National Fire Estimation 

Using NFIRS Data

White Paper

May 2017

National Fire Estimation 

Using NFIRS Data

White Paper

May 2017

This white paper was produced under contract GS-10F-0195X, order HSFE20-12-F-0240 

between 2013 and 2017 by PG Public Services, LLC for the U.S. Fire Administration, Federal 

Emergency Management Agency.

This paper was peer-reviewed by the following: Professor Charles Jennings, Ph.D., MIFireE, 

CFO in the Department of Security, Fire and Emergency Management at the John Jay College 

of Criminal Justice and Professor Susan Simmons, Ph.D., in the Department of Mathematics 

and Statistics at the University of North Carolina at Wilmington.

Mission Statement

We provide national leadership to foster a solid foundation for 

our fi re and emergency services stakeholders in prevention, 

preparedness and response.

Table of Contents i

Table of Contents

Summary ............................................................................................................................ 1

Overview............................................................................................................................. 1

Introduction to National Fire Estimates......................................................................... 3

National Fire Incident Reporting System...................................................................... 4

About the National Fire Incident Reporting System ............................................ 4

Representativeness of the National Fire Incident Reporting System Data ...... 4

Review of the Literature................................................................................................... 7

Outdoor fires — Fuel, land use, topography and weather factors........................... 10

Structure fires — Demographic and socioeconomic factors .................................... 11

Vehicle fires — Population and socioeconomic factors ............................................. 11

New factors ...................................................................................................................... 12

Developing a National Fire Incident Reporting System-Based National Estimates 

Methodology............................................................................................................... 13

ZIP code versus ZIP Code Tabulation Areas ................................................................. 14

Imputation methods ....................................................................................................... 15

Fires from the National Fire Incident Reporting System..................................... 16

Range errors .............................................................................................................. 17

Aid given data............................................................................................................ 17

True zeroes................................................................................................................. 20

Missing data and late data....................................................................................... 21

Cumulative effect of data adjustments ................................................................. 21

Scaling model ................................................................................................................... 22

Regression model ............................................................................................................ 23

Relating demographic and socioeconomic data .................................................. 26

Relating weather data, land use, fuel and topography ....................................... 26

Relating business population data......................................................................... 26

Relating vehicle crash data ...................................................................................... 27

Estimating fire incidents — Regression model..................................................... 28

Multiyear analysis ..................................................................................................... 32

Estimation model...................................................................................................... 32

Limitations.......................................................................................................................... 35

Conclusions and Further Work ....................................................................................... 37

References.......................................................................................................................... 39

Acronyms............................................................................................................................ 43
ii National Fire Estimation Using NFIRS Data White Paper

List of Figures and Tables

Figure 1. Comparison of ZCTA versus ZIP code boundaries ........................................ 13

Figure 2. Matching NFIRS address data to ZCTAs (2010): Incidents and ZIP codes .. 16

Figure 3. Number of businesses and fire incidence ..................................................... 28

Figure 4. Number of vehicle crashes and fire incidence.............................................. 29

Table 1. Meta-analysis of fire factors.............................................................................. 6

Table 2. NFIRS fire incidents by type of aid — All valid incidents (2010) ................... 17

Table 3. Initial match parameters for aid incidents...................................................... 18

Table 4. Matching NFIRS aid given-received incidents, model parameters (2010) .. 19

Table 5. Total unique NFIRS fire incidents (2010).......................................................... 20

Table 6. Summary of NFIRS incident census (2010) ...................................................... 22

Table 7. National estimates using scaling (2010)........................................................... 23

Table 8. Summary of data factors and sources............................................................. 24

Table 9. Additional factors not analyzed........................................................................ 25

Table 10. Variables and variable definitions used in regression model .................... 30

Table 11. Multivariate regression coefficients............................................................... 32

Table 12. Comparison to other models .......................................................................... 33

Table 13. Comparison of model across years (2009-2011)........................................... 33

Table 14. Summary of national estimates by different methods ............................... 34
Summary | Overview 1

Summary

The objective of this study is to develop a method of generating an annual national estimate 

of fire incidence for the United States based on the U.S. Fire Administration’s (USFA’s) 

National Fire Incident Reporting System (NFIRS) and other publicly available data. Imputation 

methods were used to adjust for missing or unreported data. Two estimation methods 

were analyzed: a population scaling method and a multivariate regression method. The 

scaling method determines a national estimate of fire incidence by first calculating the 

ratio of reported fire incidences to the population in the areas where those incidents were 

reported, and then comparing it to the total U.S. population. For the multivariate regression 

model, fire incidence was estimated for each ZIP Code Tabulation Area (ZCTA) in the U.S. 

using a variety of socioeconomic, demographic and environmental factors. The findings 

of this study are presented in comparison with the findings of previously related analyses.

Among the major findings of this study are the following:

ĵ Both the scaling and multivariate regression methods resulted in similar national 

estimates indicating that population alone could be used to develop a national estimate.

ĵ Missing data, where a fire department reports some but not all incidents to the NFIRS, 

can materially affect the estimate.

ĵ Careful de-duplication of aid incident data within the NFIRS reveals a wealth of new 

incident data previously excluded.

ĵ The addition of data factors regarding business population and vehicle crash data 

significantly added to the identification of location and volume of fire incidents.

Overview

This white paper presents two methodologies to derive a national estimate for the total 

number of fire incidents in the U.S. using the incident data submitted to the NFIRS. The 

2010 validated fire incident data from the NFIRS was used as the basis. There were several 

reasons for this choice. First, at the time of the initial study in 2012, it was the most recent 

NFIRS fire incident data available. Second, in using the 2010 NFIRS data, there would be no 

lag between the population characteristics collected from the 2010 Census and the 2010 

fire incidents as reported in the NFIRS. Lastly, demographic data at appropriate geographic 

levels was available for geographies in 2010.

A subsequent application of the methodology to 2009 and 2011 NFIRS fire incident data 

was undertaken to assess the robustness of the methodology.

After a brief introduction to national fire estimates and the NFIRS, the report begins 

with a review of literature on fire incidence modeling to understand the broad scope of 

factors across the fire problem. A discussion of the NFIRS data itself follows. Because of 

known limitations of NFIRS data, it was also necessary to develop techniques for data 

adjustments that can be applied to the NFIRS to address these limitations. These techniques 

are discussed, as well as two methods — a scaling method that uses population, and a 

multivariate regression method that uses variables derived from a review of relevant 

research on the topic of fire incidence — to describe how NFIRS data, in combination with 

other publicly available data, can be used to create national estimates of fire incidence.
2 National Fire Estimation Using NFIRS Data White Paper
Introduction to National Fire Estimates 3

Introduction to National Fire Estimates

This white paper presents a comparison between two methodologies that derive a national 

estimate for the total number of fire incidents in the U.S. using the incident data submitted 

to the NFIRS in conjunction with other publicly available data. The term “national estimates” 

refers to annual estimates of the numbers of fires, deaths, injuries and dollar loss. Currently, 

these high-level summary national estimates on the number of fires, deaths, injuries and 

dollar loss are based on the National Fire Protection Association’s (NFPA’s) annual Survey of 

Fire Departments for U.S. Fire Experience. Lower-level estimates for a particular fire statistic 

are based on a scaling method employing both the USFA’s NFIRS data and national fire 

estimates derived from the NFPA’s annual Survey of Fire Departments for U.S. Fire Experience.

The NFIRS represents the world’s largest national annual database of fire department 

incident information. Each year, approximately 23,000 fire departments from all 50 states 

and the District of Columbia voluntarily report data on one million fires and 22 million 

other fire department-responded incidents, such as hazardous material incidents or 

smoke scares. The NFIRS is not a census of all fires, and it is not based on a statistically 

derived sample. NFIRS raw totals do not reflect the whole of the U.S. fire problem. The 

NFIRS contains incident data derived from voluntary reporting of fire incidents in the U.S.

The NFPA survey produces national level fire loss statistics, as well as estimates by major 

incident type. The NFPA raw survey data are proprietary and are not made available to 

the public or to the USFA.

Generally, a national estimate for a particular fire statistic is derived by computing a 

percentage of fires, deaths, injuries or dollar loss in a particular NFIRS category and 

multiplying it by the corresponding total estimate from the NFPA annual survey.1 One 

issue with this approach is that the proportions of fires and fire losses differ between the 

NFIRS-submitted data and the NFPA survey sample. This approach leads to inconsistencies 

because of the differing proportions of fires and fire losses between the NFIRS and the 

NFPA estimates.2 Nonetheless, this method of scaling up is the current practice accepted 

by national fire data analysts, despite the fact that the two sources have different 

methodologies for collecting data. Without access to the NFPA survey data, it is difficult 

to ascertain why these differences exist. Ideally, all of the fire incident data would come 

from one consistent data source — the NFIRS. These inconsistencies will remain until all 

estimates can be derived from the NFIRS data.

To date, the NFIRS is not a complete source for fire incident data. Its data is neither complete 

nor a statistical sample. Calculating proportions based on the NFIRS is challenging because 

the NFIRS does not include the population represented by the reporting fire departments, 

which is a critical piece of information. This “residential population protected” is not 

reported to the NFIRS, nor is the data easy to come by, especially where a county or other 

jurisdiction is served by several fire departments that each report their fires independently.

