a statistical analysis of the dynamics of household...

A statistical analysis of the dynamics of householdhurricane-evacuation decisions

Md Tawfiq Sarwar1 • Panagiotis Ch. Anastasopoulos2 •

Satish V. Ukkusuri3 • Pamela Murray-Tuite4 •

Fred L. Mannering5

� Springer Science+Business Media New York 2016

Abstract With the increasing number of hurricanes in the last decade, efficient and timely

evacuation remains a significant concern. Households’ decisions to evacuate/stay and

selection of departure time are complex phenomena. This study identifies the different

factors that influence the decision making process, and if a household decides to evacuate,

what affects the timing of the execution of that decision. While developing a random

parameters binary logit model of the evacuate/stay decision, several factors, such as, socio-

economic characteristics, actions by authority, and geographic location, have been

& Md Tawfiq [email protected]

Panagiotis Ch. [email protected]

Satish V. [email protected]

Pamela [email protected]

Fred L. [email protected]

1 Department of Civil, Structural and Environmental Engineering, Engineering Statistics andEconometrics Application Research Laboratory, University at Buffalo, The State University ofNew York, 204 Ketter Hall, Buffalo, NY 14260, USA

2 Department of Civil, Structural and Environmental Engineering, Institute for SustainableTransportation and Logistics, Engineering Statistics and Econometrics Application ResearchLaboratory, University at Buffalo, The State University of New York, 241 Ketter Hall, Buffalo,NY 14260, USA

3 Lyles School of Civil Engineering, Purdue University, West Lafayette, IN 47907-2051, USA

4 Department of Civil and Environmental Engineering, Virginia Tech, 7054 Haycock Road,Falls Church, VA 22043, USA

5 Department of Civil and Environmental Engineering, University of South Florida, 4202 E FowlerAvenue, ENC 3300, Tampa, FL 33620, USA

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TransportationDOI 10.1007/s11116-016-9722-6

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considered along with the dynamic nature of the hurricane itself. In addition, taking the

landfall as a base, how the evacuation timing varies, considering both the time-of-day and

hours before landfall, has been analyzed rigorously. Influential factors in the joint model

include the relative time until the hurricane’s landfall, height of the coastal flooding, and

approaching speed of the hurricane; household’s geographic location (state); having more

than one child in the household, vehicle ownership, and level of education; and type of

evacuation notice received (voluntary or mandatory). Two time intervals from 30 to 42 h

and 42 to 66 h before landfall resulted in random parameters, reflecting mixed effects on

the likelihood to evacuate/stay. Possible sources of the unobserved heterogeneity captured

by the random parameters include the respondents’ risk perception or other unobserved

physiological and psychological factors associated with how respondents comprehend a

hurricane threat. Thus, the model serves the purpose of estimating evacuation decision and

timing simultaneously using the data of Hurricane Ivan.

Keywords Emergency management � Dynamics of hurricane evacuation � Joint modeling

of evacuation decision and timing � Unbalanced panel data � Random parameters � Binarylogit model

Introduction

Hurricanes are among the most dangerous as well as costly natural disasters in the United

States. In the 2005 season, there were 14 hurricanes, three of which were among the most

powerful and costly in the 154 years of record keeping in the Atlantic Basin (Wolshon

2006). For instance, the 2005 Atlantic hurricane season in the United States had an esti-

mated direct social cost of approximately 1700 deaths and damages of over $100 billion

(Beven et al. 2008). Hurricane Ivan was the third most costly disaster in the US, with

nearly $14.2 billion in damage and 92 deaths (Franklin et al. 2006). Hurricane evacuations

are becoming increasingly problematic due to the steady population growth along the

Atlantic and Gulf coasts as well as the inability of the transportation infrastructure to keep

pace with demand. As a result, congestion is usually a characteristic of evacuation and

could cause 10–20 h delays if the total evacuation is not managed properly (Lindell et al.

2005). Moreover, if the evacuation routes run parallel to surge prone bays and rivers, storm

surge and inland flooding could cause massive loss of life among the people trapped in

congestion. For example, during Hurricane Ivan, a portion of the Interstate 10 bridge

system over Pensacola Bay was severely damaged; about a quarter-mile of the bridge

collapsed into the bay. US Highway 90 was also heavily damaged (Franklin et al. 2006).

Better management of hurricane evacuations requires thorough understanding of

households’ reliance on information sources, the factors affecting their decision to evac-

uate, their departure timing, their preparation time, and their choice of routes. This paper

focuses on the second and third issues. The evacuate/stay decision is a complex dynamic

process which depends on various inter-related factors, such as the characteristics of the

hurricane, the hurricane’s trajectory, hurricane warning system and information propaga-

tion, the characteristics of the evacuees and their households (Baker 1991; Gladwin et al.

2001; Petrolia and Bhattacharjee 2010; Lindell et al. 2011), household risk perception, and

decisions of influential people (such as family or friends). Sorensen (2000) summarizes the

literature’s support for a lengthy list of factors and characteristics influencing the decision

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to evacuate/stay. Recently, Ozguven et al. (2015) reviewed the aging population-focused

emergency literature utilizing a knowledge base development methodology—supported

with a geographic information system-based case study—to indicate the paramount

importance of special attention for aging populations.

