Abstract
Purpose
The purpose of this paper is to demonstrate an improved method for forecasting the US Army recruiting.
Design/methodology/approach
Time series methods, regression modeling, principle components and marketing research are included in this paper.
Findings
This paper found the unique ability of multiple statistical methods applied to a forecasting context to consider the effects of inputs that are controlled to some degree by a decision maker.
Research limitations/implications
This work will successfully inform the US Army recruiting leadership on how this improved methodology will improve their recruitment process.
Practical implications
Improved US Army analytical technique for forecasting recruiting goals..
Originality/value
This work culls data from open sources, using a zipcodebased classification method to develop more comprehensive forecasting methods with which US Army recruiting leaders can better establish recruiting goals.
Keywords
Citation
McDonald, J.L., White, E.D., Hill, R.R. and Pardo, C. (2017), "Forecasting US Army enlistment contract production in complex geographical marketing areas", Journal of Defense Analytics and Logistics, Vol. 1 No. 1, pp. 6987. https://doi.org/10.1108/JDAL0320170001
Publisher
:Emerald Publishing Limited
Copyright © 2017, In accordance with section 105 of the US Copyright Act, this work has been produced by a US government employee and shall be considered a public domain work, as copyright protection is not available.
Introduction
Since the formal elimination of the draft by Congress in 1973, the USA Army has maintained an AllVolunteer Force (AVF) (Waddell, 2005, pp. 413442). At the lowest echelon of the Army recruiting system, US Army Recruiters are tasked to help fill the ranks of the AVF by actively pursuing qualified future soldiers with the ultimate goal of generating required enlistments. At higher echelons of recruiting leadership, however, a fundamental concern arises in how best to distribute recruiting goals to subordinate recruiting echelons throughout the country.
Implied in the latter concern is an assumption that a quantitative relationship between numerous recruiting factors – both within and outside of the recruiters’ control – and enlistment production in each geographical recruiting area exits, can be satisfactorily established and can be exploited for forecasting purposes. If so, recruiting leadership can then maximize potential recruiting contracts by altering recruiting goals subject to a set of organizational constraints. Thus, the two primary steps of setting recruiting goals consist of:
defining an appropriate quantitative relationship that is robust to extrapolation into the future; and
maximizing the outputs based on organizational constraints and the quantitative model parameters found in the first step. We use the acronym US Army Recruiting Command (USAREC) to refer to the corporate, goalsetting body of Army recruiting leadership.
This article focuses on the first of recruiting leadership’s tasks – the development of a quantitative relationship between recruiting market factors and enlistment production – as it is fundamental to successful execution of the second task, optimizing production. We are not the first to do this; USAREC has used and currently uses such quantitative models in the past. We do however offer an improved methodology for achieving a useful quantitative model.
We first establish the extent to which we can accurately forecast the relationship between enlistment supply and demand factors and enlistment contract production. We assume as supply factors those which are outside of the recruiters’ control; local unemployment rates are an example. Enlistment demand factors, by contrast, are those over which the Army and recruiters have some control; numbers of recruiters onhand and recruiting goals are examples. In terms of the response, we focus specifically on Regular Army (RA) enlistment contracts in 38 recruiting regions that span the USA, territories excluded. We subdivide the enlistment contracts into three mutually exclusive categories of interest to USAREC:
highaptitude high school graduates (GA);
highaptitude high school seniors (SA); and
all others (OTH) (Flesichmann and Nelson, 2014).
These are not the standard responses used by USAREC in their forecasting model, but we address in this paper why changing to these make sense.
We analyze data from both recruiting organizations and open sources for the period Fiscal Year (FY) 20102014. We take advantage of open source data at the county level and map this countylevel data to each ZIP codebased recruiting market boundary. To complete this mapping, we introduce a way to compress data from over 3,000 counties and 42,000 ZIP Codes into 38 markets. We then apply principal components analysis (PCA) and mixed stepwise regression to the remapped data to develop adequate, parsimonious models for each recruiting market and contract type. The application of PCA represents a significant contribution to the level of statistical rigor in our model development methodology over previous efforts.
Quantitative prediction models are useful when they yield accurate predictions. We use holdout samples for model validation. We use only the first 75 per cent of the data to estimate ordinary least squares models; the latter 25 per cent of the data are used in forecast validation. To obtain a better appraisal of model stability during validation, we create additional realism by using simple linear trend forecasts of market supply variables. At the conclusion of this step, we achieve our penultimate objective by rendering quantitative market and contractspecific comparisons of model performance within the context of a forecasting scenario. As a brief concluding excursion, we compare our multivariate forecasting approach to several univariate time series models.