1

The NFPA summary estimates are used for the overall U.S. fire losses; fire losses from structure, vehicle, 

outside, and other fires; and as the basis for USFA’s estimates of residential and nonresidential building fires. 

The alternative approach for these summary numbers is to use the relative percentage of fires (or other loss 

measures) from the NFIRS and to scale up (multiply by) the NFPA estimate of total fires. 

2The inconsistencies in the relative proportions of subsets of the fire problem, between the large NFIRS data 

set and the NFPA survey, result in differing estimates for these subsets. For example: In 2010, the NFPA survey 

resulted in an estimate of 294,000 one- and two-family residential structure fires — where most of the casualty 

losses occur. Using the NFIRS proportions to derive an estimate results in estimates of 253,000 or 258,000 

fires, depending on the scaling method.
4 National Fire Estimation Using NFIRS Data White Paper

Other issues also prevent the NFIRS from being a complete source for fire incident data, 

such as reporting deadlines, data access, and budgetary considerations. However, the 

USFA believes it is possible to harness the NFIRS data to produce national estimates of 

the U.S. fire problem.

National Fire Incident Reporting System

The Federal Fire Prevention and Control Act of 1974 (Public Law 93-498) authorizes the USFA’s 

National Fire Data Center (NFDC) to gather and analyze information on the magnitude of 

the nation’s fire problem, as well as its detailed characteristics and trends. The Act further 

authorizes the USFA to develop uniform data-reporting methods, and to encourage and 

assist state agencies in developing and reporting data. In order to carry out the intentions 

of the Act, the NFDC established the NFIRS.

About the National Fire Incident Reporting System

The NFIRS has two objectives: to help state and local governments develop a fire reporting 

and analysis capability for their own use, and to obtain data that can be used to more 

accurately assess and subsequently combat the fire problem at a national level. To meet 

these objectives, the USFA has developed the NFIRS data collection standard. This NFIRS 

package, maintained by the USFA, includes forms, a coding structure for data processing 

purposes, a standard system specification, manuals, computer software and procedures, 

and documentation for using the system.

The NFIRS collects fire incident data from state fire data systems. The state systems, in 

turn, collect data from their individual fire departments. State participation in the NFIRS 

is voluntary, and the guidelines for departmental participation within each state are 

determined by the state fire marshal’s office or the equivalent agency. These guidelines 

can vary significantly from state to state. In most states, reporting by local departments 

is not mandatory; the departments that report are those that are willing to participate 

and can afford the additional commitment necessary to collect the data.

Participating local fire departments fill out the incident reports as emergency responses 

occur. They forward the completed reports via paper forms or digital transactions to their 

state reporting authority and to the USFA, where the data is validated and consolidated 

into a single computerized database.

The database is used to answer questions about the nature and causes of injuries, deaths 

and property losses resulting from fires. This information is disseminated through a variety 

of means to the public, as well as to government and private organizations.

The NFIRS is a model of successful federal, state and local partnerships. The database 

constitutes the world’s largest national annual collection of incident information.

Representativeness of the National Fire Incident Reporting System Data

The percentage of fire departments participating in the NFIRS varies from state to state, 

with some states not participating at all in some years. Even in this case, individual fire 

departments are currently able to submit incident data directly to the USFA. Thus, all fire 

departments in the country are able to participate, regardless of whether the state in 

which it is located participates. To the best that the USFA can determine, the distribution 

of participants, even though it is not a scientifically selected sample, is reasonably 
Introduction to National Fire Estimates 5

representative of the entire nation. The data set is large. It is reasonably distributed 

geographically and by size of community so that fire data analysts can use the data to 

analyze the U.S. fire problem on a national level.

Most of the NFIRS data exhibits stability without radical changes from one year to another. 

Results based on the full data set are generally similar to those based on part of the 

data — an indication of data reliability.3

3Data Sources and Methodology Documentation, USFA, NFDC, March 2014: https://www.usfa.fema.gov/

downloads/pdf/statistics/data_sources_methodology.pdf.
6 National Fire Estimation Using NFIRS Data White Paper
Review of the Literature 7

Review of the Literature

Prior research has shown that climate, demographic and socioeconomic characteristics can 

be useful in predicting the magnitude and nature of fire problems in different geographic 

areas. This research has typically focused on a single aspect of the fire problem, such 

as urban or wildland fires, rather than incidence as a whole. It has also focused on the 

likelihood or the risk of fire rather than the magnitude of fire incidence. The focus of the 

current research is to analyze the fire problem for the entire country in a single model. 

This is a unique undertaking. To identify potential explanatory variables, a meta-analytic 

review was undertaken concerning available journal literature on fire-incidence modeling 

to understand the broad scope of factors across the fire problem.

A search was conducted using Mendeley, a reference management software package, 

with the following search terms: ‘fire frequency’, ‘fire hazard’, ‘fire risk’, ‘fire incident’, ‘fire 

management’, ‘fire regime’, ‘fire occurrence’, ‘fire activity’, ‘vehicle fire’, ‘wildland fire’, ‘urban 

fire’, ‘predicting fire’, ‘estimating fire’, ’residential fires’, ‘residential fire factors’, ‘structure 

fires’, and ‘socioeconomic fire’.

In all, 64 papers were analyzed. For each paper, any significant demographic, socioeconomic 

or environmental factors that had been analyzed were recorded. Additionally, the type 

of fire that was being analyzed (structure, vehicle or outdoor) was recorded. In some 

analyses, the type of fire was comingled for both structure and vehicle, and these were 

recorded as ‘structure/ vehicle.’ Factors were organized into common families (behavior, 

fuel, land use, population, socioeconomic, topography, vehicle and weather), and names 

of variables were associated with a common factor.

A meta-analysis was developed concerning the identified factors that were found. The 

result of that analysis is in Table 1. The table represents an ontology of fire factors, as well 

as a count of the number of times that each factor appeared in the analyses. Occasionally, 

a paper might include individual factors that were joined into a common factor. Within 

a given category, counts can be seen as identified major variables that contribute to the 

cause category.
8 National Fire Estimation Using NFIRS Data White Paper

Table 1. Meta-analysis of fire factors

Category Factor Outdoor Structure Structure/ 

Vehicle Vehicle Grand total

Behavior Alcohol use 1 1

Playing with fire 5 5

Smoke alarm 

presence 1 1

Smoking 3 3

Fuel Biomass 11 11

Soil moisture 5 5

Forest stand age 1 1

Time from last 

fire 1 1

Land use Distance to 

campsite 2 2

Distance to 

farmland 1 1

Distance to road 7 7

Distance to town 1 1

Industrial 1 1

Livestock units 3 3

Park 3 3

Paths 1 1

Privately owned 1 1

Road density 2 1 3

Secondary 

housing 2 2

Urban 1 1

Population Age 9 1 10

Population 1 3 4

Population 

density 2 3 5
Review of the Literature 9

Table 1. Meta-analysis of fire factors — continued

Category Factor Outdoor Structure Structure/ 

Vehicle Vehicle Grand total

Socioeconomic Age of structure 7 7

Car ownership 1 1 2

Education level 7 1 8

Employment 1 1

Home ownership 9 1 10

Home value 1 1

Household 

income 29 1 2 32

Household size 4 3 7

Housing density 2 2

Married no 

children 1 1

Minority 

population 8 2 10

Residential 

structures 3 3

Single-parent 

household 10 1 11

Single person 1 1

Telephone 

ownership 1 1

Unemployment 

rate 3 3

Vacancy 9 9

White population 1 1

Topography Altitude 4 4

Aspect 3 3

Elevation 2 2

Slope 6 6

Vehicle Age of vehicle 1 1

Number of 

vehicles 1 1

Type of vehicle 1 1

Weather Lightning 1 1

Precipitation 10 1 1 12

Relative 

humidity 6 1 7

Temperature 17 2 1 20

Wind speed 6 6

Grand total 110 114 17 6 247
10 National Fire Estimation Using NFIRS Data White Paper

Outdoor fires — Fuel, land use, topography and weather factors

There has been extensive research linking weather data, land use, fuel and topography 

to fire risk and outdoor fires, specifically wildfires.

Of all the factors contributing to outdoor fires/wildfires, weather is the most commonly 

identified contributing factor. Common weather factors include precipitation, relative 

humidity, temperature, wind conditions and lightning. Temperature is the most commonly 

analyzed weather factor. Common temperature factors include annual mean temperature 

(Guyette, Stambaugh, Dey, & Muzika, 2012), average temperature in the warmest month 

(Amatulli, Rodrigues, Trombetti, & Lovreglio, 2006), minimum temperature (Serra, Saez, 

Juan, Varga, & Mateu, 2013), and maximum temperature (Serra et al., 2013) (Dutta, Aryal, 

Das, & Kirkpatrick, 2013). Common precipitation factors include mean annual precipitation 

(Guyette et al., 2012) (Amatulli et al., 2006); mean summer precipitation (Wotton, Martell, 

& Logan, 2003); evapotranspiration (Dutta et al., 2013); rainfall (Harris, 2012); and indices, 

such as a drought or moisture codes (Wotton et al., 2003). Relative humidity was analyzed 

by a number of studies (Harris, 2012) (Mandallaz & Ye, 1997) (Dutta et al., 2013) (Garcia, 

Woodward, Titus, Adamowicz, & Lee, 1995). Common wind condition factors include 

wind speed (Harris, 2012) (Dutta et al., 2013) (Garcia et al., 1995), wind direction (Harris, 

2012), and wind velocity (Mandallaz & Ye, 1997). Lightning strike was also identified as a 

contributing factor (Xin J. & Huang, 2013).

