NIST Technical Note 1845

Identifying Residential Fires Involving 

Upholstered Furniture within the 

National Fire Incident Reporting 

System 

Douglas S. Thomas

David T. Butry

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Technical Note 1845

Identifying Residential Fires Involving 

Upholstered Furniture within the 

National Fire Incident Reporting 

System

Douglas S. Thomas

David T. Butry

Applied Economics Office

Engineering Laboratory

September 2016 

U.S. Department of Commerce 

Penny Pritzker, Secretary

National Institute of Standards and Technology 

Willie E. May, Under Secretary of Commerce for Standards and Technology and Director

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Certain commercial entities, equipment, or materials may be identified in this

document in order to describe an experimental procedure or concept adequately.

Such identification is not intended to imply recommendation or endorsement by the

National Institute of Standards and Technology, nor is it intended to imply that the

entities, materials, or equipment are necessarily the best available for the purpose. 

National Institute of Standards and Technology Technical Note 1845

Natl. Inst. Stand. Technol. Tech. Note 1845, 43 pages (September 2016) 

CODEN: NTNOEF 

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Abstract

This Technical Note develops a method for identifying residential fire incidents, reported 

to the National Fire Incident Reporting System (NFIRS), with missing information 

regarding the “item first ignited” (IFI) or “item most contributing to flame spread”

(IMCFS) that were likely to have involved upholstered furniture. Using NFIRS data, 

upholstered furniture involvement can only be identified using the IFI or IMCFS fields; 

however, it is not uncommon for these fields to contain missing values or to be coded as 

unknown (undetermined). Current statistical methods address this issue by allocating the 

missing and unknown incidents proportionally over the distribution of those known. The 

appropriateness of this depends on the representativeness of the known incidents. This 

Technical Note explores a data imputation method to determine the likelihood of

upholstered furniture involvement based on statistical correlations with other factors 

describing the fire incident. A number of competing statistical models are evaluated using 

the data imputation approach, with the best performing models selected based on the 

minimum out-of-sample root mean squared prediction error. The optimum models based 

on this criterion are then used to estimate the number of U.S. residential upholstered 

furniture fires, related occupant fatalities, injuries, and property and content losses, and 

the results are compared to the conventional scaling-based techniques currently used by 

the National Fire Protection Association.

Keywords: fire; fire statistics; NFIRS; upholstered furniture; residential upholstered 

furniture; economics; imputation
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Preface

This study was conducted by the Applied Economics Office in the Engineering

Laboratory at the National Institute of Standards and Technology. The study develops an 

imputation approach to determine the expected values of missing or unknown data 

elements, found within the National Fire Incident Reporting System, based on observed 

patterns found within the non-missing data fields.

Disclaimer

Certain trade names and company products are mentioned in the text in order to adequately specify the 

technical procedures and equipment used. In no case does such identification imply recommendation or 

endorsement by the National Institute of Standards and Technology, nor does it imply that the products are 

necessarily the best available for the purpose.

Cover Photograph Credits

Microsoft Clip Art Gallery Images used in compliance with Microsoft Corporation’s non-commercial use 

policy.
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Acknowledgements

The authors wish to thank all those who contributed so many excellent ideas and 

suggestions for this report. Special appreciation is extended to Dr. William Pitts, Dr. 

Richard Gann, and Dr. Anthony Hamins of the Engineering Laboratory’s Fire Research 

Division; and William Guthrie of the Information Technology Laboratory’s Statistical 

Engineering Division. Special appreciation is also extended to Dr. Stanley Gilbert and 

Dr. Robert Chapman of the Engineering Laboratory’s Applied Economics Office for their 

thorough reviews and many insights and to Shannon Takach for her assistance in 

preparing the manuscript for review and publication. The authors also wish to thank Dr. 

Nicos Martys, of the Materials and Structural Systems Division, for his review. Finally, 

we to acknowledge the thoughtful comments and suggestions provided by: Christina 

Holcroft, Kathleen Almand, and members of the National Fire Protection Association; 

Brad Peabody of the U.S. Fire Administration; and Rohit Khanna, Stephen Hanway, 

David Miller, Andrew Stadnik, and Kathleen Stralka from the U.S. Consumer Product 

Safety Commission.
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Table of Contents

ABSTRACT .................................................................................................................................................i

PREFACE ...................................................................................................................................................ii

ACKNOWLEDGEMENTS ...........................................................................................................................iii

TABLE OF CONTENTS.......................................................................................................................iv

LIST OF TABLES.................................................................................................................................. v

LIST OF FIGURES................................................................................................................................ v

EXECUTIVE SUMMARY ............................................................................................................................vi

1 INTRODUCTION .............................................................................................................................. 1

2 DATA AND METHODS ..................................................................................................................... 5

2.1 DATA.................................................................................................................................................. 5

2.2 IMPUTATION METHOD......................................................................................................................... 10

2.3 MODEL SPECIFICATION & SELECTION ...................................................................................................... 14

3 UPHOLSTERED FURNITURE FIRE ESTIMATES ................................................................................. 19

4 A COMPARISON OF ESTIMATES PRODUCED BY THE SCALING AND IMPUTATION APPROACHES ... 23

5 SUMMARY .................................................................................................................................... 31

APPENDIX A: A COMPARISON OF THE SCALING & IMPUTATION APPROACHES...................................... 37

APPENDIX B: COVARIATES & Z-SCORES.................................................................................................. 41
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List of Tables

Table 1.1 Number of non-confined, residential fire incidents reported to NFIRS identified 

by Item First Ignited and Item Contributing Most to Flame Spread (U.S. Fire 

Administration, National Fire Data Center, 2010). ..................................................... 3

Table 2.1: Non-Confined Residential Fires Recorded in NFIRS that Involve Upholstered 

Furniture ...................................................................................................................... 9

Table 2.2: Confined Residential Fires Recorded in NFIRS that Involve Upholstered 

Furniture ...................................................................................................................... 9

Table 2.3: NFPA Residential Fire Estimates.................................................................... 10

Table 2.4: Indicator Variables Statistically Significant at the 5 % Level......................... 17

Table 3.1: Estimated Number of Confined Residential Fires Involving Upholstered 

Furniture .................................................................................................................... 20

Table 3.2: Estimated Number of Non-Confined Residential Fires Involving Upholstered 

Furniture as Item First Ignited (Imputation Approach) ............................................. 20

Table 3.3: Estimated Number of Non-Confined Residential Fires Involving Upholstered 

Furniture as Item Contributing Most to Flame Spread (Imputation Approach)........ 21

Table 3.4: Estimated Number of Confined and Non-Confined Residential Fires Involving 

Upholstered Furniture either as Item First Ignited or Item Contributing Most to 

Flame Spread ............................................................................................................. 22

List of Figures

Figure 3.1: Minimum, Maximum, and Average of the Estimated Number of Confined and 

Non-Confined Residential Fires Involving Upholstered Furniture either as Item First 

Ignited or Item Contributing Most to Flame Spread ................................................. 22

Figure 4.1: Estimated Number of Fire Incidents, Along with their 95 % Confidence 

Interval, of Confined and Non-Confined Residential Fires Involving Upholstered 

Furniture either as Item First Ignited or Item Contributing Most to Flame Spread, 

Compared with NFPA Published Estimates.............................................................. 27

Figure 4.2: Estimated Number of Civilian Fire Fatalities, Along with their 95 % 

Confidence Interval, of Confined and Non-Confined Residential Fires Involving 

Upholstered Furniture either as Item ......................................................................... 28

Figure 4.3: Estimated Number of Civilian Fire Injuries, Along with their 95 % 

Confidence Interval, of Confined and Non-Confined Residential Fires Involving 

Upholstered Furniture either as Item First Ignited or Item Contributing Most to 

Flame Spread, Compared with NFPA Published Estimates...................................... 29

Figure 4.4: Estimated Direct Fire Losses, Along with their 95 % Confidence Interval, of 

Confined and Non-Confined Residential Fires Involving Upholstered Furniture 

either as Item First Ignited or Item Contributing Most to Flame Spread, Compared 

with NFPA Published Estimates................................................................................ 30
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Executive Summary

In 2011, there were an estimated 386 000 residential structure fires, representing nearly 

28 % of all fires in the United States. These fires resulted in approximately 2550 deaths, 

14 360 injuries, and 7.1 billion dollars in losses (Karter 2013). Many of these fires 

involved upholstered furniture, which is ignitable and can contribute significantly to the 

growth/spread of a fire. As a result, the National Fire Protection Association (NFPA) has 

been summarizing the consequences of fires in which upholstered furniture was the first 

item ignited. This report develops performance metrics, enabling comparisons between 

the use of new fire mitigation technologies and their impact on the U.S. fire losses, with a 

particular focus on residential fires involving upholstered furniture.

The U.S. Fire Administration’s National Fire Incident Reporting System (NFIRS), the 

most comprehensive accounting of individual fire incidents in the world, provides 

detailed information on more than one million fire incidents, requiring a fire department 

response, in the U.S. each year. Yet, it represents only a partial census, as many fire 

incidents, are not reported. In addition, a large number of the reported fire incidents 

contain incomplete descriptions. The current (‘scaling’) method used to produce national 

fire statistics assumes the fire incidents with complete data are representative of those 

with incomplete data—i.e., the occurrence of missing or unknown data is a completely

random process.

