From Right to Left it Had No End: Clusters

 

SSA is also appropriate to many psychological studies, as psychological hypotheses are usually about the relative associations between entities rather than their absolute differences. The resulting SSA geometric representation is thus often more amenable to direct interpretation in relation to a set of hypotheses than procedures using metric algorithms or specific, externally defined axes. Another advantage that SSA has over other procedures is that SSA only takes into account the positive co-occurrence between variables. For example, if two variables are both absent from the records, this will not increase the association. As such, SSA is deemed to be the appropriate statistical procedure to measure the association for data drawn from police records, because it is not known whether absent information was recorded.

 

The general hypotheses central to this research are:

1. Serial murderers will display certain crime scene behaviors that they share in common;

2. There will be groups of serial murderers who will consistently display signature behaviors that are more typical than any other group;

3. The analysis of the data will reveal four thematic, mutually exclusive regions that make up the offender’s modes of interaction with his victims. The four themes of behavior are:

• Affective-Vehicle

• Affective-Object

• Cognitive-Vehicle

• Cognitive-Object  

It is possible that the four thematic modes occur in any combination across a range of murders. This would suggest that none of the explanations provides a basis for distinguishing among serial murder offenses. A completely random combination of any behavior with any other would suggest that there is no consistently coherent distinction among the four crime scene themes above. Hence, a null hypothesis would suggest that no interpretable relationships will be found between the actions that occur in serial murder offenses.

 

A second possibility is that a subset of conceptually related actions — for example, sadistic acts where the offender has a personal attachment to his victim — will consistently occur together. Such a grouping would support the hypothesis of the specific theme of victim as an object related to that behavior. However, in the event that different methods of killing the victim (e.g., bludgeon and ligature) co-occur but the style of sexual assaults (e.g., post-mortem sex, attempted sexual assault) were independent of each other, there would be support for the impersonal attachment towards the victim as a vehicle as a coherent salient aspect of the offender’s focus. A grouping such as this would support the theme related to that behavior. Finally, a third possibility is that all of these aspects of offense behavior might be identified in details of an actual event and they therefore would combine to provide a composite model of serial murderers’ offense behavior. Such an empirical model would be expected to have an interpretable structure to it. For example, those types of behaviors that are likely to be associated with a cognitive thought process, such as planning the crime, disfiguring the victim’s body, and postmortem sexual activity would be expected to have some empirical relationship distinctive from the affective elements where more impulsive behaviors, such as blitz attack and non-completed sex acts, are likely to be found. Scientific evidence for the second or third possibility discussed above would contribute to an empirical model of serial murder practical for police investigations and for building a linking database to identify murders committed by one offender.

 

Details about serial murderers and their offenses are generally found in writ ten form in state and local police files and court records; during the last few years, most police records have been maintained and stored in computerized databases. Because serial murder cases often remain unsolved for months and even years, the process of maintaining accurate information in police files becomes problematic. This dilemma is further compounded by the fact that most data collected by police are not intended for research purposes, and therefore the information is not organized in an orderly fashion. In recent years, though, the management of case data for all crimes has greatly improved due to the development of computerized police databases.

 

Sixty-five crime scene variables were selected for the analysis and coded as dichotomous data, where the score of “0” represents absence of the behavior in the crime, and “1” the presence of the behavior in the crime. The data in this study do not represent categorical variables. Coding the data in dichotomous form enabled a particular association matrix of co-occurrence to be produced, thus permitting the SSA program to construct the distance matrix from which geometric mapping is reproduced. Coding the raw data matrix in binary format made the data amenable to a suitable association coefficient. Dichotomous decision-making in content analysis has the tendency to raise inter-rater reliability from around 60% to above 90%. Three sample raw data matrixes of 96 offenders and 96 offenses formed the association matrix that was analyzed by SSA. The SSA program computes correlations, or in the case of this study, offense behavior of association coefficients of the co-occurrence of behaviors. The SSA then rank–orders these correlations, transforming the original rectangular input data matrix to a triangular distance matrix. Subjecting variables of a content universe to SSA had two major roles. The first role was exploratory in nature. The exploratory approach is appro priate when the subject matter is relatively new, or where there are no empirical studies arising from the literature. For this research, it is important first to establish that, on an empirical level, there are themes of behaviors in the crime scene actions of serial murderers.

 

Smallest Space Analysis (SSA-I) is a non-metric multidimensional scaling procedure most frequently used in facet theory. SSA is appropriate in many psychological studies, such as the present one, as psychological hypotheses are usually about the relative associations between entities rather than their absolute differences. SSA was used to determine the underlying structure in the crime scene actions of serial murderers. The SSA technique examines the structure of the offenders’ behaviors, and not the offenders themselves. The SSA representation of the coefficients matrix is non-metric, meaning that no attempt is made to specify in advance a particular monotonic function that transforms the coefficients into distances. It is only the rank order of the coefficients, not their numerical values, that is preserved by SSA mapping.

 

Other methods of showing relationships between variables of behavior could have been performed on the data in a process of variable-to-variable analysis. For example, cross-tabulation of every variable with every other would have found some co-occurrence, but the results would have not been multivariate and would have been very difficult to interpret. Homogeneity analysis using alternating least squares (HOMALS), factor analysis, or cluster analysis could have been performed on the data. However, SSA has advantages over these techniques, because it imposes little a priori structure on the data. Also, qualitative, dichotomous data are not amenable to examination by methods which assume distribution and mathematically manipulate mean. Rather, a multivariate analysis of the covariance between the variable behaviors is the most interpretable and robust method for data that are produced as qualitative, non-parametric categories in dichotomous form. The SSA program works by computing iterations, comparing the rank order between the correlation matrix and distance matrix, and adjusting the spatial representation until the minimum of stress is reached within a designated number of iterations. Such a matching of ranks can be shown to give a mathematically more efficient solution as well as being less sensitive to extreme values, and is the reason the procedure is called smallest space analysis. The analysis provides a stress measurement called the coefficient of alienation, which is used to end the iterations. The coefficient of alienation gives a general indication of the degree to which the variables’ inter-correlations are represented in the plot by their corresponding spatial distances. The smaller the coefficient of alienation, the better the fit of the variables in the SSA plot.

 

SSA configurations are interpreted as regions rather than dimensions. The SSA configuration was examined to identify regions of the plot in which crime scene behaviors appeared to have coherent interrelationship. . The plot can be rotated, stretched, translated, and reflected without any effect on the meaning of the solution, because the information is con tained in the distances between the variables and not the dimensions.

 

Therefore, the orientation of the axes in the SSA plot is not meaningful, although as an artifact of the program the axes may correspond to the principal components of the correlation matrix. It is also worth mentioning that SSA regions are not considered clusters. Cluster analysis would not be able to recognize empty spaces in the sampling as the SSA does, because it is a structure-imposing procedure. For example, no indication of empty spaces containing variables which might be conceptually related would be obtained by cluster analysis since the clustering solution is created by iteratively looking at each value in the association or correlation matrix in series, unlike the SSA solution, which looks at them in parallel.

 

Acknowledgements:

 

www.aivd.nl    AIVD ©

 

Algemene Bestuursdienst – @Erik Akerboom ©

 

www.politie.nl  Politiekorpschef  @Janny Knol©

 

www.politie.nl WEB Politie - @Henk van Essen©

 

https://english.marechaussee.nl  Royal Netherlands Marechaussee    @Willem-Alexander King of the Netherlands©

 

PolitieAcademie - https://www.politieacademie.nl/en©

 

Author: W.R. Łaskawiec ©

 

 

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