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The effect of temperature on arson incidence in Toronto, Ontario, Canada

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Studies of crime and weather have largely excluded arson from empirical and theoretical consideration, yet weather could influence arson frequency over short time frames, influencing the motivation and activity of potential arsonists, as well as the physical possibility of fire ignition. This study aims to understand the role of weather on urban arson in order to determine its role in explaining short-term variations in arson frequency. We use data reported to the Ontario Fire Marshall's office of arson events in the City of Toronto between 1996 and 2007 to estimate the effect of temperature, precipitation, wind conditions and air pressure on arson events while controlling for the effects of holidays, weekends and other calendar-related events. We find that temperature has an independent association with daily arson frequency, as do precipitation and air pressure. In this study area, cold weather has a larger influence on arson frequency than hot weather. There is also some evidence that extremely hot and cold temperatures may be associated with lower day-time arson frequency, while night-time arson seems to have a simpler positive linear association with temperature.
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The effect of temperature on arson incidence in Toronto, Ontario, Canada
NikoYiannakoulias PhD (corresponding author)
Associate Professor
School of Geography and Earth Sciences
McMaster University
Hamilton, Ontario
L8S4K1
Email: yiannan@mcmaster.ca
Phone: 905-525-9140 x20117
Ewa Kielasinska MA
School of Geography and Earth Sciences
McMaster University
Hamilton, Ontario
L8S4K1
Citation: Yiannakoulias N, Kielasinska E. The effect of temperature on arson incidence in
Toronto, Ontario, Canada. International Journal of Biometeorology 2016; 60:651-661.
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Abstract
Studies crime and weather have largely excluded arson from empirical and theoretical
consideration, yet weather could influence arson frequency over short time frames, influencing
the motivation and activity of potential arsonists, as well as the physical possibility of fire
ignition. This study aims to understand the role of weather on urban arson in order to determine
its role in explaining short term variations in arson frequency. We use data reported to the
Ontario Fire Marshall's office of arson events in the City of Toronto between 1996 and 2007 to
estimate the effect of temperature, precipitation, wind conditions and air pressure on arson events
while controlling for the effects of holidays, weekends and other calendar-related events. We
find that temperature has an independent association with daily arson frequency, as do
precipitation and air pressure. In this study area, cold weather has a larger influence on arson
frequency than hot weather. There is also some evidence that extremely hot and cold
temperatures may be associated with lower daytime arson frequency, while night-time arson
seems to have a simpler positive linear association with temperature.
Keywords: arson, temperature, weather, crime, behaviour
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Introduction
Over long time frames, legal, economic and demographic processes can explain temporal
patterns in crime, but short term variabilityat the scale of days, weeks and monthsrequires
other explanation (Cohn 1990). Variation in weather has been used to explain short-term
variations in crime for at least as far back as the mid nineteenth century, inspired by a mixture of
environmental determinism, and a growing interest in the science of human behaviour and
psychology (Cohen 1941). Connections between weather and human behaviour have a long
cultural history as well. The English language is full of metaphors that describe human feelings
in a meteorological context. “Tempers flare,” “in the heat of passion,” and getting hot under the
collar” all describe the interaction between physical sensations of heat and intense emotion
(Anderson, 1989).Weather conditions have also provided a backdrop for human storytelling,
sometimes as a sense of foreboding (“it was a dark and stormy night) and at other times as an
archetypal settingsuch as the uncomfortable heat of a private investigator's office.
Empirical evidence for the association between crime and weather is plentiful, the bulk of
which has focussed largely on temperature (Anderson 1989). Cotton (1986) and Cohn (1993)
observed a positive correlation between temperature and violent crime. Field (1992) found a
similar correlation between temperature and both violent and property crime. A large and recent
review by Hsiang (2013) suggests not only a relationship between temperature and violence, but
the potential of a longer-term shift to increased violence associated with climate change. In spite
of the large body of published evidence of some correlation between temperature and crime, the
explanation for this association continues to be debated, and generally falls into one of two
theoretical frameworks. The first hypothesizes a direct association between environmentally
induced discomfort, aggressive affect (emotion), and a greater predilection for crime (Harries
and Stadler 1983). This temperature-aggression theory is supported by some laboratory
evidence (Baron 1972; Baron and Bell 1976; Bell and Baron 1976) and is consistent with other
studies of aggressive behaviour and heatsuch as traffic accidents (Stern and Zehavi 1990),
horn-honking among drivers (Kenrick and MacFarlane 1986), and aggression in members of law
enforcement (Vrij et al., 1994). Within this general framework there are differing perspectives
about the precise nature of the temperature-aggression relationship. For example, the negative
affect escape model suggests that increasing heat is associated with a general tendency towards
aggression, but at levels of extreme heat this effect is mediated by a preference for escaping
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discomfort (Bell and Baron 1976; Bell 1992). Another perspective describes amore linear
relationship (Anderson 1989; Anderson and DeNeve 1992) linking environmental discomfort
directly to crime through emotional arousal (Anderson and Anderson 1998).