This Technical Note offers an alternative (“data imputation”) method for handling the 

unknown data. It exploits correlations between the fire incident’s characteristic of 

interest (e.g., item first ignited) and other reported fire incident factors (e.g., area of 

origin) found in the data, to impute values for those incidents with missing or unknown 

data. Specifically, this Technical Note develops a method for identifying residential fire 

incidents, reported to the NFIRS, with missing or reported as unknown information 

regarding the “Item First Ignited” (IFI) or “Item Contributing Most to Flame Spread”

(ICMFS) that were likely to have involved upholstered furniture. A number of competing 

statistical models are evaluated using the data imputation approach, with the best 

performing models selected based on the minimum out-of-sample root mean squared 
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prediction error. The optimum models based on this criterion are then used to develop 

alternate estimates of the number of incidents, fatalities, injuries, and direct property 

losses from residential fires involving upholstered furniture from 2006 to 2010. 

Methodologically, the scaling and data imputation approaches will yield similar results 

should the fire incidents with known data be representative of the data with unknown and 

missing information. However, if there are systematic differences between the known 

and unknown data (e.g., if upholstered furniture involvement occurs more frequently in 

the known data), and if these differences are correlated with other, more frequently 

reported data, the two approaches will yield different results. While the data imputation 

approach offers the potential for greater accuracy, it is computationally expensive in

comparison to the scaling approach.

The imputation method estimates 10 100 home fires involving upholstered furniture 

resulted in 440 occupant fatalities, 1100 occupant injuries, and $510 million, on average 

each year, from 2006 to 2010. (Annual estimates, with uncertainty ranges, are shown in 

Section 4.) By comparison, the scaling method estimates 8900 home fires involving 

upholstered furniture resulted in 610 occupant fatalities, 1120 occupant injuries, and $565 

million, on average each year, from 2006 to 2010.

In general, the scaling and imputation methods produce similar statistical results for the 

number of residential home fires involving upholstered furniture, as well as for the 

resulting number of occupant injuries and direct property losses. However, the 

disagreement between estimated numbers of occupant fatalities using these two methods 

is statistically significant. The imputation method estimates about a third fewer occupant 

fatalities, the difference being in the number of fire fatalities resulting from upholstered 

furniture involvement due to a direct ignition (i.e., not from flame spread). 
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1 Introduction

In 2011, there were an estimated 386 000 residential structure fires, representing nearly 

28 % of all fires in the United States. These fires resulted in approximately 2550 deaths, 

14 360 injuries, and 7.1 billion dollars in losses (Karter 2013). Many of these fires 

involved upholstered furniture, which is ignitable and can contribute significantly to the 

growth/spread of a fire. In the past, upholstered furniture has contributed significantly to 

residential fires. In recent years, however, there has been efforts to reduce the fire risk of 

these products, and the National Fire Protection Association (NFPA) has been 

summarizing the consequences of fires in which upholstered furniture was the first item 

ignited (Ahrens, 2011). Unfortunately, it is difficult to understand the fire risk of 

upholstered furniture or the effect that reduced flammability might have on these fires, as 

a complete database of residential fire incidents does not include information on details 

of the type, size, or material composition of fires involving furniture.

The U.S. Fire Administration‘s National Fire Incident Reporting System (NFIRS) 

provides detailed information on more than one million fire incidents each year (on 

average) from 2002 to 2010. While NFIRS is the most comprehensive accounting of 

individual fire incidents in the world, it represents only a partial census. Many incidents 

are not reported. Out of an estimated 30 125 fire departments, approximately 23 000

departments report in NFIRS each year; however, some have occasional participation and 

many do not report at all, as it is a voluntary system. In addition, many of the reported 

fire incidents contain incomplete descriptions.

The conventional national fire statistics are based on NFIRS incident data—with 

complete/known data—that are scaled using two ratios, based on the work of Hall and 

Harwood (1989), although the approach has been modified over time to account for 

versioning changes in NFIRS (e.g., see Ahrens [2011]). (The conceptual approach has 

remained consistent.) The first ratio scales the NFIRS-based fire statistics to account for 

the sizeable number of reported fire incidents with unknown or missing data (“allocating 

the unknowns”). A proportional scaling is used to ensure that the total number of fire 
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incidents (or fatalities, injuries, economic loss) with known values equals the total 

number of fire incidents (or fatalities, injuries, economic loss) reported to NFIRS. The 

second ratio (“national scaling ratio”) scales the NFIRS-based fire statistics into national 

estimates using fire department survey data from the National Fire Protection Association 

(NFPA). 

Survey data is often weighted using an adjustment technique such as iterative 

proportional fitting (i.e., raking), to address statistical issues resulting from missing 

(incomplete) data (Izrael et al. 2004). Raking has been applied to NFIRS data (Greene 

2001), and offers a number of advantages over the scaling method. Raking allocates the 

missing and unknown observations over multi-dimensional cross tabulation data (e.g., 

item first ignited by cause of ignition) using an iterative procedure. This procedure 

eliminates results that are sensitive to the adjustment (allocation) order, a known issue 

with the non-iterative, scaling method (Greene 2001). In addition, raking preserves the 

conditional probability distribution of the cross tabular data, meaning correlations 

between the data dimensions are the same for the input and imputed datasets. However, 

this technique poses some statistical challenges, as discussed in Greene (2001), when 

there is high dimensionality and sparse counts. Further, the iterative process requires the 

data to be arranged in a cross tabular structure, making it inappropriate to allocate 

unknowns over a single data dimension (e.g., item first ignited). Finally, while raking 

preserves the conditional probability distribution of the data dimensions included, it is 

susceptible to sample selection bias should correlated data dimensions be omitted from 

the procedure. 

In this report, we explore the use of a new data imputation technique as an alternative 

method to “allocate the unknowns.” To accomplish this, we evaluate the likelihood of 

involvement of residential upholstered furniture (RUF) in residential home fires. Using 

NFIRS data, upholstered furniture involvement can only be identified using the “Item 

First Ignited” (IFI) or “Item Contributing Most to Flame Spread” (ICMFS) fields; 

however, it is not uncommon for these fields to contain missing values or to be coded as 
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unknown. Table 1.1 shows the number of non-confined1, residential fire incidents with 

IFI and ICMFS data listed as upholstered furniture, missing or unknown, or known, but 

not upholstered furniture (“other”). Both IFI and ICMFS data fields contain a significant 

number of incidents with missing or unknown (undetermined) values. Over the five-year

period, 3363 fires or 673 on average per year had both IFI and ICMFS indicating 

upholstered furniture was involved in the fire. 

Table 1.1 Number of non-confined, residential fire incidents reported to NFIRS identified by Item 

First Ignited and Item Contributing Most to Flame Spread (U.S. Fire Administration, National Fire 

Data Center, 2010).

Item Contributing Most to 

Item First Ignited Flame Spread*

Upholstered 

Furniture

Missing / 

Unknown Other Upholstered Furniture

Missing / 

Unknown Other

Year

2006 3105 51441 83523 659 74 096 16 888

2007 3053 58114 89540 641 80 903 17 441

2008 2937 61908 88941 641 85 160 16 683

2009 2566 62371 81261 579 79 995 16 508

2010 2714 71131 91011 608 92 699 18 085

* Excluded are incidents (A) with the Item Contributing Most to Flame Spread the same as the Item First Ignited, and (B) without fire 

spread.

Given the relative number of incidents with missing or unknown values and their 

potential influence on national RUF estimates, we investigate the usefulness of allocating

the unknowns based on statistical correlations with other, non-missing, information 

describing the fire incident. Unlike raking, the allocation approach can be performed on 

a single data array, and limits selection bias through the inclusion of all other, relevant, 

non-missing information. A number of competing statistical models are evaluated, with 

the best performing models selected based on the minimum out-of-sample mean squared 

prediction error (Makridakis, 1998). The optimum models based on this criterion are then

used to estimate the number of residential upholstered furniture fires, related occupant 

fatalities and injuries, and property and content losses, by year, from 2006 to 2010. In 

1 Confined fires include fires confined to a cooking container, chimney or flue, incinerator, burner, 

compactor, or trash area.
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addition, nonparametric bootstrapping techniques (e.g., see Kennedy 2003) can be used 

to produce uncertainty ranges associated with the estimates.

This analysis is a part of a larger research effort to develop statistics and uncertainty 

measures for characterizing, tracking, and better understanding the root causes of the total 

burden of fire in the United States. The purpose of these statistics will be to provide 

details on the circumstances, causes, and development of fires and the related deaths, 

injuries, and property damage by major fire incident category (residential structure, nonresidential structure, natural vegetation, vehicle), as well as to provide details on the costs 

related to fire protection and loss mitigation (e.g., fire protection of constructed facilities; 

standards and codes development, testing, and implementation; wildland fuel treatments, 

etc.). This information will be used to develop performance metrics, enabling 

comparisons between the use of new fire mitigation technologies and their impact on the 

U.S. fire losses, with a particular focus on residential fires involving upholstered 

furniture.
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2 Data and Methods

2.1 Data

This analysis utilizes data from the National Fire Incident Reporting System (NFIRS), 

which is a product of the National Fire Data Center, an entity of the U.S. Fire 

Administration (USFA). The USFA is authorized to gather, analyze, and standardize fire 

information and data through the Federal Fire Prevention and Control Act of 1974 

(FEMA 2010). The reporting format in NFIRS is, generally, consistent with the National 

Fire Protection Association Standard 901, “Uniform Coding for Fire Protection”

(National Fire Protection Association 2011). Approximately 1 million fires are reported 

to NFIRS each year by over 22 000 fire departments. NFIRS is the world’s largest, 

national database of fire incident information; however, fire department participation in 

NFIRS is voluntary. Consequently, not all fire departments participate in NFIRS, making 

the incident data a partial, and potentially non-random, census. 

