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Factors contributing to tourists' length of stay in Dalian northeastern China — A survival model analysis
Tourism Management Perspectives 4 (2012) 67–72
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Tourism Management Perspectives journal homepage: www.elsevier.com/locate/tmp
Factors contributing to tourists' length of stay in Dalian northeastern China — A survival model analysis Erda Wang a,⁎, Bertis B. Little b, 1, Beverly Ann DelHomme-Little c a b c
Department of Human Resource and Tourism Management, School of Business Management, Dalian University of Technology, Dalian, China Computer Science and Mathematics, Tarleton State University, Stephenville, TX, USA DelHomme & Associates, 3333 Lee Parkway, Suite 600, Dallas, TX 75219, USA
a r t i c l e
i n f o
Article history: Received 9 March 2012 accepted 11 March 2012 Available online xxxx Keywords: Survival analysis Tourist's length of stay Cox model Regression analysis
a b s t r a c t Length of stay is one of the most important determinants of the overall impact of tourism in a given economy. However, due to its statistical nature and complexity such as censoring and non negativity, it is rarely systematically analyzed in economic research literature. This article estimated an econometric parametric survival analysis model to learn the determinants of length of stay, in a novel way in the tourism demand literature. In the process, a number of tourist's socio-demographic characteristics were analyzed in order to disclose the most important factors that can contribute to the length of tourist stays. All findings' policy implications are addressed accordingly. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction Length of stay is one of the most important determinants of the overall impact of tourism on a given economy. The number of days tourists stay at a particular destination is likely to influence their expenditures. One simple reason is that lodging and dining expenses account for nearly 40% of aggregated tourist expenditures (Wang, Yang, Little, & Li, 2010). Obviously, both factors are directly related to the length of stays, and yet the number of possible experiences to be undertaken by tourists also depends on their length of stay (António & José, 2009; Barros, Correia, & Crouch, 2008; Barros & Machado, 2010; Kozak, 2001; Legoherel, 1998). Understanding the determinants of length of stay is important to fully characterize tourism demand and its impact on a given tourist destination (António & José, 2009; Machado, 2010). In addition, Carlos and Richard (2010) argue that the importance of disclosing the determinants of length of stay and concomitant gains to policymakers and researchers alike has grown with the increasingly pervasive pattern of shorter lengths of stays. António and José (2009) claim that uncovering the economic determinants of length of stay is critical to the design of marketing policies that effectively promote longer stays, which are associated with higher occupancy rates and revenue streams. In fact, income from tourism might be falling in many destinations despite the increase in visitor arrivals due to a decrease in the length of stay. Length of stay has also increased interest beyond its importance as an expenditure determinant. For instance, in the tourism sustainability literature, length ⁎ Corresponding author. Tel./fax: + 86 411 84707090. E-mail addresses: [email protected] (E. Wang), [email protected] (B.B. Little). 1 Tel.: + 1 254 968 9463 (office); fax: + 1 254 968 9509. 2211-9736/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.tmp.2012.03.005
of stay is important in the context of carrying capacity analysis (Manning, 2001; Prato, 2009; Saveriades, 2000; Tassiopoulos & Haydam, 2008), which is a critical issue associated with eco-tourism and sustainable tourism research. However, there are relatively few studies that estimate the determinants of length of stay in economic research literature resorting to econometric techniques. This paper contributes to fill this gap. The main aim of this paper is to estimate the determinants of length of stay, in particular, how individual socio-demographic profiles and trip experiences influence length of stay. Length of stay is one of the questions resolved by tourists when planning or while taking their trips (Martinez-Garcia & Raya, 2008; Menezes, Moniz, & Vieira, 2008; Zhou & Grumbine, 2011). Hence, it follows that length of stay is best recorded when tourists depart, and, quite likely, is influenced by tourists' socio-demographic profiles (António & José, 2009; Bargeman & Poel, 2006). 2. Determinants of length of stay: a parametric survival analysis Length of stay is an enduring research topic in tourism studies (Crouch, 1994; Crouch & Louviére, 2000; Lim, 1997; Thrane, 2011). Tourism demand is a broadly defined subject and includes tourist arrivals, tourist expenditures, travel exports, nights spent in tourist accommodations, and length of stay. Length of stay is an interesting research topic for two reasons. First, length of stay conditions the overall socioeconomic impact of tourism in a given economy. In fact Davies and Mangan (1992) found that an increased length of stay may allow tourists to access a larger number of experiences or activities, which may affect their overall spending, sense of affiliation, and satisfaction. Hence, several authors consider length of stay an important market segmentation variable in estimating the determinants of tourist
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spending (Davies & Mangan, 1992; Legoherel, 1998; Mok & Iverson, 2000). Second, modeling length of stay is important to tourism sustainability analysis (Gokovali et al., 2007; Saarinen, 2006). Sustainability has recently become an important policy issue in tourism. The worldwide continuous growth of tourism has triggered an intense debate on the socioeconomic and environmental impacts that tourism has on destination areas. Sustainability focuses on destination areas' carrying capacity, generally defined as the maximum number of people who can use a site without unacceptable alteration in the physical environment and without unacceptable decline in the satisfaction perceived by tourists. The concept of carrying capacity occupies a key position with regard to sustainable tourism, because many of the latter's principles are based on this theory and research practice. Models of the determinants of length of stay are important to research on sustainable tourism because they are useful to forecast tourists' on-site time and, concomitantly, the stress of tourism activity on local resources. Alegre and Pou (2006) argue that most studies on tourism demand fail to analyze length of stays, at least at the microeconometric level, where it is possible to control for individual behaviors. Descriptive studies on the length of stay (Oppermann, 1997; Seaton & Palmer, 1997; Sung, Morrison, Hong, & O'Leary, 2001) show that it varies with nationality, age, occupation (SES), repeat visit behavior, stage in the family life cycle, and physical distance between place of origin and destination. Descriptive studies lack formal inference tests on the causal relationships between individual sociodemographic profiles and actual trip experiences and length of stay. Econometric models to estimate the determinants of length of stay have employed a Tobit model to estimate the determinants of the vacation taking decision process for a group of Israeli senior citizens (Fleischer & Pizam, 2002). The Tobit model in Fleischer and Pizam overcomes the fact that several individuals in the study group do not take vacations at all. Thus the model allows a corner solution case, with many individuals experiencing zero days of vacation. Fleischer and Pizam conclude that age, health status, and income have a positive effect on the length of stay. In the present case, only departing tourists were surveyed, and, hence, all tourists experienced a strictly non-zero positive length of stay. Therefore, the Tobit model, employed in Fleischer and Pizam, is not applicable. Length of stay for tourists visiting the Balearic Islands where the explanatory variable is binary (0 if length of stay is shorter than 1 week, and 1 otherwise) find, among other results, that labor status, nationality, and repeat visitation rate are statistically significant determinants of length of stay (Alegre & Pou, 2006). Gokovali et al. (2007) estimated parametric survival models of the proportional hazard analysis. For a cross section of tourists departing from the Turkish region of Bodrum, experience as a tourist, past visits to destination, overall attractiveness, and image of destination country, all increase the probability of staying longer (Gokovali et al., 2007).
