Sample

Details of the sampling procedure have been reported extensively elsewhere [29, 30] and are summarized here. The Study of Peers, Activities and Neighborhoods (SPAN) is a two-wave panel study among adolescents in The Hague, the Netherlands, and its suburbs. Data collection of the first wave took place between October 2008 and May 2009. Data collection of the second wave took place between November 2010 and June 2011. The study included a self-report questionnaire and a personal space-time budget interview, both of which were administered at the schools that the respondents attended. In the second wave, if respondents had left school, the interviews were held at other semi-public locations. All instruments were based on the materials of the Peterborough Adolescent and Young Adult Development Study (PADS) [31, 32]. In the present analysis, only the space-time budget data collected in the first wave is used, because this maximizes the time period over which offences could be observed that were perpetrated after the space-time budget interviews in which activity space was reported.

In the first wave of the study, 40 schools for secondary education were approached, of which 10 agreed to participate in the study, allowing students to participate in the study during school hours. The main reasons why schools refused to participate in the study were ongoing or recent participation in other research, and concerns about interference with regular school activities. The parents of the students were informed about the study and could easily refuse participation in both waves (passive consent).

The sample was designed to be conducted among a cohort of 1st graders (ages 12–13) and a cohort 4th graders (ages 15–16). In the second wave, two years later, most members of the younger cohort were in 3rd grade, while those of the older cohort were either in 6th grade of secondary education, in the 1st or 2nd grade of follow-up education, employed or jobless).

The sample was representative for adolescents in The Hague of these age groups in terms of gender and ethnic background. However, due to the selection of the 10 schools it contained an overrepresentation of adolescents enrolled in schools preparing for lower-level educational qualifications (18% against 15% in the population) and higher-level educational qualifications (23% against 19% in the population) and an underrepresentation of the intermediate group (59% against 66% in the population). Reference data for The Hague were calculated from data accessed at website https://denhaag.buurtmonitor.nl.

In total, 843 pupils participated in the first wave and 615 (73%) participated again in the second wave. The main reason for the 27% attrition rate is that students who had left the school they attended in the first wave were difficult to contact. Nonresponse analysis shows that boys, older and more delinquent respondents have somewhat higher attrition rates.

At the end of the second wave questionnaire, respondents were informed that the researchers were interested in collecting information about them from authorities like school, municipality and police, and they were asked for their written consent. Of the 615 that participated in the second wave, 517 (84%) gave their consent.

Space-time budget interview

A space-time budget interview is a structured face-to-face interview conducted by a trained research assistant. I used a translated version of the materials developed in the Peterborough Adolescent and Young Adult Development Study (PADS+) The interviews took place during weekdays and involved the reconstruction of all major activities and whereabouts of the adolescents over four recent days, with a Friday and Saturday always being included, and Sundays always being excluded (e.g., interviews on Monday would cover the previous Wednesday to Saturday, interviews on Wednesday would cover the previous Friday, Saturday, Monday and Tuesday). Relative to the reference proportion of 1/6 = .167, the day-of-week selection procedure generates an overrepresentation of Fridays (.249) and Saturdays (.250) and underrepresentation of Mondays (.106), Tuesdays (.114), Wednesdays (.152) and Thursdays (.129). To correct for this potential bias, in all subsequent analyses, Mondays through Saturdays were weighted by their inverse proportions (the weights are 1.57, 1.47, 1.10, 1.29, 0.67 and 0.67 respectively. Despite the considerable variations between these six weights, the descriptive results and the model estimates presented below were almost indistinguishable from the unweighted versions that I used for comparison and robustness checks.

As for most people the start of the day is when they wake up, a day was defined to start at 6am in the morning. Interviewers were suggested to start the interview with the most recent day and proceed backwards in time, but this was not strictly required and other sequences were acceptable if they seemed more convenient for the participant.

