Modeling Rape Reporting Delays Using Spatial, Temporal and Social Features
Abstract
We present a novel approach to estimate the delay observed between the occurrenceand reporting of rape crimes.
We explore spatial, temporal and social effects insparse aggregated (area-level) and high-dimensional disaggregated (event-level)data for the cities of New York and Los Angeles.
Focusing on inference, we apply
Gradient Boosting and Random Forests to assess predictor importance, as wellas Gaussian Processes to model spatial disparities in reporting times.
Our resultshighlight differences and similarities between the two cities.
We identify at-riskpopulations and communities which may be targeted with focused policies andinterventions to support rape victims, apprehend perpetrators, and prevent futurecrimes.
Introduction
With the Harvey Weinstein scandal and the #metoo hashtag campaign, 2017 brought the attentionof the general public once again to the issue of sexual violence.
While the last decades haveshown progress on destigmatization, victims of sexual violence still suffer from substantial socialrepercussions.
This manifests itself in extremely low reporting numbers for sexual crime, the mostsevere of which is rape.
In 2012, a survey conducted by the parenting forum mumsnet found that 10%of women had been raped and 35% had been sexually assaulted [1].
Compounding the problem isonly a small proportion of rape crimes are reported to police: the Rape, Abuse & Incest National
Network (RAINN) estimates that only around 30% of all sexual assault is reported [2], and ouranalysis of New York City crime data (described below) reveals that approximately 30% of rapes thatwere reported to police had a lag of 30 days or more between occurrence and reporting time.
Giventhe substantial problem of under-reporting, it is of crucial importance to understand the underlyingprocess of reporting sexual violence in general, and rape in particular.
This issue is reiterated by arecent study that showed that the longer a victim hesitates to report, the more unlikely it becomes forthe crime to be reported at all [3].
Additionally, reporting delays complicate investigation efforts,making it more difﬁcult to convict perpetrators.
With this study, we seek to tackle the problem ofdelayed rape reporting from a machine learning (ML) perspective.
In recent years, ML has emerged asa powerful toolkit for criminology research [4], for instance helping to predict domestic violence [5].
We apply Random Forests and Gradient Boosting to assess the importance of multiple socioeconomicand temporal factors in predicting reporting time.
We observe substantial spatial dependence, thusapplying Gaussian Processes to model the correlation structure and to examine whether there isresidual spatial dependence, after controlling for neighborhood-level demographic and socioeconomicfeatures.
This paper contributes to current research by providing a new dataset of predictors of rape reportingdelays compiled from open data sources, exposing spatial variation in rape reporting and gatheringnovel insights into the importance of spatio-temporal and socioeconomic factors.
Our research has the
[Figure]
potential to motivate policies and support community policing practices.
Subsequently, we introduceour dataset, test for spatial and temporal effects, present the results for our predictive models andﬁnally suggest potential future research directions.
Data
We access historical crime records for New York City (NYC) and Los Angeles (LA), from theiropen-data portals.
To ensure a sufﬁcient sample size for regional aggregation, we extract rape crimesfrom 2012 to 2017.
To ensure representativeness of our predictors, we select only rape which occurredin the domestic or professional space, i.e. where we can assume that victim and perpetrator wereacquainted.
This amounts to a total of 7,242 reported rapes for NYC and 4,649 for LA.
Note thatwhile we experimented with shorter time periods as well (due to the static nature of our predictors),model performance did not vary substantially.
For each crime i we compute the reporting delay indays ∆ t i =
t occi − t repi as the difference between the day the crime occurred and the day it wasreported to authorities.
We then create binary values indicating whether a crime was reported withinone day or within one month respectively:
[Equation]
The LA crimes come with point location data for each rape case, normalized to block level.
Wecan hence use these points without further processing for our disaggregated model .
The NYCdata, however, comes with police precincts as the most granular geography.
For each of the
NYC precincts j , we compute the proportion of crimes reported within the two selected intervalsp day j = 1 m j (cid:80) i ∈
j d dayi and p month j = [Table] d [Table]
, where m j represents the number of observedrapes in each area.
We also create an aggregated dataset for LA, aggregating on the police department’s”basic car district” level (169 basic car districts in total).
Each of these three datasets (aggregated NYC, aggregated LA, disaggregated LA) were enriched with the following features: demographic(age, sex, race), housing (household size, occupants per room, single households, rent as percentageof income), education (high-school degrees) and economic (income, unemployment, insurance).
Forthe disaggregated dataset, we collect statistics from the census tract within which the crime wascommitted.
For the aggregated data, we apply population-weighted data aggregation from censustracts to police precincts (NYC) or basic car districts (LA).
Lastly, the LA data provides informationon the victim’s age, gender and ethnicity which we use in the disaggregated model.
Results3.1 Spatial and Temporal Effects
We start our analysis by examining geographical and temporal patterns in rape reporting delays.
Our hypothesis is that reporting delays are in fact not i.i.d. , but rather exhibit spatial and temporal
2017 Reporting month
M ed i an r epo r t i ng de l a y
V a l en t i ne ' s D a y
H a
ll o w een
T han ks g
i v
i ng     1 − J an 1 − F eb 1 − M a r 1 − A p r 1 − M a y 1 − J un 1 − J u l 1 − A ug 1 − S ep 1 − O c t 1 − N o v 1 − D e c Occurrence day
M ed i an r epo r t i ng de l a y dependencies [6].
We measure local spatial autocorrelation for the proportions p j of crimes reportedwithin the intervals { day, month } using the Local Moran
’s I statistic [7], deﬁned as
[Equation]
where ¯ p represents the mean of p j and w j,k represents the spatial weight between the features j andk .
