Modelling the probability of building fires
Vojtěch Bartáka (corresponding author),

Kateřina Gdulováa, Olga Špatenkováa, Aleš Bártab and Petra Šímováa

aDepartment of Applied Geoinformatics and Spatial Planning
bDepartment of Land Use and Improvement

Faculty of Environmental Sciences, Czech University of Life Sciences Prague,
Kamýcká 129, 165 21 Praha 6 – Suchdol, Czech Republic

bartakv@fzp.czu.cz

Abstract

Systematic spatial risk analysis plays a crucial role in preventing emergencies.
In the Czech Republic, risk mapping is currently based on the risk accumulation
principle, area vulnerability, and preparedness levels of Integrated Rescue System
components. Expert estimates are used to determine risk levels for individual
hazard types, while statistical modelling based on data from actual incidents and
their possible causes is not used. Our model study, conducted in cooperation with
the Fire Rescue Service of the Czech Republic as a model within the Liberec and
Hradec Králové regions, presents an analytical procedure leading to the creation of
building fire probability maps based on recent incidents in the studied areas and
on building parameters. In order to estimate the probability of building fires, a
prediction model based on logistic regression was used. Probability of fire calculated
by means of model parameters and attributes of specific buildings can subsequently
be visualized in probability maps.

Keywords: spatial risk analysis, Integrated Rescue System, building fire probability

1. Introduction

Emergencies, whether caused by forces of nature or human activity, have accompanied hu-
manity throughout its entire history. Nevertheless, developed societies endeavour to prevent
emergencies and mitigate their negative effects. A key role in these efforts is played by sys-
tematic spatial risk analysis, an integral part of preventive security measures used in crisis
and emergency planning. Such analyses take advantage of possibilities currently offered by
modern technology and geographic information systems (GISs) along with the availability of
many suitable mapping resources. Risk analysis therefore enables efficient readiness planning
for Integrated Rescue System units and more rapid responses to emergencies when they occur.
That, in turn, contributes to improved protection for the population.

In other countries, exceptional attention is devoted to developing measures to map risks in
order to protect inhabitants, although the procedures in individual countries differ in the
depths of analysis used as well as in the extent of applying the results of those analyses [15].
In Finland, for example, detailed risk mapping is required by law and is carried out through
uniform procedures at the level of municipalities. A basic GIS application was developed for
these purposes [11], and it is being further elaborated through academic research (e.g. [1], [12],
[18]). Attention is focused mainly on input values with the objective of creating a realistic risk
model corresponding to actual emergencies. Recent records on conducted interventions are

Geoinformatics FCE CTU 13, 2014, doi:10.14311/gi.13.5 37

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http://dx.doi.org/10.14311/gi.13.5


Barták, V. et al.: Modelling the probability of building fires

therefore used in this development. Significant predictors are determined using sophisticated
methods of spatial analysis which also consider how the studied phenomena vary over time.

In the Czech Republic, risk mapping is currently based on a methodology developed by
a team at the Department for Population Protection and Emergency Management of the
Fire Rescue Service (FRS) of the Moravian–Silesian Region [13] based on a methodology
recommended by the European Union. The methodology for creating risk maps is based on the
risk accumulation principle, area vulnerability, and preparedness levels of Integrated Rescue
System components in order to minimize emergencies’ negative impacts. The resulting risk
maps represent existing risk levels in the given territory expressed as values between 0 and 1.
To determine risk rates for individual hazard types, expert estimates based on statistical data
and the expert team’s experience are used. The methodology therefore does not use current
spatial data on actual interventions by the FRS, which could provide detailed information on
the events’ distribution across space and time. Although the resulting risk maps therefore
present theoretical values of accumulated risk, they are static and do not account for either
actual events’ constantly changing spatial pattern or their possible causes.

