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

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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

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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