while still offering plenty of shopping, bars, and restaurants. There are more than 10 coastal environment-oriented recreational parks where natural environment elements such as water, flowers, forests, trails, and turf grass, and activities such as fishing and swimming are major tourist attractions. Native and foreign visitors enjoy sunbathing, swimming, diving, camping, boating, fishing, and outdoor cooking. Tourism in Dalian has experienced rapid development in the last 20 years, especially the last decade. Tourist arrivals have increased from 12.15 million in 2000 to 35.17 million in 2009. Among the total of 35.17 million arrivals, domestic tourists account for 97% and the remaining 3% belong to overseas tourists including tourists from Hong Kong, Macao, Taiwan, and the rest of the world. In the same period tourism revenue increased from $1345 million to $7442 million. For the total of $7442 million of tourism revenue in 2009, 90% was contributed by domestic tourists and 10% was contributed by overseas tourists. Statistics indicates that tourists from overseas stay in Dalian for 3.40 days per person per trip on average while domestic tourists stay for 3.09 days per person per trip on average. In terms of tourism expenditures, on average each overseas tourist spent $204 per person per day and $693 per trip. By contrast, domestic arrivals spent $63 per person per day and $196 per person per trip (Dalian Statistics Yearbook, 2010). No large differences are observed in terms of lengths of stays between overseas tourists and domestic tourists. One possible reason is that a vast majority of tourists in Dalian are from Asian countries (>75%). The travelers from Asian countries generally have less than 10 h of flight. The other reason may be due to the fact that Dalian is a relatively small tourism city (5.5 million people) where most tourism sites are located fairly close to each other and it does not take many days to have a complete tour although some travelers may stay for 2 to 3 days at one site. One observation which causes concern in terms of regional economic impact consideration in Dalian is that the length of tourism stays of inbound tourists has been decreasing for the last 10 years except for Taiwan's tourists. For instance, in 1997 the number of days' stay for tourists coming from the rest of the world (excluding Hong Kong, Marco, and Taiwan) was shortened to 3.27 days in 2008 from 4.55 days in 1997. The length of stay for Hong Kong's tourists was reduced to 3.32 days in 2008 from 3.77 days in 1997. And similarly, the length of stay for tourists from Marco was shortened to 3.27 days in 2008 from 3.74 days in 1997. Only the length of stay of tourists from Taiwan increased slightly from 3.39 days in 1997 to 3.44 days in 2008 (Dalian Statistics Yearbook, 2009) (Fig. 1). A similar situation happens for domestic tourists and there is no indication that this pattern will change in the near future. The short length of tourist stay is certainly a negative sign regarding the tourism development, which naturally becomes a concern to both local government and tourism business operators. In recent years devising a good strategy to increase tourists' length of stay is a top priority for
3. Contextual setting and data 5 4.5 4
No. of Days
Dalian is located in the southernmost part of the Liaodong Peninsula in northeast China, with the Yellow Sea to the east and the Bohai Sea to the west. It is one of the most important industrial cities in the region and a main seaport of China. Dalian is extolled as the “Romantic Capital” and “Northern Pearl of China.” Dalian was given the honor of being named a “Model Environmental City” by the United Nations on June 5, 2001. It was the first city in China to receive this honor and only the second in Asia. Dalian is also a modern tourism city. It is famous for fashion, football, and its annual beer festival. China's ancient cities (i.e., Beijing, Xian, Hangzhou, and Nanjing etc.), that have numerous historical relics and ruins, temples and museums focus tourism on their long history and rich culture. Dalian, on the other hand, offers a different experience for visitors. It is a famous summer resort with beautiful scenery and pleasant environment providing the visitor a chance to relax by the sea and enjoy the clean air,
3.5 3 Foreigners Hongkang Marco Taiwan
2.5 2 1.5 1 0.5 0
1997 98 99 00 01 02 03 04 05 06 07 2008
Year Fig. 1. Length of stay of inbound tourist in Dalian.
E. Wang et al. / Tourism Management Perspectives 4 (2012) 67–72
the local government tourism administration department. Tourists' length of stay is perceived as critical to increase occupancy rates and make operations run more efficiently. Discovering determinants of length of stay is critical to improve the effectiveness of regional tourism policy. The questionnaire used to construct the dataset used in the present analysis was done in the summer of 2009. It was designed to be a representative, stratified sample of the tourists who visited Dalian, by nationality, routes, and gateways used. The tourist surveys took place at several traffic port areas including the airport, sea ports, railway station, and long-distance coach/bus station. A total of 1576 questionnaires were attempted and 1261 questionnaires were completed and returned (80.2% success ratio). Questionnaires given in port and terminal areas were administered in two languages: Mandarin Chinese and English. A partial list of items covered in the survey include gender, age, education, occupation sector, income, travel party composition, travel motive, alternative destinations considered, and repeat visitation rate. Table 1 lists the frequencies of length of stay. As expected, the highest frequency is three-day stays, typically associated with domestic tourists (frequency: 23.31%). Lengths of stays of 2 and 4 days are frequent: 19.35% and 16.02%, respectively. Seven days of stays was 14.99%. Most surveyed tourists are from northeastern China including the Liaoning province, Jilin province and Heilongjiang province, as well as a small portion from provinces outside northeastern China and overseas. Table 2 contains additional selected, self-explanatory, descriptive statistics for the data gathered. The mean stay is about 3.86 days; (median stay: 4 days) while the standard deviation is 1.83 days.
4. Study methods: an overview of survival analysis Survival analysis is a statistical method for analyzing longitudinal data on event occurrence. In classic medical application survival analysis events may include death, injury, onset of illness, recovery from illness (binary variables) or transition above or below a meaningful threshold. Survival analysis accommodates data from randomized clinical trials or cohort study design, or economic events. The economic meaning of survival analysis is opposite from medicine. The engineering sciences have contributed to the development of survival analysis, which is called “reliability analysis” or “failure time analysis” in this field because the main focus is in modeling the time it takes for machines or electronic components to fail. Likewise, survival analysis has long been a cornerstone of biomedical research. Huygens (1669) curve shows how many out of 100 people survive until 86 years. Survival analysis is commonly used in biological and medical research, and is especially used to test drug efficacy for patient treatments. In tourism economic analysis, days of visit can be modeled as time and outcomes of interest (money spent) can be analyzed as covariates. One of the strengths of using survival
Table 1 Distribution of length of stays. Lengths of stays
Observations (total = 1261)
Frequency (%)
Frequency
1 2 3 4 5 6 7 10
90 244 294 202 176 65 189 1
7.14 19.35 23.31 16.02 13.96 5.15 14.99 0.08
7.14 26.49 49.80 65.82 79.78 84.93 99.92 100.00
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Table 2 Descriptive statistics for independent variables. Stat.
Days of stay
Edu.a
Travel (km)
Income ($)
Ageb
Sexc
Visit times
Mean Std. dev. Median Mode Min Max No. of obs.
3.87 0.05 4 3 1 10 1261
3.12 0.03 3 4 1 6 1261
1026 25.73 850 397 5 10,000 1261
304 9.08 232.56 77.52 38.76 3101 1261
3.23 0.03 2 2 1 5 1261
0.58 0.01 1 1 0 1 1261
3.30 0.07 3 1 1 20 1261
a 1 = primary school, 2 = middle school, 3 = high school, 4 = college, 5 = graduate school. b 1 ≤ 14-years old, 2 = 15–24 years old, 3 = 25–40 years old, 4 = 41–60 years old, 5 ≥60-years old. c 1 = male, 0 = female.