Fuel factors include biomass composition, soil conditions, forest stand age, and time from 

last fire. Biomass factors include the type of vegetation (Fox et al., 2015), tree species (Xu 

et al., 2006), areas of grass or deciduous cover and buildup (Garcia et al., 1995), burned 

land cover (Diaz-Delgado, Lloret, & Pons, 2004), and canopy density (Xu et al., 2006). Soil 

condition measures include dryness index (Mandallaz & Ye, 1997), fine fuel moisture index 

(Wotton et al., 2003) (Garcia et al., 1995), and soil moisture (Dutta et al., 2013). Additionally, 

stand age (Xu et al., 2006) and time from last fire (Brotons, Aquilué, de Cáceres, Fortin, & 

Fall, 2013) have been analyzed as contributing to the risk factors for wildfires.

Land use factors have also been identified as contributing to outdoor fire risks. Most often, 

these factors include distance to roads or road density (Romero-Calcerrada, Barrio-Parra, 

Millington, & Novillo, 2010) (Amatulli et al., 2006) (Xu et al., 2006) (Garcia et al., 1995), distance 

to the nearest town (Garcia et al., 1995), distance to farmland (Xu et al., 2006), distance 

to campsites (Romero-Calcerrada et al., 2010) (Garcia et al., 1995), as well as specific land 

uses, such as industrial (Romero-Calcerrada et al., 2010), parks (Romero-Calcerrada et al., 

2010) (Amatulli et al., 2006) (Garcia et al., 1995), and urban (Romero-Calcerrada et al., 2010). 

Additionally, specific types of farm use and the livestock count, such as sheep, goats and 

cattle, have also been analyzed (Romero-Calcerrada et al., 2010).

Topography factors were also frequently identified in fire risk studies. These factors 

included altitude, aspect, elevation and slope. Slope was the most common topography 

factor and was identified by a number of studies (Harris, 2012) (Amatulli et al., 2006) (Serra 

et al., 2013) (Xu et al., 2006) (Diaz-Delgado et al., 2004). Altitude (Serra et al., 2013) (Xu et al., 

2006) (Amatulli et al., 2006) (Diaz-Delgado et al., 2004), aspect (Serra et al., 2013) (Amatulli 

et al., 2006) (Xu et al., 2006), and elevation (Guyette et al., 2012) (Garcia et al., 1995) were 

also common topography factors.
Review of the Literature 11

Structure fires — Demographic and socioeconomic factors

There has been extensive research linking demographic and various socioeconomic factors 

with structure fires.

Demographic factors were commonly identified factors in urban fire rate studies. In 

particular, the presence of children (Roberts, 1996) and the presence of older adults 

(Jennings, 1996) (Shai, 2006), as well as the total population (Hall, 1993) (Munson, 1975) and 

population density (Munson, 1975) (Jennings, 1999), are frequently identified as factors.

The most widely studied set of factors for structure fires are socioeconomic factors. These 

factors are wide-ranging and include household income, household makeup, housing 

stock, education levels, and minority population.

Household factors were the most common factors identified, particularly the following: 

household income (Runyan et al., 2005) (Harvey, 2004) (Jennings, 1999) (Lizhong, Heng, 

Yong, & Tingyong, 2005) (Gunther, 1981) (Shai, 2006), as well as related factors including the 

percentage of households that were renting (Runyan et al., 2005) (Roberts, 1996) (Harvey, 

2004), and the number of households that were in poverty (Gunther, 1981) (Jennings, 1999) 

(Fahy & Norton, 1989) (Munson & Oates, 1983) (Runyan et al., 2005) (Karter & Donner, 

1978) (Schaenman, 1977).

The composition of the household is important. Single parent households and parental 

presence were common factors (Lizhong et al., 2005) (Chhetri, Corcoran, Stimson, & 

Inbakaran, 2010) (Jennings, 1999) (Karter & Donner, 1978) (Schaenman, 1977).

The common housing stock data factors include age of structure (Xin & Huang, 2013) 

(Lizhong, Xiaodong, Zhihua, & Weicheng, 2002) (Jennings, 1999) (Shai, 2006), residential 

and commercial structure mix, and housing density (Jennings, 1999).

Education level was also a common factor (Corcoran, Higgs, & Higginson, 2011) (Shai, 2006) 

(Lizhong et al., 2005) (Jennings, 1999) (Schaenman, 1977).

Minority population factors, such as the percentages of the indigenous population (Chhetri 

et al., 2010), African American population (Jennings, 1999) (Munson & Oates, 1983), and 

foreign-born population (Shai, 2006) (Jennings, 1999), have been identified as well — in 

particular, as interaction factors with education and poverty (Jennings, 1999).

Additionally, behavioral factors, such as smoking (Runyan, Bangdiwala, Linzer, Sacks, & 

Butts, 1993) (Jennings, 1999) (Xin & Huang, 2013), the presence of smoke alarms (Clare, 

Len, Plecas, & Jennings, 2012), playing with fire (Xin & Huang, 2013) (Lizhong et al., 2002), 

and alcohol use (Jennings, 1999) have been identified with increased fire risk.

Vehicle fires — Population and socioeconomic factors

In general, the vehicle fire problem is under-researched. The research has often overlapped 

with the analysis of residential structure fires. Common factors have been identified, such as 

population age, home ownership, household income, household size, minority population, 

single parent households, and education level (Corcoran, Higgs, Brunsdon, Ware, & Norman, 

2007). Some specific factors have been analyzed around vehicle fire occurrences, including 

number of vehicles (Bunn, Slavova, & Robertson, 2012) (Corcoran et al., 2007), type and age of 

vehicle (Bunn et al., 2012) (Ahrens, 2005), and highway passenger vehicle traffic (Ahrens, 2005).
12 National Fire Estimation Using NFIRS Data White Paper

New factors

Supported by this background research, it appears the location and volume of the fire 

problem in the U.S., with the exception of some wildland fires, is largely a factor of human 

presence. Existing research has focused on measures where people live; however, it does 

not measure where they work, play, or the areas that they traverse. To supplement this 

gap in the research, additional variables and data sources were identified. The identifiers 

include business population and vehicle crash data, which might potentially explain this 

previously unanalyzed aspect of the fire problem.
Developing a National Fire Incident Reporting System-Based National Estimates Methodology 13

Developing a National Fire Incident 

Reporting System-Based National 

Estimates Methodology

Most prior research examined fire incidences over small areas and identified factors that 

correlate to fire incidences for specific types of fires. The research was mainly on residential 

fires or urban fires. The focus of these research efforts was at a city level where the analysis 

used census blocks and corresponding socioeconomic data. The current research objective 

is to create a more complete national estimate for all types of fires, including residential, 

nonresidential, vehicle and wildland fires.

This analysis focuses on ZIP code data rather than census block data. Initially, the census block 

approach was chosen to reduce the computational complexity of the model, but data quality 

issues in geocoding incidents to the correct census block favored a ZIP code based model.

Two major estimation methodologies to generate a national fire estimate were explored: a 

population-based scaling model and a multivariate regression model based on population, 

as well as other independent variables.

Hall and Harwood discuss a technique for producing a national estimate based on population 

protected (1989). This technique relies on each fire department having accurate counts 

of the number of people protected. With that data, it would be possible to create an 

estimate for nonfire incident reporting fire departments by calculating the ratio of fires 

per protected person for reporting fire departments, and multiplying it by the number of 

people protected by nonreporting fire departments.4 However, population protected is 

a difficult statistic to gather, as is a full census of fire departments.5 NFIRS provides fires 

by ZIP code, and the U.S. Census Bureau’s American Community Survey (ACS) provides 

population by ZCTA, which is very similar to ZIP code. By using this data, a scaling model 

can be deployed to estimate national fire incidence.

In the scaling model, the population coverage data for the existing NFIRS data was improved 

by using ACS data for population by ZIP code (or more correctly, ZCTA). With a more accurate 

count of population coverage, the total incident data that is reported in the NFIRS is “scaled 

up” to estimate national fire incidence.

4Population protected applies to municipal fire departments (whether paid or volunteer). Hall and Harwood 

assume that the number of fire departments is known. Several estimates on the total number of fire 

departments exist, notably by the NFPA and the USFA. However, these estimates include different categories 

of fire departments (military, industrial brigades, and the like, as well as municipal), not all of which have 

“populations” associated with them. Hall and Harwood also assume a community basis for fire rates, i.e., those 

fire departments protecting similar sized populations will have similar fire rates.