In summary, we introduce an improved methodology for model development and assessment. To this end, we introduce an improved way to generate appropriate response data, and we demonstrate the use of principle components analysis to reduce model dimensionality and demonstrate an improved level of statistical rigor in our model development methodology. We also present an empirical study comparing our model to other common models.
Background
There is a vast literature on military recruitment, enlistment and retention. We focus on macro and microeconomic studies. Macroeconomic studies are highly aggregated geographically, involving only a handful of national regions. Microeconomic studies are geographically disaggregated, typically at the ZIP code level. Due to space limitations, we here provide general findings based on a detailed discussion found in McDonald (2016).
Our review of pertinent literature on Armed Forces recruiting spans a 26year period from 1985 through 2011. In total, macroeconomic studies of enlistment supply are helpful in describing the “big picture” of recruiting models. There seems to be some general agreement between these studies in the significance of a few select factors: unemployment, qualified military available population, veteran population and recruiter strength are of particular importance in this regard (Asch et al., 2009; Warner et al., 2001; Dertouzos and Garber, 2006, 2008; Dertouzos, 1985). However, these works have limited capacity to predict contract production for geographical areas corresponding to recruiting market boundaries. We therefore acknowledge the added value of microeconomic models in both their geographic specificity and use of validation data despite their reduced specificity in the response and difficulties in comparing fit adequacy (Gibson et al., 2011, 2009).
There are useful conclusions derived from the prior literature. First, the literature is dominated by econometric methodology. The econometric studies share a common objective of describing socioeconomic effects on recruiting over time. In nearly every study, this involved some form of regression. We use a similar quantitative modeling methodology albeit with useful extensions.
Second, there is some broad agreement that several factors are correlated with recruit production. Of these, geography appears to be statistically significant (Dertouzos and Garber, 2006, 2008). Unfortunately, we cannot conclude how nongeographic factor effects change with respect to geographic location; each study uses different geographic boundary definitions, none of which correspond to actual USAREC definitions. In any case, geography is statistically significant based on the total body of empirical results. We do note with some caution that statistics gathered at the microeconomic level may have greater measurement error (Murray and McDonald, 1999). Thus, our methodology seeks an appropriate balance between required geographic specificity with respect to recruiting markets and data measurement errors inherent in higher resolution. We maintain a variable set broadly consistent with previous literature to provide a general basis for comparison.
Interestingly, relatively little of the previous research specifies predictive models designed to produce forecasts into future time periods. Recruiting – like any privatesector marketing effort—requires decisionmaking (i.e. an irrevocable allocation of resources) in the face of uncertainty (Howard and Abbas, 2015, pp. 119). While the studies we reviewed provided some indication of how variables respond to time, most did not explicitly describe model performance in an outofsample time period or provide any kind of probabilistic statement regarding future behavior. This observation is a primary motivator for our methodology, specifically with regard to our model validation efforts.
Methodology
Data description and cleaning
We collected data from USAREC and open sources. Our goals were to use variables mentioned in previous literature and provide a representative sample of pertinent supply and demand factors. In all, we collected data on 26 separate metrics for the period FY10 to FY14. See Table I for the definition of these first 26 variables. While data from recruiting leadership was available at the market level, open source data were collected almost universally at the county level. This presented us with a fundamental difficulty because recruiting market boundaries – defined by a set of ZIP codes – are incompatible with political boundaries.
Because the market level data provided the greatest level of resolution, we devised a method of weighting countylevel data to express it in terms of recruiting market boundaries. Let Z_{i} ⊆ Z be the subset of (m = 1, 2, 32846) ZIP Code Tabulation Areas (ZCTAs) within each unit i boundary. Let C be the set of (n = 1, 2, 3141) counties in the USA. Let
We implemented equation (1) only for fractional data, applying [equation (1)] separately to the numerator and the denominator prior to dividing. We explored weighting a raw value such as population but found that aggregating to market levels produced a total value greater than the original. This is likely due to some doublecounting in our formulation of z_{i}′. However, we assume that similar overestimation errors applied to the numerator and denominator of a single rate are likely to cancel each other out. The reasonability of our resulting weighted values further increased our confidence in this method.
We also took care to ensure our sample size of time series data were adequate. A common rule of thumb is to have at least 50 observations for model estimation (Montgomery et al., 2015, p. 39). Recruiting data in the model estimation set provided a suitable N = 45 observation. However, much of the countylevel data proved available only at annual, semiannual or quarterly intervals. We therefore expanded the countylevel data to that of its recruiting counterpart by applying stochastic mean value imputation to the county data. This involved creating random realizations of monthly countylevel data points along a trendline between the observed annual data (Montgomery et al., 2015, pp. 1819).
To illustrate the imputation, let
Modeling methodology
A common approach in the past research builds a linear regression or time series model involving numerous potential variables, seemingly without regard to multicollinearity. We used a more rigorous modeling process.
