A hierarchical mixed logit model of individuals' return decisions after Hurricane Katrina

Author’s Accepted Manuscript A Hierarchical Mixed Logit Model of Individuals' Return Decisions after Hurricane Katrina Da Hu, Wenbing Yu, Junxuan Zhao, Weibo Liu, Fenglei Han, Xin Yi www.elsevier.com/locate/ijdr

PII: DOI: Reference:

S2212-4209(18)31176-2 https://doi.org/10.1016/j.ijdrr.2018.12.015 IJDRR1053

To appear in: International Journal of Disaster Risk Reduction Received date: 14 October 2018 Revised date: 14 December 2018 Accepted date: 14 December 2018 Cite this article as: Da Hu, Wenbing Yu, Junxuan Zhao, Weibo Liu, Fenglei Han and Xin Yi, A Hierarchical Mixed Logit Model of Individuals' Return Decisions after Hurricane Katrina, International Journal of Disaster Risk Reduction, https://doi.org/10.1016/j.ijdrr.2018.12.015 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

A Hierarchical Mixed Logit Model of Individuals’ Return Decision after Hurricane Katrina Da Hub, Wenbing Yua,c,*, Junxuan Zhaob, Weibo Liuc, Fenglei Hana, Xin Yid a

School of Civil Engineering, Chongqing Jiaotong University, Chongqing, China Department of Civil, Environmental and Construction Engineering, Texas Tech University, Lubbock, TX, USA c State Key Laboratory of Frozen Soil Engineering, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou, China d School of architecture and surveying & mapping engineering, Jiangxi University of science and technology, Ganzhou, China b

*

Corresponding author Email address: [email protected]

Abstract This study examines how factors affected individual return decision after Hurricane Katrina struck New Orleans City in 2005. Survey data from a representative sample of pre-Katrina New Orleans residents collected in the Displaced New Orleans Residents Pilot Survey (DNORPS) was used. The individual return decision was separated into three categories, namely, return, relocate and possible. Mixed logit model revealed that increasing age decreases the possibility of relocation and increases the possibility of return. Model estimation results also found that marital status, housing damage, housing tenure, education background, race and employment status are important predictors of individual decision. It was also determined that random-parameter approach is plausible in the return decision model. Housing damage and age are random parameters which were estimated using one-sided triangular distribution. Heterogeneity in the random parameter means were tested as a function of sex. The results further demonstrate the potential of the model to address unobserved heterogeneity in the analysis of return decision. Keyword: Hurricane Katrina; Return decision; Random parameter; Mixed logit; Heterogeneity 1. Introduction Hurricane Katrina, which struck New Orleans in August 2005, lead to an enormous number of people displaced from the Gulf Coast. Katrina caused one of the largest relocations of people in US history, approximately 1.5 million people aged 16 years and older evacuated from their

homes [1,2]. Whether or not to return to New Orleans is an important decision that people confront when a disaster damages the built environment. Many factors could affect the decisionmaking process, employment status for example, which have been widely studied. A large body of literature has examined what factors affected the decision-making process in the wake of Katrina [2–6]. Black residents returned to New Orleans at a much slower pace than white residents [4]. It should be also noted that housing and jobs are critical for a resident’s return decision after the evacuation is over [5]. Age is an important parameter when it comes to the decision, suggesting that the older residents are more likely to return to the damage regions in the first year. Another important factor affecting the decision-making is the education background, which proposed that residents with higher level of education backgrounds were more inclined to return to the city [2,6]. Temporal compression accounts for the variation of the housing recovery, promoting the return of homeowners over renters and further homeownership diminished the likelihood of relocation [3,7]. Apparently, the degree of housing damage is an important factor for a household's decision-making, because higher levels of damage indicate higher cost and more challenges to rebuild [8]. The existing literatures have utilized a lot of analytical methods to analyze the relationship between the decision and related factors following disasters. In order to determine the trade-off among the variables in a decision to relocate, the basic set of independent variables were entered into a series of stepwise regression models [9]. Logistic regression has been widely used to examine factors that might explain individual’s or household’s decision to return to damage regions or relocate to other places [2,4,5,10–12]. A multi-level modeling approach was used to associate individual relocation decisions with block group-level predictors [13]. Nejat [14] introduced the least absolute shrinkage and selection operator (LASSO) analysis method, which performs both variable selection and regularization, to identify important factors after Hurricane Sandy. In addition, an inductive analysis of the decision as for whether to return or relocate by persons in a disaster was proposed to identify the dimensions of decision-making process [15]. A spatial lag model was used to accommodate spatial effects in the analysis, which connected vulnerability and disaster-related migration [8]. However, those existing studies assume that parameters are completely fixed, and do not consider unobserved heterogeneity across individuals by incorporating random-parameters. Such