As seen in existing research focused on emergency management ([5], [6], [8], [9], [19]), when
mapping risks it is necessary to distinguish individual hazard types and determine risk levels
separately for each type [13]. Research usually focuses on such phenomena as traffic accidents
([3], [14], [21]), forest fires ([4], [7], [17]), and building fires ([19], [20], [22], [23]). The main
objective of our study was to contribute to current risk mapping methodology by preparing
and testing an analytical procedure that would identify the factual context of building fires
based on actual incidents recorded by FRS units. The objective was therefore to find and
verify a suitable procedure beginning with input data quality analysis and continuing through
GIS analysis and statistical modelling. A partial objective was to determine which building
attributes are significant in fire incidents and are suitable for consideration as predictors when
creating building fire probability maps, or whether such detailed attributes can be at least
partially replaced by easily accessible data. This model study was performed within the
Liberec and Hradec Králové regions and was worked out in cooperation with the FRSs of the
two regions.

2. Methods

2.1. Building fires data and data quality analysis

Fire incidents data (covering 2010–2012) and the building layer were provided for the purposes
of the project by the FRSs of the Liberec and Hradec Králové regions; the building layer
originally comes from the Czech Statistical Office and results from the Population and Housing
Census 2011. The authors originally intended also to use detailed data on households’ socio-
economic characteristics from the same census, but at the time the study was prepared such
data was not yet available from the Czech Statistical Office. The analysis only included
records on fires in buildings, i.e. records with the attributes “low-rise buildings”, “high-rise
buildings” and “industrial and agricultural buildings and warehouses”. False alarms, tactical
trainings, testing trainings, and technology tests were then removed from the selected records
according to other attributes, as were inter-regional and international interventions which
extended beyond the model territory’s borders.

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Barták, V. et al.: Modelling the probability of building fires

Due to the known fact that the results of an analysis are affected by the quality of the input
data (see Shi et al. [16]) and considering possible errors in designating a fire’s location made
at the operating centre or in the field (not all vehicles are equipped with GPS receivers), the
first step was to subject the data to detailed quality analysis to examine their accuracy in
terms of location and attributes. Most of the errors determined in the fire records layer were
from 2010 and 2011, while data from 2012 had the fewest deficiencies. This demonstrates
the effectiveness of changes in data collection methodology implemented by the FRS between
these years. After removal or correction of erroneous records, data from 2012 was therefore
used for analyses to create probability maps.

Deficiencies in the position component consisted primarily of missing coordinates in certain
records, switching of x and y axes, use of multiple coordinate systems, and records’ inaccurate
localization. Inaccurate localization consisted of two error types: the first type designated the
location using only such data as the municipality’s name, thus resulting in the intervention’s
being placed in the centre of the municipality and in most cases also several records with
identical intervention positions, and the second inaccurately designated coordinates which
would place a building fire outside of a building. Prior to further analysis, records with
positions in identical locations where it was verified that the interventions had occurred at
various locations and records with a missing positional component were removed, records
with switched coordinates were corrected, and the coordinate system was unified to that of
the Czech and Slovak system known as S-JTSK.

Deficiencies in the data’s attribute component appeared particularly in the building layer,
especially due to incorrect or inconsistent completion of attribute values. An example of an
obvious error can be seen in the number-of-storeys attribute, according to which most mu-
nicipalities would contain 13-storey buildings. Attributes (columns) with probably erroneous
values were not considered in subsequent analyses to be used as possible predictors. In cases
of redundancy among attributes, attributes were selected as possible predictors if they had
more completed elements or if they could be more easily interpreted. An example can be seen
in a pair of attributes describing the building owner, one of which included 13 levels, while
the other, which was selected, only 5.

For purposes of regression modelling, the two data layers needed to be interconnected so that
a building was unambiguously assigned to each fire record. The connection was performed as a
GIS overlay analysis (using the Spatial Join tool in the ArcGIS 10.2 program). Records within
50 m of the nearest building were assigned to said nearest building, while the remaining records
were removed. The connection’s result was a layer of buildings containing a binary attribute
with information on whether or not a fire occurred in the given building. No situations
occurred in which a single building would be assigned to multiple records. The last reduction
in the data layer was to remove as potential predictors for the regression model all elements
(i.e. buildings) for which complete data was not provided for all of the selected attributes
(see the Statistical Analysis section below). The required data filtration was automated using
Python scripts.

