PREDICTING THE TIME REQUIRED FOR CNMP DEVELOPMENT FOR SWINE FARMS USING STATISTICAL METHODS AND REAL DATA

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1 PREDICTING THE TIME REQUIRED FOR CNMP DEVELOPMENT FOR SWINE FARMS USING STATISTICAL METHODS AND REAL DATA R. W. Kloot, J. D. Rickman, W. M. Evans ABSTRACT. Between June and December of 2002, a private company conducted a pilot project wherein it developed 40 comprehensive nutrient management plans (CNMPs) for confined swine operations in seven states. The time taken to develop a CNMP ranged from 45 to 262 h, with a mean of 130 h. Approximately 66% of these CNMPs took between 104 and 143 h to develop. Linear regression modeling, using site specific operational variables for 29 of the swine operations, produced a number of equations that explained between 54% and 87% of the variability in CNMP development time. The regression modeling shows that while land based variables (e.g., crop rotation, number of fields) tended to be better predictors than animal based variables (e.g., number of head, animal units), the use of interaction terms (e.g., number of fields times animal units) was most successful in explaining variability in CNMP development time. The regression exercise and the resulting equations show that the relationship between single operational variables and CNMP development time is neither simple nor linear. Keywords. Acres, Animal units, CNMP development, Cost, Fields, Linear regression, Time, Workload. Strategic issue 1 from the Unified National Strategy for Animal Feeding Operations (USDA and USEPA, 1999) was documented as Building Capacity for Comprehensive Nutrient Management Plan (CNMP) Development and Implementation. In September 2002, the USDA Natural Resources Conservation Service (USDA NRCS) initiated a study that examines: (1) the cost of upgrading facilities and practices, and (2) the technical assistance needed to plan, design, implement, and follow up on needed structures and practices (USDA, 2003). This article provides a broad view of the costs of nationwide CNMP implementation on a macro scale. On a site specific (or micro ) scale, both private and public organizations have an essential budgetary need for more detailed estimates of specific CNMP development costs. To date, there are no known cost models for CNMP development time that are based on site specific or on farm operational details using empirical data. Between June and December 2002, Environmental Management Solutions LLC (EMS LLC) conducted a pilot project wherein it developed approximately 40 CNMPs for swine operations across seven states (Arkansas, Iowa, Kansas, Michigan, Minnesota, Missouri, and Pennsylvania). Each operation was assigned a team of two to three experienced planners, agronomists, and engineers under a team leader, and each team produced a comprehensive nutrient management plan (CNMP), including a document Article was submitted for review in August 2003; approved for publication by the Structures & Environment Division of ASAE in March The authors are Robin W. Kloot, Research Assistant Professor, and William M. Evans, Research Associate, Earth Sciences and Resources Institute, University of South Carolina, Columbia, South Carolina; and James D. Rickman, Consulting Environmental Engineer, Environmental Management Solutions LLC, Des Moines, Iowa. Corresponding author: Robin W. Kloot, 402 Byrnes Building, Columbia, SC 29208; phone: ; fax: ; e mail: (typically 50 to 150 pages) for each operation, conforming to state standards, policies, and regulations (USDA, 2000). In this article, this process is called CNMP development and should not be confused with the other activities (e.g., record keeping) associated with the actual implementation of CNMPs. The Earth Sciences and Resources Institute of the University of South Carolina (ESRI USC) used the data from the pilot project to develop a number of regression based cost models for EMS LLC. This article discusses the data, methods, and limitations of the findings and sensitivity of CNMP development time to some of the more important variables. METHOD The method employed multiple linear regression modeling techniques. The model building process had two aims: (1) to develop a series of regressions that shows how each variable accounts for changes in CNMP development time, and (2) to develop the best possible linear regression model to predict CNMP development time. The process of model building required preparatory steps of data acquisition, sorting, analysis, and checking for the effect of location (i.e., which state) before any regression modeling took place. Various features in SAS and MINITAB were used in the analysis, as described below. It must be noted that this process was iterative in nature, and each iteration required significant interaction between the authors. DATA ACQUISITION, SORTING, AND ANALYSIS Of the original 40 operations for which CNMPs were developed, only the data from 29 swine operations were used in the analysis. Missing or incomplete data prevented the use of the remaining 11 records. Of the 11 data sets discarded, some of the operations included other animal operations (i.e., dairy, poultry, beef stockers). The numbers of operations considered in the regression models from each state Transactions of the ASAE Vol. 47(3): American Society of Agricultural Engineers ISSN

