Introduction to the special issue on Bayesian journey-to-crime modelling

In this special issue of the Journal of Investigative Psychology and Offender Profiling, we explore a Bayesian approach to journey-to-crime (JTC) estimation with an emphasis on the statistical models used. The approach conceptualises the probability that an offender lives at one location as the product of the probability distribution from a JTC estimate along with the probability distribution of other offenders who committed crimes in the same locations. The Bayesian approach is appropriate as the second part is conditional on the first part. The introduction gives the background behind the methodology and suggests how future improvements can be made by integrating new information. Finally, the papers in the special issue are introduced. Copyright © 2009 John Wiley & Sons, Ltd.     

Bayesian journey-to-crime modelling of juvenile and adult offenders by gender in Manchester

This study tested the Bayesian journey-to-crime (JTC) model by gender and age for serial offenders from Manchester, England. The data were 4056 crimes committed by 171 serial offenders between 2003 and 2006. The data were subdivided by gender and age group to examine whether accuracy and precision varied by these subgroups. In general, the centre of minimum distance was found to be the most accurate measure, but the Bayesian risk and product measures were found to be the most precise measurements. The traditional ‘distance decay’ type of JTC function did not produce estimates that are as accurate nor as precise as the Bayesian approach. Tests were conducted on whether specific gender and age group JTC functions and origin–destination matrices improved predictability. With the exception of juvenile male offenders, the general functions were more accurate and precise. In terms of building an accurate and precise geographical profiling methodology, the results point to the need to include information on the likely predisposition of neighbourhoods to produce offenders as well as information on the crime opportunities available to offenders. Copyright © 2009 John Wiley & Sons, Ltd.     

The mathematics of geographic profiling

We begin by describing some of the mathematical foundations of the geographic profiling problem. We then present a new mathematical framework for the geographic profiling problem based on Bayesian statistical methods that makes explicit connections between assumptions on offender behaviour and the components of the mathematical model. It also can take into account local geographic features that either influence the selection of a crime site or influence the selection of an offender's anchor point. Copyright © 2009 John Wiley & Sons, Ltd.     

Distance patterns and disposal sites in rural area homicides committed in Finland

The present study examined offender characteristics, distance patterns, and the nature of disposal sites in rural area homicides. Pre‐trial investigation files of cases where victims' bodies were found in rural areas in 1994–2005 (n = 46) and forensic psychiatric examination reports of the offenders were content‐analysed. Psychopathy Check List‐Revised was used to assess psychopathy. Investigators of these homicides filled out a questionnaire on the offender's familiarity with the body disposal area, and MapInfo was used to measure offender/victim‐residence‐to‐crime‐to‐body‐disposal‐site distances. Rural area homicides more frequently involved multiple offenders who were significantly younger than offenders in other homicides. Of the victims, 73% were found in woods and 27% in water. Offenders were familiar with disposal sites in over half of the cases. The victim's gender, close relationship with the offender, and the offender's violent crime history were associated with longer homicide‐scene‐to‐body‐disposal‐site distances. The number of inhabitants and offender's violent crime history were related to longer offender‐residence‐to‐body‐disposal‐site distances. Offender's age, intelligence, or psychopathology bore no significant association with the distance patterns. The results can be applied when searching missing persons in homicide investigations and in prioritising suspects in rural area homicides. Copyright © 2008 John Wiley & Sons, Ltd.     

