1 -3.0 -3.2

40 1910 22.7 24.0 23.6 26.0 1.3 0.9 3.91971 2S.7 21.7 25.2 25.0 -2.0 -0.5 -0.71912 26.4 24.3 c6.1 25.~ -2.1 -0.3 -0.51973 24.8 25.2 26.7 26.7 0.4 1.9 1.91974 16.1 25.5 26.1 26.6 A.~ 10.0 9.91975 21.1 24.5 23.2 23.2 -2.6 -3.9 -3.91976 2c;.1 25.3 23.9 24.0 0.2 -1.2 -1.11977 2R.O 25.5 24.1 24.1 -2.5 -3.9 -3.91978 2S.8 26.2 26.0 26.2 0.4 0.2 0.41979 21.8 2fl.3 26.5 25.6 -1.5 -1.3 -2.2

51

APPE~'[) IXBOOTSTRAP TEST PES..ULTSFOQ SOYBEA~ YIELDS INTO~A. ILLINOIS. AND INDIANACO~p~~ING STQA~MAN MODELSSM I=STpAW MAN 1 S~ 2=ST~A~ MAN 2 S~ 3=STRA~ ~AN 1

STATE: C~OACTIIAL

't'I ~U)YE"l\R ((,)/11)

pqEIJICTEDYIELO (Q/H)

S"1 1 S'-1 '2 C:;'-1 3

0=J~F.OICTE)-4CTUAL') '-1 1 S '-1 2 S r-1 3-------------------------------------------------------------

ILLINOIC; 50

60

70

80

197019711972197319741975197619771978197919701971197219731974197519761977197819'79

19701C)7 119721973197419751976197719781979

1970197119721973197419751976197719781979

21 .023.324.02?017.824.323.026.623.127.1

18.319.621 • 7lq.6IS.221.622.324.221.924.7lR.O17.220.017.215.421.617.923.118.823.1

22.422.:'23.323.924.123.42'+.224.325.125.322.622.423.023.723.923.524.124.124.424.319.619.620.020.72u.820.32/).821.221.721.917.8l~.O18.41'1.319.519.520.319.920.219.9

52

22.124.126.526.225.222.524.123.42S.425.822.323.323.-'24.124.2?1.723.323.424.223.921.620.220.421.M20.319.820.220.723.023.718.618.818.919.018.R18.019.119.019.920.~

21.720.B20.122.121.119.119.:;21.~22.324.018.6IB.318.218.819.318.1+19.519.420.720.3

-0.7-3.2-1. 11.26.5- 3. 00.5-J.O0.3-1.1

l.b-0.9-1.01.7

6.1-0.131 • 1-2.51.3-2.81.30.0-1.72.15.6

-1.J-1.5-3.0-0.1-2.8-0.20.8-1.62.14.1-2.12.4-.3.21.4-3.2

-1.0-1.62.13.5

7.6-3.-.1

0.4-3.90.6-0.61.30.0

-0 • .32.1S.4-2.60.3-3.?1 • 1-3.23.3O.t=--1."33.2=5.1-l.B-2.1-3.51.2

-1.00.6) .6

-1.11.83.4

-3.61.2-'+.11• 1-2.5

O.r:I-1.62.13.57.7

-4.1-0.6-4.0

0.0-1.42.3-O.f>

-1.01.65.7-2.2-0.7-4.20.9-e.l3.'+1.2-1.(,3.5~.q-2.:;

-2.8-3.00.5-0.7

O.f.1• 1-l.R1• f,3.9

-3.21.6-3.71.9-2.~

APPEt..JOIX800TSTR~P TEST RESULTSFOP SOYBEAN YIELDS It..JIOw~. ILLINOIC;. AND INDIANA.CO~PARING STRAWMA~ MODELSSM I=STRA\tIMAN 1 SM 2=STRA~ ~AN 2 S~ 3=STRAW '''AN '3

