Francçois J. Lescreve
Belgian Armed Forces' Center for Recruitment and Selection

The Belgian Armed Forces organize an annual recruitment of non-commissioned officers (NCO's) . Actually, the Forces are undergoing a major restructuring resulting in severe cuts in the number of applicants which can be enlisted. Given these circumstances, the Services, and in particular the Army, decided to emphasize the recruitment of candidates for combat arms. Once this is known by the applicants, it can be feared however that a number of them will give false information overestimating their combat-disposition in order to be enlisted. It therefore appeared interesting to investigate whether it would be possible to identify such a trait as "combat-disposition" and whether this trait could be related to more objective measures than the expressed preferences of the candidates.

The data for this study were collected during the annual NCO recruitment of 1995. For these data, we can assume that the applicants were not aware of the fact that candidates showing a higher combat-disposition would have a much higher probability of enlistment. So the expressed preferences and choices can be considered as true.

From the approximately 2400 original applicants, we kept the 1054 records of the acceptable applicants. Those are the one's who were still in the running after the medical, physical, intellectual and scholar tests and who passed the final interview successfully. These data have the advantage of being complete for each applicant.

Next table gives an overview of the considered variables.

During the selection procedure, the applicants were asked to express their preference towards the different enlistment possibilities (infantry, Armor, …, equipment supply, computer operator) on a 99-points scale. A 2-dimensional scaling of the Euclidean distances between the preferences yielded a solution which showed a clear cut between the so called combat arms and the support arms. Next figure shows that solution.

TWO-DIMENSIONAL SCALING OF THE EXPRESSED PREFERENCES

Although in reality the "combat-ness" of the different specialties is less dichotomous, it is interesting to denote that in the perception of applicants it seems quite dichotomic. This finding suggests that the construction of a latent class model with a limited number of classes (probably 2) could prove useful to explain the preferences towards all specialties expressed by the applicants.

After reviewing the available data, we considered the variables PARA, ABROAD, COMB_JOB and COMB_ARM as possible candidates to function as indicators for the latent variable "combat-disposition" These data were obtained at different stages of the selection procedure and although they seem highly related, they are not fully redundant. The first latent class model represented in next figure was set up postulating 2 classes for the latent variable.

As shown by the output¹, this model doesn't fit (p-value of L²=0.0000). Further trials consequently will consider either an increase of the number of latent classes, or a modification in the structure of the indicators. Since for identifiability reasons the number of parameters to be independently estimated cannot be larger than the number of the observed cell frequencies, the number of possibilities is limited. Next table gives an overview of some relevant data concerning those possible models.

The bold p-values of the log-likelihood ratio chi-square statistics indicate the latent class models that do not fit the observed data ( a = 0.05) . These models will no longer be considered. One should notice that we cannot use conditional tests here since we have no hierarchically nested models in which the unrestrictive model can be considered to be valid in the population.

To choose one of the three latent class models that fit the data reasonably well, we'll take the number of latent classes, the significance of L² and the E values into account together with the interpretability of the parameters. Although the model with 3 latent classes fits reasonably, we'll prefer a more parsimonious model, especially since the multi-dimensional scaling (MDS) solution presented in figure 1 so clearly suggests a dichotomous combat-disposition. For interpretability reasons, as will become clear in a while, together with the L² and E-values, we preferred the model with C J A as indicators This will be referred to as model B. We now will proceed with the interpretation of the model and reproduce in table 3 the latent and conditional probabilities for convenience.

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¹The program Outputs can be made available. Requests should be addressed to the author, Center for Recruitment and Selection, BRUYNstraat, B-I 120 BRUSSELS (N-O-H), BELGIUM.
²This Condition is necessary but on itself not sufficient.

As shown by table 3, the model classifies 37% of the people in latent class 1 and the remaining 63% in class 2. People belonging to class 1 are characterized by a preference for support arms (C2>C1), a low interest for combat jobs (Jl>J2) and a slight interest in being posted abroad (A3>A2>A1). Compared to the people in class 2 however, they appear not to be as interested in a job abroad as the people in class 2 are (for class 2: A3>A2>Al) The people in class 2 are characterized quite in the opposite way. They prefer combat arms (C1>C2), have interest for combat jobs (J2>Jl) and are willing to be posted abroad (A3>A2>A1)

When looking at the odds ratios, one can state that the odds of preferring combat arms rather than support arms is 22.97 times higher for the people from the second (x=2) than for those of the first class (X=1) ³. The odds of preferring non-combat jobs rather than combat jobs is 87.95 times higher for the people from the first latent class (X=1) than for those from the second class (x=2) ⁴ . The odds of not volunteering for a job abroad are 22.13 times higher for the people from the first latent class (X=1) than for those from the second class (x=2)⁵ As one can see, the variable COMB_JOB has the strongest ties with the latent variable. On the other hand, it came a bit as a surprise that the variable PARA didn't appear to be necessary to make the model fit.