The second theoretical framework, routine activity theory (Felson 1987), suggests a more
indirect mechanism behind the temperature-crime relationship. Under this framework, weather
conditions are thought to influence the behaviours of potential offenders (and sometimes victims)
in ways that increase or decrease the likelihood of a crime being committed. For example,
comfortable weather may be associated with increased outdoor activity and increased
opportunities for potential offenders to identify victims for violent and property crimes (Field
1992). Most treatment of the role of weather in routine activity theory is based on the
assumption that, all else being equal, crime levels peak at temperatures that maximize the
circumstances and opportunities for committing crime. For violent crimes, this could involve
contacts between offender and victim such that contact between them is more likely at certain
temperatures and less likely at others. For crimes against property, temperature could influence
whether or not 'guardians' (such as the residents of a home) are present in a way that would
discourage a criminal to act. Routine activity theory does not specify a particular functional
relationship between temperature and crime (e.g., curvilinear or linear), and is highly dependent
on context and type of offense. As such, part of the success or failure of routine activity to
explain crime is dependent on how well it differentiates crime patterns. According to Anderson
and Anderson (1998) if routine activity theory is an important influence on crime, then temporal
and geographical differences in crime should vary according to the specific differences in routine
activity patterns. For example, if persons living in hot climates are more adaptable to hot
temperatures, then their routine activities are less likely to change during a heat wave, and in
turn, not produce a resulting change in crime patterns.
There remain many challenges to developing a generalizable theory or even describing
findings consistent with any particular theory about the relationship between crime and weather
conditions. Chief among them is evidence that the crime-temperature relationship is dependent
on the type of crime, and most broadly, the contrast between property and violent crime.
Generally speaking, violent crimes against persons (such as assaults and homicide) seem more
strongly associated with temperature than crimes against property (Cohn 1990). According to
negative affect escape theory, most types of property crime are less likely to be motivated by
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affect, so seem less able to explain associations between temperature and crime (Cohn and
Rotton 2000). On the other hand, warm temperatures are associated with vacation time, which
could make properties more suitable targets for potential offenders looking to commit property
offenses on unguarded residences.
Deliberately set firesor arsoncan be viewed as both violent and property crime, and
can be motivated by a number of factors, including: vandalism, revenge, thrill seeking, political
activism, financial gain and obscuring evidence of other criminal acts (Labree et al., 2010).
Arson profiling literature often focusses on individual determinants of crime, including
psychiatric morbidity, substance abuse and fire-setting pathologies such as 'pyromania' (Dickens
et al., 2009; Anwar et al., 2011) in order to improve treatment and prevention (Labree et al.,
2010). However, there is comparatively little understanding of instrumentally motivated arson
for example, insurance fraud, intimidation/extortionsince it is harder to identify offender
motivations in these instances (Blumberg 1981; Barnoux and Gannon 2014). From a fire control
perspective, understanding the explanations for short-term variability in arson incidence is
important for understanding and predicting future arson activity, and distinguishing background
variation in arson from serial arson activity. Understanding such variations could also help with
resource allocation, surveillance and even public education. However, is rarely possible to
leverage information about the individual motivations of arsonists into these predictions since the
motivations of arsonists are rarely known a priori, if at all. For this reason, the historical focus
on arson as a result of pathologies or instrumental motivations offer an incomplete perspective,
particularly if larger environmental influences play an important role in explaining temporal or
geographic variations in arson.
There is some reason to think that weather may play an important role in understanding
day to day variations in arson activity independent of arsonist motivation. The feasibility of
outdoor fire setting is clearly connected to weather conditionsas lighting fires in very wet
conditions can be impractical, even with the aid of accelerants. However, very little research has
specifically studied the role of weather in predicting arson activity in urban environments. One
important exception is the work of Corcoran et al., (2011), who studied fire incidence in
Australia, and found some evidence of a relationship between extreme temperatures and all types
of fire (including suspected arson). However, the study area (South East Queensland, Australia)
has relatively limited seasonal variation in temperature, with daily averages between 20 and 30 C
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throughout the year. This small temperature range limits the generalizability of findings, and
furthermore, makes it hard to fit their results into existing theories of crime. For example,
routine activity theory could predict less arson on very cold days because potential arsonists are
more inclined to stay inside their homes when it is cold, but this effect can only be observed in
settings that get sufficiently cold to observe this effect.