Review of previous work

The evacuate/stay and departure timing decisions can be treated in two steps or one in

order to determine time dependent demand (Wilmot and Mei 2004; Pel et al. 2012). The

two step approach is more frequently used, with estimates of the number of evacuating

households produced by a variety of techniques including neural networks, participation

rates, and logistic regression (Murray-Tuite and Wolshon 2013). Wilmot and Mei (2004)

compared these techniques and found participation rates to be the least accurate and no

clear preference among the other two approaches. In the second step, evacuees are dis-

tributed over time, often based on cumulative departure S-curves (Murray-Tuite and

Wolshon 2013).

Among the few joint (one step) models to estimate evacuate/stay and departure time

choices, Fu and Wilmot (2004) developed a sequential logit model to estimate the prob-

ability of a household evacuating considering a few dynamic characteristics of the hurri-

cane. However, this model has two restrictive assumptions. First, the choice made by a

household in time period t is independent of choices in other time periods. However, this

evacuation decision making process is complex where one would expect the unobserved

factors that affect the choice in one time period would persist in the next one, resulting in

the error terms not being independent over time periods. The second assumption is that

households display the same taste or value in evaluating the attributes of alternative

choices. This assumption ignores the heterogeneity that exists among households.

Recently, Gudishala and Wilmot (2012) developed a nested logit model in which they

relaxed their previous assumptions. This model assumes that the household will take into

account the conditions existing in time period t1 as well as the anticipated conditions in the

next periods t2 and t3, which may not be suitable for longer durations. Nested logit models

are typically used to overcome the independence of irrelevant alternatives (IIA) limitation

in multinomial logit models. Nests do not typically incorporate the utility of future choices

in the current one. Gudishala and Wilmot (2012) noted that the nested approach was

computationally expensive even with only a few intervals.

To extend Fu and Wilmot’s (2004) work and overcome these limitations, two alter-

native approaches to Gudishala and Wilmot’s (2012) method can be taken. As the data

structure is panel type, a random effects model could be used, which allows for an indi-

vidual specific disturbance term (in addition to an overall disturbance term) to account for

random disturbances specific to each individual (Washington et al. 2011). For example, for

each time interval, the variables related to the hurricane change while the socio-demo-

graphic ones (i.e., income, age, number of children, etc.) do not vary. As the model would

be estimated on the basis of observations from all time intervals collectively, repeated

observations of the same household are in the estimation data and this causes the potential

for correlation among the error terms. Also, the assumption of having greater impact of the

hurricane characteristics than the other parameters is not fully justified because the total

decision is a complex procedure and different people may give emphasis to different

attributes. An alternative approach, and the one selected in this paper, is to consider a

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random parameters model to account for the influences of unobserved heterogeneity among

individuals. When a parameter varies significantly across observations, model estimation

becomes considerably more complex because a unique parameter for each observation is

estimated for the variable in question.

A random parameter approach was previously used by Hasan et al. (2011) in their esti-

mation of a mixed logit model to understand households’ decision to evacuate or stay based

on several socio-demographic characteristics. Although it provides important insights, it has

some shortcomings. One of which is that all the variables in the model are static in nature and

do not change within the short period of evacuation (age, income, gender, etc.). But, the

hurricane itself is dynamic. During the hurricane, the National Hurricane Center (NHC)

provides frequent advisories analyzing the hurricane, its movement, wind speed, rainfall,

coastal flooding, category, etc. The local and national radio and television channels also

provide details about the present condition of the hazard. When the situation becomes worse,

people may decide to evacuate if they have not evacuated already. Also, different people

perceive the risk differently. They may give higher importance to some information sources

than to others. All these factors, especially the dynamic nature of the hurricane, should have

considerable influence on the decision of the household. In another paper, Hasan et al. (2013)

developed a hazard-based duration model to critically analyze the timing behavior of the

evacuees with the same static dataset.

Moreover, a number of simulation studies on large-scale evacuation events have also been

conducted, shedding some light in the evacuation decision-making mechanisms. For

example, Koot et al. (2012) developed a latent class multinomial logit model to predict

evacuation behavior based on a stated preference experiment. Dobler et al. (2012) andDobler

(2013) conducted simulation studies on large scale evacuation events, including detailed

analyses of human behavior in such events. And Widener and Horner (2013) examined how

various types of social networks influenced participation in evacuation, using geographic data

within an agent based model of hurricane evacuation in Bay County, Florida.

The contribution of the current paper is that the evacuation decision and timing behavior

of households are modeled jointly in a dynamic context considering unobserved hetero-

geneity (both time and individual/household) using unbalanced panel data from Hurricane

Ivan. A binary logit model is developed to estimate the probability of a household evac-

uating in a certain discrete time interval of 3, 6, 12, 18, or 24 h based on the dynamic

characteristics of the hurricane and statistical significance. The analysis period is from the

first public advisory to the hurricane’s landfall. Using the panel data binary logit approach

with random parameters, the dynamics of the event are captured appropriately. Thus, this

model can be used to determine dynamic demand for use in traffic simulation models. This

model also provides insights into the influential socioeconomic factors, effect of evacua-

tion notices, and effect of locations in evacuation decisions.

The remainder of this paper is divided into four sections. First, the modeling methodology

is outlined, followed by a discussion of the Hurricane Ivan survey data. Then the results are

presented and discussed. Finally, the paper is summarized and conclusions are presented.