analysis in tourism economics is the use of covariates and the ability to assess the magnitude of specific influences which can be analyzed and used in strategic planning to maximize tourism dollar spent. Estimation of time-to-event for a group of individuals may involve how long a tourist must stay until the target amount of money they spent can be analyzed. Time‐to‐event can be analyzed between two or more groups, such as local residents vs. long‐range travelers, and to assess the relationship of covariates to time‐to‐event (e.g., age, education). There are certain aspects of survival analysis data, such as censoring and non normality that may confound data analysis using traditional statistical models such as the linear regression model and tests. The variable of interest in the analysis of the length of time that elapses from the initiation of the study to some event occurs and the study is terminated. Individual observations that do not have an event are censored. This survival analysis naturally lends itself to the study of length of stay. The length of time that elapses between the tourist's arrival on a given tourist destination and his departure is survival time. Logistic regression is not appropriate because it ignores time, and time to event is highly important in tourism economics. Survival analysis is a relative newcomer to economic literature. Economists have only recently applied the same body of techniques to strike duration, length of unemployment, time until business failure, agricultural insurance claims, etc. (Hosmer & Lemeshow, 1999; Kieffer, 1988; Wang et al., 2010). Censoring includes lost to follow up, dropping out of the study, or if the study ends before subjects have an outcome of interest. The dataset employed in the present article was collected at transportation ports or stations from tourists who were departing from their trips. Hence, there is no censoring in the data since all interviewees reported their length of stay. Therefore, the discussion that follows is not concerned with censoring. Let Ti represent the duration of tourist at the destination. It is a random variable with a known probability distribution. Different models for survival data are distinguished by different choice of distribution for Ti subset, or days of visit to tourist site. Parametric survival analysis is based on time to event or “Waiting Time” distributions (e.g., exponential probability distribution). Time-to-event for individuals in the dataset is assumed to follow a continuous probability distribution. For all possible times, Ti, after baseline, there is a probability that an individual will have an event at time Ti which is, by design, a non-negative variable. Ti is a continuous probability distribution f(t), where t is a realization of T. One is usually interested in the probability that the visit is of length at least t, which is given by the survival function S(t)= Pr (T ≥t). The hazard rate, h(t), in turn, answers the following question: given that
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the visit has lasted until time t, what is the probability that it will end in the next short interval of time: f ðt Þ ¼ lim
Δt→0
P ðt≤Tbt þ Δt Þ : Δt
ð1Þ
Eq. (1) shows the probability of the failure time (or dollar spending threshold in economics) occurring at exactly time t (out of the whole range of possible ts). The hazard function can be written as, hðt Þ ¼ lim
Δt→0
P ðt≤Tbt þ Δt=≥t Þ Δt
ð2Þ
which is the probability that if you survive to t, you will succumb to the event in the next interval. That is the probability that the visitor will spend ≥x dollars in the next time period: Hazard f rom density and survival : hðt Þ ¼
¼
f ðt Þdt : Sðt Þ
ð3Þ
pðt≤Tbt þ dt&T≥t Þ P ðt≤Tbt þ dt Þ ¼ P ðT≥t Þ P ðT≥t Þ
5. Model specification Although Cox PH assumption is accepted, it would still be enlightening to estimate parametric survival models. Hence exponential, Weibull and Gompertz regression should be carried out and one of them should be selected as best fitting model according to AIC criteria. Then comparison of the results of Cox estimation and best fitting parametric models would give more insights. Notice that the multiplicative or proportional hazards (PH) model is one of the commonly used parametric regression techniques. Parametric regression technique is used to model the underlying hazard/survival function, assuming that the dependent variable (time-to-event) takes on some known distribution, such as Weibull, exponential, or lognormal. Each selected model is utilized to estimate parameters of these distributions (e.g., baseline hazard function) and covariate-adjusted hazard ratios (HRs). Many times interest is more about comparison group than about estimating absolute survival. Generally, several models can be used in the estimation process and their performance can be evaluated via maximum likelihood if parametric models are nested. When parametric models are nested, the likelihood-ratio or Wald tests can be used to differentiate among them. This can certainly be done in the case of Weibull versus exponential, or Weibull versus lognormal. When models are not nested, however, these tests are
Table 3 PH model comparison. Model
Statistics
Nested models Wald test
AIC
Exponential (PH)
LL = − 355.90 χ2(11) = 62.36 (p.v. = 0.0007) LL = − 350.90 χ2(11) = 11.48 (p.v. = 0.0007) LL = − 405.17 χ2(11) = 83.68 (p.v. = 0.0000)
None
877.80
H0:p = 1 → χ2(1) = 162 (p.v. = 0.0000) → Reject Exponential None
660.57
Gompertz (PH) (γˆ = 0.0157)
hi ðt Þ ¼ h0 ðt Þe
:
ð4Þ ð5Þ
Here log hi(t) and h0(t) can take on any form. Overall, 11 covariates were selected given the available data and modeling results are presented in the next section.
Intuitively, the hazard rate is the rate at which visits are completed after duration t, given that they last at least until t.
Weibull (PH) (ˆp = 1.8027)
loghi ðt Þ ¼ logh0 ðt Þ þ β1 xi1 þ … þ βk xik β 1 xi1 þ…þβk xik
f ðt Þ : Sðt Þ
Eq. (3) is derived from Bayes' rule: hðt Þ ¼ pðt≤Tbt þ dt=T≥t Þ ¼
inappropriate and the task of discriminating between models becomes more difficult. Empirical studies show that, in general, there is no one specific parametric model that can perform better than any other parametric model in all statistical test criteria. For this reason, in this paper we choose Cox regression model which is a semiparametric test, that models the effect of predictors and covariates on the hazard rate but leaves the baseline hazard rate unspecified. Cox model is also called proportional hazard regression and it does not assume knowledge of absolute risk; it estimates relative rather than absolute risk. A baseline hazard function that is left unspecified must be positive (equal to the hazard when all covariates are 0). A linear function of a set of k fixed covariates that is exponential (equals the relative risk) is given as:
858.34
6. Results Table 3 presents the summary results of three PH models' log likelihood estimation, ancillary parameters, model discriminating Wald tests and AIC values. The Weibull model dominates the exponential model in all criteria considered. The log likelihood obtained under the Weibull model is higher than the log likelihood obtained under the exponential model. In addition, the AIC value obtained under the Weibull model is lower than the AIC value obtained under the exponential model. Hence, the exponential model is not used elsewhere in this paper, since it is dominated by the Weibull model. The Weibull model yields a higher log likelihood and a lower AIC value than the Gompertz model. Hence, the Weibull model is preferred to the Gompertz model and is the preferred PH model. Now, we can make a comparison of the results of Cox estimation and Weibull model estimation. Table 4 reports the results obtained from the Cox model and Weibull model — the preferred PH model. It should be noted that the coefficients are directly comparable between the models. Both models are presented in PH form and the coefficients may be interpreted as a hazard ratio. Intuitively, and focusing on binary variables, the coefficients presented are of the form exp(βk) and represent the ratio between the hazard rate when the variable takes the value of one and the hazard rate when the variable takes the value of zero. Hence, a coefficient higher than one means that an increase in the variable leads to an increase in the hazard rate and, thus, to a lower expected duration. Inspection of Table 4 reveals that, in fact, the Cox mode tends to produce better results than the Weibull model based on the statistical test performances. For example, the Cox model produces a higher value of Log likelihood than it does by Weibull model, −346.28 versus −350.90, and yet most explanatory variables in Cox model are statistically higher and significant than they are in the Weibull model. Thus, for the sake of saving paper space, we now turn to discuss the Cox model results only. Table 5 reports the results obtained from the Cox regression model. The regression results show that most explanatory variables included in the model are statistically significant at 5% or lower levels of significance (except for Sex, Education (1) primary education, as well as Education (5) graduate education) where Education (1) reaches 10% of significance. Income has a direct relation to the lengths of stay, suggesting that “tourist stay” is a good indicator, and, a higher income earner tends to stay longer than a lower income earner with all else held constant. Male tourists seem to stay longer than female tourists (Sex was designed as a binary variable with ‘0’ for female and ‘1’ for male). These results have important policy implications given the
E. Wang et al. / Tourism Management Perspectives 4 (2012) 67–72 Table 4 Regression results. Variables
Cox (PH) estimation Weibull (PH form; exp(βk))
Sex Age Income/month Education (1) Education (2) Education (3) Education (4) Education (5) Travel (km) Travel times Expt./day($) p Ancillary parameter Weibull γ Ancillary parameter Weibull Log likelihood N
0.022 (0.049) 0.351 (50.57***) 0.000 (8.167***) 0.412 (4.353*) 0.571 (8.363**) 0.414 (5.067**) 0.612 (6.708***) − 0.04 (0.002) 0.000 (48.364***) 0.051 (8.631***) 0.001 (249.54***) 1.9027***
0.0081 (0.541) 0.0124 (0.681) 0.168 (2.254**) 1.051 (1.035) 1.061 (2.497**) 1.242 (2.763**) 1.054 (2.541**) 1.105 (1.556) 0.895 (2.241**) 0.654 (1.762) 0.012 (3.254**) 0.2687*** − 350.90 1261
− 346.28 1261
Figures in parentheses are t-stats in Weibull (PH) model and Wald statistic in Cox (PH) model; Weibull coefficients are hazard ratios; ***, **, and * means significant at the 1%, 5% and 10% level, respectively.