This research aims to advance understanding of the relationship between weather and
arson independent of seasonal holidays and other calendar effects. Arson puts lives and property
at risk, with per-offense economic costs behind only homicide, aggravated assaults and robbery
(McCollister et al., 2010), and a frequency equivalent to 8 times that of murder and attempted
murder combined (Statistics Canada 2012). Our study area, Toronto Ontario Canada, has
considerable seasonal variability in temperature, with both summer heat waves, and periods of
winter weather well below 0 C. This setting is useful for studying the relationship between
weather generally (and temperature specifically) on arson frequency since temperature-induced
discomfort at both cold and warm temperature extremes may influence arsonist behaviour. In
the case of routine activity theory, extremely warm or cold temperatures may reduce residential
arson by encouraging people to stay home, making some properties less desirable targets at those
times, but also by reducing the activity levels of potential arsonists. On the other hand,
temperature induced aggression may be higher at very warm temperatures, and induce more
arson under these conditions. Based on previous work, we propose one general hypothesis:
arson frequency is associated with measures of weather independent of calendar effects (such as
holidays), and one specific hypothesis that temperature has a non-linear 'inverted-U'
relationship with arson frequency. We approach these questions using data on suspected arson
events reported in the City of Toronto between 1996 and 2007. We use Poisson regression with
nested day and week random effects to predict the number of arson events as a function of
weather and calendar effects. Our study area, Toronto Ontario, is particularly well suited to this
question since it experiences a wide range of temperatures over the yearboth prolonged heat
waves in the summer, and temperatures well below freezing in the winter.
Methodology
Study Area
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The City of Toronto (including the formerly independent municipalities of Etobicoke, York,
North York East York, Scarborough and Old Toronto) is the largest city in Canada, with a
population of roughly 2.5 million people. Located in Southern Ontario, Toronto experiences
significant temperature variability over the course of the year. Daytime highs in the summer can
reach temperatures in excess of 32 C for extended periods of time, and winter cold periods can
drop below -20 C. Both extreme heat (Pengelly et al., 2007) and extreme cold (Anderson and
Rochard 1979) contribute to excess mortality in Toronto, a finding found in other regions of the
world with large annual variations in temperature (Guo et al., 2013). On average the mean daily
temperature (ambient, or measured temperature) in January is -4.5ºC and 22ºC in July.
Fire Data
The data used in this analysis were acquired from the Ontario Office of the Fire Marshal
(OFM) for the current geographic boundary of the City of Toronto between 1996 through 2007.
This dataset includes all deliberately set or initiated fire excluding those started by children 11
years or less in age. The dataset includes fires suspected of being deliberately set as determined
by the fire department personnel attending the fire scene. While these data consist of the count
of fire events in hourly intervals, the average hourly number of arson events is quite small.
While aggregating data to daily counts was possible, daily level analysis would exclude intra-day
variations, particularly between day and night periods. As a compromise, our data are stratified
into day and night periods to account for some intra-day variation, but without creating very
small counts per unit time. For our analysis, day and night are defined based on the time of
sunrise and sunset on each particular day, with day time covering arson events occurring during
daylight hours, and night time covering arson events during non-daylight hours. For this reason,
each night record in our analysis includes an interval spanning two calendar days based on the
times of sunset and sunrise. All weather data are linked to the fire records based on the date and
period of time (either day or night).
Weather effects
Environment Canada maintains an online archive of hourly weather data from various
weather stations across the country. We acquired all weather data for the years 1996 through
2007 from the weather station at Toronto’s Pearson International Airport, and aggregated these
data into the same time periods as the arson data. We use average temperature per time period to
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estimate the direct effect of temperature on the number of arson events. In order to test our
second hypothesisthat temperature has a non-linear relationship with arson frequency, we
include 2nd, 3rd and higher order polynomials of temperature to the model. We include
precipitation as a dichotomous variable, where 1 equals any precipitation in the time period, and
0 equals none. Precipitation may influence immediate decisions of potential fire-setters, as well
as affect the flammability of materials outside. For this reason, we also include a lag term for
precipitation in the previous 24 hours. Longer lags were also tested, but were not statistically
significant, and were therefore not included. Finally, we include average wind speed (measured
in kilometres per hour), and average air pressure (measured in kilopascals) per period of time.
All weather data are added together in the model as a block referred to as 'weather effects', and
all fixed terms are retained in the model if significant at the 0.05 level. Interactions and
polynomial effects are tested and retained in the model only if significant at the 0.01 level.
Calendar data
Weekends and holidays may create opportunities for the commission of crime because of
both increased free time, decreased activity of emergency service personnel and holiday related
absences (Cohn and Rotton 2000). Most calendar events occur at the same time every year, and
are therefore season (and, in turn, weather) specific, so it is important to control for the potential
confounding calendar events may have on our understanding of weather effects on arson
frequency.
We account for the day of week effect by including a term for weekend in our model. We
account for the effect of holidays by first identifying all provincial and national public holidays
during our study period, then treating the day prior and day following the holiday as part of the
holiday period. These days are then used to create a single dichotomous variable in our analysis
such that a single holiday spans a period of three days. This large window of time may attenuate
apparent holiday effects, however we believe it is important to account for the potential spill over
effect of holidays, particularly when they occur immediately before or after a weekend. Our
analysis also includes a term for when schools are typically out of session, which includes the
months of July and August, a period in the middle of March ('Winter Break') and the holiday
between the end of December and the beginning of January ('Christmas Break'). There is some
overlap between these two holidays, so we specified that any statutory holiday during the school
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holiday period would be coded as a statutory holiday. This results in three mutually exclusive
setsschool holidays, statutory holidays and non-holidays, the latter of which is used as a
reference category in our model.