Methodology

The household decision to evacuate or stay in specific departure-time intervals is a discrete

binary choice (evacuate or stay), with hurricane characteristics changing from one

departure-time interval to the next. When the intent is to model binary choices as a function

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of explanatory variables, binary logit and probit models are obvious possibilities. The

binary logit model has been widely used in transportation research (Hamed and Mannering

1993; Young and Liesman 2007). One of the assumptions typically made in the derivation

and application of a binary logit model is that the parameters of variables are fixed across

all the observations. However, this fixed-parameter assumption may be incorrect in hur-

ricane-evacuation modeling, especially in the presence of unobserved heterogeneity. To

account for the unobserved heterogeneity, a random parameters model, such as the binary

random parameters (mixed) logit model, can be specified. Following Train (2003) and

others, a function that determines the probability that household n will evacuate in time

interval t is defined as,

EVACint ¼ bitXint þ eint ð1Þ

where, EVACint is a function determining evacuation likelihoods, i is the alternative

(evacuate or not evacuate); Xint is a vector of explanatory variables (household charac-

teristics, storm characteristics, etc.); bit is a vector of estimable parameters; and eint is theerror term. If the error terms are assumed to be generalized extreme value distributed,

McFadden (1981) has shown that the binary logit model is,

Pnt Eð Þ ¼ EXP bEtXEnt½ �EXP bEtXEnt½ � þ EXP bNEtXNEnt½ � ð2Þ

where, Pnt(E) is the probability household n will evacuate in time interval t; XEnt and XNEnt

are vectors of explanatory variables that impact the decision to evacuate (E) or not

evacuate (NE) in time interval t, respectively; (household characteristics, storm charac-

teristics, etc.); bEt and bNEit are corresponding vectors of estimable parameters. Without

loss of generality, bNEtXNEt can be set to zero (Washington et al. 2011). With this,

parameter variations across households (variations in bEnt across households, with sub-

script n added), can be accounted for with a mixing distribution giving Eq. 3 (Train 2003),

Pnt Eð Þ ¼Z

1

1þ EXP �bEntXEnt½ � f bEntjuð ÞdbEnt ð3Þ

where, f(bEnt|u) is the density function of bEnt with u referring to a vector of parameters of

the density function (mean and variance), and all other terms are as previously defined. For

this random parameters (or mixed) logit model (Eq. 3), bEnt can now account for house-

hold-specific variations of the effect of XEnt on evacuation probabilities in time t, with the

density function f(bEnt|u) used to determine bEnt.

Because maximum likelihood estimation of mixed logit models is computationally

cumbersome, a simulation-based maximum likelihood method is used (see Washington

et al. 2011). The most popular simulation approach uses Halton draws (Greene 2007). The

estimation process for mixed logit models is well documented in many sources (Train

1999; Bhat 2003; Anastasopoulos and Mannering 2011, 2015; Anastasopoulos et al.

2009, 2011). Herein, we estimate Eq. 3 by specifying a functional form of the parameter

density function f(bEnt|u) and using simulation-based maximum likelihood with 200

Halton draws—this number of draws has been empirically shown to produce accurate

parameter estimates (Anastasopoulos and Mannering 2009; Russo et al. 2014). As with

previous studies (Anastasopoulos et al. 2012a 2012b, 2012c, 2012d), for the functional

form of the parameter density functions, consideration will be given to normal, Weibull,

lognormal, triangular and uniform distributions, and those that provide the best statistical

fit will be used. With the functional forms of the parameter density functions specified,

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values of bEnt are drawn from f(bEnt|u), logit probabilities are computed, and the likelihood

function is maximized.

Data

To study household-level evacuation decisions, data are used from a household survey

conducted after Hurricane Ivan made landfall in the region of Gulf Shores, Alabama, in

September 2004 (Morrow and Gladwin 2005). Hurricane Ivan, the third and most dangerous

storm to hit Gulf Shores in 2004, was a long-lived storm that reached Category 5 strength

three different times before its first landfall as a Category 3 storm in Alabama at 2 a.m. CDT

on September 16th (Stewart 2005). Hurricane warnings and evacuation orders for Hurricane

Ivan varied from region to region. For example, a mandatory evacuation was ordered on

September 10th in the Florida Keys. According to the advisories on the NHC website at 11

p.m. EDT (10 p.m. CDT) a watch was issued for the coast between Louisiana and the Florida

panhandle (public advisory 47), and then the area was placed in HurricaneWarning at 4 p.m.

CDT on September 14th (public advisory 50), making land fall at 2 a.m. on September 16th.

Ivan was the most destructive hurricane to impact this region in more than 100 years. The

Alabama coastline was included in the warning area on September 14th. A mandatory

evacuation was ordered for Gulf Shores, Orange Beach, and Fort Morgan of Alabama. A

mandatory evacuation was also ordered for the 78 miles of coastline ofMississippi. The New

Orleans area of Louisiana was included in the warning on September 14th and 1.4 million

residents were urged to leave. It is estimated that about 600,000 citizens of NewOrleans tried

to evacuate during Ivan (Morrow and Gladwin 2005).

The data used in this study were collected from two sources. First, data were collected

in a post storm assessment of the impact of Hurricane Ivan on households in four states:

Louisiana, Alabama, Florida, and Mississippi (Morrow and Gladwin 2005). Several

counties and parishes adjacent to the path of Hurricane Ivan in the four states were

included in the original data collection. Complete data were available for 3031 households

from these regions. The data included household socio-demographic information, gender,

age, race, income, education, number of household members, number of children, number

of elders, pet ownership, number of vehicles available, housing type and location, house

ownership status, past hurricane experience, reasons for evacuating or not evacuating,

whether a hurricane evacuation notice was received, type of notice received (mandatory or

voluntary), media through which the evacuation notice was received (television/radio,

friends, relatives, etc.), time of evacuation if evacuation occurred, destination, and normal

travel time to reach the destination, among others.