Finding a serial burglar's home using distance decay and conditional origin–destination patterns: a test of empirical Bayes journey-to-crime estimation in the Hague

Can we tell where an offender lives from where he or she commits crimes? Journey-to-crime estimation is a tool that uses crime locations to tell us where to search for a serial offender's home. In this paper, we test a new method: empirical Bayes journey-to-crime estimation. It differs from previous methods because it utilises an ‘origin–destination’ rule in addition to the ‘distance decay’ rule that prior methods have used. In the new method, the profiler not only asks ‘what distances did previous offenders travel between their home and the crime scenes?’ but also ‘where did previous offenders live who offended at the locations included in the crime series I investigate right now?’. The new method could not only improve predictive accuracy, it could also reduce the traditional distinction between marauding and commuting offenders. Utilising the CrimeStat software, we apply the new method to 62 serial burglars in The Hague, The Netherlands, and show that the new method has higher predictive accuracy than methods that only exploit a distance decay rule. The new method not only improves the accuracy of predicting the homes of commuters—offenders who live outside their offending area—it also improves the search for marauders—offenders who live inside their offending area. After presenting an example of the application of the technique for prediction of a specific burglar, we discuss the limitations of the method and offer some suggestions for its future development. Copyright © 2009 John Wiley & Sons, Ltd.     

Statistical modelling in the investigation of stranger rape

A sample of stranger rape offences (n = 271) registered in the Dutch Violence Crime Linkage Analysis System database in the Netherlands between 1997 and 2007 was studied with the objective of developing statistical models, which give an indication of the probability of basic offender characteristics. Observable crime characteristics concerning the modus operandi, interaction between the offender and the victim, violence, precautionary measures, and sexual behaviours were selected in the dataset. Offender characteristics were selected based on their usefulness for the police organisation in narrowing the scope of a criminal investigation. Spatial behaviour, criminal history, and living situation of the offender were selected. From the predictive models, four out of five achieved a correct rate of over 70%, and all models predicted better than the best guess method. The proposed models for distance and prior convictions for violence seem particularly promising. Both these models show an improvement of correctly predicted offender characteristics of more than 20 percentile points compared with that which could have been estimated based on the average in the total sample. The predictive value of the models needs to be tested further with ‘new offences’, which were not used to construct the model. In general, the current study supports the finding that crime characteristics can be used to get an indication of the probability of certain offender characteristics. Nevertheless, for an understanding of the relationship between the crime characteristics and offender characteristics, a further development of a theoretical framework is urgently necessary. Copyright © 2009 John Wiley & Sons, Ltd.     

Grounding Bayesian accounts of numerosity and variability effects in a similarity-based framework: the case of self-organising maps

ABSTRACT

In this paper, we propose self-organising maps as possible candidates to explain the psychological mechanisms underlying category generalisation. Self-organising maps are psychologically and biologically plausible neural network models that can learn after limited exposure to positive category examples, without any need of contrastive information. They reproduce human behaviour in category generalisation, in particular, the Numerosity and Variability effects, which are usually explained with Bayesian tools. Where category generalisation is concerned, self-organising maps deserve attention to bridge the gap between the computational level of analysis in Marr's hierarchy (where Bayesian models are often situated) and the algorithmic level of analysis in which plausible mechanisms are described.     

A step forward: Bayesian hierarchical modelling as a tool in assessment of individual discrimination performance

Individual assessment of infants’ speech discrimination is of great value for studies of language development that seek to relate early and later skills, as well as for clinical work. The present study explored the applicability of the hybrid visual fixation paradigm (Houston et al., 2007) and the associated statistical analysis approach to assess individual discrimination of a native vowel contrast, /aː/ - /eː/, in Dutch 6 to 10-month-old infants. Houston et al. found that 80% (8/10) of the 9-month-old infants successfully discriminated the contrast between pseudowords boodup - seepug. Using the same approach, we found that 12% (14/117) of the infants in our sample discriminated the highly salient /aː/ -/eː/ contrast. This percentage was reduced to 3% (3/117) when we corrected for multiple testing. Bayesian hierarchical modeling indicated that 50% of the infants showed evidence of discrimination. Advantages of Bayesian hierarchical modeling are that 1) there is no need for a correction for multiple testing and 2) better estimates at the individual level are obtained. Thus, individual speech discrimination can be more accurately assessed using state of the art statistical approaches.     