As described in the NFIRS reference guide, the NFIRS data system is broken into 11 

modules2 with the Basic Module as the primary one (FEMA 2010). In this module, 

general information is captured for every reported incident (emergency call). There are 

additional modules for different types of incidents. Information is generally obtained at 

the scene by emergency response personnel. Within each module there are required fields 

and optional fields. Frequently, fire departments will provide aid to one another. In these 

instances, an indication is made in the NFIRS system. For this analysis, only the non-aid 

fires recorded in NFIRS are counted as a fire incident.

Not every module is relevant to all incidents (e.g., the Structure Fire module might not be 

relevant to an outside fire incident); therefore, only some modules are mandatory (e.g., 

the Basic Module), while others are not (e.g., the Arson Module). Even within the 

mandatory modules, only some of the field elements are mandatory (e.g., Incident Type 

2 The modules include the following: basic module, fire module, structure fire module, civilian fire casualty 

module, fire service casualty module, EMS module, hazardous materials module, wildland fire module, 

apparatus or resources module, personnel module, and the arson module.
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within the Basic Module). The Basic Module is completed for every reported emergency 

call to which the participating department responds. It requests information about the 

location of the incident, incident type, alarm time and response time, actions taken (e.g., 

extinguishment), property losses, casualties, and property use. 

For non-confined fires (see footnote 1), the fire department is required to fill out the Fire

Module or the Wildland Fire Module. These modules request information about the 

ignition (e.g., Area of Origin, Heat Source, Item First Ignited), cause, and factors 

contributing to ignition. The Structure Fire Module is required for all non-confined 

structure fires. Structures can include “buildings, open platforms, bridges, roof 

assemblies over open storage or process areas, tents, air-supported structures, and 

grandstands” (p. 5-3, U.S. Fire Administration 2010). This module requests information 

about the structure type, building status, building height and floor size, fire origin, fire 

spread, and the presence and operation of smoke detectors and automatic fire sprinklers. 

There are additional fields in each of the modules above; however, most of them are 

optional fields. 

For this analysis, a number of variables (i.e., incident factors) are utilized, which are 

reported within the module categories described above. They are listed below with the 

definition provided by the NFIRS reference guide (U.S. Fire Administration 2010):

Area of Fire Origin: “The primary use of the area where the fire started within the 

property. The area of origin may be a room, a portion of a room, a vehicle, a portion of a 

vehicle, or an open area devoted to a specific use. Every fire has an area of fire origin.”

Cause of Ignition: “The general causal factor that resulted in a heat source igniting a 

combustible material. The cause could be the result of a deliberate act, mechanical failure, or 

act of nature.”

Factors Contributing to Ignition: “The contributing factors that allowed the heat source 

and combustible material to combine to ignite the fire.”
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Fire Spread: “The extent of fire spread in terms of how far the flame damage extended. The 

extent of flame damage is the area actually burned or charred and does not include the area 

receiving only heat, smoke, or water damage.”

Heat Source: “The heat source that ignited the Item First Ignited to cause the fire.”

Human Factors Contributing to Ignition: “The human condition or situation that 

allowed the heat source and combustible material to combine to ignite the fire.”

Incident Type: “This is the actual situation that emergency personnel found on the scene 

when they arrived. These codes include the entire spectrum of fire department activities from 

fires to EMS to public service.”

Item First Ignited: “The use or configuration of the item or material first ignited by the 

heat source. This [variable] identifies the first item that had sufficient volume or heat 

intensity to extend to uncontrolled or self-perpetuating fire.”

Item Contributing Most to Flame Spread: “The item contributing most to flame spread, 

if different from the Item First Ignited.” This includes objects such as a sofa, bedding, or a 

structural component.

Type of Material First Ignited: “The composition of the material in the item first ignited 

by the heat source. The type of material ignited refers to the raw, common, or natural state of 

the material. The type of material ignited may be a gas, flammable liquid, chemical, plastic, 

wood, paper, fabric, or any number of other materials.”

Type of Material Contributing Most to Flame Spread: “The type of material 

contributing most to flame spread, if different from the Type of Material First Ignited.” This 

includes materials such as fabric, wood, or gasoline.
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Property Use: “Each individual property has a specific use, whether a structure or open 

land. This entry refers to the actual use of the property where the incident occurred, not the 

overall use of mixed use properties of which the property is part. The intent of this entry is to 

specify the property use, not the configuration of the building or other details of the 

property.”

Residential fires involving upholstered furniture can be identified two ways – based on 

the Incident Type and Property Use, to determine if the incident is a residential structure 

fire, and either by (1) Item First Ignited or (2) Item Contributing Most to Flame Spread.

(Item Contributing Most to Flame Spread is an optional field, which tends to get 

populated less than mandatory fields.) For this analysis, residential refers to 1- and 2-

family detached dwellings (NFIRS code: 419) and multifamily dwellings (NFIRS code: 

429). Structure fires are categorized into non-confined (NFIRS codes: 111-112 and 120-

123) and confined (NFIRS codes: 113-118). For both Item First Ignited and Item Most

Contributing to Flame Spread, upholstered furniture is identified by code 21

(“upholstered sofa, chair, vehicle seats”). This category excludes items such as cabinetry,

desks, and non-upholstered chairs. It also does not include mattresses, pillows, or

bedding. For this analysis, data from 2006 to 2010 are used. A summary of the (raw)

NFIRS data for non-confined residential fires involving upholstered furniture is shown in

Table 2.1 while that for the confined fires is shown in Table 2.2.

3

3 A confined fire in NFIRS is a fire confined to 1) a container, 2) chimney, 3) incinerator, 4) burner/boiler, 

5) compactor/rubbish or 6) trash. If a fire is confined to these items it is not clear how upholstered furniture

is involved, but there are fires with these designations; therefore, they are calculated separately.
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Table 2.1: Non-Confined Residential Fires Recorded in NFIRS that Involve Upholstered Furniture

2006 2007 2008 2009 2010

IFI

Incidents 3105 3053 2937 2566 2714

Injuries 346 291 354 322 275

Fatalities 120 126 106 110 95

Losses ($ million) 198.3 101.8 106.9 93.5 81.0

ICMFS

Incidents 659 641 641 579 608

Injuries 94 81 81 110 78

Fatalities 29 35 38 16 36

Losses ($ million) 29.2 39.1 33.9 29.3 26.6

Table 2.2: Confined Residential Fires Recorded in NFIRS that Involve Upholstered Furniture

2006 2007 2008 2009 2010

IFI

Incidents 25 29 18 30 24

Injuries 0 1 1 0 0

Fatalities 0 0 0 0 0

Losses (dollars) 3282.0 7207.0 8650.0 12305.0 10913.0

ICMFS

Incidents 1 0 1 0 2

Injuries 0 0 1 0 0

Fatalities 0 0 0 0 0

Losses (dollars) 501.0 0.0 800.0 0.0 22000.0

In addition to NFIRS data, both the conventional scaling method and the data imputation 

method developed in this report utilize data from the National Fire Protection Association 

(NFPA) to scale the aggregated NFIRS data into national statistics. (The two methods 

only differ in how they allocate the unknowns within the NFIRS data.) The NFPA 

collects annual survey data from municipal fire departments. It is a survey sent to more 

than 20 000 of the approximate 30 000 total fire departments. The data from the 

approximate 3000 fire departments that respond is used to produce nationwide estimates 

of residential and non-residential structure fires, vehicle fires, and outside and other fires 

(Karter 2010). NFPA’s estimates for residential fires, which are appropriate for scaling 

NFIRS data involving upholstered furniture, are shown in Table 2.3. The NFIRS data for 

residential fires between 2006 and 2010 (i.e., fires with incident type 111 through 123 

and have property use 419 or 429) represents approximately 67 % of the fires estimated 

by the NFPA.
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Table 2.3: NFPA Residential Fire Estimates

2006 2007 2008 2009 2010

Fires 412500 414000 403000 377000 384000

Injuries 12925 14000 13560 13050 13800

Deaths 2620 2895 2780 2590 2665

Losses ($billion) 7.0 7.5 8.6 7.8 7.1

2.2 Imputation Method

The data imputation technique ultimately allocates the unknowns using (two) statistical 

models relating non-missing, reported fire incident factors to the likelihood that the (1) 

Item First Ignited (IFI) or the (2) Item Contributing Most to Flame Spread (ICMFS) was 

upholstered furniture. The parameters in each statistical model are estimated using a 

sample of incidents with known IFI or ICMFS data. 

The conventional scaling and data imputation approaches will yield similar results should 

the fire incidents with known data be representative of the data with unknown and 

missing information. However, if there are systematic differences, and if these 

differences are correlated with other, more frequently reported data, the two approaches 

will yield different results. While the data imputation approach offers the potential for 

greater accuracy, it is computationally expensive in comparison. 