The second type of data gathered, were related to hurricane characteristics (such as wind

speed, rainfall, coastal flooding) and were collected from the website of the National

Hurricane Center in 3-h intervals, from September 12, 2004, to hurricane landfall on

September 16, 2004. The 3-h time interval was chosen as a reasonable trade-off between

relatively constant hurricane conditions and a time interval large enough to ensure that a

sufficient number of household evacuation decisions were observed. For the available data,

information on the advisories published during the hurricane were archived on the website,

and these data are also used. A total of forty 3-h time intervals (from 2 a.m., September 12

to 11 p.m., September 16, 2004) were combined with the 3031 household-data records

collected from the survey. In these data, a non-evacuating household would generate 40

observations (one evacuate/stay decision in each of the forty 3-h time intervals). If a

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household decided to evacuate in a time interval before the last 3-h interval, then there

would be no responses for the later intervals. Thus, the dataset becomes an unbalanced

panel based on the dynamic characteristics of hurricane and the actual decisions of the

households, which can be readily handled in the model-estimation process. Note that, for

model estimation, only the statistically significant time indicator variables were used (i.e.,

3, 6, 12, and 24 h intervals). Table 1 presents all the available dynamic characteristics of

Hurricane Ivan, Table 2 presents summary statistics of key variables (those used in the

presented models), and Fig. 1 presents some of the socio-economic characteristics of the

affected region.

In Fig. 2, the trajectory of Hurricane Ivan is presented (from formation to its end). In

Fig. 3, the analysis period is isolated. This is the period of interest in this paper, as the

advisories were published to the public for evacuation consideration. In both Figures, the

category (strength) of the hurricane at particular time period is shown with symbols H1 to

H5. For example, H4 reflects a 4-strength hurricane category for Ivan.

Model estimation results

The estimation results of the random parameters (mixed) binary logit model for the

evacuation decision and timing and the corresponding marginal effects (averaged across

the observations) are presented in Table 3. Note that a parameter is generally considered to

be random when both the mean and the standard deviation of the parameter density

function are statistically significant (even though, the mean does not necessarily have to be

statistically significant). For the random parameters, several distributions were tested (i.e.,

Weibull, triangular, uniform, log-normal, etc.) and normal distributions were found to

provide the best statistical fit, which is common for mixed logit models. The model was

estimated using 200 Halton draws because this number of Halton draws produces

stable estimates of the parameters (Bhat 2003). It should be noted that a likelihood ratio

test showed that the random parameters approach provided a superior statistical fit relative

to a simple fixed-parameter model (the hypothesis that the two models are equivalent was

rejected with over 99.99 % confidence, and the test results are presented in Table 4). A

discussion of the results in Table 3 is presented by variable type below.

Timing behavior

A number of time-indicator variables are used to capture the dynamic effect that the time

until the hurricane’s landfall has on household evacuation decisions. Using the information

starting from the first advisory broadcasted at 2 a.m., September 12, 2004, to the last one

broadcasted at 11 a.m., September 16, 2004, the evacuation timing behavior is explored in

two ways. First, with the landfall as a reference point, it is sought to understand how a

household’s decision varies from just before landfall to several hours or days before

landfall. Second, the effect of time-of-day (morning, afternoon, night, and late night) is

observed in the evacuation timing behavior. The total time period is divided into non

uniform intervals, such as 6, 12, 18, 24 h, and so on (note that several time intervals and

time interval combinations were tested, and those that were statistically significant are

presented in this paper). This allows capturing dynamic hurricane intensity and evacuation-

decision timing effects.

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Table

1Dynam

icsofHurricaneIvan

inrelationship

withevacuated

households

Date

Tim

eTim

ing

Hurricane

movem

entspeed

(mph)

Wind

speed

(mph)

Category

Min.central

pressure

(inches)

Averagecoastal

flooding(ft)

Average

rainfall

(inches)

Number

of

evacuated

households

Cumulative

evacuation

12-Sep-04

2:00

18

165

526.87

22

10

33

5:00

29

155

427.11

22

10

36

8:00

39

155

427.14

22

10

11

17

11:00

49

155

427.14

22

10

623

14:00

510

150

427.2

22

10

730

17:00

610

150

427.05

22

10

434

20:00

710

150

427.02

22

10

135

23:00

89

160

527.08

22

10

540

13-Sep-04

2:00

99

160

527.17

22

10

242

5:00

10

9160

527.17

22

10

951

8:00

11

9160

527.14

22

10

19

70

11:00

12

8160

527.02

22

10

979

14:00

13

8160

526.99

22

10

584

17:00

14

9160

526.93

22

10

892

20:00

15

9160

526.99

22

10

496

23:00

16

9160

526.99

22

10

6102

14-Sep-04

2:00

17

9160

527.23

22

10

11

113

5:00

18

9160

527.29

17

10

28

141

8:00

19

9155

427.31

17

10

84

225

11:00

20

8140

427.52

17

11

69

294

14:00

21

9140

427.49

17

11

64

358

17:00

22

9140

427.43

13

12

51

409

20:00

23

10

140

427.43

13

12

24

433

23:00

24

12

140

427.52

13

12

47

480

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Table

1continued

Date

Tim

eTim

ing

Hurricane

movem

entspeed

(mph)

Wind

speed

(mph)