Simulation and multi‐attribute utility modelling of life cycle profit

Investments on capital goods are assessed with respect to the life cycle profit as well as the economic lifetime of the investment. The outcome of an investment with respect to these economic criteria is generally non‐deterministic. An assessment of different investment options thus requires probabilistic modelling to explicitly account for the uncertainties. A process for the assessment of life cycle profit and the evaluation of the adequacy of the assessment is developed. The primary goal of the assessment process is to aid the decision‐maker in structuring and quantifying investment decision problems characterized by multiple criteria and uncertainty. The adequacy of the assessment process can be evaluated by probabilistic criteria indicating the degree of uncertainty in the assessment. Bayesian inference is used to re‐evaluate the initial assessment, as evidence of the system performance becomes available. Thus authentication of contracts of guarantee is supported. Numerical examples are given to demonstrate features of the described life cycle profit assessment process. Copyright © 2001 John Wiley & Sons, Ltd.     

Assessing the evidence for a cue-induced trade-off between capacity and precision in visual working memory using mixture modelling and Bayesian model comparison

There is considerable debate regarding the ability to trade mnemonic precision for capacity in working memory (WM), with some studies reporting evidence consistent with such a trade-off and others suggesting it may not be possible. The majority of studies addressing this question have utilized a standard approach to analysing continuous recall data in which individual-subject data from each experimental condition is fitted with a probabilistic model of choice. Estimated parameter values related to different aspects of WM (e.g., the capacity and precision of stored items) are then compared using statistical tests to determine the presence of hypothesized differences between experimental conditions. However, recent research has suggested that the standard approach is flawed in several respects. In this study, we presented participants with behavioural pre-cues informing them about the upcoming number of to-be-remembered items (high- vs. low-load) with the goal of inducing a trade-off between capacity and precision. The data were then analysed using the standard analytical approach and a more rigorous Bayesian model comparison (BMC) approach. The second approach involved generating a set of probabilistic models whose priors reflect different hypotheses regarding the effect of our key experimental manipulations on behaviour. Our results demonstrate that these two approaches can produce notably different results. More specifically, the standard analysis revealed that a high- versus a low-load cue resulted in higher capacity and lower precision parameter estimates, suggesting the presence of a trade-off between capacity and precision. However, the more rigorous BMC analysis revealed that it was very unlikely that participants employed a behavioural strategy in which they sacrificed mnemonic precision to achieve higher storage capacity. In light of these differences, we advocate for a more stringent approach to model selection and hypothesis testing in studies implementing mixture modelling.     

Scoring Depression on a Common Metric: A Comparison of EAP Estimation,Plausible Value Imputation,and Full Bayesian IRT Modeling

There are a growing number of item response theory (IRT) studies that calibrate different patient-reported outcome (PRO) measures, such as anxiety, depression, physical function, and pain, on common, instrument-independent metrics. In the case of depression, it has been reported that there are considerable mean score differences when scoring on a common metric from different, previously linked instruments. Ideally, those estimates should be the same. We investigated to what extent those differences are influenced by different scoring methods that take into account several levels of uncertainty, such as measurement error (through plausible value imputation) and item parameter uncertainty (through full Bayesian IRT modeling). Depression estimates from different instruments were more similar, and their corresponding confidence/credible intervals were larger when plausible value imputation or Bayesian modeling was used, compared to the direct use of expected a posteriori (EAP) estimates. Furthermore, we explored the use of Bayesian IRT models to update item parameters based on newly collected data.     