5Several initiatives, including one at the NFPA and one at the USFA, have tried to tackle the census of fire 

departments. The NFPA’s effort is the Fire Service Inventory. From published data from the Inventory, there 

were 30,125 fire departments in 2010 (http://www.nfpa.org/research/reports-and-statistics/the-fire-service/

administration/fire-departments (accessed January 31, 2016)). The USFA National Fire Department Registry 

can be considered a nearly complete census. The National Fire Department Registry is a voluntary program 

and only includes those fire departments that have chosen to register with the program. To date, the National 

Fire Department Registry database includes over 27,100 fire departments. If the NFPA Fire Service Inventory 

reflects a full census of fire departments, not all fire departments in the U.S. are registered with the National 

Fire Department Registry. These departments, however, represent about 90 percent of the fire departments 

estimated by the NFPA to be in the U.S. Because the registry is a voluntary program, the USFA continues 

to encourage fire department participation. In addition, about one-fifth of the registered departments are 

contacted each year (on a rotating basis over a five-year period) to provide updates to their data, with about 

20 percent of these departments providing updates. (USFA Staff).
14 National Fire Estimation Using NFIRS Data White Paper

In the regression model, multiple independent variables, identified from the fire factor 

meta-analysis, were analyzed to develop a best-fit regression model with existing NFIRS 

data. This model was used to calculate an estimate of fire incidence for areas where no 

NFIRS data was reported. These estimates were then added to the NFIRS data to generate 

an overall national fire estimate.

In this analysis, NFIRS fire incident data for 2010 was used as the basis for the estimate 

methodology, in conjunction with five years of ACS estimate data (2007 to 2011). Five-year 

ACS estimate data includes data for all areas, is the most reliable, and is recommended 

where precision is more important than currency — as is the case in this analysis.6

ZIP code versus ZIP Code Tabulation Areas

One complication in using ZIP code level data for estimation is that the U.S. Census Bureau 

releases population and other demographic and socioeconomic estimates using ZCTA 

rather than ZIP codes.

The U.S. Postal Service ZIP codes are not area features, but rather a collection of mail 

delivery routes. The U.S. Census Bureau developed ZCTAs to approximate ZIP codes by 

taking the most frequently occurring ZIP code in each 2010 census block and assigning 

it to a ZCTA with the same designation as that ZIP code (e.g., a ZCTA with 22030 as its 

primary ZIP code would be designated ZCTA 22030). As such, ZCTAs are aggregations of 

2010 census blocks, where a plurality of addresses in the block have the same ZIP code. 

Since census blocks are not split across ZCTAs, some addresses at the edge of a ZIP code 

boundary may have a ZCTA different from its ZIP code, as shown in Figure 1.

Figure 1. Comparison of ZCTA versus ZIP code boundaries

Source: Phil Hurvitz, “What is the difference between ZIP code “boundaries” and ZCTA areas?” http://gis.washington.edu/phurvitz/

zip_or_zcta/.

6U.S. Census Bureau, “When to use one-year, three-year, or five-year estimates,” http://www.census.gov/acs/

www/guidance_for_data_users/estimates/ (accessed January 31, 2016). 

ZIP code boundary ZCTA boundary
Developing a National Fire Incident Reporting System-Based National Estimates Methodology 15

As an initial foray into creating an estimation methodology, the working assumption is that 

a ZCTA-based estimation model will be sufficient at the state and national levels, as these 

differences will cancel out across large geographic areas because of the relatively small 

geographic differences between ZIP codes and ZCTAs. In addition, using a ZIP code level 

based area as a preliminary avenue of investigation has the advantage of computation 

efficiency and the ease to tie directly to the NFIRS data. For the purposes of this initial 

analysis, ZIP codes and ZCTAs are treated as synonymous.

ZCTAs may not be sufficient when dealing with the subparts of the fire problem, such as 

county or fire cause, but it is believed to be sufficient as an initial avenue of investigation. 

As geocoding processes are refined and assessed, it may be possible to transition to a 

census tract based estimation methodology. Census tracts provide more granularity, 

geographic coverage, and statistical uniformity than ZCTAs and are generally preferred 

for such analysis. In addition, using census tracts eliminates the translation issues from 

ZIP codes to ZCTAs.7 At this time, however, the current geocoding of NFIRS addresses is 

not sufficiently accurate to use census tracts for national estimates.

Imputation methods

Imputation, a process of replacing missing data with substituted values, is a common 

statistical technique that is used by many government agencies to adjust for various types 

of nonresponse in survey data. For example, the U.S. Census Bureau employs “count 

imputation” for nonrespondents and “characteristic imputation” to generate a complete 

population count, as well as to impute other demographic data where respondents omit 

race, age or other personal information. In the 2010 census, count imputation added 1.2 

million people, which represented 0.39 percent of the total U.S. population as determined 

by the U.S. Census Bureau (Cohn, 2011).

In its Current Population Survey, the U.S. Census Bureau also uses several imputation 

methods for nonresponse (Imputation of Unreported Data Items, 2013). The Bureau of 

Labor Statistics and the Bureau of Economic Analysis have developed several imputation 

methods for nonresponse (Eltinge, Kozlow, & Luery, 2003). With respect to fire data, analysts 

at the Consumer Product Safety Commission use imputation for distributing unknown 

fire cause entries (Greene, Smith, Levenson, Hiser, & Mah, 2001).

Generally, the U.S. Census Bureau uses averages from similar households within a particular 

census tract to estimate the nonrespondents. In between censuses, the U.S. Census Bureau 

uses a combination of birth, death and immigration/emigration records to estimate the 

current population (Cohn, 2011). A similar technique can be used to fill in the NFIRS data 

by identifying similar areas.

For this effort, 2010 validated fire incident data from the NFIRS was used as the basis for 

developing a methodology to estimate the annual overall U.S. fire incidence. There were 

several reasons for this choice. First, at the time of the initial study in 2012, it was the 

most recent NFIRS fire incident data available. Second, in using the 2010 NFIRS data, there 

would be no lag between the population characteristics collected from the 2010 census 

and the 2010 fire incidents as reported in the NFIRS. Lastly, ACS data at the ZCTA level was 

available for all ZCTAs in 2010. 

The NFIRS fire incident data was adjusted to account for the following: certain additional 

aid incidents (incidents where one fire department assists another), fire departments and 

ZIP codes where no fires occurred but other types of incidents were reported, potential 

missing data, and late submission data.

7https://www.census.gov/geo/reference/pdfs/GARM/Ch10GARM.pdf (accessed January 31, 2016).
16 National Fire Estimation Using NFIRS Data White Paper

Fires from the National Fire Incident Reporting System

The NFIRS dataset is fluid and constantly changing as fire departments update, upload 

and submit their data. Once the fire department of record validates its data, it “releases” 

the data, making it available for analyses at the national level. The most common set of 

released NFIRS data is the Public Data Release (PDR). This annual subset of NFIRS data is a 

compilation of a calendar year’s incident data which has been validated for release by the 

fire department of record and submitted to the NFIRS database by July 1 of the following 

year. The annual PDR is not re-released to reflect subsequent incident submissions after 

the reporting deadline. The PDR does not contain all validated data submitted by fire 

departments; it only contains released, validated data.

The validated incidents that the PDR does not contain are simply unreleased incidents. 

Generally, the reason for not releasing data is just an oversight on the part of the state 

NFIRS program manager. In terms of input to a national estimates methodology, using all 

validated data — released and unreleased — represents the most complete set of incidents 

from U.S. fire departments.

There were 1,227,719 validated fire department fire runs (records) reported in the NFIRS 

in 2010. A run, a record of each time a fire department responds to a service call, is not 

equivalent to an incident, as more than one department may respond to the same incident. 

This situation is called “aid.” Using the USFA accepted definition of a fire incident, 1,003,556 

of these runs were validated fire incidents in 26,669 ZIP codes (Figure 2).8 In the data, several 

of the ZIP codes reported were invalid for various reasons. Of those, 314 ZIP codes were 

invalid because they were not five-digit numbers greater than zero. There were 34,671 

fires reported for these 314 ZIP codes (3.3 percent of fires; 1.1 percent of ZIP codes). In 

addition, since both the scaling and the regression model rely on data from the ACS, only 

ZIP codes that match ZCTAs could be used in the analysis. This requirement meant that 

the 26,396 fires reported for the 1,832 ZIP codes that did not match a ZCTA were also 

removed from the data set (2.6 percent of fires; 6.9 percent of ZIP codes). After removing 

invalid ZIP codes and matching ZIP codes to ZCTAs, there were 972,489 fires (94.1 percent 

of all reported fires) in 24,523 ZIP codes/ZCTAs.

8The USFA accepted definition of a fire incident only includes records of the primary fire department in whose 

jurisdiction the incident occurred. This is achieved by excluding records reflecting aid given. The theory is 

that, in essence, not excluding aid incidents when analyzing incidents will result in double counting those 

incidents where both the giving and receiving departments report to the NFIRS. See USFA’s National Fire 

Incident Reporting System Version 5.0 Fire Data Analysis Guidelines and Issues.

It is important to note that this definition does not indicate how to count incidents where the aid receiving 

department does not report to the NFIRS, but the aid giving department does.
Developing a National Fire Incident Reporting System-Based National Estimates Methodology 17

Figure 2. Matching NFIRS address data to ZCTAs (2010): Incidents and ZIP codes

Incidents 

in NFIRS

that match

a ZCTA

Less: 

Incidents

that do not

match a 

ZCTA

Less: 

Incidents 

in invalid

ZIPs

Incidents

in NFIRS

ZIPs that

match

a ZCTA

Less:

ZIPs that

do not

match

a ZCTA

Less:

Invalid ZIPs

ZIPs in

NFIRS

1,033,556 34,671 26,396 972,489 26,669 314 1,832 24,523

Range errors

To identify whether these fires were reported in the correct ZIP code, a novel approach was 

developed for identifying a “range” error for the ZIP code data. This approach calculated an 

estimated geographic position of a particular fire department and measured the distance 

of incident data to check if they appeared to be “out of range.” A “weighted center” latitude 

and longitude for the fire department was calculated by using the latitude and longitude 

from the ZIP codes covered by the incidents. This “weighted center” was then used to 

evaluate incident data at a fire department level and to flag incidents that might have 

been misidentified to a particular ZIP code.