2.2.1 Statistical Model

This analysis uses a type of statistical model known as a logistic regression model

(StataCorp 2007), often referred to as a “logit” regression. The logistic regression models

used here relate the probability that residential fire incident j has upholstered furniture as 

IFI (or ICMFS)—as a function of other reported incident factors (e.g., Area of Origin). 

The logit model is fit to the data via Maximum Likelihood (Greene 2008) and has the 

following general form:
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Pr(yj,t = 1|xj) =

exp(xj,tβt)

1 + exp(xj,tβt)

(1)

where y is a (0/1) binary variable indicating the involvement of upholstered furniture by 

fire incident factor t (IFI, ICMFS) for residential fire incident j, x is a vector of variables 

correlated with the involvement of upholstered furniture, and  is a vector of parameters.

Each model is fit to a sample of the NFIRS data that has non-missing data entered for 

Incident Factor, Property Use, Item First Ignited, and Item Contributing Most to Flame

Spread. Each of these models is estimated for non-confined structure fires.4 To avoid 

double-counting, incidents with reported upholstered furniture as both the item first 

ignited and item contributing most to flame spread were included in the IFI model. 

The IFI variable sets include the following categories (xIFI):

 Factors Contributing to Ignition

 Heat Source

 Area of Fire Origin

 Type of Material First Ignited

 Item Contributing Most to Spread

 Type of Material Contributing Most to Spread

 Human Factors Contributing to Ignition

 Cause of Ignition

 Incident Type

 Fire Spread

The ICMFS variable sets include the following categories (xICMFS):

 Item First Ignited

 Factors Contributing to Ignition

4 Due to the limited number of confined fires, the imputation method was only applied to non-confined 

fires.
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 Heat Source

 Area of Fire Origin

 Type of Material First Ignited

 Type of Material Contributing Most to Spread

 Human Factors Contributing to Ignition

 Cause of Ignition

 Incident Type

 Fire Spread

The variable sets are derived from the NFIRS categories. Each NFIRS category has a list 

to select from. For example, there are six items to select from for the cause of ignition: 1) 

Intentional; 2) Unintentional; 3) Failure of equipment or heat source; 4) Act of nature; 5) 

Cause under investigation; 6) Cause undetermined after investigation. For statistical 

analysis, the categorical and ordinal items were converted into indicator (binary) 

variables. The data conversion meant that each variable set included multiple binary 

variables (e.g., cause of ignition set included seven binary variables—the six items above 

plus one for incidents with missing values—with one held out of the model to ensure the 

parameters have unique values that can be identified5). If data were missing for a 

specified variable set, then all the indicator variables in the model were zero and a 

separate variable indicated a missing value. This resulted in hundreds of potential 

variables (covariates) to include in the statistical modeling. A constraint of the logit 

model is it cannot include variables that perfectly predict an outcome—here, the presence 

or absence of upholstered furniture involvement. Thus, binary variables that describe fire 

conditions that only occur either with or without upholstered furniture involvement were 

excluded from analysis.6 However, this information could be exploited to narrow the 

5

If the models are allowed to be over-parameterized, the values of the ’s in Eq. (1) cannot be determined 

uniquely. Instead there will be an infinite number of different solutions. This situation is sometimes 

referred to as the dummy variable trap (Greene 2008) when it arises in regression analysis with categorical 

predictor variables.

6

It is important to note that a “perfect predictor” is a misleading term, as the variable could not be used as a 

proxy for IFI or ICMFS. For more information on this, please see the Stata manual (StataCorp 2007).
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universe of possible fire incidents involving upholstered furniture. This is left for future 

analysis. 

2.2.2 Estimated Probabilities

After estimating the values of the parameters in the model given by Eq. 1 using data

randomly sampled from the NFIRS database, the fitted model can be used to produce 

estimated probabilities of upholstered furniture involvement for any particular fire using 

Eq.2:

p̂j,t =

exp(xj,tβt

̂ )

1 + exp(xj,tβt

̂ )

(2)

where p̂denotes the predicted probability of incident factor t being upholstered furniture, 

and β̂ is the vector of estimated parameters. These estimated probabilities can be 

interpreted as the likelihood of upholstered furniture involvement, given other fire-related 

information.

2.2.3 Estimated NFIRS Residential Fires Involving Upholstered Furniture

Based on the estimated probabilities, the total number of non-confined fire incidents, F,

of factor t (Ft), involving upholstered furniture can be computed as:

Ft = ∑ yi,t

nn,t

i + ∑ p̂j,t

nu,t

j

(3)

where nn,tis the total number of fire incidents with known incident data on factor t, nu,t

is the total number of fire incidents with missing or unknown incident data on factor t, 

and nn + nu = N, the total number of NFIRS-reported non-confined fire incidents.

The total number of fatalities, injuries, and economic loss (property and content loss) 

from fires involving residential upholstered furniture can be computed as:
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Ot,k = ∑ (yi,t ∗ oi,t,k)

nn,t

i + ∑ (p̂j,t ∗ oj,t,k)

nu,t

j

(4)

where Ot,k is the total number of outcomes of k (fatalities, injuries, losses) resulting from 

fire incidents of factor t, involving residential upholstered furniture, and oi,t,k and oj,t,k are 

the incident-level outcomes. As shown in Eq. 4, the missing and unknown outcomes are 

allocated based on the likelihood that the incident involved upholstered furniture, and 

resemble expected values. The likelihood is determined by other variables in the NFIRS 

data. 

The values resulting from Eqs. 3 and 4 can be scaled using the “national scaling ratio,” as 

detailed above to produce national fire statistics, at least for the non-confined fires. (See 

Appendix A for more detail.) Again, because the number of non-missing confined fires 

with known IFI or ICMFS information is so few, it does not lend itself to the imputation 

technique. Therefore, we allocate the unknown and missing confined fires involving 

upholstered furniture similar to the method used by NFPA.

2.3 Model Specification & Selection

2.3.1 Model Specification

For IFI, fourteen different model specifications were evaluated—i.e., different 

combinations of predictor variables were included in Eq. 1 to determine the combination 

that produced the most accurate prediction of upholstered furniture involvement.

Combinations of variables were created from the 10 variable sets (listed in Section 2.2.1) 

plus a variable indicating the state where the fire occurred along with month and year

dummy variables. Some variables were removed due to collinearity. The model 

comparison exercise required in excess of seven days of computation time using Stata SE 

12 (64-bit) on a desktop computer with a 64-bit Windows 7 Enterprise operating system 

with two processors running at 2.4GHz.
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The comparison of multiple model specifications (i.e., the fourteen discussed above) was 

only done for the IFI model. Multiple ICMFS model specifications were not compared 

due to the observed lack of variation in IFI accuracy (results not shown) and to time 

constraints.7 Thus, the model specification selected for IFI is used in modeling ICMFS. 

2.3.2 Model Selection

Each model specification was evaluated using random samples of 20 000 residential fire 

incidents with known IFI from the five years examined. These training samples were 

used to fit the statistical models (Eq. 1). Validation samples were created by randomly 

sampling an additional 20 000 observations with known IFI data that were not part of the 

training data.

8

 The validation samples were used to create estimated probabilities of 

upholstered furniture involvement based on the statistical modeling results from the 

training data (Eq. 2). The sum of the estimated probabilities of the validation sample was 

then compared to the total number of fire incidents involving upholstered furniture in the 

validation sample. This process was repeated 1000 times. 

To identify the most accurate specifications, for the purposes of this analysis, the root 

mean squared error (RMSE) (Makridakis, 1998) was computed.9 Again, due to 

computing demands, this was limited to the IFI model. The best performing model (i.e., 

lowest RMSE related to the number of fire incidents) was selected. This model had an

average relative prediction error rate of 3.6 % for the number of fire incidents.10 Applying 

a similar specification to the ICMFS resulted in an average relative prediction error rate 

of 5.4 %.11 For the estimation of deaths, injuries, and losses the average relative 

7

In addition, an earlier version of the ICMFS model, for which multiple model specifications were 

compared, produced results qualitatively similar to the IFI results.

8 Occasionally, training and validation samples were less than 20 000 observations each due to missing 

covariate data. 

9 There are two primary categories of modeling that utilize regression: explanatory models and predictive 

models. This paper presents the latter. Extreme caution should be exercised when drawing conclusions 

regarding causation from a predictive model, as it is not designed for this purpose. The predictor variables 

in the regression part of this model do not in any way explain why or how fires with upholstered furniture 

occur. Any correlating variable can be used as a predictor.

10 Relative prediction error rate is computed as (100 %)*|(predicted value – actual value)/(actual value)|.

11 The final specifications differ between the IFI and ICMFS models in the following ways: (1) the IFI 

model includes variables describing the item contributing most to flame spread; the ICMFS model includes 
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prediction error rates for the IFI model were 23.9 %, 12.1 %, and 14.5 %, respectively. 

For the estimation of deaths, injuries, and losses the average relative prediction error rates

for the ICMFS model were 42.3 %, 27.9 %, and 10.5 %. The average relative prediction 

error rates for deaths and injuries are higher than for incidents because there are fewer 

occurrences of deaths and injuries, making them more difficult to estimate. The average 

numbers of deaths were 25 for IFI and 19 for ICMFS out of 20 000 observation samples. 