Category

Min.central

pressure

(inches)

Averagecoastal

flooding(ft)

Average

rainfall

(inches)

Number

of

evacuated

households

Cumulative

evacuation

15-Sep-04

2:00

25

12

140

427.58

13

12

47

527

5:00

26

12

140

427.7

13

12

84

611

8:00

27

12

140

427.73

13

12

159

770

11:00

28

13

135

427.73

13

12

80

850

14:00

29

14

135

427.73

13

12

139

989

17:00

30

14

135

427.55

13

12

107

1096

20:00

31

13

135

427.49

13

12

19

1115

23:00

32

12

135

427.55

13

12

98

1213

16-Sep-04

2:00*

33

12.5

132.5

427.75

13

12

01213

5:00

34

14

115

327.96

13

12

11214

8:00

35

14

80

128.5

13

12

01214

11:00

36

14

75

128.64

13

12

01214

14:00

37

14

70

028.79

10

12

01214

17:00

38

14

60

028.94

10

12

01214

20:00

39

14

40

0-999

10

11

01214

23:00

40

14

35

029.12

10

10

01214

*Landfalloccurs

at2:00a.m.September

16,2004

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Note that inclusion of all parameters in the model, including the time interval indicators,

was based on their statistical significance, and on the overall improvement of the model’s

fit. With several variable interactions and transformations tested, the model estimation

results in Table 3 include the parameters that were statistically significant at 95 percent

level of confidence. With respect to the time interval indicators, all intervals before the

landfall of the hurricane (the first thirty-two 3-h time intervals among the available forty,

with the last eight occurring after landfall of the hurricane) were tested in the model.

(Because the study focuses on evaluating evacuation decision and timing before the

landfall of the hurricane, the base time intervals were identified as those measured after the

landfall—even though evacuation may still have occurred after landfall, due to shortage of

supplies, medical emergencies, and so on.)

Among the first thirty-two 3-h time intervals (commencing at 96 h before the landfall),

the time intervals between 96 and 66 h to landfall (in all possible combinations, such as, 3,

Table 2 Descriptive statistics of key variables

Variable description Mean SD Minimum Maximum

Timing behavior

Time indicator (1 if time interval was from 6 h before landfallto the occurrence of landfall, 0 otherwise)

0.039 – 0 1

Time indicator (1 if time interval was from 18 h before landfallto 6 h before landfall, 0 otherwise)

0.160 – 0 1


0.020 – 0 1


0.088 – 0 1


0.030 – 0 1

Hurricane specific dynamic characteristics

Predicted height of coastal flooding (for each time period –observation) above normal tide level (ft)

16.925 4.639 10 22

Actual hurricane movement (approaching) speed (mph) 10.788 2.205 8 14

Evacuation notice indicators

Notice indicator (1 if respondent has received mandatoryevacuation notice, 0 otherwise)

0.235 – 0 1

Notice indicator (1 if respondent has received voluntaryevacuation notice, 0 otherwise)

0.183 – 0 1

Location indicator (risk level)

Louisiana indicator (1 if household from Louisiana, 0otherwise)

0.279 – 0 1

Socio-economic characteristics

Vehicle ownership indicator (1 if respondent has 1 or morevehicles, 0 otherwise)

0.412 – 0 1

Education indicator (1 if respondent has a post graduatedegree, 0 otherwise)

0.153 – 0 1

Children indicator (1 if respondent has more than one child, 0otherwise)

0.328 – 0 1

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6, 9, 12 or 24 h intervals) were found to be statistically insignificant. On the contrary, most

of the time intervals within 66 h before the landfall (i.e., between 66 h before landfall, and

time of landfall) are statistically significant. Interestingly, some of the adjacent time

female50%

male

50%

Gender

50 - 6538%

> 6521%

NA4%

<201%

20 - 295%

30 - 3911%

40 - 4920%

Age

some high school 6%

high school graduate

24%

some college26%

college graduate

25%

post graduate15%

NA4%

Educationless than $15,000

8%

$15,000 to $24,999

9%$25,000 to

$39,99915%

$40,000 to $79,999

26%

over $80,00020%

NA22%

Income level

115%

242%

317%

415%

57%

>53%

NA1%

Number of household members

053%

113%

211%

35%

>32% NA

16%

Number of children (<17 years)

01%

112%

223%

37%>3

2%

NA55%

Number of vehicles available

Evacuated45%

Not Evacuated

55%

Evacuation decision

Fig. 1 Key socio-economic characteristics of the affected households

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intervals were found to have almost identical coefficients and standard errors; thus, such

intervals were combined. To support the combination of these intervals, likelihood ratio

tests (Washington et al. 2011) were conducted, and in all cases the time interval combi-

nations were verified with a greater than 99.99 percent level of confidence. As such,

heterogeneous time intervals (i.e., 6, 12, or even 24 h intervals) were found to provide the

best model fit.