2.2. Factors potentially affecting fire probability

The next step involved analysing factors potentially affecting fire probability and selecting
suitable predictors to create probability maps. Basic demographic data about the territory

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Barták, V. et al.: Modelling the probability of building fires

and building attributes were examined.

For potentially significant building attributes, we considered building type (low-rise, high-rise,
industrial), house type (apartment, single-family, semi-detached, row), number of apartments
(category), supply of gas (yes/no), boiler room presence (yes/no), heating type (in-house, in-
apartment, remote, other), building age (before 1920, 1920–1945,1946–1960, then categories
by decade up to 2000, individual years distinguished after 2000), elevator presence (yes/no),
owner (individual, cooperative, municipality, other legal entities). The examined demographic
data were spatially related to administrative units of various degrees (municipality, munici-
pality with a delegated municipal office, municipality with extended jurisdiction, districts).
The number of inhabitants, territorial unit size, population density, and unemployment rate
were considered, given the assumption that a higher fire probability corresponds to a larger
population, larger territory, greater population density, and higher unemployment rate. For
this part of the analysis, layers from the freely accessible ArcČR500 3.0 database were used.

2.3. Statistical analysis

First, correlation between the number of fires and the number of inhabitants, population
density, territorial unit size, and unemployment rate were evaluated. As usual for data ex-
pressing abundance, the distribution of the number of fires within territorial units differed
significantly from the normal distribution and was skewed towards small values. The strength
of the relationship between fire incidents and demographic data was therefore evaluated using
Spearman’s rank correlation coefficient.

To determine significant building attributes, relative fire frequencies within individual building
attribute levels were tested, i.e. absolute fire frequency within individual levels was always
divided by the absolute frequency of buildings with the given attribute level. Differences
between frequencies were tested using a test for homogeneity of several binomial distributions
(always as many as the given attribute had levels). In this case, the tested hypothesis is that
fire probability is the same within all of the attribute’s levels. All hypotheses were tested at
a significance level of α = 0.05. These analyses resulted in a list of potential predictors –
building attributes that were then entered into fire probability modelling.

Subsequent probability map creation was based on a regression model which displays the
relationship between fire probability and a combination of building attributes. Considering
the binary nature of fire data, we used logistic regression (see Agresti [2]). Only buildings
with completed attributes (i.e. ca half of the records) were entered into the model. Based on a
simple visualization of omitted and retained buildings, we verified that the omitted buildings’
spatial pattern is similar to that of the retained buildings, i.e. that the necessary omission
of half of the records would only minimally affect the subsequent spatial expression of fire
probability. Predictors which satisfied the logistic model’s conditions (i.e. that the logits of the
selection’s quantitative variables follow an approximately linear trend) and which significantly
contributed to model quality were included into the resulting model. Predictors were chosen
by means of backward selection, i.e. using successive model simplification. The initial model
contained all considered predictors without their interactions. The basic criterion for model
selection was the lowest Akaike information criterion value (see Agresti [2] for method details).

To evaluate a model’s discriminating power, we used a generally acknowledged summary
statistic: the area under the receiver operating characteristic curve. This value is identical to

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Barták, V. et al.: Modelling the probability of building fires

Figure 1: Relationship between the number of fires in low-rise buildings and (a) number of
inhabitants and (b) territorial extent (ha) of municipalities with extended jurisdictions

Figure 2: Relationship between the number of fires in low-rise buildings and (a) number of
inhabitants and (b) territorial extent (ha) of municipalities with a delegated municipal office

so-called concordance, which is the relative frequency of “concordant” pairs, i.e. such pairs
where if the first is from those records with event (fire) incidence and the other is from those
without it, then the estimated probability is higher for the first than for the second. It is
clear that a usable model’s concordance value must be substantially greater than 0.5. Hosmer
and Lemeshow [10] presented the following interpretations of such values: 0.7–0.8 acceptable
discrimination; 0.8–0.9 excellent discrimination; above 0.9 “outstanding discrimination”.