The average number of injuries was 75 for the IFI and 59 for the ICMFS. Losses also 

have a higher average relative prediction error rate, which is possibly related to sporadic 

reporting of losses and variance in loss assessment. The indicator variables that were 

statistically significant at the 5 % level in the final statistical models are listed in Table 

2.4. 

Appendix B presents the z-scores12 from the logit models averaged over the 1000 runs for 

each model type. The z-scores provide a measure of association between each of the 

variables and the probability of upholstered furniture involvement, with their signs 

indicating direction, and their absolute magnitude indicating strength. For IFI, the three 

variables with the largest positive (also in absolute terms) z-scores are (1) type of 

material fire ignited – fabric, fiber, cotton, blends, rayon, wool; (2) area of fire origin –

common room, den, family room, living room, lounge; and (3) item contributing most to 

flame spread – upholstered sofa, chair, vehicle seat. For ICMFS, the three variables with 

the largest positive (also in absolute terms) z-scores are (1) area of fire origin – common

room, den, family room, living room, lounge; (2) area of fire origin – function area, other; 

and (3) item first ignited – undetermined.

variables describing the item first ignited; and (2) due to collinearity, some variables in the IFI model were 

dropped in the ICMFS model, while some variables in the ICMFS model were dropped in the IFI model.

12 For each variable its z-score (‘standard score’) equals its estimated parameter divided by the estimated 

parameter’s standard error. Scores equal to or exceeding the absolute value of 1.96 indicate statistical 

significance at the 5% level.
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Table 2.4: Indicator Variables Statistically Significant at the 5 % Level

IFI NFIRS Category

Common room, den, family room, living room, lounge Area of Fire Origin

Function area, other Area of Fire Origin

Cooking area, kitchen Area of Fire Origin

Vehicle storage area; garage, carport Area of Fire Origin

Exterior balcony, unenclosed porch Area of Fire Origin

Courtyard, patio, porch, terrace Area of Fire Origin

Sawn wood, including all finished lumber Type of Material First Ignited

Fabric, textile, fur, other Type of Material First Ignited

Fabric, fiber, cotton, blends, rayon, wool Type of Material First Ignited

Undetermined Type of Material First Ignited

Upholstered sofa, chair, vehicle seats Item Contributing Most to Flame Spread

Mattress, pillow Item Contributing Most to Flame Spread

Bedding; blanket, sheet, comforter Item Contributing Most to Flame Spread

Heat source too close to combustibles. Factors Contributing to Ignition

Mechanical failure, malfunction, other Factors Contributing to Ignition

Electrical failure, malfunction, other Factors Contributing to Ignition

Equipment unattended Factors Contributing to Ignition

ICMFS NFIRS Category

Common room, den, family room, living room, lounge Area of Fire Origin

Function area, other Area of Fire Origin

Cooking area, kitchen Area of Fire Origin

Laundry area, wash house (laundry) Area of Fire Origin

Item First Ignited, Other Item First Ignited

Furniture, utensils, other Item First Ignited

Non-upholstered chair, bench Item First Ignited

Electrical wire, cable insulation Item First Ignited

Magazine, newspaper, writing paper Item First Ignited

Rubbish, trash, or waste Item First Ignited

Undetermined Item First Ignited

Sawn wood, including all finished lumber Type of Material First Ignited

Fabric, textile, fur, other Type of Material First Ignited

Fabric, fiber, cotton, blends, rayon, wool Type of Material First Ignited

2.3.4 Imputation of Unknown & Missing Data

Based on the IFI model specification, a procedure analogous to the validation procedure 

was replicated for residential fire data with unknown and missing IFI fields; then the

fitted models, using the specification with the lowest RMSE from the validation 

procedure, were used with this data to impute the missing values. Some observations 

were dropped due to issues of collinearity. This process produced, for each fire incident 

with missing information, the probability that the IFI was upholstered furniture, given the 
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other fire data reported for that incident. (The same procedure was performed using the 

ICMFS, using a similar model specification.) The probabilities were then used to estimate 

the number of fatalities, injuries, and economic losses. For each model, this process was 

repeated 1000 times. Iterating this process provides a distribution of values of the total 

number of fire incidents, fatalities, injuries, and economic losses, rather than just point 

estimates, as produced from the conventional scaling method. This information is useful 

in assessing significance of time trends, for example.
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3 Upholstered Furniture Fire Estimates

Applying the model specification to fire incidents with known Item First Ignited (IFI) and 

Item Contributing Most to Flame Spread (ICMFS), two statistical models were used to 

estimate the probability that IFI or ICMFS were upholstered furniture fires for those fire 

incidents with missing IFI or ICMFS data. The predicted probabilities were used to 

estimate the total number of incidents, fatalities, injuries, and losses from non-confined 

fires that involved upholstered furniture, but had missing or unknown data. Combining

the incident, fatality, injury, and loss data from those incidents with known IFI and 

ICMFS information with the allocated confined fires with missing IFI and ICMFS data, 

these numbers were ‘scaled-up” to represent statistics for the U.S., using the procedure 

consistent with Ahrens (2011). 

The confined fires with missing or unknown IFI and ICMFS data [see Table 2.2] were 

allocated over the distribution of the known, similar to Ahrens (2011). 

The small number of confined fires made it difficult to estimate the number of fires using 

a logit regression; thus, the number of confined fires involving upholstered furniture was

estimated using the method used by NFPA. The annual totals of confined fires that 

involved upholstered furniture as the Item First Ignited (IFI) ranged between 180 and 390 

(see Table 3.1), making them a relatively small proportion of the total number of 

upholstered furniture fires. Those that involved upholstered furniture as the Item 

Contributing Most to Flame Spread (ICMFS) ranged between 0 and 1300. The small 

number of confined fires with a known ICMFS combined with the very few fires with 

ICMFS values that were designated as upholstered furniture resulted in a wide range for 

the confined fires where upholstered furniture was the item contributing most to flame 

spread. This is true for all four categories (i.e., incidents, injuries, fatalities, and losses).

The number of non-confined fires was scaled into national estimates using a method 

consistent with Ahrens (2011), but the allocation of incidents with missing or unknown 

IFI or ICMFS data was performed using a logit regression, as described in Section 2. The 

estimated number of non-confined residential fires involving upholstered furniture as IFI,
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Table 3.1: Estimated Number of Confined Residential Fires Involving Upholstered Furniture

2006 2007 2008 2009 2010

IFI

Incidents 390 320 180 290 190

Injuries 0 6 5 0 0

Fatalities 0 0 0 0 0

Losses ($thousand) 21 33 45 51 57

ICMFS

Incidents 1300 0 450 0 400

Injuries 0 0 110 0 0

Fatalities 0 0 0 0 0

Losses ($thousand) 96 0 83 0 1000

for the U.S., is shown in Table 3.2. Since the allocation of the missing or unknowns were 

made using a sampling technique, the minimum, maximum, average, and median value 

were selected from the 1000 iterations described in Section 2.3 to provide some context. 

For example, in 2010, the average number of non-confined residential fire incidents with 

upholstered furniture as the Item First Ignited is estimated at 5000. Given the uncertainty 

in allocating the missing or unknown, based on the modeling approach, the actual number 

of fires is likely between 4500 and 5700. 

Table 3.2: Estimated Number of Non-Confined Residential Fires Involving Upholstered Furniture as 

Item First Ignited (Imputation Approach)

2006 2007 2008 2009 2010

Incidents

Minimum 6200 5700 5300 4600 4500

Maximum 7400 7300 6700 5700 5700

Average 6800 6400 5900 5100 5000

Median 6800 6400 5900 5100 5000

Injuries

Minimum 780 680 760 650 570

Maximum 870 810 890 740 670

Average 820 740 810 690 610

Median 820 740 810 690 610

Fatalities

Minimum 290 300 270 240 210

Maximum 330 370 340 280 260

Average 310 330 290 260 230

Median 310 330 290 260 230

losses 

($million)Minimum 500 230 280 240 200

Maximum 570 340 390 320 270

Average 530 280 330 280 230

Median 530 280 330 280 230
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Table 3.3 is similar to Table 3.2, but for Item Contributing Most to Flame Spread. The 

values in Table 3.3 exclude any fires where the Item First Ignited was upholstered 

furniture. The values from Table 3.2 and Table 3.3 are, therefore, additive. Together, 

these represent the total number of fires where upholstered furniture played a significant 

role in either the ignition or spread of the fire. The number of fires incidents that involved 

upholstered furniture as the Item Contributing Most to Flame Spread had a larger range 

than that for the Item First Ignited. Table 3.4 provides the total estimated number, for the 

U.S., of confined and non-confined residential fires involving upholstered furniture either

as the Item First Ignited or as the Item Contributing Most to Flame Spread. Figure 3.1

graphs the minimum, maximum, and average estimated number of residential fires

involving upholstered furniture from 2006 to 2010. Based on the figure, it appears the

numbers of fires are slightly decreasing. Despite this decrease, residential upholstered

furniture fires cause more deaths per fire than the average residential fire. According to

NFPA data in Table 2.3, there were 6.9 deaths per thousand residential fires. According

to the estimates in Table 3.4, there are 39.2 deaths per thousand residential upholstered

furniture fires.