Dissociation of algorithmic and heuristic processes in language comprehension: Evidence from aphasia

Three groups of aphasic patients, Broca's, Conduction, and Wernicke's, and a nonaphasic patients control group were tested for comprehension of object-relative center-embedded sentences. The sentences were of three types: sentences in which semantic constraints between words allowed the subjects to assign a correct semantic reading of the sentence without decoding the syntax, sentences in which semantic constraints were relaxed and for which a correct reading was only possible with knowledge of syntactic relationships among words, and sentences which described highly improbable events. The subjects' task was to choose which of two pictures captured the meaning expressed in the sentence. Broca's and Conduction aphasics performed near perfectly on sentences where they could use semantic information. Their performance dropped to chance when they had to use syntactic information. These results support a neuropsychological dissociation of heuristic and algorithmic processes based primarily, though not exclusively, on semantic and syntactic information, respectively.     

Naming in aphasia: Interacting effects of form and function

The naming difficulties of Broca's and anomic aphasics were explored in relation to a recently developed model of the normal mental lexicon which stresses the importance of integrating perceptual and functional information in the act of naming, and equally stresses the inherent vagueness of conceptual categories based on such information. Subjects were shown line drawings of various food containers varying in physical features such as height and width; they were required to select a name for the object from a multiple choice list (cup, bowl, or glass). Prototypical as well as nonprototypical objects were shown. The Broca's aphasics showed relatively normal naming profiles. In contrast, the posterior patients were unable to integrate perceptual and functional information and were insensitive to the fuzzy boundaries between conceptual categories. The results obtained for the posterior patients are interpreted as reflecting an impairment in the underlying conceptual organization of the lexicon rather than retrieval difficulties.     

Feasibility of a Simplified and Dynamic Bayesian System for Use in Structured Diagnostic Interviews

An important goal of clinical assessment is to balance cost-effectiveness, administration demands, and accuracy (G. Young, J. O'Brien, E. Gutterman, & P. Cohen, 1987). The incorporation of Bayesian logic into diagnostic interviewing may assist with this goal, but in previous examinations, such methods have been prohibitively complex. In this study, analysis of a simplified Bayesian system showed overall classification error rates as good or better than traditional structured interviewing, and reduction in error was positively related to the psychometric properties of the predictor used in the actuarial functions. A dynamic system using simplified Bayesian logic appears to function well in the context of a structured interview and requires comparatively less data than previously tested Bayesian approaches. This type of system appears suitable for further research with clinical populations to determine its performance in applied settings.     

A Comparison of ML,WLSMV, and Bayesian Methods for Multilevel Structural Equation Models in Small Samples: A Simulation Study

Multilevel structural equation models are increasingly applied in psychological research. With increasing model complexity, estimation becomes computationally demanding, and small sample sizes pose further challenges on estimation methods relying on asymptotic theory. Recent developments of Bayesian estimation techniques may help to overcome the shortcomings of classical estimation techniques. The use of potentially inaccurate prior information may, however, have detrimental effects, especially in small samples. The present Monte Carlo simulation study compares the statistical performance of classical estimation techniques with Bayesian estimation using different prior specifications for a two-level SEM with either continuous or ordinal indicators. Using two software programs (Mplus and Stan), differential effects of between- and within-level sample sizes on estimation accuracy were investigated. Moreover, it was tested to which extent inaccurate priors may have detrimental effects on parameter estimates in categorical indicator models. For continuous indicators, Bayesian estimation did not show performance advantages over ML. For categorical indicators, Bayesian estimation outperformed WLSMV solely in case of strongly informative accurate priors. Weakly informative inaccurate priors did not deteriorate performance of the Bayesian approach, while strong informative inaccurate priors led to severely biased estimates even with large sample sizes. With diffuse priors, Stan yielded better results than Mplus in terms of parameter estimates.     

Impairment of auditory perception and language comprehension in dysphasia

Men with chronic focal brain wounds were examined for their ability to discriminate complex tones, synthesized steady-state vowels, and synthesized consonant—vowel syllables. Subjects with left hemisphere damage, but not right hemisphere damage, were impaired in their ability to respond correctly to rapidly changing acoustic stimuli, regardless of whether stimuli were verbal or nonverbal. The degree of impairment in auditory processing correlated highly with the degree of language comprehension impairment. The pattern of impairment of the group with left hemisphere damage on these perceptual tests was similar to that found in children with developmental language disorders.     