strategic importance of these markets in the overall policy context. However, this finding is different from the report by António and José (2009) in which they concluded that female tourists tend to stay longer than male tourists in their Azores tourism study of Portugal. Age also has a statistically significant positive influence on the lengths of stay; older tourists have a tendency to stay more nights than younger ones. This may owe to the inclusion of other covariates closely related with age such as level of income. As indicated in Table 2, age is a categorical variable with a mean of 3.23, which means that most surveyed tourists are between 25 and 45 years of age. Middle school through college education experience of tourists has direct relations to the length of stay, but it is interesting to note that tourists who had postgraduate education have shorter lengths of stay. This result is consistent with the one found by António and José (2009) where they concluded that higher levels of education are associated with shorter stays and a high level profession is also associated with shorter expected duration of stays. Travel distance exhibits a significant effect on the length of stay. In fact, an ex ante one would imagine that tourists who live far away would experience longer stays, to make up for the increased overall travel cost. Hence, it is indeed the case that tourists who live close to Dalian, such as Anshan, Liaoyang, Panjin, etc. do tend to experience shorter stays than tourists who live farther away as, say, tourists from Jilin and Heilongjiang provinces. Travel time is a numerical variable to reflect the actual repeated number of times a tourist took to visit Dalian. Quite interestingly, it is found that repeat visitors stay for longer periods. As a matter of fact, the more times a tourist visits the area, the longer the stay he or she takes. Repeat visitor behavior has aroused interest in recent years (Kozak, 2001; Lehto, O'Leary, & Morrison, 2004), has its
Table 5 Regression results predicting length of stay (days). Indept. var.
Sex Age Income/month Education (1) Education (2) Education (3) Education (4) Education (5) Travel (km) Travel times Expt./day. ($)
B
0.022 0.351 0.000 0.412 0.571 0.414 0.612 − 0.04 0.000 0.051 0.001
SE
0.100 0.049 0.000 0.197 0.197 0.184 0.236 1.016 0.000 0.017 0.000
Wald
0.049 50.57 8.167 4.353 8.363 5.067 6.708 0.002 48.346 8.6310 249.54
df
1 1 1 1 1 1 1 1 1 1 1
* 5% level of significance;** 1% level of significance.
HR Sig.
HR
.824 .000⁎⁎ .004⁎⁎
1.022 1.42 1.000 1.51 1.769 1.513 1.844 0.961 1.017 1.052 1.001
.081 .037⁎ .004⁎⁎ .010⁎⁎ .968 .000⁎⁎ .003⁎⁎ .000⁎⁎
95% CI for HR Lower
Upper
0.841 1.289 1.000 1.025 1.202 1.055 1.161 0.131 0.999 1.017 1.001
1.243 1.564 1.000 2.223 2.605 2.17 2.931 7.033 1.000 1.088 1.001
71
relationship with future visiting behavior (destination loyalty) and word-of-mouth recommendation carries important policy and marketing implications. Lastly, expenditure per tourist per day exhibits a strong effect on the length of stays. This makes intuitive sense since more expenses in general could result from more days of stay. Certainly, there are some other important determinant factors that should be considered in the investigation of the length of stay if they are available in the dataset. These include but are not restricted to: whether the tourist is domestic or international, marital status, types of accommodation (bed and breakfast, bed only, or all inclusive type, etc.), travel companies, characteristics of tourism product (such as level of hospitality, standard of entertainment, quality of services and facilities, standard of safety and security etc.). Each of them may have a significant effect on the length of stay. Unfortunately, most of those questions are not included in our survey questionnaire mainly due to the consideration of interviewees' cooperation. 7. Conclusion One of the most important decisions made by tourists before or while visiting a given destination concerns their length of stay. In fact, length of stay most likely conditions overall tourists' expenditure and stress imposed on local resources; just to name a few of the implications of varying lengths of stays. However, and as Alegre and Pou (2006) document, despite the rich literature on tourism demand, very few studies have resorted to econometric models in order to shed light on the determinants of length of stay. This paper estimated an econometric parametric survival analysis model to learn the determinants of length of stay, in a novel way in the tourism demand literature. The results suggest that survival analysis may be a fertile ground to analyze tourism demand if time dimension is of the essence, as is obviously the case with length of stay studies. An interesting avenue for future research may lie on tourism demand modeling strategies where time is explicitly modeled, with structural models of consumer demand theory leading to reduced form survival analysis regression exercises, as the ones found in this paper. The results in this paper are statistically significant and economically important. Quite interestingly, a number of covariates, pertaining to detailed individual socio-demographic profiles and actual trip experiences of the representative tourists interviewed, were considered in the regressions in order to control for heterogeneous individual behavior. Concomitantly, the richness of the information embedded in the covariates used allows the design of effective marketing policies, in the sense that the regression results allow one to estimate, for a given synthesized, policy relevant individual or target group, not only mean or median expected stays, but also the probability that stays exceed a given threshold. Hence, policymakers and private operators may benefit from such tools that disclose individual socio-demographic profiles and trip attributes that promote longer stays and act or advertise accordingly. Among the several results found, it can be argued that being a repeat visitor and having a far travel distance are important criteria to identify tourists who are likely to experience longer stays. Thus, future research should characterize such groups and their economic and activity involvement. Level of tourist income and age also play highly statistically significant roles in determining length of stay. This result is very important as the Dalian government, in its quest to promote high quality tourism to attract more higher income tourists to come, is expanding and upgrading airport, and railway station and encouraging the construction of more five-star hotels, and therefore, the government must assess the socioeconomic implications of such proposals. Apparently, such policy is successful in terms of promoting longer stays. A higher degree of education is associated with shorter expected stays. It would be interesting to investigate if this result follows from the idea that better educated tourists face more stringent time constraints or is purely due to differences in preferences across education levels.
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References Alegre, J., & Pou, L. (2006). The length of stay in the demand for tourism. Tourism Management, 27, 1343–1355. António, G., & José, C. (2009). Determinants of length of stay — A parametric survival analysis (pp. 85–104). Bargeman, B., & Poel, V. (2006). The role of routines in the decision making process of Dutch vacationers. Tourism Management, 27, 707–720. Barros, C. P., Correia, A., & Crouch, G. (2008). Determinants of the length of stay in Latin American tourism destinations. Tourism Analysis, 13(4), 329–340. Barros, C. P., & Machado, L. P. (2010). The length of stay in tourism. Annals of Tourism Research, 37(3), 692e706. Carlos, P. B., & Richard, B. (2010). The length of stay of golf tourism: A survival analysis. Tourism Management, 31, 13–21. Crouch, G. (1994). A meta-analysis of tourism demand. Annals of Tourism Research, 22, 103–118. Crouch, G., & Louviére, L. (2000). A review of choice modeling research in tourism, hospitality, and leisure. Tourism Analysis, 5, 97–104. Dalian Statistics Yearbook. (2009). Dalian Statistics Yearbook. (2010). Davies, B., & Mangan, J. (1992). Family expenditure on hotels and holidays. Annals of Tourism Research, 19, 691–699. Fleischer, A., & Pizam, A. (2002). Tourism constraints among Israeli seniors. Annals of Tourism Research, 29, 106–123. Gokovali, U., Bahar, O., & Kozak, M. (2007). Determinants of length of stay: A practical use of survival analysis. Tourism Economics, 14(1), 205–222. Hosmer, D., & Lemeshow, S. (1999). Applied survival analysis. New York: Wiley. Huygens, Christiaan (1669). Annual review of psychology, Vol. 52. (pp. 305–335). Kieffer, N. (1988). Economic duration and hazard functions. Journal of Economic Literature, 26, 646–667. Kozak, M. (2001). Repeaters' behavior at two distinct destinations. Annals of Tourism Research, 28, 785–808. Legoherel, P. (1998). Toward a market segmentation of the tourism trade: Expenditure levels and consumer behavior instability. Journal of Travel and Tourism Marketing, 7, 19–39. Lehto, X., O'Leary, J., & Morrison, A. (2004). The effect of prior experience on vacation behavior. Annals of Tourism Research, 31, 801–818.