ACTIJAb PREDICTED 0=Ylf.L YIELD (Q/f1) ~~EDICTED-ACTUALSTATE CRD YEAR (Q/f1) S~'"1 5"'1 2 C;M 3 SM 1 C;~ 2 SM 3~---~-----~-----~-------------------------------------------.ILLINOIS 90 1970 15.6 16.5 17.0 15.5 0.9 1.4 -0.11971 16.~ 16.6 15.8 15.4- 0.4 -0.4 -0.81972 U~. 17.0 16.1 15.5 -1.7 -2.6 -3.1lC)73 15.2 17.6 16.8 18.0 2.4 ] .6 2.~1974 13.9 17.6 16.5 17.2 3.7 2.6 3.31975 19.0 17.4 15.9 15.-} -1.6 -3.1 -3.11976 18.1 17.8 16.7 17.2 -0.3 -1.4 -0.91977 20.3 17.7 17.1 17.7 -2.6 -3.2 -2.61978 15.1 18.1 17.8 19.7 3.0 2.7 4.61979 21.7 17.5 18.1 18.0 -4.2 -3.6 -3.7STATE MODEL 1970 20.8 21.2 21.0 22.9 0.4 0.2 2.11971 22.2 21.2 23.0 22.4- -1.0 0.8 0.21972 23.2 21.7 22.C) 21.0 -1.5 -0.3 -0.21973 21.2 22.5 23.8 23.9 1.J 2.6 2.71974 16.5 22.7 23.1 23.3 6.2 6.6 6.81975 24.2 22.1 21.6 21.0 -2.1 -2.6 -3.21976 22.2 22.8 22.3 21.4- 0.6 0.1 -0.81977 25.6 22.8 22.5 21.6 -2.8 -3.1 -4.01978 22.5 23.4 23.2 23.8 0.9 0.7 1.31979 25.9 23.4 23.~ 23.J -2.5 -2.1 -2.9

CRDS AGGR. 1970 20.8 21.2 21.5 22.7 0.'+ O. I 1.91971 22.2 21.2 22.3 22.2 -1.0 0.1 0.01972 23.2 21.7 23.0 22.8 -1.5 -0.2 -0.4-1973 21.2 22.5 23.6 23.7 1.3 2.4 2.5lc)74 16.5 22.6 23.0 23.1 6.1 6.5 6.61975 24.2 22.0 20.9 20.9 -2.2 -3.3 -3.31976 22.2 22.7 22.0 21.6 0.5 -O.? -0.61977 25.6 22.6 21.C) 21.9 -3.0 -3.7 -3.71978 22.5 23.3 23.4 23.4- 0.8 0.9 0.91979 25.9 23.3 23.8 ?3.7 -2.6 -2.1 -2.2

53

4PP E 'J f) Ix.Rl)'nSTRAP TEST ~F.SUt.T<;fO~ SOYHF.~"JYIELD<; If\l

IQ,oiA. tLLINOI~. A~O INDIANACO~PARING STRAW"1AI\J1\.10 nF: LSS>.1 l=STRAW MAI\J1 SM 2=5 TOA'" MAN 2 SI.13=<;TKAtJ"'fAN1

ACTUAL PPEOICTED 0=YIELD YHLD (()/'-i) J~EDICTf)-ACTUALSTATE CRD YEAR «()/rl) SM 1 5~"2 SM 3 Sr~ 1 S"'f2 SM 3-----~-------------------------------------------------------INDIANA 10 1970 21.7 20.3 19.Q ?1.0 -1.4 -1.8 -0.71911 22.8 20.5 22.1 2~.:; -2.3 -0.7 -0.3lQ72 20.2 21.2 23.7 ~4.4 1.0 3.5 4.?1973 21.1 21.4 ?2.~ 23.1 0.3 1•7 2.01974 17.3 21.7 22.6 ~2.9 4.4 5.3 5.5lY75 23.1 21.2 20.2 20.3 -1.9 -2.9 -2.A1976 22.1 21.8 21.~ 22.1 -0.3 -0.5 0.01977 25.4 22.0 22.4 21.3 -3.4 -3.0 -4.11978 2~.7 23.0 22.8 ~3.7 0.3 0.1 1.0lQ79 25.7 23.1 23.7 23.~ -2.6 -2.0 -1.8

20 1970 20.7 lq.4 19.1 19.~ -1.3 -l.A -O.A1971 ?l.S 19.5 21.0 ?1.2 -2.0 -O.t; -0.3lCH2 19.6 20.0 22.1 22.5 0.4 7.7 2.91973 21.3 20.3 21.9 ?1.~ -1.0 0.6 0.61974 15.A 20.1 22.2 22.2 4.9 6.4 6.41975 21.8 20.1 19.3 20.2 -3.7 -4.5 -3.~1976 21.8 20.9 21.~ 21.7 -0.9 -0.3 -0.11977 ~C::;.121.2 22.0 21.1 -:3.9 -3.1 -4.!)1978 20.9 22.2 24.2 21.:; 1.3 3.3 2.61979 2t:\.O 22.2 2.i.l 23.2 -2.~ -1.9 -1.830 1970 19.9 18.4 18.0 19.2 -1.5 -1.~ -0.71971 20.5 1~.5 1~.8 19.~ -2.0 -0.7 -0.61972 19.2 1"3.9 20.6 20.9 -0.3 1.4 1.71973 20.5 1~.3 20.9 ?O.'1 -1.2. 0.'+ 0.31974 15.9 19.A 21.2 21.2 3.~ 5.3 5.31975 20.7 19.3 19.5 19.2 -1.4 -1.2 -1.5197t> 21.3 1~.9 19.11 19.3 -1.4 -1.5 -2.01977 24.9 20.2 20.6 ?O.O -4.7 -'+.3 -4.Q1978 21.4 21.3 23.3 23.2 -0.1 1.9 1.A1979 24.0 21.6 23.5 23.4 -?4 -o.e; -0.640 1970 21.2 20.6 22.1 ?1.3 -O.h 0.9 0.119n 24.0 20.9 21.7 ~2.3 -1.1 -2.3 -1.3lQ72 21.b 21.8 25.1 ?4.-5 0.2 3.5 2.91973 22.4 2i?3 24.1 24.!+ -0.1 1•7 2.01974 1t;.4 22.8 24.1 ?4.3 7.4 8.7 8.91975 23.4 22.0 20.9 ~O.'i -1.4 -2.5 -2.61976 24.2 22.6 21.4 ~1.l+ -1.6 -?.A -2.A1977 ?4.4 23.2 21.9 22.0 -1.2 -2.5 -2.41978 24.5 23.8 23.f) 23.~ -0.7 -O.~ -O.h197Y 24.3 24.1 24.9 25.2 -0.2 O.h O.~