2 Table 1. Summary statistics of raw data for dataset of operations considered in the regression (r 2 and p value are the Pearson correlation coefficients and significance levels, respectively, of each of the individual variables when regressed against HR). Variable Description Mean 95% CI for Mean Standard Deviation r 2 (against HR) p value (against HR) HR CNMP development time (h) (111,144) AC Acreage (ac) 879 (554, 1204) NFLD Number of fields and subfields 37.4 (15, 60) AU Animal units (avg. lb./1000) 1100 (743, 1457) HEAD Number of animals in operation 6323 (3926, 8720) BLDG Number of confinement buildings 8.5 (6, 11) ROT Crop rotation index 2.2 N/A < FAI Field times animal unit interaction term (18970, 83955) < FBI Field times building interaction term 358 (106.9, 608.2) < RFI Rotation times field interaction term 103 (40.0, 165.6) < were as follows: Arkansas (4), Iowa (5), Kansas (4), Michigan (5), Minnesota (2), Missouri (5), and Pennsylvania (4), for a total of 29 sample operations. All records pertained to swine operations. Table 1 lists the summary statistics and the results of the SAS routine Proc Corr, which provides the Pearson correlation coefficient (r 2 ) and significance level (p value) of each variable when individually regressed against CNMP development time (HR). A p value of <0.05 is considered significant. A frequency distribution of CNMP development time is provided in figure 2. Data on CNMP development time (HR) were acquired from the company s administrative records, while the other operational data (AC, NFLD, HEAD, and BLDG) were acquired via questionnaires filled out by the team leader responsible for CNMP development on each operation. Indicators of Operation Size The land based size variables, namely acreage (AC) and number of fields or subfields (NFLD) were naturally correlated. However, because field sizes ranged from 3 to 160 acres, this correlation was not perfect. In the same way, animal based variables, namely number of animals (HEAD) and animal units (AU), were indicators of herd size, where the number of head per AU varied from 2.4 to 21, depending on the animal size. Because each of these variables captures a different aspect of the operation, they were all included as possible model building variables. Indicators of Complexity In order to reduce uncertainty due to subjective assessments acquired in the questionnaires (e.g. simple, complex, pasture, etc.), the crop rotation index (ROT) was developed to reflect crop complexity, where values for ROT were as follows: 1 Single crop 2 Two crops or two crops + grass 3 Three crops or three crops + grass 4 Four or more crops. The data for crop complexity were readily available from the software applications (ESRI USC s AFOPro or Purdue University s Manure Management Planner) used in the CNMP development. The number of confinement buildings in the operation (BLDG) was an indicator of total number of animals, and it was felt to be an indicator of the complexity of the animal production operation both in terms of the number of animal production phases and the possible number of storage systems. For example, a simple feeder or finish operation may have two buildings, while a farrow to feed operation may have had 14 buildings or more. Existing On Farm Information Pre existing on farm information (e.g., record keeping, conservation plan, on farm environmental assessment [OFAER]) was reluctantly discarded from the analysis because it was difficult to compare the added value of this information to the CNMP development process. For instance, a conservation plan for each operation will usually be unique with respect to the author, which resource concerns are addressed, and which best management practices are recommended and implemented. Interaction Terms Interaction terms can be considered multiplicative hybrids between two separate variables as given in table 1. Seven interactive terms were tested for significance; of these, three terms were found to be the most significant at = 0.05: Field times animal units interaction term (FAI = NFLD AU) Field times building interaction term (FBI = NFLD BLDG) Rotation times field