Lim, C. (1997). An econometric classification and review of international tourism demand models. Tourism Economics, 3, 69–81. Machado, L. P. (2010). Does destination image influence the length of stay in a tourism destination? Tourism Economics, 16, 443–456. Manning, R. (2001). Visitor experience and resource protection: A framework for managing the carrying capacity of national parks. Journal of Park and Recreation Administration, 19(1), 93–108. Martinez-Garcia, E., & Raya, J. M. (2008). Length of stay for low cost tourism. Tourism Management, 29, 1064–1075. Menezes, A. G., Moniz, A., & Vieira, J. C. (2008). The determinants of length of stay of tourists in the Azores. Tourism Economics, 14, 205–222. Mok, C., & Iverson, T. (2000). Expenditure-based segmentation: Taiwanese tourists to Guam. Tourism Management, 21, 299–305. Oppermann, M. (1997). First-time and repeat visitors to New Zealand. Tourism Management, 18, 177–181. Prato, T. (2009). Fuzzy adaptive management of social and ecological carrying capacities for protected areas. Journal of Environmental Management, 90, 2551–2557. Saarinen, J. (2006). Traditions of sustainability in tourism studies. Annals of Tourism Research, 33, 1121–1140. Saveriades, A. (2000). Establishing the social tourism carrying capacity for the tourist resorts of the east coast of the Republic of Cyprus. Tourism Management, 21, 147–156 (2000). Seaton, A., & Palmer, C. (1997). Understanding VFR tourism behavior: The first five years of the United Kingdom tourism survey. Tourism Management, 18, 345–355. Sung, H., Morrison, A., Hong, G., & O'Leary, J. (2001). The effects of household and trip characteristics on trip types: A consumer behavioral approach for segmenting the US domestic leisure travel market. Journal of Hospitality & Tourism, 25, 46–68. Tassiopoulos, D., & Haydam, N. (2008). Golf tourists in South Africa: A demand-side study of a niche market in sports tourism. Tourism Management, 29, 870–882. Thrane, C. (2011). Analyzing tourists' length of stay at destinations with survival models: A constructive critique based on a case study. Tourism Management, 33(2012), 126–132. Wang, E. D., Yang, Y., Little, B. B., & Li, Z. Z. (2010). Crop insurance premium design based on survival analysis model. International Conference on Agricultural Risk and Food Security 2010. Elsevier ScienceDirect, Available online at www.sciencedirect.com Zhou, D. Q., & Grumbine, R. E. (2011, May). National parks in China: Experiments with protecting nature and human livelihoods in Yunnan province, People's Republic of China (PRC). Biological Conservation, 144(5), 1314–1321.
Contents lists available at SciVerse ScienceDirect
Tourism Management Perspectives journal homepage: www.elsevier.com/locate/tmp
Factors contributing to tourists' length of stay in Dalian northeastern China — A survival model analysis Erda Wang a,⁎, Bertis B. Little b, 1, Beverly Ann DelHomme-Little c a b c
Department of Human Resource and Tourism Management, School of Business Management, Dalian University of Technology, Dalian, China Computer Science and Mathematics, Tarleton State University, Stephenville, TX, USA DelHomme & Associates, 3333 Lee Parkway, Suite 600, Dallas, TX 75219, USA
a r t i c l e
i n f o
Article history: Received 9 March 2012 accepted 11 March 2012 Available online xxxx Keywords: Survival analysis Tourist's length of stay Cox model Regression analysis
a b s t r a c t Length of stay is one of the most important determinants of the overall impact of tourism in a given economy. However, due to its statistical nature and complexity such as censoring and non negativity, it is rarely systematically analyzed in economic research literature. This article estimated an econometric parametric survival analysis model to learn the determinants of length of stay, in a novel way in the tourism demand literature. In the process, a number of tourist's socio-demographic characteristics were analyzed in order to disclose the most important factors that can contribute to the length of tourist stays. All findings' policy implications are addressed accordingly. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction Length of stay is one of the most important determinants of the overall impact of tourism on a given economy. The number of days tourists stay at a particular destination is likely to influence their expenditures. One simple reason is that lodging and dining expenses account for nearly 40% of aggregated tourist expenditures (Wang, Yang, Little, & Li, 2010). Obviously, both factors are directly related to the length of stays, and yet the number of possible experiences to be undertaken by tourists also depends on their length of stay (António & José, 2009; Barros, Correia, & Crouch, 2008; Barros & Machado, 2010; Kozak, 2001; Legoherel, 1998). Understanding the determinants of length of stay is important to fully characterize tourism demand and its impact on a given tourist destination (António & José, 2009; Machado, 2010). In addition, Carlos and Richard (2010) argue that the importance of disclosing the determinants of length of stay and concomitant gains to policymakers and researchers alike has grown with the increasingly pervasive pattern of shorter lengths of stays. António and José (2009) claim that uncovering the economic determinants of length of stay is critical to the design of marketing policies that effectively promote longer stays, which are associated with higher occupancy rates and revenue streams. In fact, income from tourism might be falling in many destinations despite the increase in visitor arrivals due to a decrease in the length of stay. Length of stay has also increased interest beyond its importance as an expenditure determinant. For instance, in the tourism sustainability literature, length ⁎ Corresponding author. Tel./fax: + 86 411 84707090. E-mail addresses: [email protected] (E. Wang), [email protected] (B.B. Little). 1 Tel.: + 1 254 968 9463 (office); fax: + 1 254 968 9509. 2211-9736/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.tmp.2012.03.005
of stay is important in the context of carrying capacity analysis (Manning, 2001; Prato, 2009; Saveriades, 2000; Tassiopoulos & Haydam, 2008), which is a critical issue associated with eco-tourism and sustainable tourism research. However, there are relatively few studies that estimate the determinants of length of stay in economic research literature resorting to econometric techniques. This paper contributes to fill this gap. The main aim of this paper is to estimate the determinants of length of stay, in particular, how individual socio-demographic profiles and trip experiences influence length of stay. Length of stay is one of the questions resolved by tourists when planning or while taking their trips (Martinez-Garcia & Raya, 2008; Menezes, Moniz, & Vieira, 2008; Zhou & Grumbine, 2011). Hence, it follows that length of stay is best recorded when tourists depart, and, quite likely, is influenced by tourists' socio-demographic profiles (António & José, 2009; Bargeman & Poel, 2006). 2. Determinants of length of stay: a parametric survival analysis Length of stay is an enduring research topic in tourism studies (Crouch, 1994; Crouch & Louviére, 2000; Lim, 1997; Thrane, 2011). Tourism demand is a broadly defined subject and includes tourist arrivals, tourist expenditures, travel exports, nights spent in tourist accommodations, and length of stay. Length of stay is an interesting research topic for two reasons. First, length of stay conditions the overall socioeconomic impact of tourism in a given economy. In fact Davies and Mangan (1992) found that an increased length of stay may allow tourists to access a larger number of experiences or activities, which may affect their overall spending, sense of affiliation, and satisfaction. Hence, several authors consider length of stay an important market segmentation variable in estimating the determinants of tourist