Table 3.3: Estimated Number of Non-Confined Residential Fires Involving Upholstered Furniture as 

Item Contributing Most to Flame Spread (Imputation Approach)

2006 2007 2008 2009 2010

Incidents

Minimum 2700 2500 2800 2500 2400

Maximum 7000 7200 7500 7200 7800

Average 4400 4300 4600 4100 4100

Median 4300 4300 4500 4000 4100

Injuries

Minimum 290 280 290 310 260

Maximum 390 380 430 410 380

Average 330 330 350 360 320

Median 330 330 350 360 320

Fatalities

Minimum 110 120 140 77 120

Maximum 150 180 220 130 180

Average 130 150 170 100 140

Median 130 150 170 100 140

losses 

($million)

Minimum 140 130 160 140 130

Maximum 220 210 290 250 230

Average 170 170 210 190 170

Median 170 170 210 180 170
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Table 3.4: Estimated Number of Confined and Non-Confined Residential Fires Involving 

Upholstered Furniture either as Item First Ignited or Item Contributing Most to Flame Spread

2006 2007 2008 2009 2010

Incidents

Minimum 11000 8600 8700 7400 7500

Maximum 16000 15000 15000 13000 14000

Average 13000 11000 11000 9400 9700

Median 13000 11000 11000 9400 9700

Injuries

Minimum 1100 960 1200 960 830

Maximum 1300 1200 1400 1100 1100

Average 1200 1100 1300 1100 930

Median 1200 1100 1300 1100 930

Fatalities

Minimum 400 420 410 310 330

Maximum 490 550 550 410 440

Average 440 480 460 360 380

Median 440 480 460 360 380

losses 

($million)

Minimum 640 360 450 380 320

Maximum 790 560 680 570 500

Average 700 450 540 460 390

Median 700 450 540 460 390

Figure 3.1: Minimum, Maximum, and Average of the Estimated Number of Confined and NonConfined Residential Fires Involving Upholstered Furniture either as Item First Ignited or Item 

Contributing Most to Flame Spread

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

2006 2007 2008 2009 2010

Incidents
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4 A Comparison of Estimates Produced by the Scaling and 

Imputation Approaches

As discussed previously, the conventional national fire statistics are based on NFIRS 

incident data—with complete/known data—that are scaled using two ratios (e.g., see 

Ahrens [2011]). In this report, we explore the use of a data imputation technique as an 

alternative method to “allocate the unknowns.” There are some differences between the 

estimates using the conventional method compared to the method in this report.

Item First Ignited

Fire incidents with missing or unknown information regarding the Item First Ignited (IFI) 

represented 40 % of all non-confined home structure fires reported to NFIRS from 2006 

to 2010. These fire incidents accounted for 57 % of all civilian (non-fire service) 

fatalities. 

The NFPA estimates (National Fire Protection Association 2013), using the scaling 

method, indicate that between 2006 and 2010 there was an annual average of 6700 home 

structure fires with upholstered furniture being the Item First Ignited. These fires caused, 

on average, 480 civilian deaths, 840 civilian injuries, and $427 million in direct property 

damage (National Fire Protection Association 2013). This report, using the imputation 

method, estimates these numbers to be 5800 fires, 300 civilian deaths, 740 civilian 

injuries, and $328 million in direct property damage. 

Item Contributing Most to Flame Spread

Fire incidents with missing or unknown information regarding the Item Contributing 

Most to Flame Spread (ICMFS) represented 75 % of all non-confined home structure

fires reported to NFIRS from 2006 to 2010 that were reported to have spread beyond the 

object of origin. (Fires that spread beyond object of origin were reported in 90 % of all

non-confined home fire incidents.) These fire incidents accounted for 69 % of all civilian

fatalities of non-confined fires that were reported. 
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Hall estimates, using the scaling method,13 that there was an annual average of 2200 

home fires with upholstered furniture as Item Contributing Most to Flame Spread and 

Item First Ignited identified as something other than upholstered furniture (Hall 2014). 

These fires produced 130 civilian deaths, 280 civilian injuries, and $138 million in losses. 

These figures are directly comparable to the statistics produced in this report, and can be 

added to the IFI figures above. This report, using the imputation method, estimates that 

there was an annual average of 4300 home fires with upholstered furniture as Item 

Contributing Most to Flame Spread and Item First Ignited identified as something other 

than upholstered furniture. These fires produced 140 civilian deaths, 340 civilian 

injuries, and $182 million in losses.

Upholstered Furniture Involvement in Residential Home Fires

The imputation method estimates 10 100 residential home fires involving upholstered 

furniture resulted in 440 occupant fatalities, 1100 occupant injuries, and $510 million, on 

average each year, from 2006 to 2010, based on data reported in Table 3.4. Using 

nonparametric bootstrapping (Kennedy 2003), 95 % confidence intervals were produced 

for each year’s estimate. Figures 4.1 to 4.4 present the estimated annual number of fires 

involving upholstered furniture (Figure 4.1) and the number of resulting occupant 

fatalities (Figure 4.2), occupant injuries (Figure 4.3), and total direct losses (Figure 4.4). 

Plotted along with these values are the combined values published by NFPA, including 

Hall’s estimates (2014), produced using the method of scaling NFIRS data, discussed in 

the previous section. (Due to data limitations, the yearly estimates pertaining to Item First 

Ignited were combined with averaged yearly estimates pertaining to Item Contributing 

Most to Flame Spread.) 

Figure 4.1 demonstrates the imputation method estimates more fires involving 

upholstered furniture than using the scaling approach, on average, although the combined 

scaling-based numbers often overlap the lower confidence interval. Confidence intervals 

13 It should be noted that the scaling method developed in Hall (2014) is different than that used in NFPA’s 

report on upholstered furniture flammability for item first ignited. Hall’s method employs allocating the 

missing and unknown within fire size groups (e.g., beyond object but confined to room of origin, beyond 

room but confined to floor of origin).
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for the NFPA estimates are not produced, but assuming even a small interval band, 

suggests that the scaling and imputation methods produced results that are not statistically 

distinguishable. Figure 4.2 shows that the combined scaling-based numbers produce 

estimates of occupant fatalities that are statistically larger than those produced using the 

imputation method. Figure 4.3 graphs the number of annual occupant injuries and shows 

a high degree of agreement between the two methods. The patterns are largely similar 

and the annual values tend to be statistically indistinguishable. Figure 4.4 presents losses 

by year; only in years 2006 and 2010 are the values statistically different between the

methods, although the difference in 2010 is far less than in 2006.

In general, the scaling and imputation methods produce similar statistical results for the 

number of residential home fires involving upholstered furniture, as well as for numbers 

of occupant injuries and direct property losses. However, the disagreement between the 

estimated numbers of occupant fatalities is statistically significant. The imputation 

method estimates about a third fewer occupant fatalities, the difference being in the 

number fires involving upholstered furniture from direct ignition rather than from flame

spread. Overall, the imputation method suggests that fires involving upholstered 

furniture resulted in fewer deaths on a per reported fire basis than currently reported, 

although residential upholstered furniture fires cause more deaths per fire than the 

average residential fire. For fires involving upholstered furniture from direct ignition, 

there were 7 deaths per 100 home fires involving upholstered furniture (via scaling) 

versus 5 deaths per 100 home fires (via imputation). For fires involving upholstered 

furniture from flame spread, the fires were less deadly, on a per reported fire basis, but 

produced the same number of fatalities, as twice as many fires were estimated – 6 deaths 

per 100 home fires with significant flame spread (via scaling) versus 3 deaths per 100

home fires (via imputation).

A difference in the estimates produced from the two methods occurs when the 

proportional allocation assumption used by the scaling approach is not supported by the 

data. The magnitude of the difference depends on the robustness of the assumption along 

with the number of unknowns requiring allocation. Of non-confined home fires, 30 % of 
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the injuries, 40 % of the fire incidents, 49 % of the economic losses, and 57 % of the 

fatalities are associated with fire incidents with an unknown or missing IFI. Therefore, if 

the proportionality assumption fails to hold (for each category), we would expect the 

greatest agreement in estimates to occur between injuries, which has the lowest 

percentage of unknowns, and the least between fatalities, which has the highest 

percentage of unknowns, with fires and economic losses falling somewhere in-between.

Further, the imputation method evaluates the likelihood that an incident involved

upholstered furniture and keeps the outcome linked (fatality, injury, economic loss) to 

produce estimates, unlike the scaling approach, where each estimate is produced

independent of the others. Of the known home fires with IFI identified as upholstered 

furniture, the rate of fatalities, injuries, and economic losses occurred at rates of 3.9, 11.0

and $4.0 million per 100 home fires, respectively. Of the unknown fires attributed to 

upholstered furniture by the scaling method, the implied rates of fatalities, injuries, and 

economic losses were 7.6, 7.1, and $5.7 million per 100 home fires, respectively. (The 

rates are implied in the sense they are an artifact of the scaling.) The scaling approach 

implies that the unknown fires were deadlier and costlier, but less injurious than the home 

fires with known IFI identified as upholstered furniture. However, it has no mechanism 

to verify these implications. By comparison, of the unknown fires likely to have involved

upholstered furniture by the imputation method, the observed rates of fatalities, injuries, 

and economic losses were actually 3.6, 7.0, and $4.9 million per 100 home fires, 

respectively. There is pretty good agreement between the two methods for injuries and 

economic losses, suggesting the proportionality assumption held for these, but not for 

fatalities, which is reflected in Figures 4.2 to 4.4. 
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Figure 4.1: Estimated Number of Fire Incidents, Along with their 95 % Confidence Interval, of 

Confined and Non-Confined Residential Fires Involving Upholstered Furniture either as Item First 

Ignited or Item Contributing Most to Flame Spread, Compared with NFPA Published Estimates.