interaction term (RFI = ROT NFLD). As can be seen later, these terms were very effective at succinctly capturing operation size and complexity. The interaction terms that were discarded (i.e., not significant at = 0.05) were as follows: AU BLDG, HEAD BLDG, AC HEAD, and ROT BLDG. Variables Denoting State and the Effect of State on CNMP Development Hours Binary (or 1/0, dummy or indicator ) variables (Neter et al., 1996) were used in the regression modeling process to indicate the state in which the operation was located because data between states varied considerably (table 2). A nonparametric method (Kruskal Wallis) was used to test the effect of state in which the operation is located on CNMP development time (HR) (Neter et al., 1996; Hollander and Wolfe, 1999, pp ). The tests showed that CNMP development times were significantly lower in Arkansas than in all other states. In Michigan, CNMP development times were significantly higher than in Iowa and Kansas (table 2). No other differences were found. On further analysis, it was found that if the dummy (or 1/0) variable for Arkansas was not included in a regression, then the four Arkansas data points would invariably cause non linearity in the regression (fig. 1), and this became known as the Arkansas effect. In order to avoid serious lack of fit problems, the Arkansas effect, essentially an offset, was always included in all regressions. 866 TRANSACTIONS OF THE ASAE

3 Table 2. Median values by state for key variables used. Variable Arkansas Iowa Kansas Michigan Minnesota Missouri Pennsylvania n [a] [b] 5 4 HR AC NFLD Acres/field AU HEAD BLDG ROT FAI FBI RFI [a] Note that n is the number of operations for the state and is the only value in the table that is not a median. [b] Mean rather than median taken in the case of Minnesota, where data for two operations were available. Figure 1. The Arkansas effect illustrated: number of fields (NFLD) and field times animal unit interaction (FAI) are on the x axes, and CNMP development time (HR) is on the y axis. Note the four Arkansas data points (circled) at the lower left of each plot. REGRESSION MODELING The regression modeling process was as follows: Each individual variable was regressed against HR; the most significant variables resulted in equations 2 to 7 in table 3. These equations measure how each variable individually affects CNMP development time, as indicated by the slope of the variable. The a priori significance level ( ) was set at Because of the Arkansas effect (see above, and in discussion under Miscellaneous Effects ), this variable had to be taken into account for each individual regression. An all possible variable approach, combined with stepwise (forward and backward) techniques was used to find the most suitable regression models of a higher order (i.e., three variables or more), resulting in equation 1 (table 3). Once candidate regression equations were built, informal model diagnostics were applied to ensure that the regressions did not violate linear regression modeling assumptions of linearity, constant error variance, independent errors, few outliers, and normal error terms (Neter et al. 1996). RESULTS The regression exercise resulted in a number of equations (table 3) that were useful at explaining the variability of CNMP development time (fig. 2). Equation Table 3. Regression equations for the expected value of CNMP development time, E(HR). Equations are sorted by RMSE. P values are shown for each variable; an a priori significance level for the p value was set at 0.05; thus, p < 0.05 is considered significant. RMSE r 2 (adjusted) Individual Variable p value Diagnostics 1 E(HR) = ROT FAI 47.1 AR ROT Good FAI < AR E(HR) = FAI 65.2 AR FAI < Okay AR < E(HR) = FBI 67.7 AR FBI < Okay AR < E(HR) = RFI 66.4 AR RFI < Okay AR < E(HR) = NFLD 71.7 AR NFLD < Errors not normal, AR < okay otherwise 6 E(HR) = ROT 36.5 AR ROT < Errors not normal, AR [a] okay otherwise 7 E(HR) = AC 69.0 AR AC Skewed residuals, AR errors not normal [a] The p value for the AR binary variable is > However, the interest lies in the significance of the variable ROT, hence the use of equation 6. Vol. 47(3):

