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. 2022 Nov 21;2(4):332–346. doi: 10.1007/s43576-022-00075-w

An Exploratory Study on Murders in the Chaos of COVID-19: An Analysis of Changes in Murder Rates and Patterns in Trinidad and Tobago

Troy Smith 1,✉, Kevin Haines 2
PMCID: PMC9684839

Abstract

The study assessed the changes in murder counts and patterns under COVID-19 conditions in The Republic of Trinidad and Tobago. Initial research indicates that crime rates and patterns have changed under the COVID-19 pandemic possibly because of government implemented restrictions. The specific impact of these responses on murder has not been examined. To fill this gap in the literature the study utilized several interrupted time-series analyses to assess the change(s) in murder trends and their possible relationship to restrictions in movement associated with COVID-19. Overall, murder decreased while under COVID-19 conditions. However, the change was not consistent across different classifications of murder, with some increasing while others continued a downward trend that started before COVID-19 restrictions. The findings suggest that the change in murder trends under COVID-19 was not based on a linear relationship with restrictions in movement. Rather the results suggest that the data contains nonlinear components, which are associated with an initial but inconsistent change in murder counts among different classifications of murder. Which was followed by a phase of diminishing return on the effect of restriction on movement on the murder count. Further, in support of the findings the forecasting of murder was found to be better achieved by an algorithm which supports continuous non-linear functions (Artificial Neural Networks) when compared to a linear approach (Bayesian Structural Time-Series).

Supplementary Information

The online version contains supplementary material available at 10.1007/s43576-022-00075-w.

Keywords: Murder trends, Covid-19, Interrupted time-series analysis, Natural experiment, Nonlinear forecasting

Introduction

The current paper seeks to add to the extant literature by performing an in-depth analysis of changes in murder patterns during the COVID-19 pandemic with a specific focus on the Republic of Trinidad and Tobago (ROTT). Identification of the effects of exogenous factors on crime rates and patterns has been a sustained topic of interest in criminology. Numerous researchers have cited the COVID-19 pandemic as one of the most impactful events or shocks (exogenous factor) to social and societal activities in recent history (Buil-Gil et al., 2020; Hawdon et al., 2020; Stickle & Felson, 2020). This paper uses both linear and nonlinear predictive algorithms to forecast and explain the observed changes (and the observed inconsistency in those changes) in crime resulting from the pandemic. However, as Stickle and Felson (2020) highlighted, criminologists can tend to overgeneralize crime, ignoring the specificity of offender decision making. Therefore, this study does not look at the effect of COVID-19 on crime in general but specifically at murder. Further, it drills deeper by examining if the effect/changes are consistent across murder belonging to different classifications, specifically the classes of gang, domestic, robbery, narcotics, altercation, revenge and other (otherwise unclassified murder).

The ROTT makes for an interesting case study because of its relatively high murder rate due to elevated levels of gang-related violence. The prevalence of murder has seen a relatively steady upward trend since the year 2000, which was itself a sharp increase in comparison to the lower murder rates between 1988 and 2000 (Clancy et al., 2019; Seepersad & Williams, 2016). Past research has shown that the increasing murder rate has been largely fueled by the emergence of criminal street-gang culture and its associated violence (Clancy et al., 2019; Pawelz, 2018). Therefore, this study not only identifies the potential correlation between COVID-19 restrictions and homicides but directly assesses a study site in which the murder rate is traditionally dependent on gang-related activities.

The analyses employed in this research improve on existing approaches in identifying the change in crime pattern with greater statistical power using time-series analysis with a longer temporal dimension than previous studies and official national statistics. This approach provides a sound quasi-experimental base for identifying the effect of the treatment (COVID-19) in this natural experiment, where randomization or use of a control group was not feasible. The analysis is further enhanced using Bayesian Structural Time-Series to provide analysis into the trend and seasonality components of murder. Further, most studies in social sciences targeting the effect of the COVID-19 pandemic on crime have focused on the resulting changes in behaviors, trends and patterns of movement due to governmental restrictions implemented to stymie the spread of the disease. However, unlike this study, they were unable to identify potential metrics to measure the changes resulting from COVID-19 over time and hence unable to empirically link changes in movement to changes in crime patterns.

Initial Findings

Initial reports suggest that crime rates have changed from as early as the beginning of February 2020, but that the nature of the change is inconsistent across countries (and even cities within a country), time frame, degree of change and among forms of criminality (Abt et al., 2020; Dolmetsch et al., 2020; Fattah, 2020; Felson et al., 2020; Shayegh & Malpede, 2020). While reports suggest that the murder rate is decreasing in the ROTT, open-source reports and recent studies show that they are either up, down, or remain constant in other countries and in some cases cities (Abt et al., 2020; Campedelli et al., 2020). For example, researchers found that a decline in the murder rate was not observed in all cities in the United States and where there was a decrease that it was unequal (Ashby, 2020; Lum et al., 2020; Mohler et al., 2020). Similarly, in Canada, while serious crimes and calls to law enforcement declined, the murder rate remained stable (Humphreys, 2020; Lum et al., 2020).

Adding to the complexity of the phenomenon is the fact that the decrease in crime may not necessarily be correlated to the stringency of stay-at-home orders. In the US where Democratic and Republican-run states took divergent paths in their adherence to restrictions and guidelines, analysis of crime trends in 59 US cities in 2020, compared to 2019 found an approximate twenty-eight (28) percent increase in the murder rate, independent of leadership (Asher & Horwitz, 2020). Similarly, when the changes in murder rates for North American, Central American, Sweden, and Trinidad and Tobago reported by various researchers and international agencies are matched with the corresponding stringency index values for the various countries they were not congruent (Online Resource 1). The change in the stringency of restrictions between Trinidad and Tobago, Costa Rica, Belize and Panama are similar, however, only Trinidad and Tobago recorded a marked decrease in murder for the first half of 2020. The United Nations Office on Drugs and Crime (UNODC) murder trend data show that levels remained relatively stable in Central America (Committee for the Coordination of Statistical Activities, 2020). Sweden, which had a consistently lower stringency level showed a decrease in murder, while the United States showed an increase in murder (Gerell et al., 2020) contrary to the traditionally predicted direction of relationships. Overall, matching the reported changes in murder to the recorded stringency indices demonstrates an inconsistent relationship between COVID-19 measures and changes in the murder rate.