7000

8000

9000

10000

11000

12000

13000

14000

15000

16000

2006 2007 2008 2009 2010

Fires

Fires

95 % CI

NFPA
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Figure 4.2: Estimated Number of Civilian Fire Fatalities, Along with their 95 % Confidence Interval, 

of Confined and Non-Confined Residential Fires Involving Upholstered Furniture either as Item 

First Ignited or Item Contributing Most to Flame Spread, Compared with NFPA Published 

Estimates.

300

350

400

450

500

550

600

650

700

2006 2007 2008 2009 2010

Fatalities

Fatalities

95 % CI

NFPA
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Figure 4.3: Estimated Number of Civilian Fire Injuries, Along with their 95 % Confidence Interval, 

of Confined and Non-Confined Residential Fires Involving Upholstered Furniture either as Item 

First Ignited or Item Contributing Most to Flame Spread, Compared with NFPA Published 

Estimates.

800

900

1000

1100

1200

1300

1400

2006 2007 2008 2009 2010

Injuries

Injuries

95 % CI

NFPA
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Figure 4.4: Estimated Direct Fire Losses, Along with their 95 % Confidence Interval, of Confined 

and Non-Confined Residential Fires Involving Upholstered Furniture either as Item First Ignited or 

Item Contributing Most to Flame Spread, Compared with NFPA Published Estimates.

300

400

500

600

700

800

900

2006 2007 2008 2009 2010

Loss ($ million)

Loss

95 % CI

NFPA
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5 Summary

This Technical Note was developed in an attempt to explore alternative ways to identify 

the missing information regarding the “item first ignited” (IFI) or “item most contributing 

to flame spread” (IMCFS) that were likely to have involved upholstered furniture for 

residential fire incidents reported to the National Fire Incident Reporting System 

(NFIRS). This approach differs from the conventional scaling approach that allocates the 

missing data using the distribution of incidents with known values. The approach 

described employed a data imputation technique to determine the likelihood of 

upholstered furniture involvement based on statistical correlations with other, nonmissing, information describing the fire incident. This model utilized data from 2006 

through 2010, but did not examine the effect of including more or less data from adjacent 

years. More data often results in more accuracy; however, the correlations could 

potentially change over time, making it unclear whether additional data from adjacent 

years would improve accuracy. Extensive validation data was used for selection of the 

form of the IFI model and demonstrated that the imputation method is relatively accurate, 

with an average relative prediction error rate of  3.6 % for IFI and  5.4 % for ICMFS at 

predicting the total number of fires by year. The average relative prediction error rates for 

fatalities, injuries, and losses are higher than for incidents. These were  23.9 % for

fatalities,  12.1 % for injuries, and  14.5 % for economic losses for the IFI model, and 

 42.3 % for fatalities,  27.9 % for injuries, and  10.5 % for economic losses for the IFI 

model. Improvements for these estimates might be made with different modeling 

techniques and specifications. The average relative prediction error rates are not 

available for statistics of the current scaling method.

It is estimated that the number of residential fires involving upholstered furniture 

averaged between 9400 to 13 000 a year during the five-year period from 2006 to 2010.

14

These fires included those for which upholstered furniture was either the item first ignited 

or the item contributing most to flame spread (and not the item first ignited). These fires 

resulted in civilian (non-fire service) fatalities that averaged between 360 to 480 per year, 

14 The averages in this section are the minimum and maximum average values from Table 3.4.
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civilian injuries that averaged between 930 to 1300 per year, and property and content 

losses that averaged between $450 million to $700 million per year.

Comparisons between national statistics produced by the imputation method developed 

within this report with the conventionally-used scaling method produced both similar and 

dissimilar results. Annual trends in the number of fires involving upholstered furniture, 

along with the results for occupant injuries and total direct property losses, were largely 

similar (generally not statistically different) between the two methods. The only 

significant difference appeared between occupant fatalities, with the imputation method 

implying fires involving upholstered furniture were less deadly on a per reported fire 

basis. Overall, the imputation method resulted in estimating the same number of 

occupant fatalities resulting from fires where upholstered furniture was the item 

contributing most to flame spread, but suggested there are twice as many fires as 

previously thought. The number of estimated occupant fatalities caused by fires 

involving upholstered furniture started by a direct ignition were fewer. The number of 

fires estimated using the conventional method was lower than that of the imputation 

method; however, it overlaps the lower confidence interval of the imputation method.

Future research is needed to understand why the imputation and scaling methods diverge 

in estimating the total number of occupant fatalities. Unlike the number of fires, 

occupant injuries, and direct property losses, fatalities occur in smaller numbers, which 

makes statistical modeling challenging. Fewer occurrences can leave statistical methods

vulnerable to influential unique or rare fire incidents, which do not represent typical fire 

conditions or occupant behaviors. Further research can evaluate the robustness of 

competing methods to outliers or abnormal reporting results.

Reporting issues related to Item First Ignited and Item Contributing Most to Flame 

Spread were the only NFIRS fields considered. Further research could be performed to 

evaluate the relative performance of the scaling and imputation method to other critical 

fields contained within the National Fire Incident Reporting System. A systematic 

comparison would allow users of NFIRS-based fire statistics to better understand the 
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robustness and limitations of findings based on a partial census of all fire incidents 

reported in the United States. Finally, both methods scaled statistics using a national 

scaling ratio, which assumes reported fire incidents contained within NFIRS are 

representative of the fires within municipalities that do not report. This may partially 

explain the similarity of the results. How much this assumption influences national fire 

statistics is not well-known and is left for future exploration.
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References

Ahrens, Marty, 2011, Home Fires that Began with Upholstered Furniture, National Fire 

Protection Association, Quincy, MA.

Federal Emergency Management Agency. 2010. National Fire Incident Reporting

System: Complete Reference Guide.

Greene, Michael A., Linda E. Smith, Mark S. Levenson, Signe Hiser, Jean C. Mah. 2001 

“Raking Fire Data.” Presented at the Federal Committee on Statistical Methodology 

Research Conference 2001. 

<http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.159.7090>

Greene, William H. Econometric Analysis. 6th edition. (Pearson Education, Inc Upper 

Saddle River, NJ 2008) 482-572, 108.

Hall, John, and Beatrice Harwood. “The National Estimates Approach to U.S. Fire 

Statistics.” Fire Technology, May 1989. 13.

Hall, John R. 2014. Estimating Fires When a Product is the Primary Fuel but not the First 

Fuel, with an Application to Upholstered Furniture. Fire Technology, February 2014. 

<http://link.springer.com/article/10.1007%2Fs10694-014-0391-8>.

Izrael, David, David C. Hoaglin, and Michael P. Battaglia. 2004 “To Rake or Not to Rake 

is Not the Question Anymore with the Enhanced Raking Macro.” SUGI 29 Proceedings. 

Montreal, Canada. <http://www2.sas.com/proceedings/sugi29/toc.html>

Karter, Michael J. 2010. Fire Loss in the United States During 2009. National Fire 

Protection Association. <http://www.nfpa.org/assets/files/pdf/os.fireloss.pdf>

Karter, Michael J, 2013, Fire Loss in the United States 2012, and previous reports in the 

series.

Kennedy, Peter. A Guide to Econometrics. 5th edition. (MIT Press: Cambridge, MA, 

2003)

Makridakis, Spyros, Steven C. Wheelwright, and Rob J. Hyndman. Forecasting: Methods 

and Applications. 3rd edition. (John Wiley & Sons, Inc: New York, NY 1998) 45-46.

National Fire Protection Association. 2011 “NFPA 901: Standard Classifications for 

Incident Reporting and Fire Protection Data.” <http://www.nfpa.org/codes-andstandards/document-information-pages?mode=code&code=901>

National Fire Protection Associations. 2013 “Upholstered Furniture Flammability.” 

<http://www.nfpa.org/~/media/Files/Research/NFPA%20reports/Major%20Causes/Upho

lsteredFurnitureWhitePaper.pdf>
35

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StataCorp. Stata Base Reference Manual. Volume 2: I-P. Release 10. (Stata Press: 

College Station, TX 2007) 178-189.

U.S. Fire Administration, National Fire Data Center, 2010. National Fire Incident

Reporting System 5.0. Federal Emergency Management Agency, Washington, DC.
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Appendix A: A Comparison of the Scaling & Imputation 

Approaches 

The purpose of this Appendix is to compare differences between the method developed 

within this Technical Note and a scaling method employed by NFPA and U.S. Fire 

Administration. The scaling method is largely based on the work of Hall and Harwood 

(1989), although the approach has been modified over time to accommodate changes in 

NFIRS (e.g., see Ahrens [2011]). An example of the scaling method is shown below. It 

is not representative of all the ways the scaling method is employed, but the general 

approach is conceptually the same.