Variables 1719 in Table I are used as dependent variables with all other variables as potential predictor or independent variables. Principle component analysis provided the basis for the response choice. Principle component analysis is also used to reduce the dimensionality of the predictor set of variables (and thus reducing multicollinearity when using the full set). The reduced set is modeled based on stepwise regression techniques using
Validation of forecasts
Data splitting
The primary purpose of our models is to predict future data. Model validation examines how well the estimated model performs in the presence of future data. Data splitting is used to conduct model validation. Observations t = 1, 2, T define the estimation set used in the model building processes, whereas observations t = T + 1, T + 2, T + τ define the validation set. In our data set, we let T = 45 and τ = 15 as 15 to 20 observations are recommended to gain an adequate assessment of prediction performance (Montgomery et al., 2012, p. 375) and recruiting leadership begins setting missions a few months prior to the next full recruiting year. By adding three months to the validation set, we effectively recreate the decision situation from the leadership’s point of view, predicting contract production over an extended planning horizon using only the data realized by the forecast origin, T.
Forecast metrics
The usual metrics of model fit such as
We assume independent model and variable forecast errors for a one periodahead forecast, providing a 100 per cent (1 – α) prediction interval as:
To implement equation (4) in a predictive role, simple trend models are used to extrapolate independent factors into the future prediction periods.
Empirical results
Response and variable determination
The first phase of the work examined the current USAREC modeling approach. The current approach involves a response constructed using some of the data in Table I. Using the variable index indicated in Table I the output response used is:
The current USAREC model is relatively parsimonious and produces a good fit (
The first step was to reconsider the range of responses available. There are seven potential responses as summarized in Table II. Note the first response comes from the current USAREC approach and the second response is the variable x_{29} removed from the current model. The other five are responses are found in Table I.
A principle components analysis was conducted on these responses and revealed loadings on two quantities, one being y_{4}. Because responses y_{1}, y_{2} and y_{7} are all ratio values, all involving the x_{19} variable, the logical choice was to use responses y_{3}, y_{4} and y_{5}. These provide meaningful responses for the model development and are easy to understand. We must note that the independent formulation of SA achieve, y_{4}, as a response variable constitutes a remarkable departure from the current USAREC model, which lumps SA and GA Achieved (y_{3} and y_{4}) together in the same response. Further discussion is devoted to why this is a sensible departure. Nevertheless, subsequent model development focused on each of these three responses, GA, SA and OTH production (i.e. contracts achieved), respectively.
Multiple regression methods using the three responses and the remaining 23 variables from Table I resulted in serious problems with multicollinearity. A principle components analysis was again used this time to reduce the dimensionality of the independent variable set. As Figure 1 indicates, five components account for approximately 79 per cent of the variance. The initial set of loadings are provided in Table III. Using the loadings and factors, along with context knowledge of the problem and a few iterations of principle component analysis, we finalized the set of five component variables as x_{4} along with the derived variables:
In general terms, x_{4} captures unemployment rates, x_{30} the ratio of appointments (a surrogate for recruiter effort), x_{31} the combined GA and OTH mission, x_{32} the SA contracts per recruiter and x_{33} a measure of the young adults available. This reduction from 23 potential variables to just 5 variables is an important modeling consideration.
To conclude this portion, we provide the final correlation matrix for the five variables selected. Of the ten offdiagonal elements in Table IV, seven are less than 0.2. We note entries of 0.37 and 0.41, but these are still both less than 0.5 and are deemed not overly troublesome. Thus, we are confident that this reduced set of five variables are adequate for final model development.
Mixed stepwise selection
An initial examination via stepwise regression ruled out quadratic models or linear models with interaction terms. Thus, a pure firstorder model is used. Further, based on BoxCox analyses, all responses were transformed via the square root transformation to improve compliance with the constant variance assumption of the residuals. Despite the transformation, autocorrelation remained present in the residuals. Adding a firstorder autoregressive term to the model alleviated this concern. Finally, we needed to model each of the battalions within USAREC. This was done using indicator variables for each market, while simultaneously allowing for the predictor effects to change between markets (i.e. we modeled categoricalcontinuous interactions). The final models, while seemingly complex, facilitated model adequacy analyses.
Figure 2 provides the pertinent results of the model adequacy analysis. The models for GA, SA and OTH contracts are ordered top to bottom. On the left, we see no reason to doubt reasonable normalcy of the residuals and on the right side we see no reason to doubt the constancy of variance. Residual analysis for outliers and influential points revealed nothing of concern. Table V provides the summary of each model fit. While value of p, the number of terms in the model, is high, the vast majority of these are the indicator variables used to derive the individual battalion models.