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spending (Davies & Mangan, 1992; Legoherel, 1998; Mok & Iverson, 2000). Second, modeling length of stay is important to tourism sustainability analysis (Gokovali et al., 2007; Saarinen, 2006). Sustainability has recently become an important policy issue in tourism. The worldwide continuous growth of tourism has triggered an intense debate on the socioeconomic and environmental impacts that tourism has on destination areas. Sustainability focuses on destination areas' carrying capacity, generally defined as the maximum number of people who can use a site without unacceptable alteration in the physical environment and without unacceptable decline in the satisfaction perceived by tourists. The concept of carrying capacity occupies a key position with regard to sustainable tourism, because many of the latter's principles are based on this theory and research practice. Models of the determinants of length of stay are important to research on sustainable tourism because they are useful to forecast tourists' on-site time and, concomitantly, the stress of tourism activity on local resources. Alegre and Pou (2006) argue that most studies on tourism demand fail to analyze length of stays, at least at the microeconometric level, where it is possible to control for individual behaviors. Descriptive studies on the length of stay (Oppermann, 1997; Seaton & Palmer, 1997; Sung, Morrison, Hong, & O'Leary, 2001) show that it varies with nationality, age, occupation (SES), repeat visit behavior, stage in the family life cycle, and physical distance between place of origin and destination. Descriptive studies lack formal inference tests on the causal relationships between individual sociodemographic profiles and actual trip experiences and length of stay. Econometric models to estimate the determinants of length of stay have employed a Tobit model to estimate the determinants of the vacation taking decision process for a group of Israeli senior citizens (Fleischer & Pizam, 2002). The Tobit model in Fleischer and Pizam overcomes the fact that several individuals in the study group do not take vacations at all. Thus the model allows a corner solution case, with many individuals experiencing zero days of vacation. Fleischer and Pizam conclude that age, health status, and income have a positive effect on the length of stay. In the present case, only departing tourists were surveyed, and, hence, all tourists experienced a strictly non-zero positive length of stay. Therefore, the Tobit model, employed in Fleischer and Pizam, is not applicable. Length of stay for tourists visiting the Balearic Islands where the explanatory variable is binary (0 if length of stay is shorter than 1 week, and 1 otherwise) find, among other results, that labor status, nationality, and repeat visitation rate are statistically significant determinants of length of stay (Alegre & Pou, 2006). Gokovali et al. (2007) estimated parametric survival models of the proportional hazard analysis. For a cross section of tourists departing from the Turkish region of Bodrum, experience as a tourist, past visits to destination, overall attractiveness, and image of destination country, all increase the probability of staying longer (Gokovali et al., 2007).
while still offering plenty of shopping, bars, and restaurants. There are more than 10 coastal environment-oriented recreational parks where natural environment elements such as water, flowers, forests, trails, and turf grass, and activities such as fishing and swimming are major tourist attractions. Native and foreign visitors enjoy sunbathing, swimming, diving, camping, boating, fishing, and outdoor cooking. Tourism in Dalian has experienced rapid development in the last 20 years, especially the last decade. Tourist arrivals have increased from 12.15 million in 2000 to 35.17 million in 2009. Among the total of 35.17 million arrivals, domestic tourists account for 97% and the remaining 3% belong to overseas tourists including tourists from Hong Kong, Macao, Taiwan, and the rest of the world. In the same period tourism revenue increased from $1345 million to $7442 million. For the total of $7442 million of tourism revenue in 2009, 90% was contributed by domestic tourists and 10% was contributed by overseas tourists. Statistics indicates that tourists from overseas stay in Dalian for 3.40 days per person per trip on average while domestic tourists stay for 3.09 days per person per trip on average. In terms of tourism expenditures, on average each overseas tourist spent $204 per person per day and $693 per trip. By contrast, domestic arrivals spent $63 per person per day and $196 per person per trip (Dalian Statistics Yearbook, 2010). No large differences are observed in terms of lengths of stays between overseas tourists and domestic tourists. One possible reason is that a vast majority of tourists in Dalian are from Asian countries (>75%). The travelers from Asian countries generally have less than 10 h of flight. The other reason may be due to the fact that Dalian is a relatively small tourism city (5.5 million people) where most tourism sites are located fairly close to each other and it does not take many days to have a complete tour although some travelers may stay for 2 to 3 days at one site. One observation which causes concern in terms of regional economic impact consideration in Dalian is that the length of tourism stays of inbound tourists has been decreasing for the last 10 years except for Taiwan's tourists. For instance, in 1997 the number of days' stay for tourists coming from the rest of the world (excluding Hong Kong, Marco, and Taiwan) was shortened to 3.27 days in 2008 from 4.55 days in 1997. The length of stay for Hong Kong's tourists was reduced to 3.32 days in 2008 from 3.77 days in 1997. And similarly, the length of stay for tourists from Marco was shortened to 3.27 days in 2008 from 3.74 days in 1997. Only the length of stay of tourists from Taiwan increased slightly from 3.39 days in 1997 to 3.44 days in 2008 (Dalian Statistics Yearbook, 2009) (Fig. 1). A similar situation happens for domestic tourists and there is no indication that this pattern will change in the near future. The short length of tourist stay is certainly a negative sign regarding the tourism development, which naturally becomes a concern to both local government and tourism business operators. In recent years devising a good strategy to increase tourists' length of stay is a top priority for
3. Contextual setting and data 5 4.5 4
No. of Days
Dalian is located in the southernmost part of the Liaodong Peninsula in northeast China, with the Yellow Sea to the east and the Bohai Sea to the west. It is one of the most important industrial cities in the region and a main seaport of China. Dalian is extolled as the “Romantic Capital” and “Northern Pearl of China.” Dalian was given the honor of being named a “Model Environmental City” by the United Nations on June 5, 2001. It was the first city in China to receive this honor and only the second in Asia. Dalian is also a modern tourism city. It is famous for fashion, football, and its annual beer festival. China's ancient cities (i.e., Beijing, Xian, Hangzhou, and Nanjing etc.), that have numerous historical relics and ruins, temples and museums focus tourism on their long history and rich culture. Dalian, on the other hand, offers a different experience for visitors. It is a famous summer resort with beautiful scenery and pleasant environment providing the visitor a chance to relax by the sea and enjoy the clean air,
3.5 3 Foreigners Hongkang Marco Taiwan
2.5 2 1.5 1 0.5 0
1997 98 99 00 01 02 03 04 05 06 07 2008
Year Fig. 1. Length of stay of inbound tourist in Dalian.
E. Wang et al. / Tourism Management Perspectives 4 (2012) 67–72
the local government tourism administration department. Tourists' length of stay is perceived as critical to increase occupancy rates and make operations run more efficiently. Discovering determinants of length of stay is critical to improve the effectiveness of regional tourism policy. The questionnaire used to construct the dataset used in the present analysis was done in the summer of 2009. It was designed to be a representative, stratified sample of the tourists who visited Dalian, by nationality, routes, and gateways used. The tourist surveys took place at several traffic port areas including the airport, sea ports, railway station, and long-distance coach/bus station. A total of 1576 questionnaires were attempted and 1261 questionnaires were completed and returned (80.2% success ratio). Questionnaires given in port and terminal areas were administered in two languages: Mandarin Chinese and English. A partial list of items covered in the survey include gender, age, education, occupation sector, income, travel party composition, travel motive, alternative destinations considered, and repeat visitation rate. Table 1 lists the frequencies of length of stay. As expected, the highest frequency is three-day stays, typically associated with domestic tourists (frequency: 23.31%). Lengths of stays of 2 and 4 days are frequent: 19.35% and 16.02%, respectively. Seven days of stays was 14.99%. Most surveyed tourists are from northeastern China including the Liaoning province, Jilin province and Heilongjiang province, as well as a small portion from provinces outside northeastern China and overseas. Table 2 contains additional selected, self-explanatory, descriptive statistics for the data gathered. The mean stay is about 3.86 days; (median stay: 4 days) while the standard deviation is 1.83 days.