Theoretical Considerations

The research to date has primarily relied on the premises of exogenous shock and dependence on activity patterns to explain any possible change to crime ‘post-COVID-19’ conditions (Boman & Gallupe, 2020). Researchers have cited that an exogenous shock such as social unrest, widespread protests, rising youth population and sharp change in economic conditions can cause a change point in the upward or downward trend of murder (Abt et al., 2020; McDowall, 2002; Rosenfeld, 2018). This framework assumes that murder rates vary over time proportional to external forces, as these forces provide the energy for the change, i.e., they postulate a (uniquely bipolar) causal relationship. Therefore, it is then assumed that removal of these forces would result in almost immediate cessation of the change and reversal to a hypothesized homeostatic state (McDowall, 2002). These postulates and assumptions have formed the basis of our theoretical and empirical analysis of the COVID-19 pandemic and the associated measures implemented by governments worldwide.

The relation of activity patterns and the effects of COVID-19 are based, to a large degree, on Routine Activities Theory (RAT). The spatiotemporal framework given by RAT suggests that the occurrence of a crime event is dependent on the confluence of a motivated offender, a suitable target and the absence of capable guardianship in time and space (Cohen & Felson, 1979; Wick et al., 2017). Given the decrease in the accessibility of targets or potential victims to offenders and the extent to which potential offenders are forced to stay-at-home, the probability for spatiotemporal convergence should also decrease. The decrease in the likelihood of this convergence should translate to a decrease in the probability of a crime event. At least this should hold for crimes that are not classified as domestic, where stay-at-home orders increase the time–space proximity of potential victim and potential offender. Similarly, there is an associated increase in the presence of law enforcement, which is primarily targeted at enforcement of restrictions placed by the government. However, their presence potentially also serves as a deterrent to would-be offenders due to increased vehicular checks, patrols and stationary postings.

The same mode of thinking presented by proponents of the effect of exogenous shock and the importance of activity patterns also implies that removal of the treatment (COVID-19 and associated safety measures) should precede a decrease or reversal of the observed effect. This hypothesis has been found to hold in some instances where the decrease in murder and crime in general stalled when stay-at-home orders were eased (Abt et al., 2020; Smith, 2022; Stickle & Felson, 2020). However, the correlation of the removal of stay-at-home orders and a return to pre-COVID murder rates is not the norm, as removal of the restrictions saw murder and crime in general in the United States remaining steady, increase slightly but remain lower than previous years or spike as was seen in neighborhoods where residents were predominantly Afro-American (Harden & Jouvenal, 2020). These findings reported above, tend to be confounding in the light of traditional criminological understanding which would postulate that the effect of the exogenous shock should be consistent and proportional. It may well be, therefore, that amongst other confounding features of the COVID-19 virus (notably the inconsistency of its impact on individuals) is the absence of any linear relationship between the COVID-19 virus, measures designed to mitigate its impact and crime (in general) and murder (specifically). As such, this paper explores the potential of nonlinear dynamics to explain the observed inconsistencies.

Non-linear Dynamics

The inconsistency in the changes in murder rates under-COVID-19 conditions led to the consideration of nonlinear dynamics in this study, as examining phenomena in their complexity and interconnectedness rather than under a deconstructive method, can offer greater insight. The application of nonlinear dynamics to murder means that the mechanism that translates exogenous shock into observable change is at least partially self-propagating. Further, the degree of the effect of the external force will be dependent on the period that immediately precedes it and as such the resultant change will not be necessarily proportional to the shock (McDowall, 2002; McDowall & Loftin, 2005). In nonlinear dynamics, this is referred to as the system's sensitivity to change in initial conditions (Kia et al., 2017; Zhang et al., 2009). For example, sudden economic changes associated with COVID-19 can have different effects depending on whether murder were already decreasing or increasing. Another important point is that unlike in linear dynamics the removal or plateauing of the does not necessarily translate to a plateauing or reversal of the observed changes. Rather the shock can be considered to have a domino effect resulting in complex, long-lasting effects (McDowall, 2002). It is entirely possible, for example, to contemplate a shock resulting in a change which is then exacerbated when the shock is removed or reversed. Therefore, nonlinear dynamics add a new layer by unlocking the complexity of interactions to understand how crime propagates, particularly as it relates to historical contingency.

Data and Methods

The methods employed in this study sought to identify the relationship between changes in murder patterns and the social and situational changes resulting from the COVID-19 pandemic. This study can be classified as a natural experiment as the experimental and control conditions are beyond the direct control of the investigator. In practice, a quasi-experimental design is adopted, a methodology often used in social sciences, to determine the relationship between an intervention and an outcome in which the intervention is not or cannot be randomly assigned, such as in the evaluation of rapid responses to outbreaks (Cook & Campbell, 1979; Harris et al., 2006; Schweizer et al., 2016).

For this study the different time periods examined in relation to COVID-19 are defined operationally as pre-COVID-19 and under-COVID-19. The use of “post-COVID-19” is avoided as it would-be inaccurate since the data used in the study was obtained while under the effects of COVID-19 and its restrictions (early 2021).

The remainder of this section is divided into three parts: identification of datasets used, descriptive statistics and an overview of the analyses performed in the study.