Overall, we achieve substantial improvement in terms of model fit – 600, 200 and 131 per cent for SA, OTH and GA contract types, respectively – as measured by the estimation data
Validation forecasts
The real test of any quantitative model is how well it performs outofsample. For this study, the most recent 15 time periods of data were held out for validation purposes. Each model was forecast out for these 15 periods at a consolidated level (all contract types and battalions combined) and at a detail level (by contract type). Two prediction interval bands are provided, 80 and 95 per cent as analysts vary in how much risk to assume with respect to the certainty of the input independent variables driving the forecast.
Figure 3 is a comprehensive look across all contract types. Within the model data, the prediction values (dark line) track nicely with the actual data (gray line). Tracking is less accurate in the validation data (as one should suspect) but overall not too bad. Figure 4 breaks this data out in the echelon format by contract type. Figure 5 provides a summary of the validation metrics defined for our effort; again, overall these results are very reasonable. We note with particular satisfaction the prediction intervals obtained using linear trend forecasts of the predictors themselves (i.e. “Unknown X”). Only during the very farthest regions of the forecast horizon do we see the actual data e xceed our prediction intervals for both 80 and 90 per cent probability.
We have included the R^{2} of each contract type at the aggregate level to compare the estimation models and previous literature for which only Dertouzos and Garber (2008) provide a reliable basis for a comparison; our validation R^{2} achieves 530, 170 and 119 per cent relative improvements over the models estimated by Dertouzos and Garber (2008) for SA, OTH and GA contract types, respectively. This is a remarkable feat, especially considering the use of forecast inputs for predictor variables in our models.
Comparative analysis
The causal models developed are based on using multivariate statistical methods to obtain appropriate responses and parsimonious models; these goals were achieved quite well. However, any modeling effort involving many independent variables must answer the question of whether a simpler model would suffice. To this end each model was compared to a naive forecast, an appropriately fit seasonal autoregressive integrated moving average model and a seasonal smoothing method (e.g. the HoltWinters or Brown’s method). Figure 6 plots the results for each of the output measures. The legend in each of the subfigures provide a specification of the univariate model fit; development details are not provided here.
For each of the GA and OTH models, it is quite clear the multivariate models are the preferred approach, realizing of course that these models do already contain a single autoregressive term. For the more seasonal SA response model, the results were not so conclusive as the seasonal time series modeling approaches are comparable options. Overall, the collective result is that our effort to develop multivariate models is indeed rewarded with improved performance.
Conclusion
We have shown, through the use of multiple linear regression aided by increased geographic data specificity through the use of our ZCTA method, mixed stepwise selection methods and PCA, that improvements over previous efforts to model US Army enlistment contract production are possible. Moreover, we have shown that forecasts produced by the multiple linear regression models – which themselves require simple linear forecasts of the predictors – are robust for a relevant forecast horizon of up to 15 months. Indeed, the fit of the forecasts alone constitute remarkable improvements over previous models which did not use validation data and are worth the development effort when compared to simple time series models.
In closing, we must note the unique ability of the multiple regression model in forecasting to consider the effect of inputs which are controlled to a degree by the decisionmaker. While the regression model coefficients and standard errors are indeed based only on past data, our models indicated rather high statistical significance of future “controllable” inputs such as recruiting goals and these inputs should be likewise considered in a futuristic sense when the firm is producing forecasts. Only a causal model such as the one afforded by lagged multiple regression affords such an opportunity for exploration. We hope to have successfully informed subsequent discussions on behalf of such a method.