4. Study methods: an overview of survival analysis Survival analysis is a statistical method for analyzing longitudinal data on event occurrence. In classic medical application survival analysis events may include death, injury, onset of illness, recovery from illness (binary variables) or transition above or below a meaningful threshold. Survival analysis accommodates data from randomized clinical trials or cohort study design, or economic events. The economic meaning of survival analysis is opposite from medicine. The engineering sciences have contributed to the development of survival analysis, which is called “reliability analysis” or “failure time analysis” in this field because the main focus is in modeling the time it takes for machines or electronic components to fail. Likewise, survival analysis has long been a cornerstone of biomedical research. Huygens (1669) curve shows how many out of 100 people survive until 86 years. Survival analysis is commonly used in biological and medical research, and is especially used to test drug efficacy for patient treatments. In tourism economic analysis, days of visit can be modeled as time and outcomes of interest (money spent) can be analyzed as covariates. One of the strengths of using survival
Table 1 Distribution of length of stays. Lengths of stays
Observations (total = 1261)
Frequency (%)
Frequency
1 2 3 4 5 6 7 10
90 244 294 202 176 65 189 1
7.14 19.35 23.31 16.02 13.96 5.15 14.99 0.08
7.14 26.49 49.80 65.82 79.78 84.93 99.92 100.00
69
Table 2 Descriptive statistics for independent variables. Stat.
Days of stay
Edu.a
Travel (km)
Income ($)
Ageb
Sexc
Visit times
Mean Std. dev. Median Mode Min Max No. of obs.
3.87 0.05 4 3 1 10 1261
3.12 0.03 3 4 1 6 1261
1026 25.73 850 397 5 10,000 1261
304 9.08 232.56 77.52 38.76 3101 1261
3.23 0.03 2 2 1 5 1261
0.58 0.01 1 1 0 1 1261
3.30 0.07 3 1 1 20 1261
a 1 = primary school, 2 = middle school, 3 = high school, 4 = college, 5 = graduate school. b 1 ≤ 14-years old, 2 = 15–24 years old, 3 = 25–40 years old, 4 = 41–60 years old, 5 ≥60-years old. c 1 = male, 0 = female.
analysis in tourism economics is the use of covariates and the ability to assess the magnitude of specific influences which can be analyzed and used in strategic planning to maximize tourism dollar spent. Estimation of time-to-event for a group of individuals may involve how long a tourist must stay until the target amount of money they spent can be analyzed. Time‐to‐event can be analyzed between two or more groups, such as local residents vs. long‐range travelers, and to assess the relationship of covariates to time‐to‐event (e.g., age, education). There are certain aspects of survival analysis data, such as censoring and non normality that may confound data analysis using traditional statistical models such as the linear regression model and tests. The variable of interest in the analysis of the length of time that elapses from the initiation of the study to some event occurs and the study is terminated. Individual observations that do not have an event are censored. This survival analysis naturally lends itself to the study of length of stay. The length of time that elapses between the tourist's arrival on a given tourist destination and his departure is survival time. Logistic regression is not appropriate because it ignores time, and time to event is highly important in tourism economics. Survival analysis is a relative newcomer to economic literature. Economists have only recently applied the same body of techniques to strike duration, length of unemployment, time until business failure, agricultural insurance claims, etc. (Hosmer & Lemeshow, 1999; Kieffer, 1988; Wang et al., 2010). Censoring includes lost to follow up, dropping out of the study, or if the study ends before subjects have an outcome of interest. The dataset employed in the present article was collected at transportation ports or stations from tourists who were departing from their trips. Hence, there is no censoring in the data since all interviewees reported their length of stay. Therefore, the discussion that follows is not concerned with censoring. Let Ti represent the duration of tourist at the destination. It is a random variable with a known probability distribution. Different models for survival data are distinguished by different choice of distribution for Ti subset, or days of visit to tourist site. Parametric survival analysis is based on time to event or “Waiting Time” distributions (e.g., exponential probability distribution). Time-to-event for individuals in the dataset is assumed to follow a continuous probability distribution. For all possible times, Ti, after baseline, there is a probability that an individual will have an event at time Ti which is, by design, a non-negative variable. Ti is a continuous probability distribution f(t), where t is a realization of T. One is usually interested in the probability that the visit is of length at least t, which is given by the survival function S(t)= Pr (T ≥t). The hazard rate, h(t), in turn, answers the following question: given that
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the visit has lasted until time t, what is the probability that it will end in the next short interval of time: f ðt Þ ¼ lim
Δt→0
P ðt≤Tbt þ Δt Þ : Δt
ð1Þ
Eq. (1) shows the probability of the failure time (or dollar spending threshold in economics) occurring at exactly time t (out of the whole range of possible ts). The hazard function can be written as, hðt Þ ¼ lim
Δt→0
P ðt≤Tbt þ Δt=≥t Þ Δt
ð2Þ
which is the probability that if you survive to t, you will succumb to the event in the next interval. That is the probability that the visitor will spend ≥x dollars in the next time period: Hazard f rom density and survival : hðt Þ ¼
¼
f ðt Þdt : Sðt Þ
ð3Þ
pðt≤Tbt þ dt&T≥t Þ P ðt≤Tbt þ dt Þ ¼ P ðT≥t Þ P ðT≥t Þ
5. Model specification Although Cox PH assumption is accepted, it would still be enlightening to estimate parametric survival models. Hence exponential, Weibull and Gompertz regression should be carried out and one of them should be selected as best fitting model according to AIC criteria. Then comparison of the results of Cox estimation and best fitting parametric models would give more insights. Notice that the multiplicative or proportional hazards (PH) model is one of the commonly used parametric regression techniques. Parametric regression technique is used to model the underlying hazard/survival function, assuming that the dependent variable (time-to-event) takes on some known distribution, such as Weibull, exponential, or lognormal. Each selected model is utilized to estimate parameters of these distributions (e.g., baseline hazard function) and covariate-adjusted hazard ratios (HRs). Many times interest is more about comparison group than about estimating absolute survival. Generally, several models can be used in the estimation process and their performance can be evaluated via maximum likelihood if parametric models are nested. When parametric models are nested, the likelihood-ratio or Wald tests can be used to differentiate among them. This can certainly be done in the case of Weibull versus exponential, or Weibull versus lognormal. When models are not nested, however, these tests are
Table 3 PH model comparison. Model
Statistics
Nested models Wald test
AIC
Exponential (PH)
LL = − 355.90 χ2(11) = 62.36 (p.v. = 0.0007) LL = − 350.90 χ2(11) = 11.48 (p.v. = 0.0007) LL = − 405.17 χ2(11) = 83.68 (p.v. = 0.0000)
None
877.80
H0:p = 1 → χ2(1) = 162 (p.v. = 0.0000) → Reject Exponential None
660.57
Gompertz (PH) (γˆ = 0.0157)
hi ðt Þ ¼ h0 ðt Þe
:
ð4Þ ð5Þ
Here log hi(t) and h0(t) can take on any form. Overall, 11 covariates were selected given the available data and modeling results are presented in the next section.
Intuitively, the hazard rate is the rate at which visits are completed after duration t, given that they last at least until t.