a fixed-parameter approach could result in biased parameter estimations and incorrect inferences in the presence of unobserved heterogeneity [16,17]. In contrast to the fixed-parameter models, random-parameter approach estimates an individual-specific as well as an observation-specific random parameter vector on the explanatory variables [18,19]. These random-parameter models can allow each parameter of the model to vary across individual observations. Compared to the conventional fixed-parameter model which fits the datasets using one regression model, randomparameter approach fits different regression models for individual sites. The random parameters are estimated by an analyst-specified continuous distribution such as the normal, triangular and uniform distribution. A variety of distributions can be estimated to determine which provides best overall fit, therein individual parameters in the model have different distributions. Moreover, it should be noted that the mean and variance of random parameters in the model might be influenced by some factors [20–22]. The neglecting of this heterogeneity would lead to biased parameter estimates and marginal effects. In this paper, we develop a hierarchical mixed logit model that can account for unobserved heterogeneity, which incorporates random parameter and explores heterogeneity in the mean of a random parameter. Since this model is based on the multinomial logistic model, it has the ability to handle situations with several discrete outcomes [23]. Mixed logit model has been widely used in highway safety studies and has been demonstrated the applicability in the discrete choice situation [21,22,24–26]. Utility theory also known as utility maximization method was integrated into the model [16]. Furthermore, heterogeneity in the mean of the random parameter was captured by the observed variables. This study used the survey data from Displaced New Orleans Residents Pilot Survey (DNORPS) to examine return migration following Katrina. The objective of this research is to specifically examine the relationship between an individual’s return decision and race and socioeconomic factors using a hierarchical mixed logit model. We begin, in the following section, by describing empirical setting and data description. Methodology and result analysis are presented in subsequent sections. Finally, discussion and conclusion are elaborated. 2. Empirical setting Survey data from the DNORPS dataset was used to extract return decision as well as individual corresponding characteristic variables after Hurricane Katrina. The pilot study collected data in

September 2006, approximately one year after Katrina. The DNORPS had completed interviews with 147 households including 388 individuals in New Orleans. The sample was stratified based on flood depth, which is a critical factor in determining New Orleans residents’ experience. In this study, a total of 281 adults aged 18+ years residing in 147 households were used for return migration analysis. Of these 281 samples we analyzed, 54.53 % resulted in returning to New Orleans, 23.19 % resulted in relocating to other places and 22.28 % resulted in possibly returning to New Orleans in one year starting from the survey (the second year after Hurricane Katrina). A total of 9 explanatory variables were developed including education, race, employment status, housing tenure, sex, housing damage, marital status, and housing type. Table 1 provides weighted summary statistics of key variables in DNORPS dataset aged 18+ years. In addition, the dummy variables 0 and 1 are created for all the variables except age. As noted in table 1, over 60 % of the DNORPS sample is black, and the rest is white or other races. The average age of the sample is 44.16 and about one-third of the sample had a bachelor’s degree or more than a bachelor’s degree. Approximately 65 % of the sample was the owner of the house, with the remainder renters. At the time of Hurricane Katrina, male residents comprised 45 % of the sample. Over half of sample (55 %) was employed full time, with the remaining 45 % part-time employed, unemployed, retiree or students. More than two-thirds (67 %) of the sampled individuals’ houses destroyed or damaged so badly that people couldn’t live in it, with the remaining 33 % not damage or damaged but someone could still live in it. Before Katrina, 43 % of the sample was married and the other was single, divorced, separated or widowed. Table 1 Descriptive statistics of key variables in DNORPS dataset aged 18+ years Variable · Individual Age Education dummy (1 if individual has bachelor’s degree or more than bachelor’s degree; 0 otherwise) Race dummy (1 if black; 0 otherwise) Employment status dummy (1 if employed full time; 0 otherwise) Sex dummy (1 if male; 0 otherwise) Marital status dummy (1 if married; 0 otherwise) · Housing Housing tenure dummy (1 if owned; 0 otherwise) Housing damage dummy (1 if housing damaged so badly that people couldn’t live in it or destroyed; 0 otherwise) Housing type dummy (1 if single family house; 0 otherwise)

Mean

Std. Dev.