Figures
Variable names and definition of original 26 variables considered
Index  Variable name  Description 

1  Voter participation rate  Votes cast for president/total adult population (2008 and 2012, County) 
2  Sponsor share  Number of Army active duty sponsors/total active duty military sponsors (20102013, Annual, ZIP code) 
3  Labor participation rate  Persons in labor force/total workingage population (20102014, Annual, County) 
4  Unemployment rate  Employed persons/persons in labor force (20102014, Monthly, County) 
5  Cohort HS graduation rate  Graduates from freshman high school class/size of freshman class (20102014, Annual, County) 
6  Violent crimes  Number of violent crimes (20102014, Annual, County) 
7  Obesity  Number of obese persons/total population (20102014, Annual, County) 
8  Illicit drug use  Number of persons using illicit drugs/total Population (2010 and 2012, County) 
9  Urban population rate  Number of persons in urban zones/total population (2006 and 2013, County) 
10  Propensity  Number of youth inclined toward military service (20102014, Semiannual, Battalion) 
11  QMA population  Number of youth aged 1724, qualified without a waiver (20102014, Annual, ZIP Code) 
12  1724 Population  Number of youth aged 1724 (20102014, Annual, ZIP Code) 
13  Battalion recruiting station identifier (RSID)  Recruiting battalion boundaries (20102014, Annual, ZIP Code) 
14  Lag1  Number of total contracts produced from previous month (20102014, Monthly, Battalion) 
15  Reg. Army GA Mission  Goal for number of GA contracts (20102014, Monthly, Battalion) 
16  Reg. Army SA Mission  Goal for number of SA contracts (20102014, Monthly, Battalion) 
17  Reg. Army OTH Mission  Goal for number of OTH contracts (20102014, Monthly, Battalion) 
18  Reg. Army GA Achieved  Number of adjusted GA contracts produced (20102014, Monthly, Battalion) 
19  Reg Army SA Achieved  Number of adjusted SA contracts produced (20102014, Monthly, Battalion) 
20  Reg. Army OTH Achieved  Number of adjusted OTH contracts produced (20102014, Monthly, Battalion) 
21  Contract share  Number of Army contracts/all DoD contracts (20102014, Monthly, Battalion) 
22  Recruiter share  Number of Army recruiters/all DoD recruiters (20102014, Monthly, Battalion) 
23  Army recruiters  Number of Army active and reserve recruiters based on PERSTAT (20102014, Monthly, Battalion) 
24  Appointments made  Number of appointments scheduled and reported to USAREC (20102014, Monthly, Battalion) 
25  Appointments conducted  Number of appointments conducted and reported to USAREC (20102014, Monthly, Battalion) 
26  Processing days  Number of days to process recruits (20102014, Monthly, Battalion) 
Responses considered in reexamination of a casual model for recruitment forecasting
Responses  How defined using Table I variables 

y_{1} (GSA_PR)  (x_{18} + x_{19})/x_{23} 
y_{2} (Vol_PR)  (x_{18} + x_{19} + x_{20})/x_{23} 
y_{3} (GA Achieved)  x_{18} 
y_{4} (SA Achieved)  x_{19} 
y_{5} (OTH Achieved)  x_{20} 
y_{6} (GA + SA Achieved)  x_{18} + x_{19} 
y_{7} (Contract Share)  x_{21} 
Labels for each of the variables used found in Table I
Principle components analysis summary for initial variable set
Variable  PC(1)  PC(2)  PC(3)  PC(4)  PC(5) 

x_{1}  0.4724  0.6486  −0.0628  −0.0948  0.2746 
x_{2}  0.5045  0.7153  0.0180  0.0579  −0.0407 
x_{3}  −0.7619  0.2076  0.2354  −0.3092  0.2346 
x_{4}  −0.0377  −0.4225  −0.6136  −0.0599  0.5270 
x_{5}  −0.4288  0.5901  0.4573  0.0041  −0.1782 
x_{6}  −0.0709  −0.2936  −0.7065  −0.3887  0.0780 
x_{7}  0.5014  0.7327  0.0519  0.1881  −0.0123 
x_{8}  −0.7177  −0.4122  0.0862  0.1361  0.2085 
x_{9}  −0.4932  −0.7896  0.0706  −0.0925  −0.2529 
