Multivariate Regression Model

This research uses two multivariate regression methods. First, a multivariate linear regression (MLR) model was developed to estimate the effects of distance on high quality enlisted accessions as measured by performance on the AFQT. Then, we used a logistic (logit) regression model to determine the probability of accessing exceptionally high quality enlisted personnel. An exceptionally high quality accession is defined as an individual enlistee who scored above the 85th percentile on the AFQT. In addition to the variables provided in the enlisted accession datasets, such as demographic characteristics, the regression models use the geospatial outputs (i.e., an enlisted accession’s distance from a Marine Corps location) from the GIS models to serve as variables. Six multivariate regression models are estimated and analyzed, as described in the subsequent Sections of this Chapter.

The enlisted accession datasets also require additional data cleaning and coding, prior to the estimating the multivariate regression models. First, we created indicator variables capturing the individuals distance from an active duty location. Specifically, we constructed cdist_10, cdist_1125, cdist_2650, cdist_51100 and cdist_100. These are all indicator variables equal to 1 if the individual accessing is within that radius distance, and 0 otherwise. For example, cdist_10 equals 1 if that individual’s home of record is between zero and 10 miles of an active duty location. The cdist_1125, cdist_2650, and cdist_51100 variables identify enlisted accessions falling between 11 and 25 miles, 26 and 50 miles, and 51 and 100 miles, respectively, of an active duty location. The

Other independent variables include standard demographic controls. We created indicator variables for gender (female), race (black), education (hs_dipl) and marital status (acc_nevmar). For instance, the female variable equals 1 if the individual accession is a female, but 0 if the accession is male. The black variable equals 1 if an accession is African American and 0 otherwise, and the hs_dipl variables equals 1 if an individual is a high school graduate, 0 otherwise. Lastly, the acc_nevmar variable equals 1 if an accession is single, but 0 if married or divorced.

a. Modeling the Data for Regressions

This study estimates two sets of regressions. First, we estimate two MLR models and one logit regression model controlling for distance with respect to all active duty USMC locations. Then, we estimate two MLR models and one logit regression controlling for distance with respect to MCRC units (active recruiting locations) only.

The first MLR model in Equation (1) estimates the effect of distance from active duty locations on high quality enlisted accessions. Then, we use this same MLR model to estimate the effect of distance from MCRC locations on high quality enlisted accessions to identify differences in active and passive recruiting processes.

_ _ _ and 51–100 miles, respectively, relative to being 100+ miles (the baseline category), on high quality accessions as measured by the AFQT.

The second MLR model in Equation (2) uses interaction terms to test for differential effects of distance from an active duty location by gender, race and education (hs_dipl). The same MLR model is then used to account for differential effects of distance from a MCRC location by female, black, and education.

_ _

hs dipl cdist hs dipl cdist hs dipl cdist

i

Third, a logit regression model (shown in Equation 3) estimates the probability of accessing exceptionally high quality enlistees by distance to an active duty station. To determine differences in active and passive recruiting efforts, this logit model is also used to estimate the probability of accessing exceptionally high quality enlisted personnel by distance to MCRC stations only.

_ _

0 1 2 3 4

_ _10 _1125 _ 2650 _ 51100

5 6 7 8 9

_ _{i female black acc nevmar} ^{acc age}

hs dipl cdist cdist cdist cdist i

This study relies on the two enlisted accession datasets described in this Chapter for the analysis. The first dataset includes all of the enlisted accession data, including the distance variables generated by the GIS model using the pooled cross-sectional data for all active duty and MCRC locations. The summary statistics for the enlisted accessions included in the active duty location models and MCRC location models are displayed in Tables 10 and 11, respectively.

Women account for nearly 8% of Marine Corps enlisted accessions between 2000 and 2014. During this same period, less than 10% of the enlisted accession population was African American, while whites comprise an overwhelming majority of enlisted accessions (80.6%). Moreover, almost all enlistees are never married (97.4%), and most have a high school diploma (92.1%) at the time of accession. The cdist_51100 variable indicates that nearly 60% of enlistees have a home of record between 51 and 100 miles from an active duty location or MCRC location.

Table 10. Summary Statistics for Active Duty Locations Model.

Table 11. Summary Statistics for MCRC Locations Model.

Variables Mean Standard

Naturally, both models utilize the same number of observations; the differences are in the summary statistics for the cdist variables. Interestingly, it appears that very little variation exists between the distance variables in the two models. One can reasonably assume that this is because all of the enlisted accessions get captured in both

the active duty locations GIS model and the MCRC locations GIS model. Thus, it initially seems that passive measures (i.e., active duty presence at installations, detachments, and independent duty stations) vs. active recruiting stations may have no differential effect on accessing high quality enlisted personnel.

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