44.16

16.99

0.33

0.47

0.61

0.49

0.55

0.50

0.45 0.43

0.50 0.50

0.65

0.48

0.67

0.47

0.31

0.46

3. Modeling methodology In order to account for the possibility that the parameters may vary across individual observations, a random-parameter logit model (also called the mixed logit model) is appropriate. All discrete outcomes can be viewed as special cases of a general model of utility maximization: An individual is assumed to have preferences defined over a set of alternatives [16,27]. Tin = βi Xin + e in

(1)

where T is a choice function determining the category  proportion (return, relocation, possible) in observation . βi is a vector of estimate coefficients for discrete outcome i, Xi is the vector of explanatory variables that determine discrete outcomes for observation n, and ein is the standard error. Pn ( i ) =

EXP ( βi Xin )

å

EXP ( β I X In ) "I

(2)

where Pn(i) is the probability of observation n having discrete outcome i. I denotes to all the possible outcomes for observation n. a mixed model with mixing distribution [28]. allowing parameter to vary across individuals, is defined as Pin = ò Pn ( i ) f ( β | φ )dβ

(3)

where f(β|j) is the density function of β with j referring to a vector of parameters of the density function (mean and variance), and all other terms are as previously defined. Pin are the weighted average of the standard MNL probabilities Pn(i) evaluated at different values of β, with the weights determined by the density function f(β|j). Mixed logit is a mixture of the logit function evaluated at different β’s with f(β|j) as mixed distribution. For model estimation, β can account for individual-specific variations of the effect of explanatory variables on outcome probabilities, with the density function f(β|j) used to determine β. Therefore, mixed logit probabilities can be estimated through a weighted average for different values of β across individuals, in which some of β are fixed and others are random distributed. The random parameters can be test using a specified distribution f(β|j), across all observations n for each included explanatory variable (various distributions can be specified to determine the best statistical fit such as normal,

lognormal, triangular, and uniform distribution). Uncorrelated parameters with heterogeneous means and variances are presented below

bik = bk + Δz i + s k vik

(4)

where βk is the population mean, vik is the individual specific heterogeneity, with mean zero and standard error one, sk is the standard deviation of the distribution of βiks around βk, D is the parameters that enter the heterogenous means of distributions of the random parameters, and zi is the observed variables that measure the heterogeneity in the means of random parameters. The model was estimated using simulation-based maximum likelihood over a set of 2000 Halton draws [28,29]. What is more, we evaluated the partial effects of key variables in the model, which measure the expected instantaneous change in the dependent variable as a function of change in a certain explanatory variable while keeping all the other covariates constant [16,22]. The partial effect is defined as (n subscripting omitted), h x = [1 ( j = i ) - Pi ] Pj bik Pj

ik

(5)

where h represents the partial effects in mixed logit model, xik is the value of the variable k for outcome I, when the function 1(j = i) equals one, representing direct partial effect, if j equals i and zero otherwise. 4. Model estimation results The mixed logit model specification is shown in Eq. (3) was estimated by simulation-based maximum likelihood. Halton draws was used to draw random values which have been shown to be significantly more efficient than purely random draws [30,31]. Mixed logit probabilities were approximated by drawing values of β from f(β|j) and using Eq. (2) to estimate simple logit probabilities. This procedure was repeated based on different drawing values and then the average mixed logit probability was computed. For our analysis, normal, triangular, uniform, one-sided triangular and lognormal distributions were tested to determine the best fit model. The result indicated one-sided triangular distribution had the best statistical fit, which is produced by forcing equality of the mean parameter and the scaling parameter.

The parameter that produces a significant standard error is treated as a random parameter. Heterogeneity in the mean of the random parameter was measured by the observed variables. If the standard deviations of parameters are not significant, the parameters were fixed as constant term. More specifically, we found that the effects of housing damage and age variables vary across individual observations which are treated as random parameter in the model. The sex dummy variable was capable of capturing the heterogeneity in the mean of the housing damage parameter. Table 2 shows the comparison of mixed logit model with heterogeneous mean and fixed-parameter model. Likelihood ratio test indicates the mixed logit model with heterogeneity in the mean is statistically superior to a fixed-parameter model. Specifically, the effects of race, marital, education, housing tenure, employment variables are increased compared with fixedparameter model. We elaborate each significant variable in the following. The positive parameter on marital indicator variable indicates that people are married are more likely to relocate to other places. Race variable suggests that black residents have possibilities to return to the New Orleans in one year since the survey. Further, the average partial effect of race indicates relocation and return possibilities are decreased by 0.075 and 0.088 respectively (Table 3). It should also be noted that people with a bachelor’s degree or higher degree are more likely to return to the New Orleans following Katrina. The housing tenure variable shows a significant effect, suggesting that homeowners are more likely to return. Furthermore, the employment status variable shows a significant positive effect indicating that the full time employed residents have higher probabilities to return. In particular, Age acts as an important role, suggesting that older adults are more likely to return to New Orleans. Finally, the housing damage caused by the hurricanes shows a significant and positive effect with regard to return choice.

