Using Spatial Information in the Design and Analysis of Experiments Used to Evaluate the Effectiveness of Precision Agriculture Management Systems By George A. Milliken, KSU Jeff Willers, USDA, ARS Chuck O’Hara, MSU

2 Department of Statistics Kansas State University Team Approach Team: Subject Matter Specialists needed to identify the problems and provide the resources for carrying out the study—GLUE THAT HOLDS THE TEAM TOGETHER GPS and Computing Artist gather all of the layers of data and construct a data set Statistician to identify the physical structures and processes (with their help) of carrying out the experiment and use the data types to formulate a model to extract useful information from the available data

3 Department of Statistics Kansas State University Objectives of Experiment Determine the effect of a plant growth regulator rates on the production of cotton for several varieties Determine the effect of a plant growth regulator rates on the production of cotton for several varieties Use landscape and plant characteristics to determine a “Prescription” for applying the plant growth regulator to the field

4 Department of Statistics Kansas State University Experiment Process Collect all of the site characteristic data Use site characteristic data to form prescription for plant growth regulator Apply the Plant Growth Regulator Plant the Cotton Varieties Harvest the Cotton These two may be reversed

5 Department of Statistics Kansas State University Distance Hillshade Slope Aspect

6 Department of Statistics Kansas State University Concavity Section of field where experiment was conducted

7 Department of Statistics Kansas State University Process for Plant Growth Regulator Collect all of the site characteristic data and use expert opinion to determine areas at which one applies the various rates of PGR These areas form a prescription that can be applied to the field with equipment using GPS and computers

8 Department of Statistics Kansas State University Example Field with Prescription for 3 rates of PGR—A, B, C B A A C B Process for Plant Growth Regulator

9 Department of Statistics Kansas State University Process for Plant Growth Regulator Sprayer Path covers 24 row at a time B A A C B

10 Department of Statistics Kansas State University Process for Plant Growth Regulator Currently have to spray entire width with same rate. Form rectangles within each sprayer path to finish prescription B A A C B A A A AA A A A A B B B B BBB B B B B BB BB C CC C CC B B B B A A B

11 Department of Statistics Kansas State University Planting The Varieties Plant 12 rows in the Planting Path—2 Planting Paths/Sprayer Path Randomly Assign Varieties to Sprayer Path B A A C B V1 V2 V1V2V3

12 Department of Statistics Kansas State University Harvesting Process B A A C B V1 V2 V1V2V3 Harvest 6 rows at a time, yield measurement each 2 seconds – 36 Harvester passes

13 Department of Statistics Kansas State UniversityModeling B A A C B V1 V2 V1V2V3 Sprayer Strip Path Planting Path Harvester Pass Yield Monitor Area EXPERIMENTAL UNITS

14 Department of Statistics Kansas State University Modeling Have data at each yield monitor site Yield (y) PGR rate (r) Site Characteristics(x1,x2,…,xp) Model Yield of Each Variety as function of PGR rate and site characteristics

15 Department of Statistics Kansas State University Modeling—Error Terms B A A C B V1 V2 V1V2V3 ε ijklmn Yield Monitor Error Similar sizes E ijk Experimental Units Very Different Sizes

16 Department of Statistics Kansas State University Modeling—Error Terms B A A C B V1 V2 V1V2V3 Sprayer Path within Variety S ij Planter Path within Variety p ijkl Harvester Pass within Planter path of a Variety h ijklm

17 Department of Statistics Kansas State University Model where y ijklmn is the yield recorded on the nth yield monitor reading in the mth harvester pass of the lth planter path of the kth experimental unit or replication within the jth spraying path of the ith variety, R ijklmn is the PGR rate, X rjklmn is the value of the rth site characteristic from the yield monitor site,

18 Department of Statistics Kansas State University Model φ i is the slope corresponding to the rate, β ri is the regression coefficient corresponding to Xrijklmn for the ith variety, s ij is the effect of the jth sprayer path of the ith variety, E ijk is the effect of the kth experimental of the ith variety within the jth sprayer path

19 Department of Statistics Kansas State University Model p ijkl is the planter path, h ijklm is the harvester pass effect, and ε ijklmn is the effect of the yield monitor area. Note: Planter Path, Harvester Pass and Yield Monitor Area are ALL nested within the Experimental Unit.