The range error analysis yielded several likely reporting problems. One particularly 

interesting case occurred in ZIP code 77201. That ZIP code is assigned to a U.S. post office 

that has no demographic data, but 1,434 incidents were reported there in 2010. Based 

on the fire department identification, it is believed that the ZIP code should actually be 

72201. This kind of pervasive and potentially systematic ZIP code error may result from 

accidental hard coding of a ZIP code within an entry screen. For purposes of analysis, this 

ZIP code error was corrected in the data, but other range errors were not corrected.

Aid given data

In general, aid is a voluntary exchange of resources and services between fire departments 

for mutual benefit or by contractual agreement. In emergency services, there are two basic 

types of aid fire departments can give or receive: mutual aid and automatic aid. Mutual 

aid is an agreement among emergency responders to lend assistance across jurisdictional 

boundaries as a need arises. Automatic aid is assistance dispatched automatically by a 

pre-arranged contractual agreement between two communities or fire districts.

The NFIRS makes a distinction between primary incident reports, which are filed by the fire 

department with a jurisdiction over the location of the fire, and “aid given” reports that are 

filed by neighboring fire departments that may assist in the fire. Aid given reports are valid 

incidents, but are not counted as fire incidents as they are considered duplicate reports. 
18 National Fire Estimation Using NFIRS Data White Paper

Primary incident reports, which include “aid received” reports, are more comprehensive 

and contain information related to cause, incident type, property use, structure type, and 

so on. In theory, aid received primary reports and aid given secondary reports can be 

reconciled and any duplicate reports can be removed from analyses. However, when the 

primary report is missing, aid given reports serve as the only record of the incident. By 

current convention,9 these aid given reports are not included in discussions and counts of 

incidents reported in the NFIRS. Therefore, aid given reports, for which there is no primary 

report, provide an additional source of fire incident data that can be explored for use in 

developing national estimates.

Table 2 gives the number of incidents by type of aid from the 2010 NFIRS valid data set. 

If aid given reports are excluded under the assumption that all aid given incidents are 

represented elsewhere in the data, the total number of incidents is 1,003,556. However, 

the number of aid given incidents is nearly twice the number of aid received incidents. 

This could be for the following reasons:

ĵ The receiving fire department does not report the aid received; the incidents are 

reported as no aid.

ĵ Multiple aid given reports are filed for the same aid received incident.

ĵ The receiving fire department does not report the incident because of nonparticipation 

in the NFIRS or missed reporting. In this case, the aid given report is the only record 

of the fire.

Table 2. NFIRS fire incidents by type of aid — All valid incidents (2010)

General aid type Incidents Percent

Aid received 128,390 10.5

Aid given 224,163 18.3

Other aid 2,091 0.2

No aid 873,075 71.2

Total 1,227,719 100.0

Likely, some portion of the aid given incidents are duplicated in the aid received incidents, 

but some portion likely is not. A methodology was developed to identify the unduplicated 

aid given incidents.

The aid given incidents were compared to the aid received incidents to find exact or 

approximate matches based on the incident identification information. As insufficient 

NFIRS information was available to identify potential matches from the identification 

information for aid given incidents, USFA-provided geocoded location data was used to 

match aid incidents on the geocoded location, date and time of the incident.10

9Currently, the convention for fire data analysis is to exclude mutual and automatic aid given incidents in counts 

of fire incidents. The assumption is that these aid given reports are duplicated in the primary incident report. 

See USFA’s National Fire Incident Reporting System Version 5.0 Fire Data Analysis Guidelines and Issues.

10While the geocode algorithm used for the 2010 NFIRS data did not yield locations with sufficient precision 

to enable the use of census tracts as the primary analytic unit, it was sufficiently reliable to use for this deduplication exercise.
Developing a National Fire Incident Reporting System-Based National Estimates Methodology 19

The methodology to identify and match aid given incidents to aid received incidents is based 

on physical and temporal distances. Physical distance between incidents is achieved using 

an SQL geography element of geocoded address data for fire records; temporal distance 

between the incidents is based upon reported incident alarm time. Various versions of 

de-duplication were attempted using multiple geocode sets, variable distance, variable 

time, and sensitivity, based on aid type and incident type. An initial baseline set of distances 

for each major incident type (structures, vehicles, outside/other) was suggested by the 

USFA. This baseline was a temporal distance of 20 minutes and physical distances of 1, 2 

and 5 miles for structure, vehicle and outside fires, respectively (Table 3).

Table 3. Initial match parameters for aid incidents

Match 

parameter Criteria

Time Within a specified date-time range, with aid received alarm time prior 

to aid given alarm time

Location

Geocoded all addresses and considered to be a match between aid given 

and aid received incidents if within 1 mile (structure fires), 2 miles (vehicle 

fires), or 5 miles (outdoor fires)

The first phase of analysis used a broad-ranged matching algorithm to pair each aid record 

with the closest primary record if there was a match within 10,000 meters that had an 

alarm time within 120 minutes. This provided a large set of matched records that could 

be analyzed at a high level to identify patterns in the distribution of matches. Analyses 

determined that the suggested baseline time and distance radii resulted in an unacceptable 

number of false positives and that automatic aid (i.e., prearranged) versus mutual aid (i.e., 

ad hoc) resulted in considerably different distribution of results.

The second phase implemented a more tightly tailored matching approach, matching 

only aid given to the primary aid received. Matches were again made by major incident 

type (structure, vehicle and outside) with the additional filter of aid type (automatic or 

mutual.) This approach limited the matches to within 2,000 meters and 40 minutes. These 

data were then spatially graphed in 50-meter physical distance intervals and five-minute 

temporal distance intervals. A random sample of matches was manually verified. This 

analysis identified distances and intervals used in this approach. For perspective, a circle 

with a radius of 50 meters is roughly equivalent to one football field, and one with a radius 

of 2,000 meters is roughly 5 square miles.

Model fidelity between the analytically derived distances and the initial USFA-suggested 

distances was analyzed. With the use of the newly proposed match distances, the model 

improved incrementally. Manual verification of both sets of distances confirmed that 

using the larger initial distances results in a substantial number of false positives without 

a substantial increase in successful matches of well-populated records.

This process yielded 49,372 matches between aid given incidents and aid received incidents 

(Table 4). That means the remaining 174,791 aid given incidents have no match in the aid 

received incidents and are potentially unique incidents.
20 National Fire Estimation Using NFIRS Data White Paper

Table 4. Matching NFIRS aid given-received incidents, model parameters (2010)

Incident-aid type Distance (m) Time (min) Matches Unmatched 

incidents

Structures — Mutual 50 15 19,024 64,596

Structures — Automatic 50 5 17,134 42,510

Vehicle — Mutual 50 5 917 6,729

Vehicle — Automatic 50 5 1,067 5,045

Outside/Other — Mutual

0 40

union 7,535 36,624

2,000 20

Outside/Other — Automatic 50 5 3,695 19,287

Aid given incidents 49,372 174,791

“Other aid” incidents — incidents where a fire department covers and responds to another 

jurisdiction or locale that has no fire department — were also analyzed. As there were no 

aid given/received pairs to match, the other aid data was searched for possible duplicates. 

There were very few; only 122 potential duplicates were identified. For consistency, these 

incidents were removed from further analyses. A summary of the count of unique fire 

incidents found in the 2010 NFIRS data is shown in Table 5.

Table 5. Total unique NFIRS fire incidents (2010)

Match group Incidents

NFIRS valid incidents 1,003,556

Unduplicated aid given fires 174,791

Less duplicate other aid given -122

Total unique fires 1,178,225

True zeroes

Reporting fire departments with no fires can be identified by reviewing the pattern of 

reported incidents. If a fire department reported other incidents — such as Emergency 

Medical Services or hazmat responses — and did not report any fires, it is understood 

that, while there was activity, there were no fires for the department that year.11 Using this 

method, 9,090 ZIP codes were identified that had no reported fires. Of these ZIP codes, 

4,373 match ZCTAs.12 The inclusion of these “true zeroes” to the model should allow for 

a more accurate estimate by reducing the number of ZCTAs for which incidents need to 

be estimated.

11USFA NFIRS Program Manager.

12Reviewing patterns of fire reporting does not identify departments that had no reported incidents of any 

type. If a department participates in the NFIRS, there is a mechanism that allows fire departments to submit 

a monthly “report of no activity” if the department experiences no calls of any type during the month. These 

“reports of no activity” were analyzed for 2010 with no material effect on the national estimate: 46 “true zero” 

ZIP codes were added, reducing the estimate by 327 incidents.
Developing a National Fire Incident Reporting System-Based National Estimates Methodology 21

Missing data and late data

Fire departments that faithfully report incidents to the NFIRS may fail to report a particular 

incident due to a variety of circumstances. Additionally, it is known that the annual data is 

incomplete. The NFIRS has a closing date of July 1 post year, but data continues to arrive 

to the NFIRS after this date. The identification of this missing and late reporting data is 

critical in calculating an accurate estimate of the fire problem. There are known issues of 

underreporting; overreporting of fire incidents is rare, if it exists at all.13

A conservative approach to identifying and adding missing data to the model was adopted, 

and a model was developed of fire incidence for each fire department that reported data 

to the NFIRS between 2006 and 2011. To account for seasonality of data submission, the 

fire incident data was analyzed on a monthly basis. A monthly average and standard 

deviation for each fire department was calculated. Using a 97.5 percent confidence band, 

if the reported number of incidents was less than two standard deviations below the 

average number of incidents for that month (suspected underreporting) then the average 

was substituted for the reported value.14 For the base analysis year of 2010, this method 

adds 85,097 fires to the total.