x_{10}  0.6309  −0.4604  −0.2794  0.2299  −0.3635 
x_{11}  −0.6595  0.3620  0.2762  −0.4695  0.1842 
x_{12}  −0.7745  0.1379  0.3073  −0.4403  0.0694 
x_{15}  0.5548  −0.2439  0.2772  −0.4699  0.4496 
x_{16}  0.2977  −0.1260  0.7181  0.1922  0.1013 
x_{17}  0.7237  −0.2960  −0.0005  −0.2013  0.2052 
x_{22}  0.3273  0.1584  −0.2562  −0.6416  −0.0017 
x_{23}  0.3109  0.2602  −0.5920  −0.5654  0.0165 
x_{24}  0.2679  −0.1399  0.3664  −0.7385  −0.3609 
x_{25}  0.3141  −0.2481  0.3994  −0.5156  −0.5592 
x_{26}  −0.0334  0.0158  0.0654  0.1292  −0.0716 
x_{27}  0.5856  −0.3851  0.6286  −0.0026  0.3038 
x_{28}  0.3848  −0.2956  0.7824  0.0378  0.2950 
Notes: Labels for variables found in Table I; Italics indicate the larger loadings
Correlation matrix R for the reduced set of independent variables
Variable  x_{4}  x_{30}  x_{31}  x_{32}  x_{33} 

x_{4}  1  –0.213  0.196  –0.370  –0.086 
x_{30}  1  –0.130  0.199  0.409  
x_{31}  1  0.073  0.079  
x_{32}  symm  1  0.077  
x_{33}  1 
Summary of fit for the final transformed, lag1 models with nonsignificant, nonhereditary terms removed
Response 


P > F_{0}  p  N 

(Reg. Army GA Achieved)^{1∕2}  0.740  0.730  < 0.001  89  1672 
(Reg. Army SA Achieved)^{1∕2}  0.698  0.679  < 0.001  100  1672 
(Reg. Army OTH Achieved)^{1∕2}  0.807  0.795  < 0.001  98  1672 
Final GA models for all Battalions
Battalion  Intercept  β_{x4}  β_{x30}  β_{x31}  β_{x32}  Lag 

BN 1A  6.0013  26.4225  −4.2724  0.0245  −2.0811  0.0028 
BN 1B  3.1563  26.4225  0.8758  0.0245  −2.0811  −0.0010 
BN 1D  3.5834  26.4225  0.8758  0.0245  −2.0811  −0.0029 
BN 1E  2.1978  26.4225  0.8758  0.0245  −2.0811  0.0020 
BN 1G  6.5452  26.4225  −7.4793  0.0245  −2.0811  0.0103 
BN 1K  4.7563  26.4225  0.8758  0.0245  −2.0811  −0.0008 
BN 1N  2.1978  26.4225  0.8758  0.0245  −2.0811  0.0069 
BN 1O  4.2881  26.4225  0.8758  0.0245  −2.0811  0.0108 
BN 3A  5.6542  26.4225  −3.0809  0.0245  −2.0811  −0.0031 
BN 3D  3.9949  26.4225  0.8758  0.0245  −2.0811  0.0070 
BN 3E  −1.9996  72.9264  0.8758  0.0245  −2.0811  0.0020 
BN 3G  0.8969  26.4225  0.8758  0.0245  −2.0811  0.0106 
BN 3H  0.8771  26.4225  0.8758  0.0245  2.9382  0.0046 
BN 3J  2.1978  26.4225  0.8758  0.0245  −2.0811  0.0058 
BN 3N  0.4258  47.3275  0.8758  0.0245  −2.0811  0.0043 
BN 3T  0.3884  26.4225  0.8758  0.0245  −2.0811  0.0199 
BN 4C  2.1978  26.4225  0.8758  0.0245  −2.0811  0.0069 
BN 4D  1.5753  26.4225  0.8758  0.0358  −2.0811  0.0021 
BN 4E  3.3289  26.4225  0.8758  0.0245  −2.0811  0.0060 
BN 4G  2.1978  26.4225  0.8758  0.0245  −2.0811  0.0087 
BN 4J  2.1978  26.4225  0.8758  0.0245  −2.0811  0.0074 
BN 4K  −1.0958  60.5243  0.8758  0.0245  −2.0811  0.0128 
BN 4P  2.6972  26.4225  0.8758  0.0245  −2.0811  0.0023 
BN 5A  1.3459  26.4225  0.8758  0.0245  −2.0811  0.0094 
BN 5C  4.1218  4.2068  0.8758  0.0245  −2.0811  0.0022 
BN 5D  2.1978  26.4225  0.8758  0.0245  −2.0811  0.0045 
BN 5H  2.1978  26.4225  0.8758  0.0245  −2.0811  0.0060 
BN 5I  −0.0926  41.0251  0.8758  0.0245  −2.0811  0.0069 
BN 5J  1.4253  26.4225  0.8758  0.0245  −2.0811  0.0151 
BN 5K  2.1978  26.4225  0.8758  0.0245  −2.0811  0.0104 
BN 5N*  2.1978  26.4225  0.8758  0.0245  −2.0811  0.0058 
BN 6F  4.947  26.4225  0.8758  0.0245  −2.0811  −0.0054 
BN 6H  2.1978  26.4225  0.8758  0.0245  −2.0811  0.0078 
BN 6I  3.7050  26.4225  0.8758  0.0245  −2.0811  −0.0056 
BN 6J  1.1932  26.4225  0.8758  0.0437  −2.0811  −0.0005 
BN 6K  3.7902  26.4225  0.8758  0.0245  −2.0811  0.0079 
BN 6L  2.4804  26.4225  0.8758  0.0245  −2.0811  0.0089 
BN 6N  3.491  26.4225  3.7986  0.0245  −2.0811  0.0034 
Coefficient for β_{x33} not provided; all less than 0.001; the * indicates baseline