54

APPEN'1IXBOQTSTRAP TEST PESULTSfOR SOYBEA~ YIELDS INIOWA, ILLINOI~. AND INDIANACO~PAqING STRAWMAN MODELSSM 1=STRA'lI/MA~ 1 SM 2=STRAW MAN 2 S~ 3=STRAW '4AN 3ACTIJAb PREDICTED D=YIfL YIELD CQ/H)

3 o~EDICTED-ACTUALSTATE CRO YfAP (o/rl) Sf\.11 SM 2 C;M St..11 S~ 2 SM 3--------------------------------------------------------.----INDIANA 50 1970 22.1 21.2 21.1 21.9 -0.9 -1.0 -0.21971 24.1 21.4 23.0 23.1 -2.7 -1.1 -1.01972 20.7 22.1 24.9 25.1 1.4 4.2 4.41973 23.6 22.2 24.0 24.2 -1.4 0.4 0.61974 17.1 22.1 24.4 24.f> 5.0 6.1 6.91975 24.4 22.2 21.1 22.S -2.2 -2.1 -1.91976 25.0 22.9 22.4 23.4 -2.1 -2.6 -1.61917 26.9 23.4 24.1 24.4 -3.5 -2.A -2.51918 26.3 24.3 25.4 25.6 -2.0 -0.9 -0.71979 2S.5 24.8 27.6 27.8 -0.1 2.1 2.3

60 1970 20.1 18.6 20.1 20.3 -1.5 0.0 0.21971 21.2 18.9 21.4 21.4 -2.3 0.2 0.21972 1A.5 19.4 22.7 22.6 0.9 4.2 4.11973 21.3 19.7 21.6 21.9 -1.6 0.3 0.61974 17.2 20.4 22.0 22.4 3.2 4.8 5.21975 22.2 20.1 20.6 2Q.~ -2.1 -1.6 -1.31976 21.0 20.R 21.5 21.7 -0.2 O.S 0.7191'7 23.1 21.0 21.7 20.4 -2.1 -1.4 -2.71978 21.1 21.7 22.6 22.7 -1.4 -0.5 -0.41979 22.0 22.3 23.1 23.4 0.3 1•1 1.470 1970 19.4 20.6 21.3 20.1 1.2 1.9 0.71971 20.4 20.9 21.5 20.1 0.5 1•1 -0.31972 19.8 21.4 21.8 20.5 ~.6 2.0 0.71973 18.6 21.7 20.9 20.5 .1 2.3 1.91974 17.7 21.7 20.~ 20.3 4.0 2.9 2.61975 21.3 21.4 20.1 19.5 0.1 -1.2 -1.81976 21.7 21.7 20.5 19.7 -2.0 -3.2 -4.01917 23.8 22.1 21.3 2j.6 -1.7 -2.5 -2.21978 22.4 22.6 22.2 2 .6 0.2 -0.2 1.21979 21.2 22.5 24.2 24.6 -0.7 1.0 1.480 1970 19.3 19.8 20.1 19.7 0.5 1.4 0.41971 19.2 20.3 20.9 19.~ 1.1 1.7 0.71972 17.6 20.8 21.1 20.0 3.2 3.5 2.41973 16.3 20.8 19.7 19.6 4.5 3.4 3.31974 16.6 20.5 113.9 19.1 3.9 2.3 2.51975 15.1 20.2 18.3 18.2 5.1 3.2 3.11976 19.6 19.6 18.0 17.7 0.0 -1.6 -1.91977 20.S 19.5 18.0 17.9 -1.3 -2.8 -2.91978 19.9 19.7 18.3 113.3 -0.2 -1.6 -1.61979 19.0 19.6 18.6 1A.5 0.6 -0.4 -0.5