4 # of CNMP s CNMP Plan Development Time (hrs) Figure 2. Frequency distribution of CNMP development time (minimum = 45 h, maximum = 262 h, mean = 130 h, and number of CNMPs = 29. Approximately 66% of the data fall between 104 and 143 h. Table 3 shows all regression equations with the expected value of CNMP development time, or E(HR), as the predicted variable. After accounting for size and complexity, the Arkansas effect (denoted by AR, where AR = 1 if the operation is located in Arkansas and 0 otherwise) was the only significant state indicator variable; all other differences between states were not significant. All variables in table 3 were significant at = Equation 1 was considered best based on the RMSE criterion, which is an estimate of the error standard deviation ( ) around the true line. Based on personal communications with D. Edwards (Professor, Department of Statistics at the University of South Carolina, February 12, 2004), RMSE provides a fairly robust operational estimate of the quality of the prediction interval where the true line ±2 RMSE contains 95% of the data. Despite an impressive r 2 coefficient (0.87) for equation 1, an RMSE of 15.5 h indicates a wide prediction interval (i.e., 95% of the data lie within the true line ±31 h); this is salutary in the sense that high r 2 values did not necessarily connote predictive accuracy. The next three best regression variables, after accounting for the Arkansas effect (using the binary variable called AR in table 3), were the interaction terms in equations 2, 3, and 4, namely field times animal units interaction (FAI), field times building interaction (FBI), and rotation times field interaction (RFI), respectively. These were followed by another distinct grouping of equations 5, 6, and 7 containing the variables number of fields (NFLD), crop rotation index (ROT), and acreage (AC). DISCUSSION This section discusses calculations using equation 1, natural groupings of different regression equations, miscellaneous effects on the variable HR, and potential uses of the results. GROUPINGS OF REGRESSION VARIABLES Table 3 shows that a series of natural groups of regression variable emerged. It appeared that some interaction terms were more useful than land based variables, which were more useful than animal based variables. The interaction terms, namely field times animal units interaction (FAI), field times building interaction (FBI), and rotation times field interaction (RFI), were significantly better than any other individual variables in explaining variation in CNMP development time (table 3). Additionally, interaction terms were successful at capturing operational size and complexity issues that affect CNMP development time, regardless of state. Land based variables, namely number of fields (NFLD), crop rotation index, (ROT) and acreage (AC), were also appreciably better than animal based variables, i.e., animal unit (AU), number of head (HEAD), or number of buildings (BLDG), in explaining variability in CNMP development time (table 3). Presumably this effect is because for each farm field, one typically needs to make a unique determination for a number of attributes such as soil loss, phosphorus index, leaching index, and fertilizer recommendations (N, P 2 O 5, K 2 O) based on soil tests and other site specific data (e.g., observed slopes, best management practices). In addition, for each field, cropping projections are usually required for five years. These data requirements can be contrasted with animal (essentially manure generation) data, which are considered steady state for the planning period. From a purely practical (and cost effectiveness) standpoint, it would make sense that the planner would, where possible, seek to reduce the planning period to the minimum length allowable that would still meet CNMP requirements. INTERPRETATION OF EQUATION 1 In order to provide a feel for how CNMP development times vary with a change in an equation variable (e.g., ROT or FAI), calculations using equation 1 are used as an example. In the calculations, the slopes for the crop rotation index (ROT) and the field times animal unit interaction term (FAI = NFLD AU) are discussed. The slope for ROT is 14.5 h per unit increase in the complexity index. For instance, one would expect to find an increase in CNMP development time of = 29 h if one increased the crop rotation index from, say, 1 to 3, or from 2 to 4, all other variables being equal. The slope for FAI is Because the field times animal unit interaction term (FAI) is the product of the number of fields and animal units in the operation, a change in one term (e.g., NFLD) will have the effect of changing the slope of the other term. For instance, if the number of fields in the operation is set at 10, then the slope for AU (all other variables being equal) becomes = h per AU unit increase. If however, the number of fields is set at 100, then the slope for AU (all other variables being equal) becomes = This is illustrated in figure 3, where AU is varied for different numbers of fields. The implication is that the true relationship between CNMP development hours and animal units or number of fields is not a simple linear relationship. For instance the increase in CNMP development time when animal units increase by 1750, given 10 fields in the operation, is 4.7 h. Given 150 fields in the operation, this difference (of 1750 AU) causes CNMP development time to increase by 71.6 h. The fact that the interaction variables were all highly significant provides strong evidence that simple linear relationships between numbers of fields or animal units versus CNMP development hours do not exist. Therefore, caution is needed in estimating time when only one factor for an operation (e.g., animal units) is known. 868 TRANSACTIONS OF THE ASAE