Final OTH models for all Battalions
Battalion  Intercept  β_{x4}  β_{x30}  β_{x31}  β_{x32}  β_{x33}  Lag 

BN 1A  3.7519  15.2018  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.004 
BN 1B  4.8331  15.2018  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0009 
BN 1D  3.3435  15.2018  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0146 
BN 1E  3.0128  15.2018  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0185 
BN 1G  4.8331  15.2018  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0039 
BN 1K  5.7101  15.2018  −0.9503  0.0200  −0.2294  −2.26 x 10^{–5}  0.0146 
BN 1N  3.7381  15.2018  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0040 
BN 1O  4.4737  15.2018  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0193 
BN 3A  4.9531  15.2018  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0056 
BN 3D  5.6615  15.2018  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0008 
BN 3E  0.5804  63.6241  −0.9503  0.0200  −0.2294  3.68 x 10^{–5}  0.0069 
BN 3G  8.3778  15.2018  −0.9503  0.0200  −0.2294  −4.67 x 10^{–5}  0.0015 
BN 3H  4.2080  15.2018  −0.9503  0.0200  3.1698  4.82 x 10^{–6}  0.0080 
BN 3J  4.6361  15.2018  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0099 
BN 3N  0.0017  39.9493  −0.9503  0.0200  −0.2294  4.95 x 10^{–5}  0.0016 
BN 3T  8.0054  15.2018  −4.3841  0.0200  −0.2294  4.82 x 10^{–6}  0.0029 
BN 4C  4.3254  15.2018  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0066 
BN 4D  3.4651  15.2018  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0146 
BN 4E  4.8331  15.2018  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0006 
BN 4G  3.5428  15.2018  −0.9503  0.0298  −0.2294  4.82 x 10^{–6}  0.0004 
BN 4J  4.7788  15.2018  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0079 
BN 4K  0.5943  64.6082  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0086 
BN 4P  2.7029  50.8070  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0055 
BN 5A  3.4791  15.2018  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0074 
BN 5C  4.2807  15.2018  −0.9503  0.0211  −0.2294  4.82 x 10^{–6}  0.0078 
BN 5D  4.0023  15.2018  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0060 
BN 5H  6.4252  15.2018  −0.9503  0.0114  −0.2294  4.82 x 10^{–6}  0.0157 
BN 5I  4.4255  15.2018  −0.9503  0.0200  −6.0886  4.82 x 10^{–6}  0.0079 
BN 5J  3.2492  15.2018  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0115 
BN 5K  3.3761  15.2018  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0106 
BN 5N*  4.8331  15.2018  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  −0.0015 
BN 6F  4.313  15.2018  −0.9503  0.0200  −0.2294  −1.71 x 10^{–5}  0.0225 
BN 6H  4.2229  15.2018  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0163 
BN 6I  4.8073  15.2018  −0.9503  0.0129  −0.2294  4.82 x 10^{–6}  0.0044 
BN 6J  0.9208  40.7777  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0190 
BN 6K  0.6777  50.6793  −0.9503  0.0200  −0.2294  4.82 x 10^{–6}  0.0185 
BN 6L  4.0834  15.2018  −0.9503  0.0200  −4.1426  4.82 x 10^{–6}  0.0160 
BN 6N  0.0084  61.7380  −0.9503  0.0200  −0.2294  −7.84 x 10^{–6}  0.0059 
The * indicates baseline
Final SA models for all Battalions
Battalion  QTR 1  QTR 2  QTR 3  QTR 4  β_{x4}  β_{x30}  β_{x31}  β_{x33}  Lag 

BN 1A  3.2325  3.5766  4.0698  2.8806  −12.7345  0.5186  0.0107  1.47 x 10^{–6}  0.0051 
BN 1B  −2.1747  −1.8306  −1.3374  −2.5265  −12.7345  7.3834  0.0107  1.47 x 10^{–6}  0.0155 
BN 1D  2.9588  3.3029  3.7961  2.607  −12.7345  0.5186  0.0107  1.47 x 10^{–6}  0.0335 
BN 1E  3.2325  3.5766  4.0698  2.8806  −12.7345  0.5186  0.0107  1.47 x 10^{–6}  0.0004 