In addition to a discrimination calculation, the resulting model also underwent internal val-
idation performed in 100 iterations. For each iteration, the entry data was divided into two
discrete sets: a calibration set (75% of records) upon which the model was fitted, and a
validation set (25% of records) upon which the model created from the calibration set was
applied. Individual models’ parameter values were summarized and thus their stabilities were
assessed (i.e. how much their values fluctuated through the iterations performed). In addi-
tion to parameter values, concordance was also calculated for each iteration, while doing so
separately for its validation and calibration sets.

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Barták, V. et al.: Modelling the probability of building fires

Table 1: Selection of prediction model for building fire probability. Backward selection was
used and the Akaike information criterion (AIC) was selected as its criterion. Individual
selection steps are divided by lines. In a given step, the model with the lowest AIC value was
selected (selected models are marked in bold). The process was repeated until all AIC values
were greater within the current step than the AIC value of the best model from the previous
step. The resulting selected model is thus the model selected as the best in the penultimate
step, i.e. model 4a. This model was subsequently used to create probability maps. Legend
for predictors: v1 – heating, v2 – owner, v3 – elevator, v4 – wall material, v5 – house type,
v6 – gas, v7 – category according to number of apartments.

Model Predictors Compared AIC Predictor removed
1 v1+v2+v3+v4+v5+v6+v7 4,460.902 Complete model without interactions
2a v2+v3+v4+v5+v6+v7 2a–1 4,456.919 Model without heating
2b v1+v3+v4+v5+v6+v7 2b–1 4,460.346 Model without owner
2c v1+v2+v4+v5+v6+v7 2c–1 4,466.768 Model without elevator
2d v1+v2+v3+v5+v6+v7 2d–1 4,454.768 Model without wall material
2e v1+v2+v3+v4+v6+v7 2e–1 4,479.949 Model without house type
2f v1+v2+v3+v4+v5+v7 2f–1 4,498.457 Model without gas
2g v1+v2+v3+v4+v5+v6 2g–1 4,461.416 Model without number of apartments
3a v2+v3+v5+v6+v7 3a–2d 4,450.268 Model without wall material and heating
3b v1+v3+v5+v6+v7 3b–2d 4,453.669 Model without wall material and owner
3c v1+v2+v5+v6+v7 3c–2d 4,464.100 Model without wall material and elevator
3d v1+v2+v3+v6+v7 3d–2d 4,473.839 Model without wall material and house type
3e v1+v2+v3+v5+v7 3e–2d 4,491.878 Model without wall material and gas
3f v1+v2+v3+v5+v6 3f–2d 4,456.074 Model without wall material and number of apartments
4a v3+v5+v6+v7 4a–3a 4,449.085 Model without wall material, heating and owner
4b v2+v5+v6+v7 4b–3a 4,460.299 Model without wall material, heating and elevator
4c v2+v3+v6+v7 4c–3a 4,468.160 Model without wall material, heating and house type
4d v2+v3+v5+v7 4d–3a 4,486.196 Model without wall material, heating and gas
4e v2+v3+v5+v6 4e–3a 4,451.167 Model without wall material, heating and number of apartments
5a v5+v6+v7 5a–4a 4,458.595 Model without wall material, heating, owner and elevator
5b v3+v6+v7 5b–4a 4,476.741 Model without wall material, heating, owner and house type
5c v3+v5+v7 5c–4a 4,486.448 Model without wall material, heating, owner and gas
5d v3+v5+v6 5d–4a 4,450.216 Model without wall material, heating, owner and number of apartments

After model selection and validation, the resulting model was used to predict fire probability
in individual buildings. Estimated probability values were added as a new attribute to the
attribute table of the building layer, which enabled their subsequent visualization in the form
of probability maps. Estimated probabilities were then averaged within territorial units and
the results were again visualized in map form. All statistical calculations described in this
section were performed using our own scripts in R, while map visualization was via the ArcGIS
10.2 program.