Datasets

This study utilized three datasets in its analyses to identify changes in murder and the possible link to governmental restrictions on the population and the public’s response to stay-at-home orders. The outcome variables were limited to those which provided measurable data representing the changes in movement in the target population and the level of implementation of stringency measures. Both variables are necessary as the researcher does not assume that the effect of Stringency Measures on movement will be consistent throughout the pandemic as the closing of schools vs businesses vs bars and limitations in the maximum capacity of personal and hired vehicles will have varied effects. Further, as time elapses the willingness to comply with restrictions may fluctuate and will be dependent on the government’s/law enforcement’s ability to maintain controls. These datasets are as follows:

Crime and Problem Analysis Branch Murder Dataset

This dataset was obtained from the Crime and Problem Analysis branch of the Trinidad and Tobago Police Service (TTPS) for the period January, 2014 to August, 2020. Such information is available upon request to the Commissioner of Police under the Freedom of Information Act. Each incident is recorded separately and dated for the period January 1, 2014 to August 31, 2020. The total dataset had 2,571 data points, corresponding to 80 months for almost 7 years. Variables regarding the demographic characteristics of victims could not be included in the analysis as the provision of such details were not consistent across the various years. However, the motive of the murder (once known) was consistently provided in the police records, hence enabling a sub-analysis into the specificity of any observed changes when the data are split by motive. The classifications of murder that were considered were Gang, Narcotics, Domestic, Robbery, Altercation, Revenge and Other. The classification of ‘Other’ accounted for murder resulting from rape, kidnapping, the murder of a state witness and for those labeled as ‘unknown’ (motivation for the murder is unknown). In this paper changes in murder were given as counts rather than rates, which was supported by the fact the estimated population remained at approximately 1,300,000 for the periods of interest. It was also useful to use counts to make the quoted values easily relatable when examining murder occurring per week.

OXFORD COVID-19 Government Response Stringency Index 4.0

This is a composite measure based on indicators, which include school and workplace closures; restrictions on public gatherings; transport restrictions; and stay-at-home requirements, rescaled to a value from 0 to 100 (100 = strictest). The index is derived from the Coronavirus Government Response Tracker (OxCGRT), which is published and managed by researchers at the Blavatnik School of Government at the University of Oxford. The score is given on a per-day basis for each country and is presented for the period January 2020 to present.

Movement Range Data

This data are a product of the Facebook for Good initiative to provide researchers with data on the response to physical distancing measures. There are two metrics, which provide perspective on movement trends, Change in Movement and Stay Put. Change in Movement looks at how much people are moving around and compares it with a baseline period (February 2020), while Stay Put looks at the fraction of the population that appears to stay within a small area during an entire day. The data are extrapolated from persons with Facebook installed on their mobile devices. There were 874 000 Facebook users in Trinidad and Tobago in January 2020, which accounted for 78.6% of its entire population over the age of 15 years (IndexMundi, 2020; Napoleon Sp. z o.o., 2020). There is one notable limitation, the data can only be obtained from users that allow locations services to share their data. This limitation does not bar the use of Facebook data in an exploratory study as the aim is to identify potential changes of interest and stimulate further research in the area. However, it does mean that the generalizability of findings may be limited.

Descriptive Analyses

This section looks at the general distribution of the datasets through the assessment of descriptive plots. In the initial assessment murder per month was plotted against time for the period 2014–2020 (Online Resource 2). While it provided an overview of murder for the period under consideration and showed clear fluctuation it did not provide much insight into patterns. Further insight was obtained into the changes to murder under COVID-19 conditions by comparing murder month-over-month for a seven-year period (Online Resource 3). This comparison showed that 2020 had the lowest count of murder for the last 7 years (excluding January, 2020). According, to the COVID-19: Government Response Stringency Index, Trinidad and Tobago’s first recorded an increase in its stringency score from zero at the beginning of February, 2020 (Hale, et al., 2020). Another interesting observation is that the murder for 2020 are almost identical to 2015 for the period February to August. Notably, the only instance in which murder were markedly lower than in 2015 after their peak in 2008 was 2011 (Seepersad & Williams, 2016). In 2011, the Government of Trinidad and Tobago implemented a State of Emergency, which was accompanied by curfews, increased police activity (patrols, raids and roadblocks) and restrictions in movement (Ramdass et al., 2015). However, after this exogenous shock the system quickly tended upwards returning to previous murder rates.

Table 1 shows the murder counts for the period February to August for the years 2014–2020. The period February to August was chosen as the COVID-19: Government Response Stringency Index suggests stringency measures began to be implemented at the beginning of February, 2020 in Trinidad and Tobago. For all classifications of murder except ‘Other’ there was a decrease in 2020 compared to 2019. The greatest change was observed in murder related to revenge followed closely by those related to gangs and robbery, all of which showed a decrease of more than 50%. The number of murders related to narcotics and revenge were the lowest in 2020 for the seven-year period. While the number of murders classified as ‘Gang’ and ‘Robbery’ were not the lowest for the seven-year period they were within two and nine percent, respectively. Murder classified as ‘Other’ not only increased in 2020 compared to 2019 but was the highest for the seven-year period. Further, the increase in the classification of ‘Other’ was not proportional to the decreases seen in the other classes of murder. Given that this class predominantly consist of unclassified murder, it suggests a displacement in the motivation of murder or law enforcement ability to classify the crimes. This could imply that conditions under-COVID-19 while restrictive to the ‘main’ classes of murder, fosters conditions for murder due to other motivations or better concealment of motives. This could theoretically be linked to increased thought given by offenders who recognize the heightened presence of law enforcement. Additionally, change in environmental factors such as decreased foot and mobile traffic, especially at night can translate into potentially longer times between murder and discovery of bodies and increased ease for offenders to find isolated locations for offending or concealment.

Table 1.