We include Halloween as a term in our model. Halloween is not a statutory holiday in
Canada, but we include it in our analysis to account for the cultural perception (and empirical
evidence) that Halloween is a day of mischief and increased vandalism (Maciak et al., 1998).
For the same reason, we include a term in our model for ice hockey events. Specifically, we
identified days in which the local professional hockey team (the Toronto Maple Leafs) played in
the National Hockey League playoffs in our study period, and included a hockey playoff term in
our analysis.
We refer to these calendar events as 'calendar effects' in our analysis and similar to above, all
fixed terms are retained in the model if significant at the 0.05 level but interactions are retained
only if significant at the 0.01 level.
Other data
We include a year term in our analysis based on the year recorded in the arson database. For
ease of interpretation, we use years from starting year (e.g., '0' for 1996 and '10' for 2007) rather
than actual year in our analysis. Year effects are intended to account for any secular trends in
arson frequency. We consider year and year squared to account for potential non-linearities in
this long-term trend.
We include a fixed effect for day and night in our analysis. Like all Canadian cities, the
hours of daylight varies considerably with season in Toronto, with roughly 9 hours of daylight in
the winter, and almost 16 hours of daylight in the summer. Since the analysis is stratified by
day-time and night-time periods, we account for variations in the length of these time periods
using the number of hours in these periods as an offset term (see below). Data on time of sunset
and sunrise were obtained from an online resource (http://www.timeanddate.com/) that includes
historical sunrise and sunset times.
Analysis
Arson events are often serial in nature, and exhibit temporal clustering because of either the same
person setting fires over a short period of time, or copy-cat and retaliatory fire-setting
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(Prestemon and Butry, 2005). This temporal autocorrelation presents several challenges to this
study. First, this could be a challenge for estimating the effect of weather on the count of arson
events per time period since some events in a time period may not be independent of each other.
This lack of independence between observations can affect the estimation of standard errors of
the coefficients in our model, either inflating or deflating these estimates depending on whether
or not the covariate is time-varying. The second challenge is that there could be brief spikes in
arson activity when a single fire setter has a particularly active period. These periodic spikes in
activity make specifying an appropriate model difficult; while it may be possible to find the
correct model for the normal background variations in arson activity, brief periods of intense
activity associated with serial arson are very likely to be under-estimated.
We use a Poisson generalized linear mixed model (GLMM) to address the problem of
clustering in arson frequency over time. GLMMs are useful for estimating the effects of
clustering in data when the structure of the clustering can be specified ahead of time. In this
application, we treated the autocorrelation as clustering in time where there are periods of high
and low arson activity explained by an unmeasured but temporally clustered processsuch as
serial and retaliatory fire-setting. We first explored the temporal clustering of arson events in the
data to find an interval of time in which most temporal autocorrelation occurs in the data set. We
did this by modelling daily arson events as a function of lags of daily arson events, and observed
that most of the temporal autocorrelation occurs within a 7 day period. We then created 7 day
(weekly) clusters of observations, and incorporated this time period as a random effect in our
model. This random effect captures week-to-week variability unaccounted for by the model
fixed effects, and could be the result of processes not explicitly identified a priori. We also
include a 'daily' random effect to account for the fact that day and night periods on the same
calendar day could be temporally autocorrelated. Therefore our final model is a nested GLMM
with two random effects: one weekly random effect and one daily random effect.
Finally, we include the natural log of period length as an offset term in our model rather
than including this term as a fixed effect. This accounts for variations in the length of time
periods by adding the term directly to the model estimated. We used the GLIMMIX procedure in
SAS version 9.2 (SAS Institute Inc., 2009) for all modelling.
Results
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Between 1996 and 2007 there was a total of 12185 arson events, 5065 of which occurred during
daytime hours, and 7120 of which occurred during night-time hours. Summary statistics of
weather measures over the study period are presented in Table 1. Since temperature, wind speed
and air pressure are measured on different scales, we chose to standardize each of these variables
to a mean of 0 and a standard deviation of 1 to simplify their interpretation in the model below.
We also reduce precipitation to a dichotomous indicator variable since the distribution of daily
precipitation is highly skewed and much of the variability is contained in the difference between
precipitation and non-precipitation days. We graph the average daily number of arson events by
quintiles of each weather variable in order to visualize associations between each weather effect
and arson (Figure 1). Average daily temperature and average daily air pressure have a positive
association with daily arson frequency, while precipitation and wind speed have a negative
association. We also note that the variation in daily arson appears largest in the low quintile
groups, and smallest in the highest quintile groups.