3. Results and discussion

3.1. Demographic characteristics and territorial extent

When using Spearman’s rank correlation coefficient to analyse associations between the num-
ber of fires and demographic characteristics and territorial extent, the selection of suitable
territorial units can present a difficulty. In such small units as a municipality there are fre-
quent duplicate fire number values (frequent repetitions of low values). The situation can be
resolved by random assignment of rank, but if there are many such values in the tested set,
then the result can be considerably distorted (and particularly the correlation coefficient’s
significance). Meanwhile, excessively large units do not provide sufficiently detailed spatial
information. Based on the results of the present study, optimal practice means using the poly-

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Barták, V. et al.: Modelling the probability of building fires

Table 2: Model parameters and measures of their stability. Model parameters in treatment
parameterization are contained in the FULL column. Values stated for individual levels of
qualitative predictors state the difference from the basic level included in the Intercept row.
Asterisks next to individual values in the FULL column indicate significance level in the test
of the non-zero parameter or, for qualitative predictors, the non-zero difference from the basic
level (*, ** and *** mean p < 0.05, p < 0.01 and p < 0.001, respectively). Other columns
summarize parameter values within 100 iterations performed during internal validation. The
QRNGdiv2 column expresses half of the inter-quartile spread as a robust alternative to stan-
dard deviation; CVar expresses in percentage the ratio of QRNGvar2 to absolute median
value, i.e. it is a robust variant of the variation coefficient and demonstrates the degree to
which the model parameters fluctuate around the median expressed as a percentage of the
median.

FULL Median QRNGdiv2 CVar Min Max
Intercept -6.43349*** -6.424 0.0415 0.65 -6.574 -6.306
Elevator 0.839882** 0.8406 0.0709 8.43 0.481 1.218
House type 1 1.133916*** 1.124 0.127 11.3 0.7181 1.451
House type 2 1.099528*** 1.09 0.078 7.16 0.8685 1.311
House type 3 -0.34709 -0.3834 0.1455 37.95 -1.428 -0.03358
House type 4 -0.27501 -0.2561 0.1061 41.43 -0.884 0.05618
Gas 1 0.95464*** 0.9647 0.0939 9.73 0.4434 1.245
Gas 2 -0.57129*** -0.5702 0.04365 7.66 -0.7622 -0.4323
Number of apartments 0.073533 0.07219 0.013325 18.46 0.02459 0.1133

gons of municipalities with a delegated municipal office (35 polygons in the Hradec Králové
Region and 21 in the Liberec Region), or, for more generalized images, the polygons of mu-
nicipalities with extended jurisdictions (15 polygons in the Hradec Králové Region and 10 in
the Liberec Region). High correlation coefficients (0.67–0.76) were achieved for associations
between the number of fires and the number of inhabitants and territorial unit extent (see
Figs. 1 and 2 for examples). For municipalities with a delegated municipal office, the number
of inhabitants had slightly greater correlation coefficients for individual fire types, and for
municipalities with extended jurisdictions correlations with territorial extent and with the
number of inhabitants are almost identical. The number of fires exhibited no association
with population density or unemployment, i.e. with any demographic variable that could
potentially be used to predict fires at the level of individual houses. Of the tested variables,
the number of inhabitants and the territorial extent are suitable predictors as to the number
of fires at the level of municipalities with a delegated municipal office and municipalities with
extended jurisdictions. These easily accessible data (territorial unit extent is always available)
can therefore be used for simple visualizations of fire hazards. These results are not in the
least surprising, however, as they only say that “the more space and potential sources (i.e.
people) there are, the more likely fire is”.

3.2. Prediction models and probability maps

When selecting a model using backward selection (see Table 1), interactions among predictors
were not considered. A model that included interactions would be too complex and for
many predictors would be prohibitively demanding computationally (which was one of the

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Barták, V. et al.: Modelling the probability of building fires

Figure 3: Results of concordance calculations during internal validation. The boxplots sum-
marize 100 iterations in which a random selection of 25% of the building records were always
used as the validation set and the remaining 75% was used to fit the model. The resulting
model was subsequently used in predictions on the validation set. Subsequently, concordance
was calculated for both the validation and calibration sets.

obstacles for internal validation based on repeated iterations). In addition, interactions among
individual variables would be very difficult to interpret and it cannot be assumed that they
would be demonstrated to be significant due to the relatively small number of events.