Murder divided by classification for the period March to August for the years 2014–2020

Classification Year % Change in murder (2019 vs 2020)
2014 2015 2016 2017 2018 2019 2020
Altercation 29 29 20* 31 35 33 27 − 18%
Domestic Violence 15 7* 20 21 24 22 18 − 18%
Gang 83 90 81 59* 114 120 60 − 50%
Narcotics 35 52 50 48 44 44 31* − 30%
Revenge 50 43 43 60 35 53 21* − 60%
Robbery 23 26 34 39 41 45 21* − 53%
Other 9 2* 8 13 12 8 28 250%
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*Lowest value in 7−year period

A comparison of changes in the Stringency Index and the murder rate for Trinidad and Tobago for the period of January – August, 2020 illustrated in Online Resource 4 shows that the changes in the murder rate do not reflect changes in the Stringency Index. Given that the Stringency Index represents a holistic measure of the intensity of government response, especially as it relates to restriction of movement, it means that changes in response and restriction of movement are not proportional to changes in the murder rate. In linear dynamics, which is normally applied to social science it would-be expected that the change resulting from an exogenous shock would remain proportional to the shock and as such an increase or decrease in this intervention should be reflected in the outcome (murder). However, not only is the effect of the change not consistent, but the change observed in May and July to August is counterintuitive as there was a further decrease in murder although the Stringency Index value decreased.

Analyses

This study is based on a natural experiment where randomization of the intervention is not possible and as such a quasi-experimental design was adopted. Quasi-experimental studies can be categorized into three categories; interrupted time-series designs, designs with control groups and designs without control groups. Krishnan (2018) describes interrupted time-series as the strongest quasi-experimental design in establishing causality. Therefore, to identify changes in murder patterns with some statistical authority interrupted time-series analyses were employed in this study, whereby the historic crime patterns can be used as a baseline for a comparative assessment.

Bayesian Structural Time-Series Analysis

The interrupted time-series was performed in the first instance using Bayesian Structural Time-Series Analysis. The Bayesian Structural Time-Series Analysis model was chosen as it can provide analysis into the trend and seasonality components of murder and its treatment of unobserved components is considered transparent as its representation does not rely on differencing, lags and moving averages. Further, this method can account for model uncertainty using posterior model probabilities averaging to make an inference, where the emergent forecast result will be better than any single model (Koop & Osiewalski, 1995; Steel, 2008). The Bayesian paradigm has also been shown to avoid overfitting and take advantage of the correlations among multiple target time-series. Further, the incorporation of machine learning in the form of the “spike and slab” variable selection technique enables feature selection in the regression component of multivariate time series (Jammalamadaka et al., 2019). Thus, it provides the ability to include known drivers, which cannot be extracted from the available data in a variable selection process (Larson, 2016). This allowed the researcher to test the ‘importance’ of the variables of ‘Stringency Index’, ‘Relative Change in Movement’ and ‘Stay Put’ in the prediction of weekly murder counts. Stickle and Felson (2020) highlighted the importance of time-series analysis and the inclusion of methods to directly link the stay-at-home measures to changes in murder.

The Bayesian Structural Time-Series analyses performed were divided into two parts. First, a time-series analysis of 2014–2020 (rate by month) to determine any change in crime pattern by visual examination of the plots and comparison of the Mean Absolute Percentage Error (a measure of prediction accuracy of forecasting methods; MAPE) pre- and under COVID-19 conditions. With the holdout period being set to 2019 and 2020, respectively. This analysis includes checks for seasonality and smoothing to identify the overall trend to further demonstrate any change visually. Second, a per week analysis is performed for the period January 1-August 31, 2020, with three variables associated with government response and two measures associated with the public response. Stringency Index, Change in Movement and Stay Put. In both cases, 500 Markov chain Monte Carlo draws were used, with the forecast being created by averaging across the draws. The credible interval was generated from the distribution of the Markov chain Monte Carlo (MCMC) draws where the first MCMC iterations (burn-in) was discarded, and a log transformation used to make the model multiplicative. The bsts (v 0.9.5; Scott, 2020) package in R (v 4.0.3; R Core Team, 2020) was used for the analysis. Further, JASP (v0.14; JASP Team, 2020) was used to perform a Bayesian Correlation analysis to confirm the relationship between these variables and changes in murder, as well as identify correlations among variables.

Artificial Neural Networks: Feed-Forward Neural Network

While the Bayesian Structural Time-Series Analysis allows for a deeper analysis of overall trends and the possibility of seasonality the study also sought to determine if linear or nonlinear forecasting would-be better suited for future predictions. To test the data for nonlinearity the BDS Test of independence was performed (Broock et al., 1996). The BDS Test for nonlinearity rejected the H0, that the time series is independently and identically distributed i.e., the data are nonlinear. To test the applicability of a nonlinear modeling method, given the result of the BDS, Feed-Forward Neural Networks with a single hidden layer and lagged inputs for forecasting univariate time series was employed, using the nnetar tool (Hyndman et al., 2020) in R (v4.0.3; R Core Team, 2020). The algorithm uses a Box-Cox transformation with λ = 0.5 to ensure the residuals will be roughly homoscedastic. The nnetar package iteratively simulates future sample paths to build knowledge of the distribution for all future values based on the fitted neural network one thousand times (default) to produce prediction intervals (Boateng, 2017).