Table 2 includes three models: a weather effects only model, a weather plus calendar
effects model, and a model of interaction and polynomial effects. While it is difficult to estimate
the 'fit' of a generalized linear mixed model using methods typical to linear regression (such as
the coefficient of determination) there is no evidence of over or under-dispersion in any of the
models, as the ratio of the generalized χ2 statistic to degrees of freedom is nearly equal to 1 for
each of the models. A value greater or less than one could suggest a poor model specification.
Of more importance are the coefficients in the model, since they reveal the specific factors that
may predict temporal variation in arson frequency, and speak most directly to the research
question. The weather effect coefficients are largely unchanged through the process of adding
the calendar effects to the model. The year effect suggests a slightly non-linear decline in arson
frequency over time. Night-time is associated with more arson; on non-holiday days in average
weather conditions, for example, the model predicts arson frequency 51 per cent higher during
the night compared to the day. Precipitation, temperature and air pressure all have an
independent association with the frequency of arson. Precipitation and precipitation in the
preceding 24 hour period are associated with a decline in arson frequency, and both increasing
air temperature and air pressure are associated with increases in arson frequency. All three
weather variables are weakly correlated with each other, but have small (< 2) variance inflation
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factors when fit in a linear regression model, suggesting that they can be interpreted
independently in a our model.
We tested 9 interactions between the groups of temperature and calendar variables that
were statistically significant as main effects, and tested 6 interactions between year and the
statistically significant weather and calendar effects. All of these estimates were near 0, and
none were statistically significant, so are not presented in these results. We also tested 6
interactions between the temperature and calendar effect variables and the night indicator, with
several interactions revealing a contrast between day and night. We observe an interaction effect
involving temperature and night where warmer temperatures at night contribute an increase in
arson frequency in addition to the additive temperature (and temperature squared) effects. In the
final model, statutory holidays, weekends, Halloween and hockey play-offs are all associated
with increased arson frequency. For Halloween, this is a purely night-time effect, since the main
effect is not statistically significant once the interaction term is included in the model. Weekend
and statutory holidays also interact with night-time, but in this case, the main effects remain non-
zero, suggesting that while night-time amplifies the effect of holidays on arson, day-time
weekends and holidays also predict higher arson frequency. Second order polynomials were
included for all continuous weather variables (temperature, air pressure and wind speed) and
temperature and air pressure were both statistically significant.
Our models include two random effects: a calendar date effect to capture any clustering
in arson frequency by calendar day, and calendar week effects. The calendar date effect is nested
within the week effect so that the week effect is independent of the clustering of calendar days
that comprise it. In the final model both of these random effects are statistically significant at the
0.001 in a pseudo-likelihood ratio test of whether or not the estimated covariance matrices could
be replaced with a value of 0. For reference, a model containing only the random effects
estimates a calendar date effect of 0.166 and a calendar week effect of 0.164. In the final model,
the calendar date effect is 0.078 and the calendar week effect is 0.129, suggesting that the
addition of fixed effects accounted for more of the clustering in arson frequency at the daily scale
than at the weekly scale.
Figure 2 illustrates the model predicted number of arson events in a 12 hour period by
temperature quintiles for day and night periods. The figure shows the difference in the
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temperature-arson relationship by day and night-time periods, and importantly, the temperature
by time period interaction effect. For these predictions, all other model variables are held at their
respective means. For night-time periods, the relationship between temperature and arson
frequency appears to be roughly linear, but for daytime periods, there is a curvilinear trend, with
daytime arson peaking at the fourth quintile, and slightly declining at the fifth quintile. The
difference in arson frequency by day and night periods is greatest at the fifth quintile, and
smallest at the first quintile. However, neither the model coefficients nor this figure reveal the
actual impact of temperature on the frequency of arson activity given the temperature profile
typically seen in the study area. To better understand the actual impact of temperature variations
on the frequency of arson given the model, we calculate the conditional mean number of arson
events per day across three temperature ranges: normal (within one standard deviation above or
below the annual mean), high (more than one standard deviation above annual mean) and low
(more than one standard deviation below the annual mean). We then compare the difference in
average daily arson events for these time periods accounting for the number of days within these
temperature ranges. Over the study period we find 423 model predicted arson events attributable
to temperatures more than one standard deviation above the annual mean, and 890 fewer model
predicted arson events attributable to temperatures more than one standard deviation below the
annual mean.
