By George A. Milliken, KSU Jeff Willers, USDA, ARS Chuck O’Hara, MSU

1. 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. 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 Department of Statistics Kansas State University

3. Objectives of Experiment 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 Department of Statistics Kansas State University

4. 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 These two may be reversed Plant the Cotton Varieties Harvest the Cotton Department of Statistics Kansas State University

5. Slope Hillshade Aspect Distance Department of Statistics Kansas State University

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

7. 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 Department of Statistics Kansas State University

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

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

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

11. V1 V3 V2 V1 V3 V2 V1 V3 V2 A B C A B Planting The Varieties Randomly Assign Varieties to Sprayer Path Plant 12 rows in the Planting Path—2 Planting Paths/Sprayer Path Department of Statistics Kansas State University

12. V1 V3 V2 V1 V3 V2 V1 V3 V2 A B C A B Harvesting Process Harvest 6 rows at a time, yield measurement each 2 seconds – 36 Harvester passes Department of Statistics Kansas State University

13. A B C A B Modeling Sprayer Strip Path V1 V3 V2 V1 V3 V2 V1 V3 V2 Harvester Pass Planting Path Yield Monitor Area EXPERIMENTAL UNITS Department of Statistics Kansas State University

14. 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 Department of Statistics Kansas State University

15. V1 V3 V2 V1 V3 V2 V1 V3 V2 A B C A B Modeling—Error Terms εijklmn Yield Monitor Error Similar sizes Eijk Experimental Units Very Different Sizes Department of Statistics Kansas State University

16. V1 V3 V2 V1 V3 V2 V1 V3 V2 A B C A B Modeling—Error Terms Sprayer Path within Variety Sij Planter Path within Variety pijkl Harvester Pass within Planter path of a Variety hijklm Department of Statistics Kansas State University

17. Model where yijklmn 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, Rijklmn is the PGR rate, Xrjklmnis the value of the rth site characteristic from the yield monitor site, Department of Statistics Kansas State University

18. Model φi is the slope corresponding to the rate, βri is the regression coefficient corresponding to Xrijklmn for the ith variety, sij is the effect of the jth sprayer path of the ith variety, Eijk is the effect of the kth experimental of the ith variety within the jth sprayer path Department of Statistics Kansas State University

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

20. Model Department of Statistics Kansas State University

21. 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, Department of Statistics Kansas State University

22. 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, Department of Statistics Kansas State University

23. Model Rijklm 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. Department of Statistics Kansas State University

24. 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); Department of Statistics Kansas State University

25. 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. Department of Statistics Kansas State University

26. 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. Department of Statistics Kansas State University

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

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

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

30. 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!!! Department of Statistics Kansas State University

31. 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 Department of Statistics Kansas State University

32. 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 Department of Statistics Kansas State University

33. Examples’ Model Rate Rate2 Interactions of all variables with variety, rate and variety by rate Backward Deletion to select final model Department of Statistics Kansas State University

34. 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; Department of Statistics Kansas State University

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

36. 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 Department of Statistics Kansas State University

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

38. Type 3 Tests of Fixed Effects in Final Model Department of Statistics Kansas State University

39. Type 3 Tests of Fixed Effects in Final Model (continued) Department of Statistics Kansas State University

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

41. 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. Department of Statistics Kansas State University

42. 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. Predictions from Model with Site Characteristics Department of Statistics Kansas State University

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

44. 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. Department of Statistics Kansas State University

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

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

47. 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. Department of Statistics Kansas State University

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

49. 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 Department of Statistics Kansas State University

50. 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 Department of Statistics Kansas State University