5 CNMP development time (Hrs) Animal Units 150 Fields 100 Fields 50 Fields 10 Fields Figure 3. The effect of animal units (AU) and number of fields (NFLD) on CNMP development time, using equation 1. The crop rotation index was kept at 2. INTERPRETATIONS FOR THE SLOPES OF EQUATIONS 2 5 Equations 2 through 4 represent interaction terms and, keeping the AR term constant (where AR = 0 or 1), the slopes of each equation may be interpreted as follows: Equation 2: Where the FAI term (number of fields times animal units) increases by 1, CNMP development time increases by an average of h; where the FAI term increases by 1000, CNMP development time increases by an average of 3.24 h. Equation 3: Where the FBI term (number of fields times number of buildings) increases by 1, CNMP development time increases by an average of h; where the FBI term increases by 100, CNMP development time increases by an average of 4.17 h. Equation 4: Where the RFI term (crop rotation index times number of fields) increases by 1, CNMP development time increase by an average of h; where the RFI term increases by 10, CNMP development time increases by an average of 1.59 h. INTERPRETATIONS FOR THE SLOPES OF EQUATIONS 5 7 Equations 5 through 7 represent individual terms and, keeping the AR term constant (where AR = 0 or 1), the slopes of each equation may be interpreted as follows: Equation 5: CNMP development time increases by an average of h for each field added. Equation 6: CNMP development time increases by an average of 32.6 h for each unit increase in the rotation index (ROT). Equation 7: CNMP development time increases by an average of h for each additional acre, or CNMP development time increases by an average of 1.76 h for each 100 additional acres. MISCELLANEOUS EFFECTS Addressing the Arkansas Effect The Arkansas effect, a downward offset of the intercept of between 47.1 and 67.7 h, was found in all cases to be statistically significant. This may be attributed to a number of factors including: The four Arkansas operations (number of buildings, number of fields, crop rotations) were by far the simplest in the entire sample set (table 2). Only two people were used to develop CNMPs in Arkansas, while three were used in the other states. Despite this, the operational variables were not able to capture this significant offset. This offset was thus observed in the data, but in terms of how the operational variables were described, it was not fully understood. The effect may be attributable to any number of human, organizational, or management causes or to some operational function that was not measured. If one were attempting to predict CNMP development hours for an Arkansas operation, then this correction factor would lessen the result of equation 1 by 47.1 h. To obtain a conservative estimate for an Arkansas operation, it would be best not to use this offset, which is for all practical purposes a downward adjustment of the intercept. This offset would naturally not be applied to estimates in other states. Potential Sources of Error in the Data Some of the measurement errors in the raw data may include discrepancies due to qualitative interpretation. For example, team leaders may classify confinement buildings differently (BLDG). The fact that the crop rotation index (ROT) is such a significant predictor of CNMP development time may be fortuitous, as this index was derived from the original data. Effects Not Taken into Account All the pilot project data were based on five year planning periods. If planning periods are shorter or longer than five years, we believe that this will have a significant effect on CNMP development time. Because these regressions were developed for swine operations only, the effect of other species on CNMP development time is unknown. The composition of the investigative team developing the CNMP will have a marked effect on the efficiency with which a plan may be produced (e.g., organizational, interpersonal). HR may also vary significantly between organizations, be they consulting companies, extension agencies, conservation districts, or NRCS field offices. The process used, tools available, and the developer s experience levels are some of the variables that would, in our estimation, significantly affect CNMP development time, and possibly outweigh the operational effects