Employment status dummy (1 if employed full time; 0 otherwise) Sex variable that measures the heterogeneity in the mean of the random parameter housing damage dummy Number of observations Restricted log-likelihood (constant only) Log-likelihood at convergence Akaike information criterion (AIC)

Age

Relocation Marital dummy (1 if married; 0 otherwise) Possible Constant Race dummy (1 if black; 0 otherwise) Return Education dummy (1 if individual has bachelor’s degree or more than bachelor’s degree; 0 otherwise) Housing damage dummy (1 if housing damaged so badly that people couldn’t live in it or destroyed; 0 otherwise) (standard error of parameter distribution) Housing tenure dummy (1 if owned; 0 otherwise)

Variable

0.358 0.009 (0.009)

0.731 0.034 (0.034)

281 -296.585 -222.395 1.647

0.392

0.454 (0.454)

-1.758 (1.758)

-1.023

0.369

0.850

0.325

0.473 0.486

-1.121 1.632

0.727

0.338

0.632

-2.60

2.24

2.04 3.70 (3.70)

-3.88 (3.88)

2.31

-2.37 3.36

1.87

Mixed logit model Std. TCoefficient error static

N/A

0.542

0.031

0.695

-1.866

0.719

-1.111 1.550

0.571

281 -305.518 -226.363 1.668

N/A

0.274

0.007

0.320

0.331

0.314

0.468 0.477

0.318

N/A

1.98

4.55

2.17

-5.64

2.29

-2.37 3.25

1.80

Fixed-parameter model Std. Coefficient T-static error

Table 2 Comparison of mixed logit model and fixed-parameter model of individual’s return decision after Hurricane Katrina

Table 3 The average partial effects of key variables of mixed logit model

*

Variable Marital dummy (1 if married; 0 otherwise) Race dummy (1 if black; 0 otherwise) Education dummy (1 if individual has bachelor’s degree or more than bachelor’s degree; 0 otherwise) Housing damage dummy (1 if housing damaged so badly that people couldn’t live in it or destroyed; 0 otherwise) (standard error of parameter distribution) Housing tenure dummy (1 if owned; 0 otherwise) Age Employment status dummy (1 if employed full time; 0 otherwise) Direct partial effect of the attribute

Relocate Possible 0.034* -0.015 -0.075 0.161*

Return -0.023 -0.086

-0.025

-0.012

0.037*

0.104

0.088

-0.192*

-0.039 -0.116 -0.030

-0.029 -0.092 -0.024

0.069* 0.208* 0.054*

5. Finds and Discussions The results indicate a significant effect of race, indicating black residents are less likely to return or relocate in the first year after a disaster. Corresponding to the change of race from the other to black, the change in return probability can be expected to be a decrease of 0.088 which is higher than relocation probability change (0.075). Furthermore, it should be noted that black people have a higher probability to return to the New Orleans in one year starting from survey date (the second year following Hurricane Katrina). This is consistent with the previous proposition that statistically significant higher percentage of non-blacks in DNORPS samples return to New Orleans by the time of the survey [2,4]. Generally, blacks experienced greater losses from a disaster and higher injury rate than whites, noting that blacks were less likely to obtain adequate aid for their recovery needs [32–34]. Furthermore, black workers from New Orleans were four times more likely than white counterparts to lose their jobs after the Katrina. The job security is an important factor affecting individuals’ decisions. Therefore, the racial difference should be paid special attention for policymakers to target assistance to those most in need residents [5]. For example, recovery efforts need to be integrated into a coherent strategy of economic and social development focused on the job creation of the areas which have been affected. What is more, this study reveals education is an important variable, suggesting that residents with bachelor’s degree or higher-level education are more likely to return than those with less than this level of education. This finding is in line with previous studies that people with higher education and income are more likely to engage in preparedness, take first aid courses, and obtain assistance after the disaster [35–37]. Poor educational backgrounds may leave many