Figure 3 is a visual representation of the relative impact of different model predictors on
the number of daily arson events (as above, holding all other effects at their respective means),
and is useful for making qualitative judgements about the relative impact of different effects on
arson frequency. The horizontal lines on the graph are model predicted arson frequency holding
all model effects at their means for day and night periods. Each pair of bars on the graph is a
model term (for day and night-time periods), and the y-axis is the model predicted number of
arson events in a 12 hour period. The first five variables on the graph are calendar effects, and
show the model predicted arson events for those days on the calendar. The number of daytime
arson events on Halloween, holidays and weekends do not appear to differ greatly from each
other or the annual average. Weekend Halloween nights predict the greatest number of arson
events per night-time period, although since there were only 4 Halloween nights falling on
weekends in the study period, the actual impact of this calendar effect on the total number of
arson events in any year is very small. In contrast, there are over 1200 weekend observations in
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the dataset, so while the difference in weekend night-time predicted arson frequency (1.914) and
the annual night-time average (1.492) is small, the impact of weekends on the total number of
arson events is noteworthy. The graph also includes model predicted arson events at the highest
and lowest temperature quintiles. Most notably, the night-time arson frequency appears sensitive
to temperature; arson frequency in the coldest quintile is half the annual average, and in the
warmest quintile, is roughly 23% above the annual night-time average.
Discussion
We had two study hypotheses: 1) that there is an association between weather and arson, and 2)
that the temperature-arson relationship is in the 'inverted-U' form observed in other research on
crime and temperature. We use a generalized linear mixed model to predict arson as a function
of two groups of fixed effects: calendar effects and weather effects. Our model also includes two
random effects in order to account for clustering in daily and weekly arson frequency that is
unexplained by the fixed effects. Our results indicate that both weather and calendar effects are
associated with the number of daily arson events. Furthermore, our model suggests the presence
of an 'inverted-U' relationship between daytime (and not night-time) arson frequency and
temperature where arson frequency peaks at moderately warm temperatures and is lower at
exceptionally cold and exceptionally hot temperatures. We discuss these findings in detail
below.
Weather and arson
Our results suggest that temperature has a curvilinear association with daytime arson
frequency. Graphs of daytime arson frequency as a function of temperature show that rising
temperatures are associated with increased arson frequency, but at the highest temperatures,
arson frequency declines. At night the relationship appears more linear; as temperatures rise,
arson frequency appears to rise as well. Generally speaking, both theories of crime and
temperature could be consistent with a curvilinear relationship between temperature and arson.
Routine activity theory may predict more arson in warm weather due to changing behaviours
(such as more time outdoors) leaving some potential arson targets less guarded. Temperature-
aggression theory (and in particular, the negative escape variant) may also be consistent with an
increase in arson frequency with temperature and then decrease in arson frequency at the highest
temperatures. We note, however, that cold temperatures have a larger absolute relationship with
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arson frequency than hot temperatures; there are roughly two fewer arson events on extremely
cold days compared to one fewer arson event on extremely hot days. Furthermore, most
discussion of temperature-aggression theory is focussed on the effects of extremely hot
temperatures on crime, for which there may be specific physiological connections between
human physiology and extreme heat (Simister and Cooper 2005). In our study area, the entire
temperature spectrum has some relationship with night-time arson frequency, but while the effect
of cold on arson frequency is particularly striking, it does not fit as well within existing
temperature-aggression theory, since cold temperatures have a less obvious physiological
association with reduced aggression. In addition, the difference between the daytime and night-
time effects suggests a more complicated process than a simple relationship between
temperature, aggression and arson.
Our analysis also suggests that precipitation and air pressure are associated with arson
frequency. For precipitation and a one day lag in precipitation the relationship is negative;
precipitation corresponds to a decline in arson frequency. One obvious explanation for this
observation is that precipitation reduces the effectiveness of fire setting. This explanation could
be confirmed were it possible to contrast indoor from outdoor fire setting. The OFM data
contains area of fire origin location, however these data were not easily classified into inside and
outside locations. Nevertheless, our observation that the previous day's precipitation is also
associated with a reduction in arson frequency suggests that at least some of the precipitation-
arson relationship is related to combustibility; when conditions are wet there is decline in fire
setting on the following day irrespective of the precipitation on that day. Routine activity theory
may also explain some of the precipitation effect. Rain, like cold and hot temperatures, may
alter behaviour by keeping people indoors, and then reducing the suitability of some potential
targets of arson.
Air pressure is positively associated with arson frequency. Low pressure conditions are
often associated with precipitation, and therefore, it is possible that the effect is partly capturing
residual confounding from the effect of precipitation. However, there is evidence that some
socially deleterious behaviour is associated with air pressure independent of other measures of
weather (Auliciems and DiBartolo 1995). Other research has suggested an association between
air pressure and mood, where higher air pressures (and the typically corresponding weather
conditions) are associated with better mood (Cunningham 1979). Consistent with these
16
observations, more recent research has suggested that specific behaviours are associated with air
pressure; suicide attempts, for example (Ruuhela et al., 2009; Hiltunen et al., 2012) are
associated with low air pressure conditions. The relationship we observe seems to suggest that
higher air pressure results in more arson, but whether a shift in mood is the intermediary is
unclear. Wind speed did not appear to have a relationship with arson frequency independent of
the other weather effects. Other research has suggested that wind speed influences fire incidence
(Corocoran et al., 2011). In an urban setting where a large number of arson events are likely to
occur indoors, the effect of wind may be particularly hard to measure. It may also be that of the
four weather conditions measured in this study, wind is least likely to affect the activity of
potential offenders, particularly under otherwise normal weather conditions.
