Subjects who have been exposed to one or more traumatic events can suffer from a conglomerate of psychological, psycho-physiological and psycho-social changes in functioning, which are called posttraumatic stress symptoms (PTSS). E.g. intrusive recollections of the events experienced, hypervigilance, startles after unexpected sounds, avoiding situations that remember the traumatic events, less efficiency at work. Parallel to these PTSS people often develop feelings of guilt, such as feeling guilt to have survived while others died (survival guilt) and feelings of guilt about the way they behaved to survive (behavioral guilt). Furthermore, they assert different claims towards authorities such as claim for recognition, compensation or punishing the persons responsible for the traumatic events. These three behavioral complexes - PTSS, Guilt and Claims - taken together are called post-traumatic stress reactions (PTSR). Other forms of comorbidity appear as well but are not discussed here.

The first purpose of this study is to describe clusters of symptoms in the three types of PTSR. Second, it will be verified if the clusters found in the PTSS item set correspond to the criteria of the nosographic classification DSM-IV. Third, unlike DSM which describes the posttraumatic stress disorder (PTSD) in a dichotomous way - i.e. presence or absence of a combination of a certain number of symptoms belonging to the different criteria - we will describe those clusters in terms of "partial posttraumatic stress disorders" (PPTSD) and assess their prevalence as well.

The population considered consists of the 360 soldiers serving as Blue Helmets at the beginning of the genocide in Rwanda in April 1994.

A questionnaire has been elaborated with among others an item set for each of the three PTSR-complexes. Each item refers to a particular behavior/feeling (Tables 1, 2 and 3). Its "intensity" is assessed by a Likert-scale. For all items the answer alternatives are: 0 = not applicable, 1 = a little bit applicable , 2 = less or more applicable, 3 = strongly applicable, 4 = very strongly applicable. The response quotum was 124.

Two different clustering techniques will be used; trees and hierarchical classes analysis.

The technique, called additive tree, is a graph-theoretical technique that searches for clusters of objects based on a similarity measure between these objects. This measure is converted into distances, satisfying some metric conditions. In our study the similarity of symptoms/feelings is expressed in the correlation between each item-pair within each of the three item-sets. Given that Likert-scales are ordinal scales, we computed the polychoric correlations, which are estimates of the correlation in the latent bivariate normal distribution underlying the two ordinal variables. The result is (among other) a graphical representation in the form of a tree, with a common root for all objects, some branches which are common to some objects- reflecting features shared by those objects- and a terminal branch for each object expressing his specificity; the leaves are the objects themselves. The (dis)similarity between two objects corresponds to the distance when "walking" from the leaf of one object over the branches to the leaf of the other object.

How well a solution reflects the structure in the data is expressed in a "stress value", which is in fact an index of "badness-of-fit" and should thus be as low as possible. A second index of goodness of fit is the percentage of variance accounted for.

The second technique is the hierarchical classes analysis which is described in my other paper for this congress: Hierarchical Classes Analysis: a set-theoretical clustering technique.

The additive tree solution is given in Figure 1. The codes and labels in the graph and in the remainder of this text refer to the lettercode of the DSM-criteria (see Table 1). The stress value is only .08, which means that the actual structure in the data is quite well reflected in the solution. This is also expressed in the percentage of variance accounted for, namely 77%. As can readily be derived from the graph by reading it from the leaves to the root, initially different couples and triplets are formed, almost between items belonging to the same DSM-criterion. E.g. the first cluster contains Cbl0 (avoithnk) and Cbll (avoisit), belonging to the cluster avoidance behavior. That they have a lot in common is shown by the long common branch. Next D16 (vigilant) cluster with D17 (startles), referring to the criterion hyperarousal. In a third and in a fourth step, all items of the criterion B (persistent reexperiencing the events) cluster together, just as do the items belonging to criterion F (impairment in functioning) but with an "interference" of D13 (difsleep) and D14 (irritat). The items Ca7 (strange) and Ca8 (inhibemo) cluster at about the same height as the former but the other symptoms of criterion C, i.e., Ca6 (lossintr), Ca9 (nofuture) enter the tree near to the root. The graph shows also that Cbl2 (memoloss) is a highly specific item because of its long branch starting at the leaf. The same holds also for Ca6 (lossintr). Items belonging to criteria C do not constitute a cluster, even not when split up in Ca and Cb nor the items of criterion D which are spread throughout the tree.

The goodness-of-fit for the Hiclas solution in the ranks 1 and 2 is too low (<.60), for the ranks 3 to 5 acceptable (.63 a .69) and for the higher ranks "good" (> .70). While the DSM-IV gives a four-criteria structure, we start with the analysis in rank 4, according to the conjunctive decomposition rule. This solution, with a GOF of .66, is represented in figure 2. The symptoms are given in the lower part of each box and described by their label; for each the individual GOF is given too. The figure in the upper part refers to the number of subjects that suffer from the symptoms in their "own" box as well as from the symptoms in the boxes lower in the hierarchy but connected to his own class. Persons have an individual GOF too (although not mentioned here).