Recent studies have demonstrated the predictive power of Artificial Neural Networks (ANN) associated with its ability to approximate any continuous function. ANN are utilized in a wide of variety of applications in engineering, technology and time series forecasting in fields such as biology, finance, medicine and economics social science (Dilek et al., 2015; Fu et al., 2018; Palmer et al., 2008; Walczak, 2021). ANN are robust in their application, which include tasks related with pattern classification, the estimate of continuous variables and time series forecasting (Kaastra & Boyd, 1996). In the latter case, ANN offer several potential advantages with respect to alternative methods such as ARIMA time series models. This is apparent when the problem involves nonlinear data/functions which do not follow a normal distribution, even when apriori information about the properties of dataset are unavailable (Hansen et al., 1999; Oancea & Ciucu, 2013). Further, ANN can perform better than most algorithms when chaotic components exist in the dataset, which is important as most relevant time series possess systematic chaotic components. Additionally, there is evidence that ANN is sufficiently flexible to accommodate for both seasonality and linear trends of a time series and as such may be considered universal function approximators (Montaño Moreno et al., 2011). The ANN consists of three layers; a layer N of input neurons, a layer M of output neurons and at least one hidden layer. In this framework information always feeds forward to the next layer in sequence, starting at the input layer and ending at the output layer. A sigmoid function is used in the hidden layer, which gives it the capacity to learning nonlinear functions, while the linear function is used in the output neuron to estimate a continuous variable.

Results

This section presents the core analyses of the study, which utilized Bayesian Structural Time-Series and Feed-Forward Neural Networks on murder data for the period 2014–2020 at both the monthly and weekly frequencies. However, this is prefaced by presenting the results of tests for normality and nonlinearity in the dataset. First, a test for normality was performed using the fitdistrplus package (v1.1.1; Delignette-Muller & Dutang, 2015) in R, which fits data to a univariate distribution using maximum likelihood estimation. The output of the fitdistrplus indicated that the monthly murder rates for the period 2014–2020 indeed follows a normal distribution. Normality in time series cannot be assumed, as in other areas of statistics, as it is necessary for accurate confidence intervals, especially for horizons greater than 1 since they are based on the distribution of a linear combination of random variables. Second, the test for nonlinearity was performed using the Brock–Dechert–Sheinkman (BDS) Test using the fNonLinear package (v 3042.79; Wuertz et al., 2017) in R. The results of the BDS Test suggest that the null hypothesis, that the data are linearly independent and identical (iid), is rejected for most combinations of m (dimensions) and the time series at the conventional significance level of 95%. Further, since there is almost no discernible linear structure in the levels of the murder time series, the results from the BDS test suggest that there may be nonlinear structures in the data. Any such non-linearity presents challenges to conventional thinking, law enforcement practices and assumptions about the generalizability of research findings. As such, demonstrable evidence of the possibility of non-linearity in the frequency of murder should stimulate further enquiry and deeper analysis to confirm and define the nature of the relationship.

The discovery that murder may contain nonlinear components adds a new lens through which the nature of this form of criminality can be understood i.e., considered as a deterministic system. If the system has nonlinear and deterministic properties, then future behavior would follow a unique evolution where the relationship between the change in inputs/interventions are not proportional to the outcome. Therefore, it would explain the greater difficulty in predicting long-term recurrent behavior in comparison to cases where systems are fully linear. Further, it is sensitive to initial conditions as this can determine the degree to which the intervention affects the outcome.

Additionally, the existence of a nonlinear system would allow the consideration of attractors and basins of attraction in future discussion of changes in murder rates and how they relate to exogenous shocks. The concepts of attractors and basin of attraction suggest that for nonlinear systems there are subsets of state space (equilibrium or steady states) called attractors which a system approaches given a set of initial conditions (basin of attraction) that facilitates long-term behavior that approaches the attractor. In the case of murder, this can potentially explain why the introduction of an exogenous shock such as COVID-19, that through its complex relationship with other initial conditions leads to long-term behaviors that approach a new steady state. This shift to a new steady state is illustrated by the lack of proportional intuitive change in the system after the changes resulting from the intervention are altered i.e., murder rates don’t spike or continue to decrease after restrictions in movement are removed.

Bayesian Structural Time-Series Analysis

Several analyses were conducted using Bayesian Structural Time-Series analyses to determine changes in murder patterns under-COVID-19, examining murder in general and split by classification. The first assessment sought to identify the presence of any deviation between the expected evolution of the frequency of murder compared to the actual frequency under-COVID-19 conditions by generating a time-series plot with 2019 and 2020 as the holdout period, respectively. Further, the underlying components of trend and seasonality were extracted and represented graphically to aid in identifying changes in the murder rate over time. In Fig. 1, which shows the results of the Bayesian Structural Time-Series forecast, it can be observed that unlike much of the plot, the model provides a poor forecast with a Mean Absolute Percentage Error (MAPE) of 36.71% for the period under COVID-19 conditions. This is in comparison to a MAPE of 14.22% when 2019 is used as the holdout period for the model (not shown). This means that the predictive accuracy of the model decreased under-COVID-19 conditions i.e., the murder rate was not in line with the expected outcome. The change in the pattern of murder is seen in Fig. 1 and represented by the section after the vertical broken line but is made clearer in Fig. 2. Figures 1 and 2 show that murder trend downwards under-COVID-19 conditions. Further, Fig. 2 shows a drop in murder in 2015 followed by a steady upward trend until mid-2019 when it started to descend. However, in 2020 the rate of descent increased markedly under COVID-19; co-incident with the onset of stringency measures such as government-mandated restriction in movement, closing of businesses and increased policing. This absence in the consistency of findings may be a more accurate representation of reality than previous homogenous results suggest.

Fig. 1.

Fig. 1

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Bayesian Structural Time Series Plot of Murder for 2014–2020, using 2020 as the holdout

Fig. 2.