Overall, our analysis suggests some association between weather conditions and arson
incidence independent of calendar effects. Mood and weather more generally have been the
subject of considerable study, with the bulk of empirical evidence suggesting a weak to non-
existent relationship (Dennison et al., 2008). Other research suggests that relative improvements
in weather (for example, from winter to spring) seem to have a greater effect on mood than
absolute weather conditions (Keller et al., 2005). Some specific behaviours have been associated
with pleasant weather, such as certain financial decisions (Saunders 1993; Hirshleifer and
Shumway 2003; Cao and Wei 2005). Many holidays correspond to seasonal changes, and could
confound observed relationships between weather and crime, however we observe that
weatherin particular, temperature, precipitation and air pressurehas a persistent association
with arson frequency independent of the calendar effects. Importantly, the effect of different
weather conditions on arson frequency can be comparatively large. Holding all other effects
constant, the model predicted difference between the most arson-inducing weather (warm, high
air pressure and dry conditions) and least arson-inducing weather (cool wet and low BP) is 2.4
and 0.07 events per day, respectively. In contrast, holding all other influences constant, the
difference between a holiday weekend evening and non-holiday week day is 3.6 and 1.8 events,
respectively. While holiday weekends predict a larger number of arson events, the variations in
arson frequency due to differences in weather are considerably larger, and may be more useful
for predicting changes in arson activity over short time frames. Furthermore, they may be more
useful for understanding deviations from the baseline trend in arson frequency. A small increase
in the number of arson events over a period of cold wet weather may be more likely to signal
17
variability of systemic concernsuch serial arsonthan an equivalent increase during periods
of warm temperature. Further research on the effects of weather on the variability in arson
frequency (independent of frequency itself) could be helpful for assisting the profiling of
arsonists in the future.
The calendar effects we observed were not part of our explicit research hypotheses, but
are worthy of some attention. Our model predicts that weekend Halloween evenings are
associated with a large increase in arson activity, a finding largely consistent with the cultural
reputation of the day. Interestingly, we did not find school holiday periods to be predictors of
arson activity even though this time of year is often associated with more arson due to warmer
temperatures. We also found a weak but statistically significant association between playoff
hockey and arson; we were unable to determine whether this effect was mediated by the local
team's success due to the small ratio of victories to losses over the study period, however our
findings seem consistent with other work that has linked behaviour to the performance of a local
sporting team (Travato 1998; Edmans Garcia and Norli 2007; Kirk 2008).
Limitations
Our study design is observational, rather than experimental, therefore we cannot rule out
the possibility that apparent relationships in the models presented are simply expressions of
relationships between arson and missing model variables. Such missing variables can bias
coefficients in the models towards or away from null. The authors are aware of no significant
temporal factors that could explain the relationships observedand in particular, the relationship
between temperature and arson frequencybut this does not preclude their existence. For this
reason, we interpret any observed relationships in terms of association rather than causation.
The arson data used in this analysis are based on the reporting of the firefighting personnel
attending the scene of the fire. The methods for characterizing a fire as arson are highly
dependent on the context, including the experience of the personnel attending the fire, the
historical frequency of arson at a given time and the costs associated with the blaze. It is likely
that some of the arson events used in this study were misclassified, and that some fires were
mistakenly excluded. If these errors are uncorrelated with any of the measures used in our
analysis, their effects are negligible, and are white noise that increase the standard errors of the
regression coefficients. On the other hand, if the errors are systematic, and more importantly,
correlated with any of the model effects specified here, then they could have an effect on our
18
results. For example, if the investigators are biased to mistakenly classify a fire on Halloween as
an arson event, this will bias the coefficient upwards. The authors are unaware of any research
describing systematic behaviours of fire investigators, particularly as it relates to classifying
arson. However, the potential effect should put caution in the interpretation of our results, as
weather may play some part influencing the decisions of investigators.
Individuals may respond to the discomfort of heat and cold in relative rather than absolute
terms. For example, exposure to unseasonably warm temperatures, but not particularly warm
when compared to annual means, may result in heightened physiological responses relative to
those later in the summer season, after individuals have had a chance to adapt to hotter
temperatures, an effect seen in the study of weather related mortality (Curriero et al., 2002).In
our final model we include only a measure of the relationship between absolute temperature and
arson frequency, rather than the effect of difference from expected temperatures. However, we
did consider the inclusion of a relative temperature variable in our analysis, specifically, the
difference between the observed temperature in a time period and the monthly average. This
effect was a statistically significant term in our model, however, it was also highly correlated to
temperature. Since it had little direct influence on other weather variables, we opted to exclude it
from our results. Nevertheless, future studies may benefit from investigating the effects of
temperature in relative as well as absolute terms.