Detailed information was collected about the main activities of the adolescents for each hour of the day. Locations of activities were recorded with the help of paper maps printed on A3-size paper. The maps were similar to regular paper maps used for wayfinding and orientation. They were overlaid with a 76×67 grid of numbered 200 by 200m cells. To indicate the location of an activity, participants could point or mention the number of the grid cell (S1 Fig). Over 93% of the time was spent inside the study area, which covered 203km² (of which 182km² are on land). The remaining hours were assigned geographical coordinates with lower resolution, typically the centroid of a town or district in another city. S2 Fig shows where the 843 participants spend their time during the four days recorded in the space-time budget instrument.

Compared to data automatically extracted from mobile phone networks (e.g., [8, 10, 20, 22]), space-time budget data has two disadvantages. First, because of the high fieldwork costs, samples sizes are generally limited to less than 1,000 whereas mobile phone network data typically include over 40,000 phone users. Second, because of participants’ memory limitations, reliable space-time budget data cannot cover more than a few days whereas mobile phone data often cover multiple months or even years. Space-time budget data have three advantages over mobile network data. First, whereas networks only record the locations of phones when they are actively used, space-time budget data include continuous (hour by hour) measures. Second, whereas the spatial resolution of mobile phone network locations is limited by the density of towers, the spatial resolution of space-time budget data can be chosen by the researcher. Third, whereas mobile network data are population data of all phone users whose phone activity level must reach a certain threshold to be useful for research, space-time budget data can be conducted samples that are representative of the population under study.

Police records

Police records were screened for evidence of crime involvement of the 517 participants who consented that additional information about them be collected. The police records allowed detailed reconstruction of the respondents’ criminal records (i.e., which offenses they had been charged with and the times and locations of these offenses).

Access to police records was provided by the unit The Hague of the Dutch National Police. The police records were drawn from the HKS information system. The HKS system is used for investigative purposes and contains data about all persons who have been suspected of having committed a crime serious enough, and supported by enough evidence, to warrant prosecution. The HKS contains information about the complete criminal record of the individuals. The system has been taken out of service in 2013, making 2012 the last year over which full and reliable crime data can be obtained.

In the police files, records of 70 (14%) of the 517 participants were traced that indicated involvement in criminal conduct. The total number of crime incidents was 178, indicating that some had been involved in multiple crimes. The crimes included a wide variety of property and violent crimes, including theft, burglary, assault, robbery, drug dealing and public order offences. No selections were made with respect to crime type.

Close inspection of the space-time structure of the crime data demonstrates that some pairs of crimes took place on the same day and at the same address. In these cases, it appears that multiple crimes have been reported that were part of the same incident (for example, theft escalating into assault, or drug dealing leading up to robbery). To prevent any conclusions about repeat locations based on artefacts, I selected only the 165 crimes that were the first to take place in a given location on a given day. S1 Table presents the number of offenses per offender. In S3 Fig, I overlaid the locations of the 165 offenses on a map of the aggregated whereabouts of the 70 offenders who committed these offenses.

The crimes took place between at least 35 days and no more than 1484 days (4 years) after the space-time budget interview was administered, with a mean of 791 days (2 years and two months, see S2 Table).

Police data are not collected for the purpose of scientific research, and they are incomplete for two reasons. First, police data on crime exclude those crimes that victims did not report to the police. Based on the International Crime Victimization Survey (ICVS), it is estimated that in western countries on average about 50 percent of crime victims report to the police, a figure that is 58 percent in The Netherlands [33]. Second, police data on offenders are incomplete because they exclude offenders who are not apprehended. Internationally, the percentage of reported crime for which an offender is identified (the clearance rate) is 34 percent, but it is only 13 percent in the Netherlands [34]. Since both selection mechanisms—reporting and clearance—are unlikely to be random, generalizations based on police data must be made with great caution.

Points of interest

I used numbers of points of interest as a generic measure of crime opportunity for each of the grid cells in the study area. The points of interest in the period 2008–2010 were extracted from the LISA, a commercially available geo-referenced dataset on all branches of businesses and facilities in The Netherlands, including both commercial and public facilities (government, education, health care, recreation; see www.lisa.nl).