20 Department of Statistics Kansas State University Model

21 Department of Statistics Kansas State University Model Q1 is the correlation structure among the sprayer paths, which can be described by a one dimensional spatial covariance matrix using the path centroids as the centers and distance between centroids to describe the covariances, Q2 is the correlation structure among the experimental units within a sprayer path, which can be described by a one dimensional spatial covariance matrix using the experimental units’ centroids as the centers and distance between centroids to describe the covariances,

22 Department of Statistics Kansas State University Model Q3 is the correlation structure among the planter paths within and an experimental unit, which can be described by a one dimensional spatial covariance matrix using the planter paths centroids as the centers and distance between centroids to describe the covariances, Q4 is the correlation structure among the harvester passes within a planter path and an experimental unit, which can be described by a one dimensional spatial covariance matrix using the harvester pass’s centroids as the centers and distance between centroids to describe the covariances,

23 Department of Statistics Kansas State University Model R ijklm is the correlation structure among the yield monitor values within a harvester pass within and experimental unit, which can be described by a one dimensional spatial covariance matrix using the yield monitor areas’ centroids of the yield monitor areas as the centers and distance between centroids to describe the covariances. The site characteristic values can include transformations (squares, reciprocals, logarithms, etc.) of the actual site characteristics and their cross products or ratios.

24 Department of Statistics Kansas State University PROC MIXED CODE PROC MIXED DATA=ONE; CLASS VARIETY SPRAY EU PLANT HARV; MODEL YIELD=RATE VARIETY*RATE X1 X1*VARIETY … XR XR*VARIETY / DDFM=KR; RANDOM SPRAY*VARIETY/SUBJECT=INT TYPE=SP(GAU)(DIST_SPRAY); RANDOM EU/SUBJECT=SPRAY*VARIETY TYPE=SP(GAU)(DIST_EU); RANDOM PLANT/SUBJECT=EU(SPRAY*VARIETY) TYPE=SP(GAU)(DIST_P); RANDOM HARV/SUBJECT=PLANT(EU SPRAY VARIETY) TYPE=SP(GAU)(DIST_H); REPEATED / SUBJECT=HARV(PLANT EU SPRAY VARIETY) TYPE=SP(GAU)(DIST_YM);

25 Department of Statistics Kansas State University PROC MIXED CODE LSMEANS VARIETY/DIFF; Provides a comparison of the varieties at the mean values of the rates and site characteristics. This is like predicting each variety’s yield at each yield monitor site over the complete field and then comparing those means -- how would the varieties compare if the whole field was planted to each variety.

26 Department of Statistics Kansas State University PROC MIXED CODE LSMEANS VARIETY/ AT RATE=2 DIFF; LSMEANS VARIETY/ AT RATE=6 DIFF; These statements provide means at the mean values of the site characteristics using the specified rate – plant the complete field with each variety and use a blanket rate of PGR (same rate over the complete field.

27 Department of Statistics Kansas State University Example TREATMENT STRUCTRUE 17 Varieties 4 levels of PIX DESIGN STRUCTURE 2 ROWS OF EACH VARIETY PIX APPLIED TO MANAGEMENT ZONES

28 Department of Statistics Kansas State University Pairs of Row for Each Variety

29 Department of Statistics Kansas State University MANAGEMENT ZONES FOR PGR APPLICATION

30 Department of Statistics Kansas State University Example’s Model Original Model New Model—only one spray path/ variety, so no S… Only one planter path per variety, so no P… Lose two subscripts!!!

31 Department of Statistics Kansas State University Example’s Model Using Rate as a continuous variable, so the E terms are absorbed in the regression part Only have two error terms Did some initial screening of the data, then used LOESS smoother down a row, deleted extreme residuals All before fitting final mixed model

32 Department of Statistics Kansas State University Examples’ Model Variables Used – All scaled to Yield Monitor Areas NDVI – normalized vegetation index NDVI_diff – difference between two dates Slo—Slope of land FAC—square meters flowing into current area DSM – Altitude CVX- convexity of area--hold water or shed water Euc – Euclidean distance from stream network

33 Department of Statistics Kansas State University Examples’ Model Rate Rate 2 Interactions of all variables with variety, rate and variety by rate Backward Deletion to select final model

34 Department of Statistics Kansas State University proc mixed data=predres1; where -800<res1<800; title 'analysis with site characteristics'; class pass variety load_id; model say = variety rate rate*rate variety*rate variety*rate*rate Slo LogFac Cvx logEuc Dsm Ndvi_dif index one_cvx ndvi_717 logfac*cvx Dsm*variety Dsm*rate Cvx*variety*rate logEuc*variety*rate ndvi_717*variety*rate LogFac*variety*rate*rate logEuc*variety*rate*rate Dsm*variety*rate*rate ndvi_717*variety*rate*rate LogFac*rate cvx*variety*rate*rate Ndvi_dif*variety*rate*rate Slo*variety*rate*rate index*variety*rate Ndvi_dif*variety*rate Slo*rate logfac*dsm slo*dsm logfac*ndvi_dif one_ndvi dsm*dsm*variety /outp=preds solution;**say is smoothed yield; random load_id/subject=variety; repeated /type=sp(GAU)(new_y) subject=load_id(rateclass*variety) local; lsmeans variety/at means diff; lsmeans variety/at rate=0 diff; lsmeans variety/at rate=2 diff; lsmeans variety/at rate=4 diff; lsmeans variety/at rate=6 diff; lsmeans variety/at rate=8 diff;