To simplify the comparison, the focus is on estimating the total number of home fire 

fatalities in the U.S. for fire incidents involving upholstered furniture (RUF) as the item 

first ignited (IFI). Differences exist only for non-confined fires. Due to the limited 

number of confined home fires that involve upholstered furniture, the data imputation 

technique cannot be used.

Scaling Method

The scaling method uses a simplifying assumption that the proportion of all fire deaths 

that is associated with RUF as the IFI is the same for the incidents with unknown IFI—

i.e., assumes the occurrence of unknown IFI is a completely random process. A national

estimate of non-confined RUF fire fatalities (NCRUFFF) is computed with the scaling

method as follows,

NCRUFFFNFPA = NCRUFFFNFIRS  (FatalitiesNFPA/FatalitiesNFIRS) 

(NCFFNFIRS/KNCFFNFIRS)

where,
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NCRUFFFNFIRS is the total number of non-confined RUF fire fatalities reported to 

NFIRS

FatalitiesNFPA is the total number of residential fire fatalities estimated by NFPA

FatalitiesNFIRS is the total number of residential fire fatalities reported to NFIRS

NCFFNFIRS is the total number of non-confined home fire fatalities reported to 

NFIRS

KNCFFNFIRS is the total number of non-confined home fire fatalities, with known 

IFI, reported to NFIRS

This can be rearranged into

NCRUFFFNFPA = (NCRUFFFNFIRS + {[UNCFFNFIRS]  [NCRUFFFNFIRS/KNCFFNFIRS]}) 

 SRF

where,

UNCFFNFIRS is the total number of non-confined home fire fatalities, with 

unknown or missing IFI, reported to NFIRS (i.e., NCFFNFIRS  KNCFFNFIRS)

SRF is the national scaling ratio for residential fire fatalities (i.e., 

FatalitiesNFPA/FatalitiesNFIRS)

It can be seen that the number of fire fatalities with unknown or missing IFI information 

is allocated to RUF based on the proportion of non-confined RUF fire fatalities to the 

total number of non-confined home fire fatalities with known IFI information.
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Imputation Method

The method develop in this Technical Note relaxes the assumption that the proportion of 

all fire deaths that is associated with RUF as the IFI is the same for the incidents with 

unknown IFI (i.e., the occurrence of unknown IFI is a completely random process). A 

data imputation technique is used to directly estimate the number of deaths with unknown 

IFI that were likely to have involved upholstered furniture as item first ignited. Instead of 

scaling, it allocates the fire fatalities reported with unknown or missing IFI information 

based on the distribution of other, known factors found correlated with the reporting of 

upholstered furniture as the IFI. (Scaling is still used to inflate the NFIRS based statistics 

into national estimates.) The imputation method assumes the fire behavior exhibited 

across those fire incidents with known IFI and other particular fixed factor values is 

similar to that of the incidents with unknown IFI with the same fixed factor values—i.e., 

it assumes the occurrence of unknown IFI is a random process conditioned on the 

correlated factors (covariates).

NIST’s estimate of NCRUFFF is computed as follows,

NCRUFFFNIST = (NCRUFFFNFIRS + {∑ Pr(RUFi = 1|Xi i

) ∗ UNCFFNFIRS,i

})  SRF

where,

Pr(RUFi = 1| Xi) is the estimated probability that fire incident i, with unknown or 

missing IFI information, involved upholstered furniture given other, known 

factors, X.

The scaling and imputation method produce equal estimates when the distribution of 

other, known factors is the same between the sample of fire incidents with known IFI and 

those with unknown or missing IFI—i.e., when the occurrence of unknown IFI is a 

random process. 
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If, for instance, the other, known factors positively correlated with RUF fires occur less 

(more) frequently in the sample of incidents with unknown or missing IFI information, 

then the estimated number of RUF fire fatalities will be less (greater) than the scaling 

method. 

The two methods offer different advantages. The scaling method is straightforward and 

quicker to compute. The imputation method utilizes additional information on the 

reported fire incidents, making it more accurate if correlations exist between upholstered 

furniture involvement and other factors. In addition, the number of fires with known IFI 

indicating RUF and unknown IFI estimated as RUF could trend differently. 
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Appendix B: COVARIATES & Z-SCORES

Table B.1. List of included covariates and their average z-score resulting from the 1000 fits of the logit 

model predicting (1) the probability of upholstered furniture as Item First Ignited or (2) the probability of 

upholstered furniture as Item Contributing Most to Flame Spread.

COVARIATES ITEM FIRST IGNITED

ITEM CONTRIBUTING 

MOST TO FLAME 

SPREAD

INCLUDED Z-SCORE INCLUDED Z-SCORE

AREA OF FIRE ORIGIN

Assembly, sales areas (groups of people)

Common room, den, family room, living room, lounge X 16.820 X 13.649

Function area

Function area, other X 13.233 X 9.662

Bedroom - < 5 persons; included are jail or prison X 0.385 X 1.492

Bedroom - 5+ persons; including barrack/dormitory X 0.832

Cooking area, kitchen X -2.982 X -3.076

Laundry area, wash house (laundry) X -2.096

Storage areas

Closet X -0.912

Storage: supplies or tools; dead storage X 0.692

Vehicle storage area; garage, carport X 3.105 X -0.444

Service, Equipment Areas

Heating room or area, water heater area X -0.574

Structural Areas

Exterior balcony, unenclosed porch X 4.336 X -1.008

Ceiling & floor assembly, crawl space b/t stories X 0.497 X 0.354

Wall assembly X 0.153 X 0.473

Wall surface: exterior X -0.977

Other area of origin

Courtyard, patio, porch, terrace X 2.891 X -0.654

Item First Ignited

Item First Ignited, Other

Item First Ignited, Other X 2.363

Structural Component, Finish

Structural component or finish, other X -0.431

Floor covering or rug/carpet/mat X 0.613

Interior wall covering excluding drapes, etc. X 0.871

Structural member or framing X -0.974

Furniture, utensils, including built-in furniture

Furniture, utensils, other X 5.492

Non-upholstered chair, bench X 2.237

Cabinetry (including built-in) X 1.236

Appliance housing or casing X 1.338

Soft goods, wearing apparel

Soft goods, wearing apparel, other X 0.717

Mattress, pillow X -0.045

Bedding; blanket, sheet, comforter X 0.541

Wearing apparel not on a person X -0.297

Curtains, blinds, drapery, tapestry X 0.266

Storage supplies

Box, carton, bag, basket, barrel X 0.947
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Liquids, piping, filters

Flammable liquid/gas - uncontainedX 0.136

Organic materials

Cooking materials, including edible materialsX-0.841

General materials

Electrical wire, cable insulationX 2.561

General materials continued

Magazine, newspaper, writing paperX 2.736

Rubbish, trash, or wasteX 1.727

Multiple items first ignitedX 1.049

UndeterminedX 5.901

Type of Material First Ignited

Plastics

PlasticX 0.300X 0.319

Natural Product

Natural product, otherX 1.171X-0.351

Wood or paper - processed

Wood or paper, processed, otherX-0.937

Sawn wood, including all finished lumberX-3.005X-1.991

Fiberboard, particleboard, and hardboardX-0.447

Paper, including cellulose, waxed paperX 0.268

Fabric, textiles, fur

Fabric, textile, fur, otherX 15.518X 1.790

Fabric, fiber, cotton, blends, rayon, woolX 19.521X 4.141

UndeterminedX 7.309X-0.447

Item Contributing Most to Flame Spread

Structural Component, finish

Interior ceiling cover or finishX 0.391

Furniture, utensils, including built-in furniture

Upholstered sofa, chair, vehicle seatsX 15.987

Soft goods, wearing apparel

Mattress, pillowX-2.288

Bedding; blanket, sheet, comforterX-2.548

Cause of Ignition

Cause, otherX-0.528

IntentionalX-1.290

UnintentionalX-0.448

Failure of equipment or heat sourceX-0.956

Act of natureX-0.754

Cause under investigationX 0.076

Incident Type

Fires in structures other than in a buildingX-0.030X-0.076

Fire in mobile prop. used as a fixed struc., otherX 0.323X 0.184

Fire in mobile home used as fixed residenceX 0.782X 1.042

Fire in motor home, camper, recreational vehicleX 0.753X 0.948

Fire in portable building, fixed locationX 1.180

Fire Spread

Confined to object of originX-1.133X-0.700

Confined to room of originX-0.670X-0.292

Confined to floor of originX-0.080X 0.166

Confined to building of originX 0.027X-0.173

Beyond building of originX-0.040
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Factors Contributing to Ignition

Misuse of material or product

Heat source too close to combustibles.X-2.512X-0.120

Improper container or storageX-1.459

Playing with heat sourceX-0.720X-0.292

Mechanical failure, malfunction

Mechanical failure, malfunction, otherX-2.559X-0.661

Electrical failure, malfunction

Electrical failure, malfunction, otherX-2.613X 0.571

Unspecified short-circuit arcX-1.679X 1.633

Arc, spark from operating equipmentX-0.644X 0.092

Operational deficiency

Equipment unattendedX-1.804X-0.468

Equipment overloadedX-1.173X 0.582

Fire spread or control

Fire spread or control, otherX 0.281X-0.381