Radius of gyration

Following prior research in human dynamics (e.g., [10]), the characteristic size of the area covered by the mobility of a single person up to time t is indicated by his or her radius of gyration where t = 1 … 96 represents the number of hours measured, starting at 6am on the first day, represents the person’s position at time i and = is the person’s center of mass. Note that measure is backward-looking only, and thus the center of mass at time t is a summary measure of the locations visited up to and including time t. For the complete four days covered in the space-time budget, t = 4 × 24 = 96.

Predictability

Following [8], the predictability of an individual’s whereabouts was derived from entropy measures of the sequence of 96 locations (i.e., 200 × 200m grid cells) reported in the space-time budget. It varies between 0 (completely random) and 1 (completely determined). Random predictability Π^rand is a measure of how well an individual’s whereabouts can be foreseen if only the set of unique locations visited is known. Temporal uncorrelated predictability Π^unc applies to the case in which the number of hours spent at each location is known as well, but not the temporal order of visits, and maximum predictability Π^max to the case where in addition the temporal order is known too. By definition, Π^max > Π^unc > Π^rand.

Statistical model

I use a discrete spatial choice approach [35] to explain the offender’s choice of a crime location and test the hypotheses. Following the random utility maximization postulate and according to a conditional logit model [36], the offender chooses a single location from the full choice set of 4558 locations (67 × 67 = 5092 grid cells of 200x200m each, minus 544 grid cells completely located on the North Sea). Offender i chooses the location j that maximizes a utility function (1) where U_ij is the utility that offender i derives from targeting at location j, V_ij is the deterministic part of utility that captures the knowledge of the analyst, and ε_ij is a random disturbance term that captures the analyst’s uncertainty. The deterministic part of utility V_ij is a linear function of the attributes of individuals and locations: (2)

The seventeen terms on the right-hand side of the equation are a weighted sum of the following attributes of locations and:

1. = subject i spent 1–4 hours in location j (0,1)
2. = subject i spent 5–16 hours in location j (0,1)
3. = subject i spent 17–96 hours in location j (0,1)
4. = subject i spent time in a location 1^st order contiguous to location j (0,1)
5. = subject i spent time in a location 2^nd order contiguous to location j (0,1)
6. = subject i spent time in a location 3^rd order contiguous to location j (0,1)
7. = subject i spent time in a location 4^th order contiguous to location j (0,1)
8. = subject i spent time in a location 5^th order contiguous to location j (0,1)
9. = subject i committed a prior crime in location j (0,1)
10. = subject i committed a prior crime in a location 1^st order contiguous to location j (0,1)
11. = subject i committed a prior crime in a location 2^nd order contiguous to location j (0,1)
12. = subject i committed a prior crime in a location 3^rd order contiguous to location j (0,1)
13. = subject i committed a prior crime in a location 4^th order contiguous to location j (0,1)
14. = subject i committed a prior crime in a location 5^th order contiguous to location j (0,1)
15. = at least one catering business in location j (0,1)
16. = at least one retail business in location j (0,1)
17. = at least one school in location j (0,1)

S4 Fig provides a visual example of how variables were coded. I calculated spatially contiguous bands up to the 6^th order. Because I did not find significant effects beyond 5^th order contiguity, and because the literature suggests proximity effects up to 2 or 4 bands (200–400 meter), I did not calculate contiguity beyond the 6^th order.

The values of β₁ to β₁₇ are parameters that are estimated from the data. Their sizes, relative to 0 and relative to each other, their directions and their standard errors determine whether the hypotheses are confirmed or rejected (according to the theory, all β > 0). The values e^β are odds ratios, and represent the factor by which the odds of being chosen increase (odds ratio > 1) or decrease (odds ratio < 1) with each one-unit increase of the right-hand side variables. As all right-hand side variables are binary, the odds ratios are ratios of the odds of the ‘1’ category and the odds of the ‘0’ category.