35 Department of Statistics Kansas State University Two passes of harvester – data are quite variable- similar side by side patterns, but lot of variability within a harvester pass

36 Department of Statistics Kansas State University Example Have only one strip per variety Replication is obtained by “crossing” PGR rates with the varieties Fit regression model using quadratic function of rate, the site characteristics, and interactions with varieties Provided a model for each variety

37 Department of Statistics Kansas State University Example Carried out a backward deletion process to simplify the model Following is AOV of variables in model

38 Department of Statistics Kansas State University Type 3 Tests of Fixed Effects Effect Nu m DFDen DFF ValuePr > F variety <.0001 rate rate*rate rate*variety <.0001 rate*rate*variety <.0001 Slo logfac <.0001 Cvx <.0001 logeuc Dsm <.0001 Ndvi_dif index one_cvx <.0001 Ndvi_ logfac*Cvx <.0001 Dsm*variety <.0001 rate*Dsm rate*Cvx*variety <.0001 Type 3 Tests of Fixed Effects in Final Model

39 Department of Statistics Kansas State University rate*logeuc*variety rate*Ndvi_71*variety <.0001 rate*rate*logf*varie <.0001 rate*rate*loge*varie rate*rate*Dsm*variet <.0001 rate*rate*Ndvi*varie <.0001 rate*logfac rate*rate*Cvx*variet <.0001 rate*rate*Ndvi*varie <.0001 rate*rate*Slo*variet <.0001 rate*index*variety <.0001 rate*Ndvi_di*variety <.0001 rate*Slo logfac*Dsm <.0001 Slo*Dsm logfac*Ndvi_dif <.0001 one_ndvi Dsm*Dsm*variety <.0001 Type 3 Tests of Fixed Effects in Final Model (continued)

40 Department of Statistics Kansas State University Predicted values from model, original data and smoothed data One Harvester Pass

41 Department of Statistics Kansas State University Example Used LSMEANS to obtain predictions of each variety at rates of 0, 2, 4, 6,8 and mean (6.17). 2 was not in the data set, but model provided predictions Following are the means and rank of the varieties within a rate.

42 Department of Statistics Kansas State University Table 3. Predicted seed cotton yield means for each of the varieties for blanket application of PGR at 0, 2, 4, 6, and 8 (oz./acre) denoted by rate_0,…rate_8 with the ranks of the mean within a rate (rank_0,…,rank_8) from the model using the site characteristics. Varietyrate_0rank_0rate_2rank_2rate_4rank_4rate_6rank_6rate_8rank_ B R Predictions from Model with Site Characteristics

43 Department of Statistics Kansas State University Example Computed the LSMEAN using mean, minimum and maximum standard deviations from comparisons within a rate

44 Department of Statistics Kansas State University Table 4. Standard deviation information for pairwise comparisons among the varieties and 0.05 LSD values computed using the mean standard deviation (mn_std), the minimum standard deviation (min_std) and the maximum standard deviation (max_std) for each of the rates of PGR from a regression model using site characteristics. ratetemn_stdLSD_mnmin_stdLSD_minmax_stdLSD_max

45 Department of Statistics Kansas State University Predicted Means from Model using Site Characteristics

46 Department of Statistics Kansas State University Example LSMEANS computed from mean, maximum and minimum standard error for comparisons made from model without the site characteristics.

47 Department of Statistics Kansas State University Table 7. Standard deviation information for pairwise comparisons among the varieties and 0.05 LSD values computed using the mean standard deviation (mn_std), the minimum standard deviation (min_std) and the maximum standard deviation (max_std) for each of the rates of PGR from model without using site characteristics. ratemn_stdLSD_mnmin_stdLSD_minmax_stdLSD_max

48 Department of Statistics Kansas State University Predicted Means from Model without Site Characteristics

49 Department of Statistics Kansas State University Summary Team approach was required to assemble all necessary knowledge about the processes and tools Built statistical model to describe data obtained from experiments ran on farms where site characteristics and management procedures are taken into account

50 Department of Statistics Kansas State University Summary Successfully put together a process that can be used to answer many of the questions being asked by researchers needing to address research problems associated with precision agricultural