55

APP£'\!Dlx.BOOTST~AP TEST RF.~ULTSFOq SOYBEAN YIELDS INIOwA, ILLINOIS, AND INDIAN~CO~PA~ING STRAWMAN MOnEL~S~ l=STpAW MA~ 1 SM 2=STRAW MAN 2 S~ACTI JAL pOEO ICTEI)YI~LD iIELO (O/rl)

STATE CRD YEAR (1/~) S~] S~ 2 S~ 3

3=STRAw "1Af\.J1D=:>~EnICrE)-~CTUALS'1 1 5"1 ~ SM 3~~~----------------------------------------------------------

INDIANA 90

STATE MODEL

CRDS A('G~.

197019711972197319741975197b1q77197819791970197119721973197419751976197719781919

1970197119721973197419751976197-'19781979

18.919.716.115.717.417.621.421.719.719.720.82;>.219.821.216.822.522.924.923.224.220.822.219.821.216.822.522.q24.923.224.2

20.120.521.020.920.520.~19.92fl.220.520.320.120.'+21.021.221.S21.021."21. Y22.723.020.120.320.921.121.521.021.622.022.823.0

56

20.921.020.119.~18.318.118.019.119.819.820.021.62).022.222.220.S21.121.723.924.720.321.~23.122.422.520.321.222.123.424.4

19.619.719.~19.318.218.118.018.4-21.021.:'20.322.023. -I22.5;>'2.52n.421.:>22.323.'+?3.~20.62) • 623.0?2.~22.620.6;>1.~21.723.'124.6

1.2O.d4.9'3.23.12.6-1.5-1.5O.H0.6-0. (-l.M

1.20.04.7-1.5-1.3-].0-().5-1.2-0.7-1.9

1• 1-0.14.7-1.'5-1.3-2.'1-0.4-1.2

2.01.34-.23.50.9O.S-3.4

-2.tio • 10.1-o.~-O.~3.?1.05.4-2. 'J-1. R-3.2

0.10.5-O.e;,-0.61.3

1.2S.7-2.2-1.7-2.90.20.2

0.70.03.83.t-0."10.5

-3.4--3.11.31.8-0.5-0.23.91.35.7-2.1-1.4-2.60.2-0.4--0.2-0.63.21.35.8-1.9-1.5-3.20.60.4

\PPE~Jf) I Xb00TSTR~P TEST RESULTSFOR SOYREA~ YIELOS INIO~A. tLLINOI~. AND INOIANACO~PAQING STqA~~AN MODELS5M 1=5TRAW ~AN 1 SM 2=STRA~ MAN 2 5~ACTUI\L PREDICTED

Y I F" LI) YI f L() ( ()/ rl )STATE CRO YEAR W/rl) 51" 1 SI\.1 2 C)M 3

3=STR~W \1AN 30=.J~EDICrED-ACTUAL

S:~ 1 S"1 2 S M 3-------------------------------------------------------------REGION MODEL

oms AGGR.

STATES AGGR.

19701971197219731974197519761977I'H81979

1970197119-/21973197419751976197719781979

1970197119721913197419751976197719781979

21.222.122.821.817.421.421.824.823.725.421.222.122.821.817.421.421.824.823.725.421.222.122.821 .817.423.421.824.823.725.4

21.021.321.822.322.622.222.722.823.423.621.021.221.722.322.622.122.7?2.723.423.~21.021.221.722.322.7?2.122.822.~23.423.7

57

21.922.323.023.523.321.222.321.523.223.821.322.322.823.n23.321.422.121.923.324.021.022.422.723.723.421.522.022.123.424.1

21.822.S23.3?3.H23.521.121.421.523.423.321.722.222.~23.623.421.322.0?1.~23.324.021.722.022.823.923.521.121.621.923.223.6

-0.2-0.8-1.00.55.2-1.20.9-2.0-0.3-1.8

-0.2-rJ.9-1.10.5

5.2-1.30.9-2.1-0.3-1.8-0.2-0.9-1.10.55.3-1.31.0-2.0-0.3-1.7

0.70.20.21.75.9-2.20.5

-3.3-0.5-1.f>

O. 10.20.01.85.9

-2.00.3

-2.9-0.4-1.4

-0.20.3-0.11.96.0

-1.90.2-2.7-0.3-1.3

0./10.50.52.06.1-2.3-0.4

-3.3-0.3-2.1

0.50.10.01.86.0-2.10.2-2.9-0.4

-1.40.5-0.10.02.16.1

-2.3-0.2-3.0-0.5-1.8