If the unobserved random utility components ε_ij are independently and identically distributed according to an extreme value distribution, the conditional logit model [36] can be derived. This statistical model allows us to estimate the β parameters from empirical data. According to the conditional logit model, the probability that offender i chooses location j is given by: (3)

Evaluation of predictions

To evaluate the quality of the prediction, I use a simple and intuitive measure. After model estimation, for each crime in the data all 4558 locations in the study area are lined up in ascending order of predicted probability P_ij according to the model estimates. The model fit measure is the rank number of the grid cell where the crime was actually committed, divided by the total number of 4558 grid cells, averaged over all crimes. It reflects the proportion of the study area with a lower average predicted probability than the locations actually chosen. The value would normally range between 1 (perfect prediction) and .50 (the expected average value for a null model with random predictions) although predictions worse than random are possible. Average rank orders are assigned in case of ties (i.e. multiple grid cells with equal predicted probabilities).

Mobility differences between sample subgroups

Before testing hypotheses, I describe four key features of the mobility of the study participants, argue that the observed patterns are consistent with those reported in prior research with different samples and methods [8, 10, 20], and demonstrate that the patterns of (future) offenders are hardly different from those of others.

For all groups, the number of unique locations roughly follows a Gaussian distribution in the range 1–15, with a median value of 6 locations. Individuals spend 60 percent of the time in their most frequently visited location (home), and another 15 percent in their second most visited location (typically school), their radius of gyration follows a lognormal distribution with a mean of 3.2 km, and their predictability Π^max equals 0.96 on average, slightly above the values found in general populations by prior research [8, 19].

As the four panels in Fig 1 also show, offenders are very similar both to non-offenders and to the two groups of whom it is unknown whether they are offenders. Except for the finding that on average the unique number of visited locations is somewhat larger for offenders than for the other groups, the cumulative numbers of locations visited, the radius of gyration and the predictability measures are similar across the four groups. Thus, as far as routine mobility is concerned, adolescent offenders are not very different from other adolescents.

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Fig 1. Key features of mobility are similar amongst subgroups of the sample.

The sample can be segmented into four mutually exclusive subgroups: (1) participants (n = 228) who could not be asked for permission to link their registry data to their survey responses, (2) participants (n = 98) who did not give permission to link their registry data to their survey responses, (3) participants (n = 447) who gave permission and did not commit crimes subsequently, and (4) participants (n = 70) who gave permission and who became offenders during the study period. (A) On average, offenders visited 1 location more than individuals in the other three groups (see S4 Table). (B) All participants spent about 75 percent of their time in their two most visited locations (home and school). (C) The radius of gyration is approximately 3km and displays minor but insignificant differences between the four groups (see S5 Table). (D) The three predictability measures differed slightly across the groups, with a very slight tendency for offenders to be less predictable (see S6–S8 Tables). Densities in (A), (C) and (D) were calculated with the Gaussian kernel density estimator proposed by Scott [37]. Values are not labeled along the Y axis is they have no useful interpretation here.

https://doi.org/10.1371/journal.pone.0210733.g001

The key features themselves are similar to those reported elsewhere on different samples and with different spatial and temporal scales [8, 10, 20], although the short observation period of four days and the fixed temporal resolution of one-hour slots are measurement limitations that likely underestimate the total number of visited locations observed [22] but not the radius of gyration. Furthermore, the young age of the sampled cohorts most likely causes the mean radius of gyration to be smaller than in the general population, because the average commute to school is shorter than the average commute to work.

Fig 2 demonstrates how the cumulative number of locations visited and the radius of gyration develop over the four days reported in the space-time budget interviews.

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Fig 2. Development of number of unique locations visited and radius of gyration over time.