The modeling of late data represents a particularly hard challenge to estimation. After the 

submission period, there can be additions, changes and deletions of incident data. Three 

years of data (2010 to 2012) were examined to understand the extent of change to the data 

after the close of the submission period.15 The average number of additional late incidents 

was 0.8 percent of the total number of incidents for the year — a non-negligible change.

It was theorized that the existing missing data model could explain some of this change. An 

analysis at the fire department level was developed to compare the number of validated, 

released incidents as reported in 2010 (the 2010 PDR); the total number of validated incidents 

for 2010 reported as of 2014 (the model input data set); and the predicted number from 

the missing data model.

The analysis showed that most fire departments make no change to their data after the 

close of the submission date (including releasing previously unreleased data) — only 7.2 

percent of fire departments in the 2010 PDR changed their total valid incidents by 2014. 

Comparing fire departments that had increases in their valid incident counts with the 

incident counts predicted by the missing data model showed 97.2 percent of the increase 

in incidents could be predicted by using the existing missing data analysis. Given the 

overall robustness of the missing data model, additional factors to account for late data 

were not added to the model.

Cumulative effect of data adjustments

In 2010, there were 1,003,556 reported fires for 26,669 ZIP codes. Applying additional 

data correction techniques increased the number of fires and the number of ZIP codes 

for which data were available. Table 6 shows the various correction techniques used and 

the estimates each respective technique produced.

13USFA NFIRS Program Manager.

14The analysis was conducted using a one-sided confidence interval because the incidence of overreporting 

is uncommon.

15Because the NFIRS fire incident data for the models contains all validated 2010 incidents as of 2014, and the 

PDR contains only released validated incidents as of 2010, an exact comparison on the effect of late submitted 

data could not be made, but a bound on the size of the late data increase could be determined.
22 National Fire Estimation Using NFIRS Data White Paper

Table 6. Summary of NFIRS incident census (2010)

Category

NFIRS 

valid 

incident 

data

NFIRS 

valid 

incident 

data 

matched 

to ZCTAs

NFIRS 

valid 

incident 

data with 

unduplicated 

aid

NFIRS 

valid 

incident 

data with 

unduplicated 

aid matched 

to ZCTAs16

NFIRS valid 

incident 

data with 

unduplicated 

aid and 

“true 

zeroes” 

matched to 

ZCTAs

NFIRS valid 

incident 

data with 

unduplicated 

aid, “true 

zeroes” and 

missing 

data added 

matched to 

ZCTAs

Fires 1,003,556 972,489 1,178,225 1,178,225 1,178,225 1,263,322

ZIP codes 26,669 30,410

ZCTAs 24,523 24,330 28,703 28,703

Scaling model

The original paper by Hall and Harwood on national estimates (1989) proposed a method 

for creating a national estimate of fire incidence by relating the population protected for 

each of the fire departments in the NFIRS to the total U.S. population and then scaling up 

the reported incidents.

Historically, the population protected data in the NFIRS was inaccurate, and the data is 

no longer collected. Since the NFIRS collects the ZIP code for each incident, it is possible 

(assuming a ZIP code — ZCTA equivalence) to estimate the total population of ZIP codes for 

areas where fires were reported and to then compare that portion to the total population. 

This approach is similar to that described by Hall and Harwood but does not require an 

estimate of population protected.

A novel approach at estimating the population associated with each fire department was 

undertaken within the NFIRS. NFIRS data was combined with ACS data to generate an 

estimate of the total population covered.

To assign the population to a particular fire department and ZIP code combination, an 

analysis was used for each ZIP code to identify all fire departments and the associated 

U.S. census population for that ZIP code. If multiple fire departments had incidents in a 

ZIP code, each fire department was allocated an equal share of the total incidents for that 

ZIP code. Future work could allocate the population on a pro-rated basis, but this was not 

undertaken for this analysis.

The resulting model produces a simple population coverage estimate for each fire 

department — one that, in concept, is mutually exclusive of any other fire department 

estimate.17

16Excludes erroneous ZCTA matches to areas other than the 50 states and District of Columbia.

17This process can be further simplified. If fires and population by ZIP code are available, there is no need to do 

any allocation to fire departments to calculate protected population. A simple proportion is possible as well.
Developing a National Fire Incident Reporting System-Based National Estimates Methodology 23

The known incidents, including “true zeroes” where applicable, represent fires in areas 

where a known number of people live. According to the ACS, the 2010 population for 

the 50 states and the District of Columbia was 309,122,569. A scaling estimate for the 

total incidence rate was developed by relating the population coverage of reporting fire 

departments to the total population and multiplying that by the incidents as reported. 

National estimates derived using the scaling method are summarized in Table 7.

Table 7. National estimates using scaling (2010)

Category NFIRS valid incident 

data matched to ZCTAs

NFIRS valid incident data 

with unduplicated aid, 

true zeroes and missing 

data added matched to 

ZCTAs

Fires 972,489 1,263,322

Population in ZCTAs with data 280,323,251 295,964,706

Estimated fires 1,072,399 1,319,486

Regression model

A regression model is a statistical approach to forecast values of a dependent variable 

based on change in one or more independent variables. However, relationships depicted 

in a regression analysis are associative only, and any cause-effect or causal inference is 

purely subjective. As with the scaling model, this model is focused on using a ZCTA as a 

preliminary avenue of investigation for computation efficiency and the ease to tie directly 

to the NFIRS data.

Research efforts identified factors that might help predict the total fire incidence: 

demographic, socioeconomic, weather, business and vehicle crash factors (Table 8). Each 

of these factors was collected from either the ACS five-year data (2007 to 2011), the 2010 

Census County Business Patterns (CBP), the Wildland Fire Assessment System (WFAS), or 

the Fatality Analysis Reporting System (FARS).
24 National Fire Estimation Using NFIRS Data White Paper

Table 8. Summary of data factors and sources

Category Factor Data source

Business Business population CBP — Number of establishments

Population Age ACS S0101 — Total estimate by age18

Population density ACS S0101 — Total population19

Socioeconomic

Age of structure ACS DP04 — Year structure built, various20

Car ownership

ACS DP04 — Calculated. Occupied 

housing units minus occupied housing 

units with no vehicles available.

Children ACS DP02 — Families with children under 

18

Education level ACS DP02 — Households with at least a 

high school graduate

Home ownership ACS DP04 — Owner occupied units (not 

found significant in this analysis)

Home value ACS DP04 — Estimated median value

Household income ACS DP03 — Median household income

Household size ACS DP02 — Average household size

Housing density ACS DP04 — Total housing units

Married, no children

ACS DP02 — Calculated. All married 

couples minus married couples with 

children under 18.

Minority population ACS DP05 — Calculated. Total population 

minus non-Hispanic white population.

Residential 

structures ACS DP04 — Year structure built, various

Single-parent 

household

ACS DP02 — Calculated. All maleheaded households without a spouse 

with children, plus all female-headed 

households without a spouse with 

children.

Single person ACS DP02 — All householders living 

alone

Unemployment rate

ACS DP03 — Calculated. One minus 

(total employed population divided by 

population 16 or over).

Vacancy ACS DP04 — Vacant housing units

White population ACS DP05 — Non-Hispanic white 

population

18Older age population was calculated by adding the total population by age statistics for age bands of 65 and 

above for a given ZCTA.

19Population density is calculated by using the total population for a ZCTA and dividing it by the total land area 

for a given ZCTA.

20Age of structure is the total number of housing units constructed in each of the time bands collected by 

census for a given ZCTA.
Developing a National Fire Incident Reporting System-Based National Estimates Methodology 25

Table 8. Summary of data factors and sources — continued

Category Factor Data source

Vehicle Fatal crashes DOT FARS — Fatal crash location

Weather

Precipitation WFAS — Fire danger index data

Relative humidity WFAS — Fire danger index data

Temperature WFAS — Fire danger index data

In addition, the research efforts identified data factors that could not be sourced with 

national-based data. These factors are detailed in Table 9.

Table 9. Additional factors not analyzed

Category Factor

Behavior Alcohol use

Playing with fire

Smoke alarm presence

Smoking

Fuel Biomass

Soil moisture

Stand age

Time from last fire

Land use Distance to campsite

Distance to farmland

Distance to road

Distance to town

Industrial

Livestock units

Park

Paths

Privately owned

Road density

Secondary housing

Urban

Topography Altitude

Aspect

Elevation

Slope

Vehicle Age of vehicle

Number of vehicles

Type of vehicle

Weather Lightning

Wind speed
26 National Fire Estimation Using NFIRS Data White Paper

Relating demographic and socioeconomic data

Data from the ACS, collected by the U.S. Census Bureau, can be used to complement the 

fire data from the NFIRS. The U.S. Census is taken every 10 years, but the ACS data is an 

ongoing, confidential survey in which results are released every year. Over two million 

surveys are conducted each year, and socioeconomic data is collected at differing geographic 

levels, including age, sex, race, income, insurance and housing.