There are on the attribute side, in terms of DSM-IV, one "pure" bottom class (1000), two "mixed" bottom classes (0100 and 0010) as well as an empty class (0001). In the class 1000 we find Ca6 (lossintr). The class 0010 regroups B3 (revive), D14 (irritat), D15 (difconc), F19 (difsoc) and F20 (difrelat). The class 0100 covers B1 (memories), B4 (assoc) and D16 (vigilant). At the second level we find one apparently empty class (1010), which is a "liaison class": the subjects of this class are characterized by the mere conjunction of the symptoms of the hierarchical lower classes 1000 and 0001. The class 0011 consists of the items B5 (physio), Ca9 (nofuture), Cbl2 (memoloss), F18 (loweffic) and F21 (difdaily) beside the items of the classes 0001 and 0010. The items proper to the class 1100 are B2 (dreams), Ca7 (strange), Ca8 (inhibemo), CblO (avoithnk), D13 (difsleep) and D17 (startles). At the third level we observe the class 1101 containing Cb11 (avoisit) as particular item and two liaison classes (0111 and 1110). The top class (1111) does not have own features neither.

Looking at the prevalences, the class 0000 regroups 23 subjects reporting none of the symptoms. Given that in fact there are only eight subjects with a full zero pattern, there is an over extension of this class by 15 persons. The latter are subjects with a response pattern containing too few or a set of too different symptoms with respect to the classes in the structure. Eight subjects report only Ca6, none mentions the group symptoms of the class 0010 and 29 subjects suffer from the group of symptoms belonging to the class 0100. At the second level the one soldier in the class 1010 suffer from the symptoms in the class 1000 (Ca6) AND the symptoms in the class 0010; i.e. in total a mixture of symptoms belonging to all four of the DMS-criteria. The subject in the class 0011 shows all symptoms of criterion F plus two symptoms of each of the other criteria. The 11 people in the class 1100 are characterized by a conglomerate of 10 symptoms but none belonging to criterion F (functioning).

The subjects of the third hierarchical level show a dominance of one or two DSM criteria in the symptom pattern. The 12 subjects in class 1101 suffer essentially of psychic numbing (Ca), avoidance behavior (Cb) and reexperiencing the events (B). Typical for the class 0111 is the presence of the nearby full criterion B (reexperiencing) and the full criterion F (functioning) while for the class 1110 it are the criteria B and D (hyperarousal). In terms of PPTSD, we can label these syndrome as type F, type BC, type BF, type BD respectively. The hierarchical highest class 1111 contains 26 persons with apparently all symptoms of all criteria. In reality there is only one subject with a full symptomatology. Thus the algorithm ascribes one or more symptoms to those persons that in fact they have not, but on the other side, they show a response pattern that is nearer to the full response pattern than to any other combination of hierarchical lower classes (given the limitation to rank 4).

It should be stressed that the syndrome as well as the prevalences have to be interpreted with caution. The degree of prototypicality of belonging to a class is given by the individual GOF.

Conclusion: about 20% report no of very few symptoms; about 20% suffer from involuntary confusing memories and distressing recollections together with increased vigilance. About 10% show a complex pattern of symptoms belonging to all criteria (except for avoiding situations that remember the events) but do not feel impaired in functioning. About 10% show the same pattern including avoiding situations. About 20% shows a complete or nearby complete pattern of symptoms.

The additive tree solution is given in figure 3. The stress value of .07 and the percentage variance accounted for of 98% indicate that the model reflects the structure in the data very well.

Items 2 (comfort), 4 (notdone) and 5 (done) are highly specific while item I (alive) and 3 (luck) are not. Items 2 (comfort) and 3 (luck) cluster first, followed by 1 (alive); this cluster can easily be labeled as survival guilt (SG). The items intended as forms of behavioral guilt (BG) do not cluster first together but enter consecutively the tree. The occurrence of these items seems to be independent one of each other or they are not spanned by the same concept.

The Hiclas solutions in rank 2 show already a good fit (.74). The disjunctive solution in rank 2 is easier to interpret than the conjunctive solution. The disjunctive solution in rank 2 is shown in figure 4a. The item 5 (done) is put in the "null class". This means that is does not appear together with any combination in the structure. This is due to the fact that the four possible answer patterns for the items 4 and 5 appear; i.e., 00, 01, 10 and 11; they can thus never belong to the same class in a solution in rank 2. The bottom class 10 consists of the items referring to SG (sensu latu) while the class 01 contains item 4 (notdone) referring to BG. There is no higher order attribute class with feelings shared by different subject classes. Regarding the individual GOF, it should be stressed that item 2 (comfort) is not very typical for SG, the GOF being only .55. The concept of SG is best reflected in item 3 (luck) with a GOF=.86.

Fifty-six subjects are put in the null class. In fact, there are 42 persons with a 00000-pattern, 13 reporting one feeling of SG and one subject reporting two of the three feelings of SG. The eight subjects belonging to the bottom class 10 suffer from SG only, while 35 subjects say that they feel guilty for not have done certain things (class 01) only; the latter probably refers to the facts that they were not allowed to provide help for their captured colleagues. The top class 11 contains the persons reporting both types of guilt. Looking at the individual GOF of those 25 subjects we see an over extension of this class with 14 subjects.