measured in this article. There is anecdotal evidence that the availability of on farm information such as good records, an existing conservation plan, or an existing on farm environmental assessment (OFAER) would help to mitigate the considerable data collection effort in developing a CNMP. How efficiencies improved with experience was not measured. Many of the CNMPs in the pilot project were developed simultaneously, and it was thus difficult to distinguish between start and end dates of each operation s CNMP in the pilot. These effects are likely to be small for the pilot (which only covered six months), but as competition drives the need for improved planning skills and technology, it is likely that a steady downward trend in the time taken to develop CNMPs will occur in the next few years. POTENTIAL USE OF THESE EQUATIONS Predictors The equations (and associated prediction intervals) can be used as a reality check (keeping in mind the miscellaneous effects that were not addressed) to estimate CNMP development time, and where data permit, equation 1 will be the best estimator. The slopes of the equations are more likely to be of use in estimating variability in CNMP development hours, given operation specifics. The intercepts reflect overhead Vol. 47(3):

6 activities that occur, regardless of the size of operation (e.g., report generation). If data for equation 1 are not available, then equations 2, 3, or 4 should be used, and thereafter equation 5 or 6. Because of severe statistical problems, equation 7 is least preferable and would be useful only in establishing general values for CNMP development time. Application to Other Cost Modeling It is hoped that these findings can serve as a useful reference to others in future cost modeling efforts, both in terms of the variables included (land based and animal based) and the effects not accounted for (planning period, species, organizational differences, availability of on farm data, and temporal effects). work can be used as a reasonable reference for private or public organizations that want to estimate costs associated with CNMP development, or for those interested in further cost modeling. ACKNOWLEDGEMENTS Our sincere gratitude to the men and women of the CNMP pilot project team at Environmental Management Solutions LLC for their help in providing data and answering questions; to Earl Dotson, CEO of Environmental Management Solutions LLC, for allowing us to use the data and publish the results; and to Senator Ernest F. Hollings for his leadership; and to the South Carolina congressional delegation for their interest and support of this research. CONCLUSIONS The EMS LLC pilot project showed that the time taken to develop CNMPs for swine operations ranged from 45 to 262 h and averaged 130 h. Approximately 66% of these CNMPs took between 104 and 143 h to develop. The regression modeling showed that while land based variables (e.g., crop rotation, number of fields) tend to be better predictors than animal based variables (e.g., number of head, animal units), the interaction terms (e.g., number of fields times animal units) were most successful at explaining variability in CNMP development time. The regression exercise and the resulting equations show that the relationships between single operational variables and CNMP development time is neither simple nor linear. The regression equations developed in this exercise were for a specific purpose (i.e., a cost model), reflecting one organization (i.e., EMS LLC), one species (i.e., swine), one time period (i.e., June to December 2002), seven states, and operation specific data. Due caution therefore needs to be used when applying these equations to situations outside any of these bounds. Nevertheless, it is believed that the findings in this REFERENCES Hollander, M., and D. A. Wolfe Nonparametric Statistical Methods. 2nd ed. New York, N.Y.: John Wiley and Sons. Neter, J., M. H. Kutner, C. J. Nachtsheaim, and W. Wasserman Applied Linear Statistical Models. Chicago, Ill.: John Wiley and Sons. USDA and USEPA Unified National Strategy for Animal Feeding Operations. Washington, D.C.: USDA and U.S. Environmental Protection Agency. Available at: Accessed 13 February USDA National Planning Procedures Handbook: Subpart E, Parts , and Subpart F, Part Draft comprehensive nutrient management planning technical guidance. Washington, D.C.: USDA. Available at: Accessed 25 July USDA Costs associated with development and implementation of comprehensive nutrient management plans: Part I. Nutrient management, land treatment, manure and wastewater handling and storage, and record keeping. Washington, D.C.: USDA. Available at: Accessed 31 July TRANSACTIONS OF THE ASAE

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