minorities, low-income households at a distinct disadvantage to obtain public financial resources [38,39]. Hence, there is a need to give more attention to those with poor education to help recover quickly from the disaster. For instance, people with low educational attainment were linked to greater posttraumatic growth about 6 months after Hurricane Katrina [40]. The community and local government should provide special help to mitigate their posttraumatic stress. It is also interesting that marital status has a positive significant effect with a regard to relocation. In addition, employment status plays a positive role with a regard to return, indicating full-time employed are more likely to return to New Orleans. This result confirmed previous literature that people who are tied to a location because of employment, social networks and schools are less likely to relocate to other places [41]. The model results also show that homeowners are more likely to return to New Orleans following Hurricane Katrina. In other words, the relocation or possible probabilities are decreased for homeowners compared with renters. This finding is supported by the previous study conducted by Peacock [41], suggesting that homeowners do generally receive the assistance, such as insurance and public funding, they need to repair and rebuild their houses. Conversely, renters are much less likely to have insurance to cover their assets and much more likely to be displaced for they have few rights to the property [42]. Further, homeowners have a chance to undertake mitigation measures through the tax rebate and finally lowering the disaster recovery costs [43]. In addition, rental properties will take significantly longer to rebuild, for owners of rental properties delay repairs to damage housing or local officials or residents block the construction of new multifamily units [44,45]. There is a need for the policy considering the difference between rental properties and homeowners. Another important finding in this study is that age has a positive significant effect on an individual’s return probability, indicating that older adults are more likely to return compared with younger residents. This is consistent with previous studies that older evacuees were more likely to return to New Orleans than younger evacuees [2,4]. According to Huerta [46], older adults are better equipped to cope, exhibiting resilience and reporting less loss than of youngers. Generally, older adults have strong local social networks which prevented older adults from relocation. Further, a higher proportion of older adults in community neighborhoods will have a less proportion of relocated households [13].

Finally, housing damage due to Katrina plays a negative significant effect on return, suggesting that a higher level of damage led to higher probability to relocate or possible return. This is because a greater amount of damage had greater difficulty in recovering from disasters, and the cost of rebuilding housing increased with the level of damages [47]. Further, housing damage effects vary across different individuals. Previous work suggested that the effect of damage was less consequential for individual decision when it comes to high-income households [13,48]. 6. Conclusions The objective of this study was to examine the relationship between socioeconomic characteristics and individual’s return decision in the New Orleans following Hurricane Katrina. A mixed logit model with heterogeneous mean was used to identify significant variables affecting an individual’s decision. Further, housing damage and age parameters are modeled as random parameter in the mixed logit framework. The comparison of the mixed logit model and fixed-parameter model indicates random-parameter approach is the better fit model. This study makes contributions to identify the race and socioeconomic attributes in terms of their impact on individual return decision. Specifically, we identified several important factors, affecting individual decision following Hurricane Katrina, including race, marital status, housing damage, age, education, housing tenure type, and employment status. These results can have significant applications in post-disaster housing recovery planning by providing guidance to policyholders and public officials. Another important contribution of this research is the consideration of unobserved heterogeneity by using random-parameter approach. By explicitly testing for, and accommodating, random parameter in our analysis, we not only arrive at a better statistical fit model, but also find evidence of random parameter (i.e., housing damage is modeled as random parameter allowing variation across individuals). There are compelling reasons to believe that the effect of housing damage on return decision would vary from individual to the next as a result of unobserved factors, such as household income, housing price, insurance, and available public funding. This finding is important on methodological and theoretical implications with a regard to individual return decisions following the disaster. Methodologically, the implication is that unobserved heterogeneity is especially an important consideration when modeling post-disaster return decision, a process that is modeled by incorporating random parameters. Theoretically, the

implication is that some of the many factors (which constitute unobserved heterogeneity) affecting the individual choice after the disaster are not likely to be available to the analyst. It should be noted that the analytic approach we undertake here suffers from several important limitations. First, the small sample size and short observation period for return migration compromised the reliability of findings. For example, smaller sample sizes get increasingly further away from the entire population and may lead to bias estimation due to higher variability. Second, only 147 of the original selected 344 households in the city of New Orleans completed interviews, affecting representative of the samples. There is a high possibility that sampled families had different characteristics compared to those that were not interviewed. Third, our approach also does not parse out differential impacts on the longitudinal nature of disaster and migration processes (we only have a ‘‘snapshot’’ of a single period). Despite of the above limitations, these findings have important implications not only for areas affected by Katrina but also for policymakers establishing recovery plan for future natural disasters. The finding also highlighted the plausibility of random-parameter approach in the modeling of individual decision-making following disasters. Acknowledge The authors gratefully acknowledge the contributions of many colleagues in designing, implementing, and analyzing the Displaced New Orleans Residents Pilot Survey. This work was supported by the national key research and development plan (2018YFC0809601), the Funds of Key Research Program of Frontier Sciences of CAS (QYZDY-SSW-DQC011), the National Natural Science Foundation of China (41571070, 41801040, and 41801053). Thank Dr. Sanjaya Senadheera and Texas Tech University for providing graduate assistantship to Da Hu. Reference [1]

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