Clearly these latent classes can be interpreted in terms of combat-disposition where class 1 is defined as "low combat-disposition" and class 2 as "high combat-disposition". In next section we'll try to set up models which can estimate the latent trait from more objective data.

This way of computing estimated cell-frequencies can be derived from the design matrix for this model which is given in table 6.7.

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⁶This value departs slightly from the one given by the Computer Output (68.835) merely because of rounding errors.

This matrix can be modified in order to impose certain relations among the variables. One could for example impose the equality among the parameters related to YF and GF. This would mean that the different classes of AGE respectively GENDER would have the same effect on PHYS. Within the context of our study, this doesn't make sense.

The next step consists of relating the obtained model to the latent class model developed previously.

We will now consider five different modified LISREL models that fit the data reasonably well They all include GENDER, AGE, PHYS, COMB_ARM, COMB_JOB, ABROAD and the latent variable with two classes. Several trials to include the other possible variables in a meaningful way failed and will not be discussed here. Next overview gives the model specification and the graphical representation concerning those models. Table 8 gives their principal data.

As said before, all these models fit. To choose one of them, we looked at the fit, the Bayesian information criterion (BIC) and the number of independent parameters. We therefore chose model K which seems a nice compromise between fit and parsimony. This is the model we will try to interpret now.

First we will check whether the link between indicators and latent variable is consistent with the model including only indicators and latent variable (model B) . Next table shows the latent and conditional probabilities for model B and for Model K

As one can see, the two models yield very similar values. This means that the interpretation we gave for model B still holds for model K. So latent class Xl is still defined as "low combat disposition" and class X2 as "high combat disposition".

When considering table 10, where we give the remainder of the latent and conditional probabilities for Model K, we can develop the interpretation further.

Now we can see that the model classifies 35% of the applicants in latent class 1 and the remaining 65% in class 2. People belonging to class 1 are generally males (Gl) . However, when compared to class 2, we see that the proportion of males is still higher for class 2. The interpretation of the proportions of the two classes for the variable AGE (Y) , is less obvious for now (it will become clear when we look at the odds ratio) . The people belonging to class Xl tend to have lower results for physical fitness (F)

When looking at the odds, one can make following statements.

The odds of belonging to class "high combat disposition" (X2) rather than class "low combat disposition" (Xl) are 2.59 times higher for the boys than for the girls (p <0.0000, Exact 95% CI l.939® 3.50l).

For the variable AGE (Y), the odds ratio between Y2 and Y3 is not significantly different from 1 (OR = 1.221, p>0.07655) . So, we collapsed the categories Y2 and Y3 for further computation of the odds ratio. The odds of belonging to the class "high combat disposition" rather than the class "low combat disposition" is 1.900 times higher for the young applicants (Y1: = 18 years) than for the older ones (Y2 or Y3: >18 years) (p <0.0000, Exact 95% CI 1.555® 2.322)

For the variable PHYS (F), the odds ratios based on the conditional probabilities can be summarized by table 11.

When we interpret the last row of table 11 for instance, we can say that the odds of belonging to the class "high combat disposition" (X2) rather than low combat disposition is 2.67 times higher for applicants with a good physical fitness (F3) than for the ones with a poor physical fitness (Fl). When looking at the values of the parameters, one notices the large (but not surprising) effect of gender on physical fitness (given by l G₁F1 = -1.4460) indicating that the males tend not to belong to the low physical fitness class).

To conclude, we can say that especially the young males who are in good physical condition tend to belong to the class of "high combat disposition". This latent disposition explains the observed answers concerning preference for combat arms, interest for combat jobs and disponibility for jobs abroad well. It does not appear to be necessary to include variables such as medical fitness, personality scores or intellectual potential to obtain a model that fits the observed data well. It seems to be possible to infer the combat disposition based on the variables GENDER, AGE and PHYSICAL FITNESS only. This study however should be repeated on a new data set, to confirm these conclusions The question also raises as to the use of the particular results of this research because AGE by definition isn't a constant quality of an individual and GENDER is a variable which is forbidden to use by law. On the other hand, the combat-disposition is something which is well perceptible within military units. So it might be possible that combat-disposition does exist but that it isn't assessed well by the expression of preferences within the actual selection procedure. This would mean that the latent variable we used wouldn't reflect true combat-disposition but merely the intention of combat-disposition expressed by applicants.

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