Similarly, other factors may affect the feeling of discomfort associated with heatin
particular, humidity. We did not include humidity in our analysis, and therefore are
underestimating the discomfort experience on some daysmost notably, those days with
moderately hot temperatures but high humidity. Other research has considered the more general
notion of discomfort and crime that includes humidity as well as temperature (typically in the
form of a 'discomfort index'), but this is in settings where the primary focus is on the effects of
heat on temperature (Harries and Stadler 1983; LeBeau 1994). It is more difficulty to employ a
single measure of temperature-related discomfort that accounts for both the influence of cold and
hot temperatures on arson over and above what is already measured by temperature itself. One
possible consequence of excluding humidity from estimating discomfort is that we have under-
estimated the effect of heat-related discomfort on arson frequency, possibly biasing our
observations towards no effect. Since we found an effect in spite of this potential bias, it is
19
possible that our results represents a lower-bound estimate of the importance of heat-related
discomfort on arson frequency.
In conclusion, variations in weather are associated with variations in arson frequency, and
perhaps unsurprisingly, cold weather significantly dampens arson activity independent of
holidays, weekends and other weather effects. The relationship between temperature and arson
interacts with time of day; at night-time, there appears to be a linear relationship between
temperature and arson frequency. During the daytime, the relationship is curvilinear, with a
slight decrease in arson frequency at the warmest temperatures. Given the diversity of
motivations behind arson events, the challenge of predicting arson as a simple linear function of
weather and calendar effects is unsurprising. However, our findings provide some insight into
the relative importance of temperature on arson when compared to holidays and weekends. Put
simply, colder weather is associated with a decline in arson activity at a magnitude similar to the
increase in arson activity associated with weekends, holidays and Halloween. Further research is
required to understand the specific effects of cold weather on crime, and the degree to which
cold weather may explain some international variations in violent crime.
20
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24
Table 1. Descriptive summary statistics for weather effects
Mean
Standard
Deviation
Q1
Q2
Q3
Q4
Max
Average daily temperature (C)
8.71
10.45
-0.80
5.35
12.53
19.10
32.99
Average daily air pressure (kPa)
99.42
1.43
98.92
99.36
99.71
100.12
102.28
Average daily wind speed (kph)
15.64
7.88
9.13
12.30
16.15
21.8
62.5
Average daily precipitation (mm)
2.09
5.31
0
0
0.2
2.4
66.4
25
Table 2. Full model with fixed, polynomial and interaction effects
Parameter
Weather main effects only
All main effects
Final model
Estimate
SE
t
Pr > |t|
Estimate
SE
t
Pr > |t|
Estimate
SE
t
Pr > |t|
Intercept
-2.410
0.025
-95.38
<.001
-2.189
0.041
-53.80
<.001
-1.885
0.061
-31.15
<.001
Night period
0.491
0.021
23.20
<.001
0.502
0.021
23.76
<.001
0.422
0.025
16.56
<.001
Year
-0.049
0.005
-10.43
<.001
-0.148
0.020
-7.49
<.001
Year2
0.008
0.001
5.14
<.001
Precipitation
-0.151
0.024
-6.19
<.001
-0.163
0.024
-6.73
<.001
-0.144
0.025
-5.81
<.001
Lag precipitation
-0.175
0.024
-7.16
<.001
-0.184
0.024
-7.60
<.001
-0.171
0.024
-7.04
<.001
Temperature
0.193
0.018
10.85
<.001
0.215
0.017
12.53
<.001
0.168
0.020
8.35
<.001
Temperature2
-0.036
0.014
-2.65
0.008
Air pressure
0.044
0.013
3.46
<.001
0.038
0.012
3.01
0.003
0.117
0.021
5.69
<.001
Air pressure2
0.006
0.001
4.56
<.001
Wind speed
-0.033
0.013
-2.58
0.009
-0.018
0.013
-1.42
0.155
0.001
0.013
0.05
0.957
Night * Temperature
0.126
0.022
5.77
<.001
Statutory holiday†
0.220
0.042
5.25
<.001
0.228
0.042
5.48
<.001
School holiday†
-0.062
0.035
-1.78
0.075
-0.048
0.035
-1.37
0.170
Weekend
0.276
0.023
11.94
<.001
0.193
0.033
5.88
<.001
Halloween
0.470
0.124
3.81
<.001
-0.014
0.239
-0.06
0.953
Hockey playoffs
0.118
0.073
1.62
0.104
0.145
0.072
2.02
0.044
Night* Weekend
0.136
0.039
3.49
<.001
Night* Halloween
0.659
0.263
2.51
0.012
Fit statistics
Generalized χ2/d.f = 0.98
Generalized χ2/d.f = 0.99
Generalized χ2/d.f = 0.98
† With non-holidays as reference category
26
Figure 1.Arson frequency by weather quintiles (including 95% confidence intervals)
27
Figure 2. Model predicted daytime and night-time arson frequency as a function of temperature quintiles
28
Figure 3. Model predicted arson frequency by time period: a comparison of effect sizes
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