In summary, there were initially thirty-two 3-h time intervals. Based on the statistical

significance of the time interval indicators, and the resulting likelihood ratio tests with

Fig. 2 Trajectory of hurricane Ivan. Source: National Oceanic and Atmospheric Administration (NOAA)with H1 to H5 indicates category of hurricane

Fig. 3 Trajectory with time for the analysis period of hurricane Ivan. Source: National Oceanic andAtmospheric Administration (NOAA) with H1 to H5 indicates category of hurricane

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respect to the combined time interval indicators, Table 3 shows that five time interval

indicator variables are statistically significant. The first and second time intervals are from

the hurricane’s landfall to 6 h before landfall (i.e., from 8 p.m. to 2 a.m.), and from 6 to

18 h before landfall, respectively, which both result in a higher evacuation likelihood

(0.166 and 0.133, respectively, as indicated by the marginal effects in Table 3). The third

time interval is from 24 to 30 h before landfall, which results in a lower evacuation

Table 3 Random parameters binary logit model estimation results

Variable description Coefficient t-statistics Marginaleffects

Constant (defined for the outcome of not evacuating) 8.384 10.68

Timing behavior

Time indicator (1 if time interval was from 6 h before landfall tothe occurrence of landfall, 0 otherwise)

1.521 11.11 0.166

Time indicator (1 if time interval was from 18 h before landfall to6 h before landfall, 0 otherwise)

0.956 9.60 0.133


-0.634 -4.21 -0.125


-0.071 -0.25 -0.012

Standard deviation of parameter density function 2.591 10.80


-1.608 -2.34 -0.359

Standard deviation of parameter density function 2.633 5.24


Predicted height of coastal flooding (for each time period –observation) above normal tide level (ft)

-0.272 -12.97 -0.010

Actual hurricane movement (approaching) speed (mph) 0.278 6.26 0.040


Notice indicator (1 if respondent has received mandatoryevacuation notice, 0 otherwise)

0.307 3.65 0.049

Notice indicator (1 if respondent has received voluntaryevacuation notice, 0 otherwise)

0.181 2.11 0.030


Louisiana indicator (1 if household from Louisiana, 0 otherwise) 0.291 3.93 0.047


Vehicle ownership indicator (1 if respondent has 1 or morevehicles, 0 otherwise)

5.997 28.43 0.757

Education indicator (1 if respondent has a post graduate degree, 0otherwise)

0.249 2.69 0.040

Children indicator (1 if respondent has more than one child, 0otherwise)

0.173 1.93 0.029

Log-likelihood at convergence -4110.883

Restricted (fixed parameter) log-likelihood -4143.450

Number of respondents 3031

Number of observations 102,065

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likelihood (the marginal effect is -0.125). The fourth and fifth time intervals are from 30

to 42 h and 42 to 66 h before landfall, respectively, which result in a mixed evacuation

likelihood (the marginal effects are -0.012 and -0.359, respectively). Both variables

resulted in statistically significant and normally distributed random parameters, with about

48.9 and 27.1 percent of the observations having an increase in the evacuation likelihood,

respectively, and about 51.1 and 72.9 percent of the observations having a decrease. Note

that the mean b of the fourth time interval (from 30 to 42 h before landfall) is statistically

insignificant (implying a zero mean); whereas the corresponding standard deviation of the

parameter density function is significant. A likelihood ratio test indicated at 0.90 level of

confidence that the model with the variable used as a random parameter is statistically

superior to the equivalent model with the variable used as a fixed parameter. This indicates

that the random parameter would likely yield about half positive and half negative bs,

which was the case as noted above.

Considering that the hurricane was intense (the category ranged from H4 to H5)

throughout the 66-h period until landfall, the timing indicator variables intuitively indicate

that as the hurricane approached, the likelihood to evacuate increased. In fact, with the

hurricane being about two to three days (42 to 66 h) away from landfall, the model shows

that the likelihood to evacuate decreased for the majority of the respondents, possibly

capturing risk averse respondents, who likely expected a change in the direction or

intensity of the hurricane. However, as discussed above, for some respondents—possibly

those accepting lower risks and whose decision to evacuate/stay was significantly affected

by the hurricane’s intensity or the time-of-day (showing a preference for daylight evacu-

ation; see Fu and Wilmot (2004))—the likelihood to evacuate increased. And as the

hurricane approached, the likelihood to evacuate increased (as indicated by the two time

interval indicators, from 6 h before landfall to the occurrence of landfall, and from 18 h

before landfall to 6 h before landfall). This is also consistent with Fu and Wilmot (2004).

Note that from the actual number of evacuees, the rate of evacuation was the highest

from landfall to 24 h before. Even up to 48 h before landfall, a significant number of

households evacuated. But before that (i.e., before 66 h from landfall), no warnings were

issued to the four affected regions, and the number of evacuating households was small.

Those time intervals are statistically insignificant and have been considered as the base for

the other five time intervals. These results are in line with Nelson et al. (1989).

It should also be noted that the time to landfall was also tested for linear, non-linear, and

combined (i.e., combination of linear and non-linear transformations with time interval

indicators) effects on the decision to evacuate/stay. However, these variable expressions

did not result in statistically significant parameters, and the time interval indicators were

used instead.

Table 4 Likelihood ratio test between the random and fixed parameters binary logit models

Likelihood-ratio test Random versus fixed parameters

LRT ¼ �2 LL bRð Þ � LL bUð Þ½ � 65.13

Degrees of freedom 2

Critical v20:0001;2 (0.9999 level of confidence) 18.42

Number of observations 102,065

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Among the different hurricane characteristics, the predicted height of the coastal flooding

(measured for each time period—observation—in feet) and the actual wind speed of the

approaching hurricane (also measured for each time period—observation—in mph) were

statistically significant. Note that several variable transformations (linear, non-linear,

indicator variables, and their combinations), and combinations of time and predicted height

of coastal flooding were explored. However, none of these variable expressions produced

statistically significant results, with the exception of the predicted height of coastal

flooding used as a continuous variable, which is included in the model. Interestingly,

Table 3 shows that one foot increase in the height of the coastal flooding, results in a 0.010

decrease in the evacuation likelihood. This implies that as the height of the coastal flooding

increased, respondents were less likely to evacuate. This result is counterintuitive and is

likely an artifact of the data; or, it may be possibly picking up the effect of the hurricane

intensity dropping from a category 5 to a category 3 as the storm approached the coastline.