The GOF of the solution in rank 3 of .850 is very satisfying. In this structure (see figure 4b) "comfort" is put in a new bottom class. It can easily be understood that "living in comfort" means something else than "having survived" or "not been injured".

A new bottom class and new higher order classes at the subject side are created. The new bottom class 001 shows that 17 soldiers report one feeling: "comfort". Thirty-two subjects (as compared to the 35 in rank 2) belonging to class 010 suffer from "notdone". Only one soldier (class 100) shows typical SG (alive and luck). The 10 people of class 011 combine "comfort" with "notdone" while five (class 110) combine "notdone" with "alive" and "luck". Three people (class 101) show the three feelings referring to SG (sensu latu). Finally 13 subjects belonging to the highest class (111) report the four feelings captured by the structure. The most striking changes are in the null class with only one misclassification (out of 14) remaining and in the top class with an over extension of only two subjects instead of 14.

The structure of the Hiclas solution do not correspond entirely with the one found with additive tree: in the latter "comfort" clusters first with "luck" while in the former "luck" clusters first with "alive", but both techniques lead to basically the same structure.

In contrast with the PTSS and Guilt item-sets, no conceptual structure has served to develop the item-set of claims. The analyses are thus pure exploratory.

The additive solution for the claim data has a stress value of only .05 and a percentage of explained variance of 90%. The graph of this solution is given in figure 5. Four couples of items can easily be recognized: first, item 2 (recogact) clusters with item 3 (considac); second, item 6 (moralsup) with item 7 (recogdif); third, item 4 (compensa) with item 5 (mataid) and, finally, item 1 (mantreat) with item 8 (punish). It should be noticed however that the first two couples cluster together before the third couple enters the tree. This larger cluster refers to a general claim for recognition. In this context moral support can be interpreted as being an expression of recognition. Next, the items 4 and 5, which constitutes a general claim for compensation (sensu latu), enter the tree and finally the items 1 and 8, being instances of a claim for justice complete the tree. At the individual level, unlike the items I (mantreat), 8 (punish) and 5 (mataid) which are highly specific, the pairs 2-3 (recogact - considac) and 6-7 (moralsup - recogdif) respectively share some common meaning as expressed in the length of their common branch.

Even in rank 1 we observe a high GOF (.80) but such a solution is not of much help while all objects are put in one class and the attributes as well (besides the null class). Although the solution in rank 2 and 3 show a very high GOF (.84 and .88) and notwithstanding the fact that the attributes in the solutions accordingly to the disjunctive rule have an individual GOF varying from good to excellent, these solutions show also a lot of misclassifications in several classes at the object side and will therefore not further be discussed. The same holds for the conjunctive solution rank 2.

The conjunctive solution in rank 3 has a null-class with nine subjects. Seven of them utter effectively no claims while the other two have in fact one claim. The bottom class 010 contains item 8 (punish); two out of the 11 subjects have this as a unique claim but nine soldiers are put in this class too, although with a rather poor fit. The class 001 concerns item 4 (compensa) together with item 1 (mantreat). Only one subject has this combination of claims, but the low fit of .50 (not shown in the graph) indicates that there is an over extension: in fact he claims only compensation. The third bottom class 100 includes item 2 (recogact) item 7 (recogdif) and finally, item 3 (considac); this class contains only one subject but with a perfect fit. In contrast with the tree solution we find a satisfying structure with three basic types of claims: a claim for justice, a claim for compensation and a claim for recognition. At the second level only the class 011 contains one additional claim, i.e. 5 (mataid). This is the specific claim of seven persons over and above the claims 8 (punish), 4 (compensa) and I (mantreat). The other two classes are linking classes with respectively nine and ten soldiers. The attributes of class 110 is the conjunction of the claims in the classes 010 and 100; i.e. claims for punishment, recognition and consideration. The class 101 is the conjunction of the classes 001 and 100; i.e., the complaint of unacceptable treatment, the claims for compensation and recognition, The top level class 111 contains the most widespread claim: moral support is claimed apparently by 74 subjects. These persons formulate also all other seven claims. It should be noted however that only 44 soldiers show a perfect fit and utter actually all the claims. The solution in rank 4 has a slightly better overall GOF and leads to only minor improvements of individual GOF but produces at the same time a more complicated structure without leading to a better insight.

We have used two cluster techniques based on different metric assumptions and on different theoretical premises. As a consequence each of them shed a particular light on the data and the structure in it. Moreover, the emerging structure is not always the same.

The results presented here are based on one sample and are thus tentative (the more that this sample contains only 33% of the military population). Further research is thus needed for evaluating the validity of the structures found.

The hierarchical classes analysis has been performed on data with a dichotomization level at zero. But DSM-IV states that people must experience a serious disturbance; it may be indicated to reanalyze the data with a threshold at I and/or 2.

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