(A) The cumulative number of visited locations grows linearly over time, remains stable during sleeping hours and does not reach an asymptotic stable level within the observation period of four days. (B) Apart from the first few hours on the first day covered, the radius of gyration grows sub-linearly, slightly decreases during sleep due to 9 hours of immobility, and reaches a stable level of approximately 3km after two days already. The adolescents slept almost 9 hours per day on average, typically at home during the night between 22:00 and 7:00.

https://doi.org/10.1371/journal.pone.0210733.g002

Modeling location choice and hypothesis tests

Within four years after completing the first space-time budget interview, 70 (14%) of the 517 who had given permission to have their data linked to other sources had committed at least one offense in the study catchment area that was brought to the attention of the police. Together these 70 participants committed 165 detected offenses in the study area. Based on their whereabouts reported in the space-time budget interview and on previously committed offences registered by the police, I attempt to predict the locations of subsequent crimes that the offenders perpetrated. I use a discrete spatial choice approach to explain the offender’s choice of a crime location and test the hypotheses.

The findings reported in Fig 3 provide support for most of the six hypotheses. Except for the presence of retail and catering businesses, estimates and confidence intervals of all attributes are far above the baseline value of 1, and are thus statistically significant. Therefore, locations in and around offenders’ activity spaces and prior crime locations are much more likely to be targeted than other locations. The estimated differences on the temporal and spatial dimensions—hours spent at a location, and distance from a location—do confirm the expected pattern, but they are not all statistically significant. For example, grid cells that are first-order contiguous to the offender’s activity space (near activity (1^st)) are not significantly more likely chosen than those that are second-order contiguous, although both are more likely chosen than those that are third-order contiguous. Similarly, differences between first-order, second-order and third-order contiguity to prior crime locations are not statistically significant. More generally, the confidence intervals around the point estimates are rather large. This is partly due to the sparseness of the data (165 crimes relative to the total number of 4558 grid cells), but it also indicates that there is a fair amount of heterogeneity that is not covered by the explanatory variables.

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Fig 3. Quality of the explanation and tests of the hypotheses.

Estimated effects (dots) and 95% confidence intervals (lines) of the conditional logit model (70 adolescents, 165 crimes and 4558 locations). H1 (activity space): All locations within activity space (activity 1–96 hours) are more likely to be chosen for committing crime than those outside activity space. H2 (usage): Frequently used locations are more likely to be targeted than locations less often used (non-significant). H3 (exploration): The likelihood of being targeted decreases with the distance from activity space. H4 (repeat location): previously targeted locations are more likely to be targeted than locations not previously targeted. H5 (near repeat location). The likelihood of being selected decreases with the distance from the previous crime (partially and non-significant). H6 (opportunity) Locations with schools, retail businesses and catering businesses are more likely targets.

https://doi.org/10.1371/journal.pone.0210733.g003

Accuracy of predictions

For six models of increasing complexity (see S10–S14 Tables), the predictive accuracy is displayed in Fig 4. Taking into account that the individuals’ activity spaces were measured during only four days and on average 21 months before their first crime during the observation period, the predictive accuracy is surprisingly high, with the true location situated in the 95^th percentile of the predicted locations in the most comprehensive model. Without the inclusion of opportunity structure measures (which are not included in the preferential return and spatial exploration model), the true location is in the 83^rd percentile, still high but substantially lower, and probably reflecting that four days is a period too short to fully capture our complete activity spaces.

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Fig 4. Accuracy of the predictions.

A simple and intuitive measure of model fit is the proportion P of potential crime locations with a lower predicted probability than the actual crime location. P = 1 in case of a model with perfect prediction, while P = .5 in case of random choice. Increasing model complexity along the horizontal axis improves predictive quality (black dots). The shape of the density (blue ‘hourglasses’) of the accuracy measure P show thats its distribution is bimodal, and that model fit improvement is a function of individuals ‘jumping’ from the ‘almost random’ category to the ‘near-perfect’ category when variables are added to a model. The accuracy measure P correlates .96 with McFadden’s R2, a common but less interpretable measure of model fit. In S15 Table I present the results of a parsimonious model that uses continuous measures of time use and proximity. This model cannot test all hypotheses, but its predictions are almost equally accurate (P = .94) as those of the most comprehensive model presented here (“+ opportunities”, P = .95).

https://doi.org/10.1371/journal.pone.0210733.g004