ACS data consists of “period estimates.” Essentially, it represents population and housing 

characteristics over a specific data collection period. For this data, the U.S. Census Bureau 

releases estimates for five years, three years, and a single year, depending on the population 

thresholds for the specific geographic areas. For geographic areas with populations of 65,000 

or more, the collected data produces one-year estimates; for geographic areas with smaller 

populations (20,000 or more), three years of data are necessary to produce estimates; for 

the smallest population areas, five years of data are necessary. These are called “one-year,” 

“three-year,” and “five-year” estimates (Guidance for Data Users Main, 2013). 

The ZCTA estimates that were selected are five-year estimates. This ACS data at the ZCTA 

level provides a rich set of demographic data that can be used to analyze and predict fire 

incidence.

Relating weather data, land use, fuel and topography

As reviewed in the background research, there has been extensive research linking weather 

data, land use, fuel and topography with fire risk and wildfires.

The U.S. Forest Service (USFS) Wildland Fire Assessment Program collects a number of these 

factors to calculate a “fire danger rating” that includes “current and antecedent weather, 

fuel types, and both live and dead fuel moisture.”21 This data is collected in their Geographic 

Information System called the WFAS. Working with a USFS researcher, shape-files from 

the U.S. Census Bureau and the WFAS were combined to develop ZCTA-based estimates 

for average annual temperature, precipitation and humidity.22

Land use, fuel or topography factors were not analyzed due to a lack of availability of this 

data on a ZIP/ZCTA basis on a national level. These factors may have additional explanatory 

power if they could be gathered.

Relating business population data

The general thesis for fire incidence estimation is that fire incidence is largely related to 

the presence of people. Demographic and socioeconomic data have been analyzed with 

respect to residential fire incidence, but additional factors are typically included when 

analyzing outdoor or wildfire incidence. For example, many of the land use factors identified, 

such as distance to towns, campsites, parks or farmland, are essentially identifying the 

locations where people work or play.

Unfortunately, ‘daytime population’ is not accurately captured on a national basis at a ZIP 

code level. It was postulated that the number of businesses could be a potential proxy for 

this information. The U.S. Census Bureau’s CBP collects the total number of businesses 

21http://www.wfas.net/index.php/fire-danger-rating-fire-potential--danger-32. 22W. Matt Jolly, Ph.D., Research Ecologist, Project Administrator, WFAS, U.S. Department of Agriculture, USFS. 

February 2015.
Developing a National Fire Incident Reporting System-Based National Estimates Methodology 27

at a ZIP code level by the North American Industry Classification System (NAICS) codes. 

NAICS was developed as the standard for use by federal statistical agencies. It is used to 

classify business establishments for the collection, tabulation, presentation and analysis of 

statistical data describing the U.S. economy. The U.S. Census Bureau assigns and maintains 

only one NAICS code for each establishment, based on its primary activity. This can be 

used as a direct measure for the number of businesses within a geographic area.23

An analysis was conducted to compare the total number of businesses located within a 

ZCTA and the fire incidence for that ZCTA. A scatter plot of those two factors is found in 

Figure 3. The simple linear regression analysis showed an R-squared (R2) value of 0.2478. 

Since roughly 25 percent of the data is accounted for by the model, business activity was 

included in the pool of variables tagged for further analysis.24

Figure 3. Number of businesses and fire incidence

0

0

500

1,000

1,500

2,000 4,000 6,000

Number of businesses

Fire incidence

Relating vehicle crash data

One of the most challenging aspects of identifying the location and volume of fire incidence 

is accounting for vehicle fires. Vehicle crash data was leveraged to identify locations that 

might have substantial travel volume that were separate and distinct from where people 

work or live. The Department of Transportation’s (DOT’s) National Highway Traffic Safety 

Administration collects fatal vehicle crash data on an incident basis in the FARS.25 There 

23In addition to the number of establishments, the U.S. Census Bureau collects employment populations as 

part of the CBP, but this data was not available in 23.5 percent of ZIP codes and was excluded from further 

consideration. 

24A log transform on fire incidence was considered, but it was discarded as it did not improve the model when 

including the other variables.

25http://www.nhtsa.gov/FARS.
28 National Fire Estimation Using NFIRS Data White Paper

are approximately 30,000 fatal car crashes per year in the U.S. One of the reported fields 

for fatal crashes is the crash location, which is recorded with a latitude and a longitude. A 

commercial geo-location service was used to transform the latitude-longitude into a ZIP 

code for each incident and to summarize the number of incidents by ZIP code. A ZIP code 

was identified for 99 percent of the latitude-longitude pairs.

An analysis was conducted to compare the total number of vehicle crashes located within 

a ZCTA and the fire incidences for that ZCTA. Figure 4 shows a scatter plot of these two 

factors. The simple linear regression analysis showed an R2 value of 0.1946 (Figure 4). As 

nearly 20 percent of the data is accounted for by the model, the variable was included in 

the pool of variables tagged for further analysis.26

Figure 4. Number of vehicle crashes and fire incidence

0

0

500

1,000

1,500

5 10 15

Number of vehicle crashes

Fire incidence

Estimating fire incidents — Regression model

The goal of the model is to estimate fire incidence in areas for which no incident data 

are available, but demographic, socioeconomic, business, vehicle crash, and climate data 

are available. Other models estimate specific incidence rates (Jennings, 1999) (Corcoran 

et al., 2011); however, this research and model look at the entire fire problem, including 

residential, vehicle and outside/wildfire incidents for the whole country. This model, 

therefore, contains elements that help predict each type of fire.

A multivariate regression model was developed using incident data, including demographic 

and socioeconomic variables (population density, older population size, housing stock age, 

vehicles present at homes, owner occupancy, housing vacancy, presence of children, single 

26A log transform on fire incidence was considered, but it was discarded as it did not improve the model when 

including the other variables.
Developing a National Fire Incident Reporting System-Based National Estimates Methodology 29

parent households rate, married with no children, minority population, unemployment 

rate), environmental variables (precipitation, temperature, relative humidity), business 

variables (business population and density), and vehicle crash data as shown earlier in 

Table 8. The incident data included the effects of all of the data adjustment techniques, 

including accounting for aid, range errors, “true zeroes,” and missing data.

This linear regression produced an estimate for any ZIP code where there was no data. 

Of the 32,989 ZCTAs in the 50 states and District of Columbia, almost 87 percent have fire 

incident data present and, under the model, would not need to be estimated.

Lastly, a variable was added that was specifically needed because of the ZCTA based 

analysis. ZCTAs vary widely by the area of land that they cover. For example, ZCTA 99557, 

an area close to the center of Alaska, has a land area of over 13,400 square miles and 

is over 10 times larger than the state of Rhode Island. To properly account for any size 

discrepancy in ZCTAs, the area of land for each ZCTA was included in the model. The full 

set of regression variables is shown in Table 10.

Table 10. Variables and variable definitions used in regression model

Variable Definition

Population density The total number of persons residing in the 

ZCTA divided by the total land area in the ZCTA.

Older population Total number of the population over the age of 65.

Total housing units built after 2010 Total number of housing units in the area built 

after 2010.

Total housing units built 2000 to 2009 Total number of housing units in the area built 

between 2000 and 2009.

Total housing units built 1990 to 1999 Total number of housing units in the area built 

between 1990 and 1999.

Total housing units built 1980 to 1989 Total number of housing units in the area built 

between 1980 and 1989.

Total housing units built 1970 to 1979 Total number of housing units in the area built 

between 1970 and 1979.

Total housing units built 1960 to 1969 Total number of housing units in the area built 

between 1960 and 1969.

Total housing units built 1950 to 1959 Total number of housing units in the area built 

between 1950 and 1959.

Total housing units built 1940 to 1949 Total number of housing units in the area built 

between 1940 and 1949.

Total housing units built before 1939 Total number of housing units in the area built 

before 1939.

Houses with vehicles The total number of occupied housing units 

with at least one vehicle available.

Owner occupied units The number of occupied housing units that are 

occupied by the owner.

Vacant unit The percentage of housing units that are vacant.
30 National Fire Estimation Using NFIRS Data White Paper

Table 10. Variables and variable definitions used in regression model — continued

Variable Definition

Children present Number of households with their own children 

under 18 years of age.

Education level Number of households with at least a high 

school degree.

Household size Average household size.

Married, no children The total number of households that are 

married, but who do not have children.

Single-parent household

The sum of the percentage of single-mother 

households with children, and the percentage 

of single-father households with children.

Minority population Total population that is not white (not-Hispanic/

Latino).

Household income Median household income.

Unemployment Total population over 16, minus the population 

that is employed.

Precipitation The yearly total precipitation for the closest 

weather station to that ZCTA.

Temperature The yearly average of mean daily temperatures 

for the closest weather station to that ZCTA.

Relative humidity

The log of yearly average relative humidity, as 

measured by the closest weather station to 

the ZCTA.

Total businesses Total number of businesses registered by NAICS 

within the ZIP code.

Fatal crashes Number of fatal vehicle crashes within a ZIP code.

Total land area The total land area contained within that ZCTA.