We assume simple weights for neighbouring and non-neighbouring areas of each district j , wherew j,k = 1 if k is a neighbour of j and w j,k = 0 otherwise.
The Local Moran’s
I statistic corresponds to a (pseudo) p-value indicating the signiﬁcance of thespatial correlation.
Both NYC and LA exhibit hot spots of spatial autocorrelation, conﬁrming ourinitial hypothesis (see Figure 1).
There are (at least) two possible explanations for this: (1) anunderlying social process disguised as a spatial process (e.g., reporting delays are driven by socioeconomic factors that vary over space), or (2) a true spatial process
(e.g., a contagious spread of rapereporting behavior over space).
We address this question in the next section.
First, however, we assess the temporal dimension.
Again, our hypothesis is that temporal featuresaffect rape reporting delays.
In particular, we examine whether rapes that occurred on weekends,holidays or during different seasons exhibit varying reporting delays.
Figure 2 shows medianreporting delays by respective reporting month and occurrence day.
Several of the observed spikesand irregularities can be explained with common policing practices.
For instance, for rapes wherethe victim cannot remember the exact occurrence date (due to trauma or long reporting delay), theﬁrst or middle day of a month is recorded as occurrence day.
This practice is consistent for NYCand LA.
However, we do ﬁnd interesting patterns from the graphical analysis: Holidays (particularlythose highlighted in Figure 2) exhibit higher median reporting delays.
Note that this pattern of longerdelays does not seem to correspond to more overall rapes during these days.
Beyond holidays, rapes reported at the beginning and end of each year appear to be reported later.
We hence decide to includeboth spatial and temporal features in our predictive model for reporting delays.
3.2 Predictive Modeling
Aggregated model: We model the aggregated data in a two-step process.
First, we estimate ouroutput p { day,month } j as a function of social features, p ∼ f ( x )+ (cid:15) where x represents a matrix of socialfeatures and (cid:15) gives the model residuals.
We then seek to predict the residual error term (cid:15) ∼ f ( g )using spatial context, where g represents the centroid coordinates of each area j to isolate additionalspatial effects that are not explained by the variation in observed demographic and socioeconomicfeatures.
We apply this to aggregate data from NYC and LA, excluding temporal features which aremeasured at disaggregated case level only.
Step 1 is carried out using Random Forests and Gradient
Boosting (choosing the best predictor by cross-validation each time), Step 2 uses Gaussian Processeswith radial basis function (RBF) kernels to learn from spatial context [8].
We apply Leave-One-Out
Cross-Validation (LOO-CV) to validate the predictions.
Our results are shown in Table 1.
For NYC,we can explain around 20% of the total variation in the data using social features.
Spatial contextexplains another 10% of the remaining variation.
In LA, the explanatory power of social featuresdrops slightly while spatial context does not further improve the predictions.
Looking at variable [Table] importance from the random forest model, we ﬁnd that economic predictors (e.g. median income,unemployment rate) are relatively unimportant, while housing characteristics (e.g. occupants perroom, household size) appear highly relevant.
African-American communities are associated withshorter reporting delays, while Hispanic communities are associated with longer reporting delays.
These ﬁndings are consistent across both cities.
Disaggregated model: We model disaggregated data as a classiﬁcation problem where we seek topredict each case’s binary indicators d { day,month } i as deﬁned in section 2.
These are modelled as afunction d ∼ f ( c, z, x, v ) where x represents social features for the census tract a rape occurred in,z represents temporal features (holiday, weekend,...) speciﬁc to the occurrence date, v representsvictim-speciﬁc information and c represent the coordinates of crime location (normalized on blocklevel).
We use Gaussian Process, Random Forest and Gradient Boosting classiﬁers to apply thismodel to the LA data.
Due to the large sample size, we use 10 -fold cross validation instead of
LOO-CV to verify the results, which are given in Table 2. model.
d ∼ f ( c ) d ∼ f ( z ) d ∼ f ( x ) d ∼ f ( v ) d ∼ f ( c, z, x, v )
[Table]
The ﬁndings indicate that predictive power of spatial, temporal and social features is limited, whilevictim information adds substantial value to the model.
We achieve our best prediction accuracy withan AUC of nearly 0.7 for p monthi from a model including all available features.
Variable importancemeasures conﬁrm ﬁndings from the aggregated model and also demonstrate that victim age is byfar the best single predictor of reporting delay, which is in line with previous ﬁndings [9].
Despitesuspected patterns, temporal features do not appear to be of particular relevance for this analysis.
Conclusion
In this paper, we present a machine learning approach to predict reporting delays of rape crime.
We train event-level (disaggregated) and area-level (aggregated) models with spatial, temporal andsocioeconomic predictors gathered for the cities of New York and Los Angeles.
Our ﬁndings suggestthat economic factors and temporal features have relatively low, and housing characteristics relativelyhigh, explanatory power.
We ﬁnd substantial evidence for spatial patterns in rape reporting, whichwe account for using Gaussian Processes to model covariance structures.
While these results mayalready serve authorities in tailoring policies and community-policing strategies, further effortsshould be undertaken to deepen the understanding of rape reporting processes.
Bayesian approachescoming with more generalizable inference might be particularly valuable.
We explore the temporaldimension of rape reporting using static features only, which could be approved upon using a dynamicapproach.
This way, effects of events such as the #metoo campaign could also be investigated.
As only some of our socioeconomic predictors appear relevant, more features quantifying culturalinﬂuences (e.g., social stigma) should be tested.
Lastly, working with open data sources limits theavailable information and is not fully representative of the data available to authorities.
Working withdetailed victim and perpetrator data might help to further isolate vulnerable subgroups who could besupported with targeted community-based interventions.
Nevertheless the potential threat of victimreidentiﬁcation from open data should also be addressed.