Fig. 2

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Trend and Seasonality component of Bayesian Structural Time Series Plot of Murder for 2014–2020

The above results show a decrease in murder, but does this change apply to murder in general regardless of their classification? Figure 3a-g shows trend components of the time-series for the classifications of ‘Domestic’, ‘Gang’, ‘Narcotics’, ‘Robbery’, ‘Altercation’, ‘Revenge’ and ‘Other’. All classifications except ‘Other’ show decreases in occurrences in 2020, however, only ‘Domestic’ shows a clear sharp decrease in occurrences during the COVID-19 pandemic. The connection between COVID-19 and the decrease in the gang, narcotics, revenge, altercations and robbery-related murder is difficult to attribute solely to stringencies imposed in the ROTT at the beginning of the COVID-19 pandemic as these crimes were trending downward before COVID-19. The degree of the relevant slopes in the trend component of the classes also do not provide a clear change in slope to suggest an enhanced effect, but rather a continuance of a downward trend. This is not to say COVID-19 did not have an additive effect to other factors which led to these downward trends, as it altered the ‘initial conditions’ that preceded the change in murder patterns. The fact that there is a clear change in murder associated with domestic violence seems somewhat counterintuitive, given that numerous reports and studies have suggested a spike in domestic violence under-COVID-19 (Campbell, 2020). Stickle and Felson (2020) highlighted that factors previously thought to drive crime are remaining constant or increasing yet crime fell steeply under-COVID-19 conditions contrary to criminological theory. This finding adds to the discourse of the difficulty of readily explaining the crime phenomenon under-COVID-19 with criminological theory. For example, the RAT suggests that an increased likelihood of the spatiotemporal convergence of an offender and a suitable target should lead to a greater probability of a crime event. However, counter to this model although stay-at-home orders would effectively increase the time victims of domestic violence spend with an offender, domestic murder decreased. Further, the circumstances often attributed to impacting crime such as strain and stress have increased during the pandemic, yet murder decreased. Even in a domestic setting where people may be confined for a prolonged period due to the government-imposed restriction in movement. If this finding is confirmed or corroborated by future research, some of criminology’s key theories and assumptions may need reevaluation.

Fig. 3.

Fig. 3

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a-g Trend analysis of the murder rate for the period 2014–2020 separated by classification

Bayesian Structural Time-Series Analysis 2020 (Per Week Assessment)

To determine the importance of the key changes in the murder rate associated with the COVID-19 pandemic as highlighted in previous research, namely changes in the mobility of the population due to governmental restrictions, a per week time series analysis was performed for the period January 1 to August 31, 2020. This both provided a dynamic assessment of changes in murder as the pandemic progressed (changes in social conditions) but was also necessary given that the external variables (regressors) of ‘Stringency Index’, ‘Stay Put’ and ‘Relative Change in Movement’ were only available for 2020. Figure 4 shows the results of the analysis, in which the trend component suggests a downward trend in murder from February to August, 2020. However, the regression component shows fluctuating levels of contribution by the regressors to the model. The changes in the overall contribution of the regressors if correlated (having a linear relationship with murder) should have a similar pattern to the trend or an inverse pattern (if regressors have negative coefficients). However, after the initial increasingly negative effect and the corresponding decrease in the murder rate, the decrease in the effect of the regressors is not accompanied by an increase or stalling of the downward trend of murder. This does not correspond to normal linear relationships, which suggests that exogenous shock has a short-term effect and once the change associated with the shock is removed the resultant change should stall and conditions may return to normal. If the data followed a linear relationship with the regressors when stringency measures decreased (corresponds to lower Stringency index, a lower relative change in movement and a lower percentage of persons Staying Put) the decrease in murder should have stalled or seen an increase.

Fig. 4.

Fig. 4

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Plot of Trend, Seasonality and Regression component of a Bayesian Structural Time Series for the Period January to August, 2020

Further an examination of the average correlation coefficient of the variables and the inclusion probabilities obtained from the regression component of the time series suggests that the probability of any of the regressors being in the true model is less than approximately 1% i.e., these variables are poor predictors of the murder count during the COVID-19 pandemic.

The possibility that the change in crime patterns under COVID-19 is not predicted by the restriction of movement attributable to the stringency of the government’s response or the adherence of the public seems counterintuitive. Therefore, an additional assessment was performed using Bayesian Correlation with robustness checks to provide further evidence. The robustness check is designed to demonstrate that the choice of priors does not bias the outcome and hence adds to the validity of the findings. The results of the test (Online Resource 5) show that there is only anecdotal evidence [lg (BF10) = 20.98] for the relationship of ‘Relative Change in Movement’ and ‘Stay Put’ to Murder. Whereas there is moderate evidence [lg (BF10) = 1.32] for a correlation between the ‘Stringency Index’ (stringency of government implemented restrictions) and murder. In the case of ‘Murder’ and ‘Stay Put’, it is still noted that, as is expected, the nature of the correlation is inversely proportional (r = -0.356) i.e., murder counts decreased as these variables increased. While murder appears to be positively correlated to ‘Relative Change in Movement’ (r = 0.233). Further, as expected there is a strong correlation between the variables of ‘Stay Put’, ‘Relative Change in Movement’ and ‘Stringency Index’. The strongest correlation being between the ‘Stringency Index’ and the variable of ‘Stay Put’ (r = 0.928), as the ‘Stringency Index’ score decreased the percentage of persons staying put also decreased. Similarly, it is expected and intuitive that ‘Relative Change in Movement’ and ‘Stay Put’ would-be correlated as they measure similar behavior patterns i.e., change in the movement of the population. Lastly, the ‘Relative Change in Movement’ is also strongly correlated to the ‘Stringency Index’, however, the strength of support for this correlation is half of the value for obtained for ‘Stay Put’. This suggests that the restriction imposed by the government may be more effective in keeping people within a set small geographic space than controlling their level of activity. Overall, the assessment of the correlation supports the findings given by the time series that the variables of ‘Stringency Index’, ‘Relative Change in Movement’ and ‘Stay Put’ are either not strongly correlated or have a weak effect on murder rate and as such are poor predictors of the change in murder rate under COVID-19 conditions.