As shown in Table 11, each of the independent variables included in the model show 

high “t” statistics for their partial regression coefficients, and they are significant at the 

0.001 level. The exception is “household income,” which was significant at the 0.01 level. 

“Household size” and “married, no children” were found to not be significant and were 

removed from subsequent analysis. A variation inflation factor test was performed and 

no multicollinearity was detected for the variables in the model. A Breusch-Pagan test was 

performed, and heteroscedasticity is not present in the model.
Developing a National Fire Incident Reporting System-Based National Estimates Methodology 31

Table 11. Multivariate regression coefficients

Coefficient

Standardized 

coefficients 

beta

Standard 

error

“t”

Intercept (186.7000) 19.5300 (9.5600)

Population density (0.0013) 0.0001 (13.3570)

Older population (0.0118) 0.0006 (18.8310)

Total housing units built 2000 to 2009 0.0079 0.0004 17.8910 

Total housing units built 1990 to 1999 0.0101 0.0006 16.3780 

Total housing units built 1980 to 1989 0.0039 0.0006 6.3680 

Total housing units built 1970 to 1979 0.0072 0.0006 11.7020 

Total housing units built 1960 to 1969 0.0135 0.0007 18.1120 

Total housing units built 1950 to 1959 0.0035 0.0007 4.7900 

Total housing units built 1940 to 1949 0.0103 0.0010 10.5900 

Total housing units built before 1939 0.0125 0.0004 32.8050 

Houses with vehicles (0.0139) 0.0005 (29.6570)

Owner occupied units 0.0072 0.0005 14.7940 

Vacant unit (19.9700) 2.0910 (9.5520)

Children present (0.0087) 0.0009 (10.0260)

Education level 0.0062 0.0003 17.8220 

Household size (0.0614) 0.7409 (0.0830)

Married, no children 0.0020 0.0013 1.5340 

Single-parent household 0.0493 0.0015 32.8070 

Minority population (0.0013) 0.0001 (16.4450)

Unemployment 0.0065 0.0003 21.4400 

Household income (0.0000) 0.0000 (3.2310)

Precipitation 0.0129 0.0013 9.6730 

Temperature 0.5334 0.0749 7.1180 

Relative humidity 11.0900 1.4930 7.4290 

Total businesses 0.0233 0.0012 19.8530 

Fatal crashes 4.2610 0.2068 20.6030 

Total land area 0.0141 0.0017 8.2140 

The R2 value calculated for the model is 0.5849, indicating that 58.5 percent of the total 

variation in the incidence of fires has been explained by the independent variables. The 

remaining 41.5 percent has not been explained. The adjusted R2 value for the model was 

0.5844. An R2 value greater than 0.35 is considered meaningful for the social sciences (Jost, 

n.d.). Additionally, this model compares favorably to other fire rate estimation models, as 

shown in Table 12 (Chhetri, 2010).
32 National Fire Estimation Using NFIRS Data White Paper

Table 12. Comparison to other models

Model R2 Adjusted R2 Residual 

standard error

P. Chhetri (2010) .451 .390 52.1

USFA .585 .584 41.2

Multiyear analysis

The same factors were analyzed across multiple years to examine the general robustness 

of the model. For each of the three years, demographic and socioeconomic data were 

retrieved from the ACS, weather data from the WFAS, business data from the CBP, and 

crash data from the FARS. The Gazetteer ZCTA data was the same over the three years, 

as the boundaries of ZCTAs were consistent through the examined period.

Overall, the model was very robust, with the average adjusted R2 value remaining over 

0.57 across the three years analyzed (Table 13).

Table 13. Comparison of model across years (2009-2011)

Model 2009 2010 2011

Adjusted R2 0.5725 0.5844 0.5669

Residual standard error 39.6 41.2 42.0

Estimation model

An estimation model was developed using the results of the regression analysis. The base 

regression model was used to estimate incidents in ZCTAs where no incident data was 

reported in the NFIRS and all associated predictive factors were available. If a negative 

estimate was predicted, a zero was substituted for the estimate of that ZCTA. There were 

751 ZCTAs where not all of the multivariate data was present. In these ZCTAs, an estimate 

was calculated by using a linear regression based on population only. A range was estimated 

based on a 95 percent confidence interval for each estimate.27

Using either the multivariate or the population-only models, estimates were calculated 

for a total of 3,399 ZCTAs. The estimates were then added to the actual responses. In 

2010, the total national estimate using the multivariate linear regression (MLR) model 

was 1,278,263. This compares to using the scaling estimate of 1,319,486 and the NFPA 

estimate of 1,331,500. This process was repeated for 2009 and 2011, and the results are 

summarized in Table 14.

27The margin of error for an individual ZCTA estimate was calculated using the standard error multiplied by 

the appropriate z-score (1.96 for 95 percent). The total range for the forecast was calculated by multiplying the 

margin of error by the total number of estimated ZCTAs, and dividing by the square root of the sample size.
Developing a National Fire Incident Reporting System-Based National Estimates Methodology 33

Table 14. Summary of national estimates by different methods

Model 2009 2010 2011

NFIRS valid incidents 948,089 1,003,556 999,457

NFIRS unduplicated aid 1,124,038 1,178,225 1,181,115

National estimate — scaling 1,283,989 1,319,486 1,326,666

National estimate — MLR 1,233,667 1,278,263 1,287,174

National estimate (MLR) — range ± 4,519 ± 4,709 ± 4,666

NFPA 1,348,500 1,331,500 1,389,500
34 National Fire Estimation Using NFIRS Data White Paper
Limitations 35

Limitations

There are some limitations to the current model, in particular with missing data and the 

application of estimates. The current model, based on the ZCTA, is capable of producing 

estimates for state and county level fire incidence, but the estimates will have higher 

margins of error because of trending and aid given effects.

The missing data model substitutes an average if the monthly reported number for that fire 

department is below two standard deviations from the mean. Currently, the model does 

not include any yearly trend factors for fire incidence; therefore, a ZCTA where population 

is changing quickly may be underestimated or overestimated. It is believed that this factor 

is not significant at the national level, but this may create errors at the county or state level.

The estimation model substitutes an estimate for a ZCTA if there is no data for that ZCTA. 

If a ZCTA has a high fire incidence and the fire department primarily responsible for that 

area does not participate in the NFIRS, the model result could be underestimated for 

that ZCTA. If the high fire incidence ZCTA has aid incidents reported by participating fire 

departments, then those aid incidents will be presumed to be the incidence for the entire 

ZCTA. A preliminary analysis was conducted to correct this underprediction. The analysis 

compared the actual numbers and estimates for each ZCTA, and substituted the prediction 

if the ZCTA was underestimated by two standard deviations from the mean. The analysis 

identified only 248 ZCTAs out of 33,120 where this post-estimation fix would be applied. 

This is within natural probability of such an error. While it is not believed that this factor 

is significant at the national level, it may be a factor for state or county level estimates.
36 National Fire Estimation Using NFIRS Data White Paper
Conclusions and Further Work 37

Conclusions and Further Work 

It is possible to develop a method of generating an annual estimate of fire incidence for the 

U.S. based on fire incident data from the NFIRS, in conjunction with other publicly available 

data. Two models were examined: a simple scaling model using population protected and 

a more sophisticated multivariate regression model using a combination of demographic, 

socioeconomic, weather, business, and vehicle use data. Both models produced similar 

estimates, within two percent of each other.

During the course of analysis, two major improvements were made relative to existing NFIRS 

data: identifying additional incidents within the NFIRS where aid is given using advanced 

geolocation techniques and imputing missing values with more reliable data from a prior 

year. The accurate identification of aid incidents reveals an additional 14 to 18 percent of 

unique incidents. The imputation of missing data further identifies an additional 7 to 9 

percent of incremental incidents. This total of 21 to 27 percent of additional incidents is a 

very substantial increase and significantly adds to the overall number of reported U.S. fires.

Population appears to be the most important predictive variable in estimating fire incidents; 

however, a greatly improved estimation model can be built by leveraging a combination 

of additional socioeconomic, climate, business and vehicle data. Identifying the location 

of population at home, work, and recreational areas, as well as their movement between 

these places, is important to accurately estimating the location of incidents at a ZCTA level.

If they could be gathered, other factors, including land use, fuel or topography, could add 

additional explanatory power to the model. Additionally, interaction and higher-order 

terms may provide additional explanatory power to the regression model.

As the estimates are made at the ZCTA level, it may be possible to create estimates at the 

state or county level by aggregating the ZCTAs appropriately. Because NFIRS participation 

is not necessarily uniform over small geographic areas and may lead to large estimation 

errors, further work may be necessary to examine the robustness of this approach.
38 National Fire Estimation Using NFIRS Data White Paper
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Acronyms 43

Acronyms

ACS American Community Survey

CBP County Business Patterns

DOT Department of Transportation

FARS Fatality Analysis Reporting System

MLR multivariate linear regression

NAICS North American Industry Classification System

NFDC National Fire Data Center

NFIRS National Fire Incident Reporting System

NFPA National Fire Protection Association

PDR Public Data Release

R2 R-squared

USFA U.S. Fire Administration

USFS U.S. Forest Service

WFAS Wildland Fire Assessment System

ZCTA ZIP Code Tabulation Area
16825 South Seton Ave.

Emmitsburg, MD 21727

www.usfa.fema.gov

May 2017