Longitudinal associations between athletes' controlled motivation,ill-being,and perceptions of controlling coach behaviors: A Bayesian latent growth curve approach

Although many scholars have argued that leadership is a dynamic process jointly produced by leaders and followers, leadership in sports is most often researched as a unidirectional process from coaches to athletes. Within self-determination theory (SDT), individual characteristics are suggested to influence how people perceive external events such as coaches' behaviors. In the present study, we examined this jointly produced leadership process by investigating longitudinal associations between athletes' controlled motivation, ill-being, and perceptions of coaches' controlling behaviors at the between- and within-person levels. The participants were 247 young elite skiers enrolled at Swedish sport high schools who responded to self-report questionnaires at three time points over the course of an athletic season. At the between-person level, increases in perceptions of coaches' controlling behaviors over the season positively predicted controlled motivation at the end of the season, and controlled motivation at the beginning of the season positively predicted ill-being at the end of the season. At the within-person level, athletes' controlled motivation positively predicted perceptions of coaches' controlling behaviors. The results at the between-person level support the unidirectional perspective and the tenets of SDT. The results at the within-person level suggest that individual characteristics such as motivation can influence how athletes perceive external events, which has been proposed theoretically but seldom examined empirically. Three plausible explanations for this reversed association are presented in the discussion.     

The Parallel Episodic Processing (PEP) model 2.0: A single computational model of stimulus-response binding,contingency learning,power curves,and mixing costs

The current paper presents an extension of the Parallel Episodic Processing model. The model is developed for simulating behaviour in performance (i.e., speeded response time) tasks and learns to anticipate both how and when to respond based on retrieval of memories of previous trials. With one fixed parameter set, the model is shown to successfully simulate a wide range of different findings. These include: practice curves in the Stroop paradigm, contingency learning effects, learning acquisition curves, stimulus-response binding effects, mixing costs, and various findings from the attentional control domain. The results demonstrate several important points. First, the same retrieval mechanism parsimoniously explains stimulus-response binding, contingency learning, and practice effects. Second, as performance improves with practice, any effects will shrink with it. Third, a model of simple learning processes is sufficient to explain phenomena that are typically (but perhaps incorrectly) interpreted in terms of higher-order control processes. More generally, we argue that computational models with a fixed parameter set and wider breadth should be preferred over those that are restricted to a narrow set of phenomena.     

A comparative evaluation of factor- and component-based structural equation modelling approaches under (in)correct construct representations

Structural equation modelling (SEM) has evolved into two domains, factor-based and component-based, dependent on whether constructs are statistically represented as common factors or components. The two SEM domains are conceptually distinct, each assuming their own population models with either of the statistical construct proxies, and statistical SEM approaches should be used for estimating models whose construct representations correspond to what they assume. However, SEM approaches have often been evaluated and compared only under population factor models, providing misleading conclusions about their relative performance. This is partly because population component models and their relationships have not been clearly formulated. Also, it is of fundamental importance to examine how robust SEM approaches can be to potential misrepresentation of constructs because researchers may often lack clear theories to determine whether a factor or component is more representative of a given construct. Addressing these issues, this study begins by clarifying several population component models and their relationships and then provides a comprehensive evaluation of four SEM approaches – the maximum likelihood approach and factor score regression for factor-based SEM as well as generalized structured component analysis (GSCA) and partial least squares path modelling (PLSPM) for component-based SEM – under various experimental conditions. We confirm that the factor-based SEM approaches should be preferred for estimating factor models, whereas the component-based SEM approaches should be chosen for component models. Importantly, the component-based approaches are generally more robust to construct misrepresentation than the factor-based ones. Of the component-based approaches, GSCA should be chosen over PLSPM, regardless of whether or not constructs are misrepresented.