Artificial Neural Network: Feed-Forward Neural Network

As indicated in the introduction, given a positive test for nonlinearity, the study also sought to determine if a nonlinear method of forecasting would provide a better prediction of murder during the COVID-19 pandemic. Similar to the time series assessment using the Bayesian methods, tests were carried out using an Artificial Neural Network (ANN) with 2019 and 2020 as holdout periods, respectively. The neural network forecast derived using the nnetar package when the hold out was 2019 resulted from the averaging of 20 networks, each of which was a 4–2-1 network with 13 weights with sigma square estimated as 1.03. The performance of the model was given by a MAPE of 11.54% compared to the MAPE of 14.2% for the Bayesian Structural Time Series model. The neural network obtained when the holdout was 2020 took the form of an averaging of 20 networks, each of which was a 5–3-1 network with 22 weights with sigma square estimated as 0.7817 (Online Resource 6). The performance of the model was given by a MAPE of 8.52% compared to the MAPE of 36.71% for the Bayesian Structural Time Series model.

It is clearly shown that in both the 2019 and 2020 versions of the ANN performed better than their linear counterparts. This means that murder rates were modelled better using a nonlinear method, which is likely reflective of it possessing nonlinear components. This can be suggestive of several factors including some murders are follow-on to other murders, diminishing returns on exogenous changes and/or seasonal effects are adjusted based on occurrence of murders in the previous season. Further, the increase in width of the neural network from a 4–2-1 with 13 weights to a 5–3-1 with 22 weights correlated to increased predictive performance i.e., a greater level of predictive complexity. Notably, there was one additional input variable (4 to 5) and an additional interaction suggested by the increase of neurons in the hidden layer (2 to 3). The increase in the number of input neurons suggests an increased number of lagged terms in the series i.e., more historical data are used in making a forecast. This is demonstrative of the degree of dependence of current crime events on previous events. The increase in the number of neurons in the hidden layer suggests an increased capacity to learn possible nonlinear functions. Thus, the increased performance in the 5–3-1 multilayer neural model further supports the existence of nonlinear components in the data.

Discussion

The analyses performed in this study have identified a change in the pattern of murder in Trinidad and Tobago while under COVID-19 restrictions. The time-series analyses performed using Bayesian Structural analysis show that the occurrence of murder in 2020 is less than expected given observed trends before the COVID-19 pandemic. Further, a comparison of murder month-over-month for a seven-year period shows that 2020 has had the lowest murder count for the seven-year period for the months February to August, which coincide with the implementation of COVID-19-related government responses. Therefore, conditions/changes resulting from the pandemic either directly resulted in a decrease in the murder count or had an additive effect on factors that previously resulted in downward trends or both.

The decrease in murder under-COVID-19 conditions compared to pre-COVID-19 conditions appears to be independent of classification to a large degree. Six of the seven classes examined saw a marked decrease in murder compared to the previous year and in some cases were the lowest in a seven-year period. The percentage decrease in these six classes ranged from18% to 60% i.e., the change was not consistent among classifications. Further, a comparison of the changes in the murder rate for each class given in Table 1 to the trend analyses in Fig. 3a-g does not suggest any link to the slope (rate and direction of change in murder) before the pandemic. However, the inconsistency in effect does not allow for a decisive statement on the consistency of the effect on the various classes.

Contrary to the other classes, the murder class of ‘Other’ showed a spike during the COVID-19 pandemic. All the murder in this class during the period February to August, 2020 were from unclassified murder i.e., murder for which the motive is unknown to law enforcement. The drastic increase in this class of murder is coincident with the implementation of COVID-19 restrictions. The only noticeable difference between murder classified as ‘Other’ and the remaining classes is that it was increasing before the pandemic. This is potentially suggestive of increased ability by offenders to conceal the motive of murder or a decrease in law enforcement’s ability to classify these criminal occurrences. Since this was increasing before COVID-19 the changes resulting from COVID-19 are not causative of the phenomena. However, given the drastic change in the rate of increase the COVID-19 changes may have acted as an exogenous shock that propagated the initial change. Future studies after a longer period would-be necessary to determine if this change was emergent and whether it led to a new equilibrium state.

While the analyses performed in this study have shown that there has been a change in murder patterns under-COVID-19, the empirical evidence does not support a linear relationship between murder and the introduction of stringency measures. The results of the study suggest that murder has non-linear components and that there is a non-linear relationship between the murder rate and COVID-19 conditions. As such, murder may be sensitive to initial conditions (deterministic) but not necessarily to a degree that an approximation of current conditions cannot be used to approximate future outcomes to a limited extent (some valuable information can be obtained from linear modelling). This is important in the international context given that differences in conditions before a shock provided by the COVID-19 pandemic can result in vastly different outcomes i.e., similar causes do not lead to similar effects. This implies a dependence on historic changes for future change, which may explain why different locations may experience different results from the same changes made due to COVID-19 both in degree and duration. This phenomenon has been seen in the varied changes of murder rate for the countries while under-COVID-19 conditions, with some locations showing a drop, some spiking and others remaining steady. The observed decline in murder in most classes before 2020 (See Fig. 3a-g) in Trinidad and Tobago may have created optimal conditions for the COVID-19-related changes to have a greater effect than in other locations. Further, even within the classifications of murder, the potential importance of initial conditions is seen as the only class (‘Other’) which trended upwards before COVID-19 showed a spike under-COVID-19 condition. Additionally, the degree of change was non-congruent with the level of change seen with the other classes, it was significantly larger.