Note that hurricane intensity variables were also elaborately explored, but did not result in

statistically significant parameters (the hurricane’s intensity is likely captured by the effect

of the other variables included in the model). Regardless of any possible interpretations,

this finding warrants further investigation, through the use of additional data from hurri-

cane Ivan or other hurricanes.

On the other hand, as indicated by the marginal effects presented in Table 3, a one mile

per hour increase in the approaching wind speed resulted in a 0.040 increase in evacuation

likelihood. This variable likely reflects the perception of the hurricane’s intensity by the

respondents, with higher approaching wind speeds increasing the likelihood for a

respondent to evacuate.


All four regions were tested as indicator variables, and only the variable representing

Louisiana was statistically significant. Given the marginal effects in Table 2, when com-

pared to Florida, Mississippi and Alabama (the other three regions), respondents whose

household was in Louisiana were 0.047 more likely to evacuate, compared to respondents

whose household was in Florida, Mississippi, or Alabama. This is likely picking up

Louisiana households’ sensitivity regarding hurricane evacuation, due to the intense

2000–2003 hurricane seasons preceding Hurricane Ivan.


The model results show that a number of socio-economic characteristics affect the decision

to evacuate/stay. For example, highly educated respondents (holding at least a post

graduate degree), parents (with two or more children), and respondents with one or more

vehicles in the household, are all more likely to evacuate (the resulting marginal effects are

0.757, 0.040, and 0.029, respectively). These variables are likely picking up low risk

tolerance or better risk assessment by the educated respondents and the parents, and

availability of a means to evacuate by the respondents with one or more vehicles in their

household. The results are consistent with a number of studies (Gladwin and Peacock

1997; Solis et al. 2010; Hasan et al. 2011).

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Finally, Table 2 shows that if a household received any type of evacuation notice—

mandatory or voluntary—from an authority, respondents were more likely to evacuate. As

indicated by the marginal effects, respondents who received a mandatory notice were

naturally more likely to evacuate by 0.049, as opposed to 0.030 for respondents who

received a voluntary evacuation notice, reflecting the more severe nature of the mandatory

over the voluntary notice. This is intuitive, and is in line with Whitehead et al. (2000) that

found that receiving mandatory or voluntary notices increases the probability to evacuate

compared to receiving no notice at all.

Note that, consideration of different locations with distinct population and socio-eco-

nomic characteristics, different extreme events, or hurricanes of different scales, is likely to

result in different model estimation results and predicted household evacuation probabil-

ities. However, the findings of this study are geared towards providing an insightful por-

trayal on how different households react or make decisions during an extreme event based

on varying socio-economic characteristics and on the nature of the event. For example,

having children, owning one or more vehicles, and being well educated (with the latter

two, also possibly capturing the effect of higher income households) are characteristics of

households that decide to evacuate. On the other hand, households with no children, no

vehicle, and non-higher education (with the latter two, in this case, possibly capturing the

effect of lower income households) are characteristics of households that decide to stay

(and not evacuate).

In terms of evacuation timing choice, households are found to select to evacuate as late

as possible (with respect to the hurricane’s time-to-landfall), but preferably in the day time

(morning or afternoon, as opposed to night time). Because the evacuation decision is a

stochastic process, which is heavily influenced by the physical characteristics of the hur-

ricane (time-to-landfall, possible change of direction, etc.), and by the sparse evacuation

facilities and resources in the post-evacuation period (e.g., shelter, food, and other

amenities), households are likely to stay and not evacuate until it seems an absolute

necessity in order for the household members to survive. And households select to evac-

uate during day time (morning or afternoon) for safety reasons, and immediately after

concluding their pre-evacuation activities.

This paper identifies the factors that can affect the decisions of households to evacuate

or stay during an extreme event, such as a hurricane. Unlike most of the previous work in

this field, this study accounts for both the socio-economic characteristics of the households,

and of the dynamic nature of the hurricane. Combination of such stationary and dynamic

elements, results in an unbalanced panel data configuration, which interestingly reveals

novel ways of exploring data structures that have the potential to address issues regarding

evacuation decision and timing behavior.

Summary and conclusion

In this paper, a unique model is developed to address two fundamental questions simul-

taneously related to hurricane evacuation: households’ decision to evacuate/stay and

selection of departure time. For capturing the heterogeneity of a household’s decision at

different time intervals and the heterogeneity present among different households, a ran-

dom parameters binary logit model of unbalanced panel is developed.

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Several factors are found to influence both the evacuation and timing decisions of a

household. These factors include the dynamic characteristics of the hurricane (relative time

until the hurricane’s landfall, height of the coastal flooding, and approaching speed of the

hurricane), household’s geographic location, socio-economic characteristics (having chil-

dren in the household, vehicle ownership, and level of education), and type of evacuation

notice received (voluntary or mandatory). Two time interval variables—time intervals

from 30 to 42 h and 42 to 66 h before landfall, respectively—resulted in random param-

eters, reflecting mixed effects on the likelihood to evacuate/stay. Possible sources of the

unobserved heterogeneity captured by the random parameters may include the respon-

dents’ risk perception or other unobserved physiological and psychological factors asso-

ciated with how respondents apprehend a hurricane threat. To further assess unobserved

heterogeneity, directions for future work can include exploration of a latent class modeling

scheme, possibly in combination with random parameters (see Ben-Akiva et al. 2002; Koot

et al. 2012; Behnood et al. 2014).