Of the examined building attributes, a combination of house type, number of apartments,
and whether a building had an elevator and gas connection best predicted fire probability
(see Table 1 describing model selection). The prediction model’s resulting parameters are
summarized in Table 2. The modest insignificance displayed by the number of apartments
(p = 0.07) could lead to doubts as to whether to retain this predictor in the model. However,
a predictor’s independent significance or insignificance is not the only criterion for retaining
a predictor in the model. It is also necessary to account for whether there is a strong reason
to believe that a predictor has in fact an influence on the explained variable, which is obvious
in the case of number of apartments and fire probability. It can therefore be argued that the
“correct” model should be based on individual apartment units rather than entire houses.
This is impossible, however, as fire data does not state specific apartment units. In addition,
such a model could not include fires in houses’ common spaces. Including the number of
apartments as a predictor therefore efficiently resolves the problem as to the unequal size of
basic spatial units (i.e. houses). Another reason to include the predictor in the model lies
in the result of the backward selection of the model, wherein including the predictor led to
a significantly better model and therefore higher-quality prediction. Including the predictor
of a house having an elevator might seem rather surprising. There is no clear interpretation
for this predictor that might offer a causative link to fires. Its inclusion is therefore based
only on comparing the model with and without it (see backward selection of the model, Table
1). The probable explanation is that it is a “placeholder” predictor, i.e. a building attribute
closely correlating with one or more attributes for which there is a causative link to fires. In
backward selection of the model, this predictor also “beat” predictors such as heating method
and wall material for which a correlation with fires could be expected. This suggests that
its inclusion is a way actually to bring indirectly into the model building properties which
influence fire probability but are not directly recorded in the building data.

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Barták, V. et al.: Modelling the probability of building fires

Figure 4: Section of the probability map created based on the prediction model, Liberec and
environs, visualization by buildings, natural breaks classification.

Figure 5: Average fire probability within municipalities with a delegated municipal office,
nature breaks classification.

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Barták, V. et al.: Modelling the probability of building fires

The calculated model concordance of 0.70 suggests acceptable model discrimination. The
stability of model parameters can be evaluated as very good based on internal validation (see
Table 2), as concordance in validation sets demonstrated an expectably larger dispersion than
that in calibration sets, and the median was surprisingly even slightly greater (see Fig. 3).
Probability maps created based on the prediction model can be used as the building layer
in visualizations and can therefore directly express fire probability in individual buildings
(see Fig. 4, section of Liberec). A second option is to average probabilities within selected
territorial units and map visualization of such acquired average building fire probabilities
within a given territorial unit (see Fig. 5).

4. Conclusions

Based on fire data recorded by FRS units, data from the Czech Statistical Office, and ac-
cessible layers of territorial units, a prediction model for fire incidents with acceptable dis-
crimination can be assembled. Logistic regression is a suitable technique which corresponds
to the binary character of the explained variable (incidence/non-incidence of fire) and also
enables estimation of fire probability in a specific building based on model parameters and
said building’s attributes. Fire probability can then be displayed in probability maps by
means of common GIS techniques and places with higher fire probabilities can be identified
by means of suitable visualizations. Maps based on the processes described come directly
from event data and can be updated using Python and R scripts created within the project.
If detailed building data is not available, classification according to the number of inhabitants
in the territorial units of municipalities with a delegated municipal office or municipalities
with extended jurisdictions or according to the extent of said units can be used for basic
visualization of building fire probability within a wider region.

Acknowledgement

This study was carried out under project no. VG20122014102 “Analytical Support of Risk
Mapping” of the Security Research unit of the Ministry of the Interior of the Czech Republic.

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