Further, the existence of nonlinear components can potentially explain the change in murder coinciding with COVID-19-related restriction yet not being found to be correlated with them for the period under investigation. Figure 4 shows that the initial decrease in murder coincided with the implementation of stringency measures, however, subsequent changes were not reflected in the murder count. The combination of evidence of resistance to fluctuation in COVID-19 conditions and seasonality can jointly suggest the existence of a basin of attraction and a process of self-organization, which exists because of the system adjusting and moving from one state of equilibrium pre-COVID-19 to a new state under-COVID-19 condition. However, it should be noted that initial observations after a shock in nonlinear systems can be misleading. For short periods the effects of changes in different systems can seem similar but eventually diverge if the initial conditions in each system are different or if the basin of attraction approaches a different attractor. As suggested here the system can move to a new phase if the external force is sufficient or change temporarily until the system reorganizes to return to the previous state of equilibrium. In this specific scenario it would suggest that restriction to movement has a point of diminishing return. This means that after a point, continued or increased restrictions will have a decreasing effect on murder. As such, long-term solutions to decreasing murder would require more than simple restriction in movement for a sustained effect (Kelly et al., 2021). Further assessment will be required to determine if the observed changes persist, which would suggest a new equilibrium or if the system will adapt to the changes and the murder rate eventually begins to return to prior levels as observed by Kelly et al. (2021).

Lastly, examination of murder for the period 2014 – 2020 demonstrated opportunities for improved performance of forecasting murder using algorithms such as Feed-Forward Neural Networks that can solve continuous nonlinear functions. In the time-series analyses, the nonlinear model outperformed the linear model for prediction of murder rate both when 2019 and 2020 were used as holdout periods, respectively. Further, even after the exogenous shock associated with the COVID-19 pandemic occurred the MAPE of the Feed-Forward Neural Network was still lower than both forecasts produced by the Bayesian Structural Time Series. Thus, making Feed-Forward Neural Network feasible for future consideration in murder rate forecasting. However, Bayesian Structural Time Series remains useful in its ability to model linear aspects and its extraction of trend, seasonality and regression components to provided deeper analysis of the time series.

There is no disputing the fact that COVID-19 conditions in Trinidad and Tobago coincided with the lowest murder rate in 7 years and further this drop started in February, 2020, the month in which the COVID-19 response first started according to Coronavirus Government Response Tracker (OxCGRT). The ongoing difficulty with explaining the changes associated with COVID-19 and the inconsistency of these changes may be associated with the restrictive assessment of changes based on linear dynamics, particularly the importance of initial conditions. However, the use of nonlinear dynamics to examine the phenomenon in its complexity rather than using deconstructive methods may hold greater insight. Further, the use of nonlinear predictive methods may provide a forecast with smaller errors and hence be more informative to stakeholders, such as law enforcement and policymakers.

Conclusion

These findings have potential implications for both criminology and crime forecasting. First, criminology must consider the possibility of a duality in the change in crime patterns. The rise and fall of murder would not be only due to the influence of exogenous shock due to linear dynamics. Rather, the translation of shocks into an observable change in murder may be partially self-generating, propagating like a disease that reaches a breaking point then spreads explosively (McDowall, 2002). The linear model makes key assumptions that are likely untrue in reality; 1) murder will change by a fixed amount after the same change in external variable and that the change will dissipate once the variable is removed, 2) long-term change is only possible due to the sustained addition of the external variable (McDowall, 2002). However, nonlinear dynamics allow the researcher to account for the possibility that the effect an external variable has on a system is dependent on the history of the series. Further, dependent on the nature of the change a new basin of attraction can form. Therefore, even after the removal of the external variable, the system will continue to self-organize to maintain the new phase state. The point being that for murder, linear and nonlinear relationships between effectors and the resulting change are not mutually exclusive.

Similarly, the predominant use of linear predictive models for the prediction of crime such as the ARIMA model may need to be revisited. Bayesian Structural Time Series models while linear have a marked edge on traditional models such as the ARIMA, as it includes uncertainty and is more transparent: it provides insight into underlying patterns and allows the assessment of the importance of variables that are not directly extractable from the data on predicting future outcomes. However, given that murder is potentially nonlinear and sensitive to small changes in initial conditions it may be better predicted by more complex nonlinear algorithms such as neural networks. As shown in this study the Feed-Forward Neural Network outperformed the Bayesian Structural Time Series mode, both pre- and under COVID-19 pandemic conditions.

This study has highlighted some novel and unexpected interactions between the COVID-19 pandemic, measures put in place by the government to mitigate the effects of the virus and murder rates (for different categories of murder) with a particular focus on Trinidad and Tobago. The available evidence suggests that these findings may have wider applicability to other countries. As the contagions caused by the virus and mitigating measures (vaccination, etc.) mature, the longer-term impact of these factors on crime will, no doubt, be of great interest to criminologists and others.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file1 (PDF 206 KB) (205.7KB, pdf)
Supplementary file2 (PDF 206 KB) (205.7KB, pdf)
Supplementary file3 (PDF 206 KB) (205.7KB, pdf)
Supplementary file4 (PDF 243 KB) (243.2KB, pdf)
Supplementary file5 (PDF 243 KB) (243.2KB, pdf)
Supplementary file6 (PDF 243 KB) (243.2KB, pdf)

Data Availability

The data that support the findings of this study are available from the corresponding author, upon reasonable request.

Declarations

Conflict of interest

None to report.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Data Citations

  1. Wick SE, Nagoshi C, Basham R, Jordan C, Kim YK, Nguyen AP, Lehmann P. 2017. Patterns of cyber harassment and perpetration among college students in the United States: A test of routine activities theory. International Journal of Cyber Criminology. [DOI]

Supplementary Materials

Supplementary file1 (PDF 206 KB) (205.7KB, pdf)
Supplementary file2 (PDF 206 KB) (205.7KB, pdf)
Supplementary file3 (PDF 206 KB) (205.7KB, pdf)
Supplementary file4 (PDF 243 KB) (243.2KB, pdf)
Supplementary file5 (PDF 243 KB) (243.2KB, pdf)
Supplementary file6 (PDF 243 KB) (243.2KB, pdf)

Data Availability Statement

The data that support the findings of this study are available from the corresponding author, upon reasonable request.

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