The findings provide a nuanced understanding of evacuation decision-making that can

potentially lead to better evacuation planning. Thus, this paper is anticipated to enable the

emergency officials and planners to plan for safe evacuation, by coordinating the existing

traffic conditions in the network, and progressively directing households (given their

characteristics, and their propensity to evacuate/stay) to evacuate in a timely fashion.

The findings in this paper, thus, reveal the factors that influence the decision to evac-

uate/stay, and how the evacuation timing behavior of the household varies. Using existing

and readily available (from census) socio-demographic information of the households in

the affected regions, the emergency officials can use updates from the National Hurricane

Center (NHC) regarding the hurricane’s trajectory and strength, prioritize and identify

high-risk regions, and broadcast voluntary or mandatory evacuation notices. More

specifically, for affected regions where the household vehicle ownership is limited,

emergency evacuation vehicles may need to be prepared and dispatched, and the evacu-

ation notices may need to be broadcasted at an early phase (considering the time required

for the emergency vehicles to arrive to the affected regions, and load the evacuees). At the

same time, based on the predicted (by the NHC) timing of the landfall of the hurricane, the

officials can plan a day time evacuation, which is the preferred option among the house-

holds, and broadcast evacuation notices accordingly. And for the regions where the

households decide to extend their evacuation to as late as possible, a contra-flow

arrangement can be considered for the major evacuation routes. Naturally, proper a priori

planning is required for a successful evacuation, especially considering the short time span

between the formation of the hurricane and the landfall.

To conclude, this paper seeks to offer important practical insights that can help improve

the evacuation process, in terms of the nature (mandatory versus voluntary) and timing

(number of hours until landfall) of the evacuation notices. In all, this paper should be

viewed as an incremental step towards identifying influential factors affecting the decision

making process to evacuate/stay, and towards improving the effectiveness and efficiency of

current and future evacuation plans.

Acknowledgments The research presented in this paper was supported by the National Science FoundationAwards SES 0826873 and CMMI 1520338; and CMMI 105544 for which the authors are grateful. However,the authors are solely responsible for the findings of the research work.

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Md Tawfiq Sarwar is a PhD candidate in the Department of Civil, Structural and EnvironmentalEnginnering at University at Buffalo, The State University of New York. He received his BS fromBangladesh University of Engineeering and Technology (BUET), Dhaka, Bangladesh, and MS from PurdueUniversity, West Lafayette, Indiana. His research interests are statistical and econometric modeling, trafficsafety, infrastructure asset management, disaster management, travel demand and behavior analysis.

Panagiotis Ch. Anastasopoulos is an Assistant Professor in the Department of Civil, Structural, andEnvironmental Engineering at the University at Buffalo, The State University of New York. He received hisBS from the Athens University of Economics and Business (Greece), and MS and PhD from PurdueUniversity. His expertise is in statistical/econometric modeling, methods and applications in engineeringproblems, transportation safety, reliability/sustainability of infrastructure systems, and engineeringeconomics.

Satish V. Unnusuri is a Professor in the Lyles School of Civil Engineering at Purdue University. Dr.Ukkusuri is recognized nationally and internationally in the area of transportation network modeling, ITS,big data and disaster management. He leads the Interdisciplinary Transportation Modeling and Analytics

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http://dx.doi.org/10.1080/01441647.2015.1082516

Lab at Purdue. His current areas of interest include: complex network modeling, coupled systems modeling,network resilience, big data analytics for transportation systems, dynamic traffic modeling, innovative signalcontrol algorithms, connected vehicles and sustainable freight logistics. Dr. Ukkusuri has published morethan 230 peer reviewed journal and conference papers. Dr. Ukkusuri has received many awards includingthe Fulbright Scholar Award and the ARTBA/CUTC New Faculty award. Dr. Ukkusuri is a member of theTransportation Network Modeling committee, Freight Planning and Logistics Committee and theEmergency Evacuation committee at Transportation Research Board (National Academies). Dr. Ukkusuriis an Area Editor for the journal, Networks and Spatial Economics, Academic Editor for PLOS One and anAssociate Editor for Transportmetrica Part B. He is on the Editorial Advisor Board of TransportationResearch Part-B and Transportation Research Part-C and was the Editor of overview papers for the journalof Transportation Research Part-C (Emerging Technologies) from January 2008–December 2011.

Pamela Murray-Tuite is an Associate Professor in the Department of Civil and Environmental Engineeringat Virginia Tech. She received her PhD in 2003 from the University of Texas at Austin. She specializes inanalyzing and modeling disasters and disruptions to the transportation system and related travel behavior.

Fred L. Mannering is currently a Professor of Civil and Environmental Engineering at the University ofSouth Florida with a courtesy appointment in the Department of Economics. Previously he was the CharlesPankow Professor of Civil Engineering at Purdue University, and a professor at The University ofWashington and the Pennsylvania State University. He received his BS from the University ofSaskatchewan, MS from Purdue University and PhD from the Massachusetts Institute of Technology. Dr.Mannering’s expertise is in the application of statistical and econometric methods to study a variety ofsubject areas including highway safety, transportation economics, automobile demand, and travel behavior.

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