BN 1G  1.8122  2.1564  2.2980  1.4604  −12.7345  0.5186  0.0107  1.47 x 10^{–6}  0.0314 
BN 1K  3.2325  3.5766  4.0698  2.8806  −12.7345  0.5186  0.0107  8.82 x 10^{–6}  0.0314 
BN 1N  3.6116  3.9557  3.5476  3.8873  −12.7345  0.5186  0.0107  1.47 x 10^{–6}  −0.0053 
BN 1O  −2.2302  −1.2794  −1.3929  −2.582  −12.7345  6.8295  0.0107  1.47 x 10^{–6}  0.0185 
BN 3A  9.5942  9.9383  10.4315  9.2424  −69.8499  0.5186  0.0107  1.47 x 10^{–6}  −0.0159 
BN 3D  −1.6317  −1.2875  −0.7943  −1.9835  −12.7345  0.5186  0.0107  1.30104 x 10^{–4}  −0.0065 
BN 3E  0.6327  0.9769  1.4701  0.2809  −12.7345  5.3432  0.0107  1.47 x 10^{–6}  0.0126 
BN 3G  3.7872  4.1313  4.6245  3.4354  −12.7345  0.5186  0.0023  1.47 x 10^{–6}  0.0179 
BN 3H  3.2325  3.5766  4.0698  2.8806  −12.7345  0.5186  0.0107  1.47 x 10^{–6}  0.0021 
BN 3J  6.9493  7.2935  7.7866  6.5975  −44.7603  0.5186  0.0107  1.47 x 10^{–6}  0.0015 
BN 3N  1.9630  2.3071  2.8003  0.9800  −12.7345  4.6567  0.0107  1.47 x 10^{–6}  0.0032 
BN 3T  3.4437  3.7878  4.281  3.0919  −12.7345  0.5186  0.0107  1.47 x 10^{–6}  −0.0221 
BN 4C  8.1182  8.4624  8.9555  7.7664  −12.7345  −4.5569  0.0107  1.47 x 10^{–6}  −0.0141 
BN 4D  6.8775  7.2216  7.7148  6.5257  −49.211  0.5186  0.0107  1.47 x 10^{–6}  −0.0095 
BN 4E  3.4288  3.773  4.2662  2.5276  −12.7345  0.5186  0.0107  1.47 x 10^{–6}  0.0082 
BN 4G  3.7728  4.1170  4.6102  3.4210  −12.7345  0.5186  0.0107  1.47 x 10^{–6}  −0.0131 
BN 4J  3.6719  3.4995  4.5093  3.3201  −12.7345  0.5186  0.0107  1.47 x 10^{–6}  0.0076 
BN 4K  3.2325  3.5766  4.0698  2.8806  −12.7345  0.5186  0.0107  1.47 x 10^{–6}  0.0037 
BN 4P  6.3981  6.2528  7.2354  6.0463  −25.392  0.5186  0.0107  1.47 x 10^{–6}  −0.0248 
BN 5A  3.2325  3.5766  4.0698  2.8806  −12.7345  0.5186  0.0107  1.47 x 10^{–6}  −0.0126 
BN 5C  5.6229  5.9670  6.4602  5.2711  −12.7345  −2.6684  0.0107  1.47 x 10^{–6}  0.0042 
BN 5D  3.2325  3.5766  4.0698  2.8806  −12.7345  0.5186  0.0107  1.47 x 10^{–6}  −0.0052 
BN 5H  2.9113  3.2555  3.7487  2.5595  −12.7345  0.5186  0.0192  1.47 x 10^{–6}  0.0128 
BN 5I  3.2325  3.5766  4.0698  2.8806  −12.7345  0.5186  0.0107  1.47 x 10^{–6}  0.0008 
BN 5J  6.2880  6.6322  7.1253  5.9362  −12.7345  −3.0345  0.0107  1.47 x 10^{–6}  0.0180 
BN 5K  3.0773  3.0012  3.9147  2.7255  −12.7345  0.5186  0.0107  1.35 x 10^{–5}  0.0042 
BN 5N*  3.2325  3.5766  4.0698  2.8806  −12.7345  0.5186  0.0107  1.47 x 10^{–6}  0.003 
BN 6F  3.2325  3.5766  4.0698  2.8806  −12.7345  0.5186  0.0107  1.47 x 10^{–6}  −0.0046 
BN 6H  3.6321  3.9763  4.4695  3.2803  −12.7345  0.5186  0.0107  −1.01 x 10^{–5}  0.0137 
BN 6I  3.5007  3.8449  4.338  3.1489  −12.7345  0.5186  0.0160  1.47 x 10^{–6}  0.0061 
BN 6J  0.2422  0.5864  1.0795  −0.1096  26.5042  0.5186  0.0107  1.47 x 10^{–6}  0.0145 
BN 6K  3.6321  3.9763  4.4695  3.2803  −12.7345  2.642  0.0107  −1.01 x 10^{–5}  0.0145 
BN 6L  3.5736  3.9177  4.4109  3.2218  −12.7345  0.5186  0.0107  1.47 x 10^{–6}  0.0209 
BN 6N  2.6417  2.9858  3.479  2.2899  15.0886  0.5186  0.0107  −2.53 x 10^{–5}  −0.0131 
The * indicates baseline
Note
Dertouzos and Garber (2008) used 68 variables for each contract type, whereas we used 100, 98 and 89 for SA, OTH and GA models, respectively.
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Acknowledgements
Disclaimer: The views expressed in this article are those of the author and do not reflect the official policy or position of the United States Air Force, the United States Army, the Department of Defense or the US Government.
The authors are indebted to the USAREC – specifically the Marketing & Mission Analysis Division – for their supply of data and willingness to let us aid their decisionmaking process.