Weibull (PH) (ˆp = 1.8027)
loghi ðt Þ ¼ logh0 ðt Þ þ β1 xi1 þ … þ βk xik β 1 xi1 þ…þβk xik
f ðt Þ : Sðt Þ
Eq. (3) is derived from Bayes' rule: hðt Þ ¼ pðt≤Tbt þ dt=T≥t Þ ¼
inappropriate and the task of discriminating between models becomes more difficult. Empirical studies show that, in general, there is no one specific parametric model that can perform better than any other parametric model in all statistical test criteria. For this reason, in this paper we choose Cox regression model which is a semiparametric test, that models the effect of predictors and covariates on the hazard rate but leaves the baseline hazard rate unspecified. Cox model is also called proportional hazard regression and it does not assume knowledge of absolute risk; it estimates relative rather than absolute risk. A baseline hazard function that is left unspecified must be positive (equal to the hazard when all covariates are 0). A linear function of a set of k fixed covariates that is exponential (equals the relative risk) is given as:
858.34
6. Results Table 3 presents the summary results of three PH models' log likelihood estimation, ancillary parameters, model discriminating Wald tests and AIC values. The Weibull model dominates the exponential model in all criteria considered. The log likelihood obtained under the Weibull model is higher than the log likelihood obtained under the exponential model. In addition, the AIC value obtained under the Weibull model is lower than the AIC value obtained under the exponential model. Hence, the exponential model is not used elsewhere in this paper, since it is dominated by the Weibull model. The Weibull model yields a higher log likelihood and a lower AIC value than the Gompertz model. Hence, the Weibull model is preferred to the Gompertz model and is the preferred PH model. Now, we can make a comparison of the results of Cox estimation and Weibull model estimation. Table 4 reports the results obtained from the Cox model and Weibull model — the preferred PH model. It should be noted that the coefficients are directly comparable between the models. Both models are presented in PH form and the coefficients may be interpreted as a hazard ratio. Intuitively, and focusing on binary variables, the coefficients presented are of the form exp(βk) and represent the ratio between the hazard rate when the variable takes the value of one and the hazard rate when the variable takes the value of zero. Hence, a coefficient higher than one means that an increase in the variable leads to an increase in the hazard rate and, thus, to a lower expected duration. Inspection of Table 4 reveals that, in fact, the Cox mode tends to produce better results than the Weibull model based on the statistical test performances. For example, the Cox model produces a higher value of Log likelihood than it does by Weibull model, −346.28 versus −350.90, and yet most explanatory variables in Cox model are statistically higher and significant than they are in the Weibull model. Thus, for the sake of saving paper space, we now turn to discuss the Cox model results only. Table 5 reports the results obtained from the Cox regression model. The regression results show that most explanatory variables included in the model are statistically significant at 5% or lower levels of significance (except for Sex, Education (1) primary education, as well as Education (5) graduate education) where Education (1) reaches 10% of significance. Income has a direct relation to the lengths of stay, suggesting that “tourist stay” is a good indicator, and, a higher income earner tends to stay longer than a lower income earner with all else held constant. Male tourists seem to stay longer than female tourists (Sex was designed as a binary variable with ‘0’ for female and ‘1’ for male). These results have important policy implications given the
E. Wang et al. / Tourism Management Perspectives 4 (2012) 67–72 Table 4 Regression results. Variables
Cox (PH) estimation Weibull (PH form; exp(βk))
Sex Age Income/month Education (1) Education (2) Education (3) Education (4) Education (5) Travel (km) Travel times Expt./day($) p Ancillary parameter Weibull γ Ancillary parameter Weibull Log likelihood N
0.022 (0.049) 0.351 (50.57***) 0.000 (8.167***) 0.412 (4.353*) 0.571 (8.363**) 0.414 (5.067**) 0.612 (6.708***) − 0.04 (0.002) 0.000 (48.364***) 0.051 (8.631***) 0.001 (249.54***) 1.9027***
0.0081 (0.541) 0.0124 (0.681) 0.168 (2.254**) 1.051 (1.035) 1.061 (2.497**) 1.242 (2.763**) 1.054 (2.541**) 1.105 (1.556) 0.895 (2.241**) 0.654 (1.762) 0.012 (3.254**) 0.2687*** − 350.90 1261
− 346.28 1261
Figures in parentheses are t-stats in Weibull (PH) model and Wald statistic in Cox (PH) model; Weibull coefficients are hazard ratios; ***, **, and * means significant at the 1%, 5% and 10% level, respectively.
strategic importance of these markets in the overall policy context. However, this finding is different from the report by António and José (2009) in which they concluded that female tourists tend to stay longer than male tourists in their Azores tourism study of Portugal. Age also has a statistically significant positive influence on the lengths of stay; older tourists have a tendency to stay more nights than younger ones. This may owe to the inclusion of other covariates closely related with age such as level of income. As indicated in Table 2, age is a categorical variable with a mean of 3.23, which means that most surveyed tourists are between 25 and 45 years of age. Middle school through college education experience of tourists has direct relations to the length of stay, but it is interesting to note that tourists who had postgraduate education have shorter lengths of stay. This result is consistent with the one found by António and José (2009) where they concluded that higher levels of education are associated with shorter stays and a high level profession is also associated with shorter expected duration of stays. Travel distance exhibits a significant effect on the length of stay. In fact, an ex ante one would imagine that tourists who live far away would experience longer stays, to make up for the increased overall travel cost. Hence, it is indeed the case that tourists who live close to Dalian, such as Anshan, Liaoyang, Panjin, etc. do tend to experience shorter stays than tourists who live farther away as, say, tourists from Jilin and Heilongjiang provinces. Travel time is a numerical variable to reflect the actual repeated number of times a tourist took to visit Dalian. Quite interestingly, it is found that repeat visitors stay for longer periods. As a matter of fact, the more times a tourist visits the area, the longer the stay he or she takes. Repeat visitor behavior has aroused interest in recent years (Kozak, 2001; Lehto, O'Leary, & Morrison, 2004), has its
Table 5 Regression results predicting length of stay (days). Indept. var.
Sex Age Income/month Education (1) Education (2) Education (3) Education (4) Education (5) Travel (km) Travel times Expt./day. ($)
B
0.022 0.351 0.000 0.412 0.571 0.414 0.612 − 0.04 0.000 0.051 0.001
SE
0.100 0.049 0.000 0.197 0.197 0.184 0.236 1.016 0.000 0.017 0.000
Wald
0.049 50.57 8.167 4.353 8.363 5.067 6.708 0.002 48.346 8.6310 249.54
df
1 1 1 1 1 1 1 1 1 1 1
* 5% level of significance;** 1% level of significance.
HR Sig.
HR
.824 .000⁎⁎ .004⁎⁎
1.022 1.42 1.000 1.51 1.769 1.513 1.844 0.961 1.017 1.052 1.001
.081 .037⁎ .004⁎⁎ .010⁎⁎ .968 .000⁎⁎ .003⁎⁎ .000⁎⁎
95% CI for HR Lower
Upper
0.841 1.289 1.000 1.025 1.202 1.055 1.161 0.131 0.999 1.017 1.001
1.243 1.564 1.000 2.223 2.605 2.17 2.931 7.033 1.000 1.088 1.001
71
relationship with future visiting behavior (destination loyalty) and word-of-mouth recommendation carries important policy and marketing implications. Lastly, expenditure per tourist per day exhibits a strong effect on the length of stays. This makes intuitive sense since more expenses in general could result from more days of stay. Certainly, there are some other important determinant factors that should be considered in the investigation of the length of stay if they are available in the dataset. These include but are not restricted to: whether the tourist is domestic or international, marital status, types of accommodation (bed and breakfast, bed only, or all inclusive type, etc.), travel companies, characteristics of tourism product (such as level of hospitality, standard of entertainment, quality of services and facilities, standard of safety and security etc.). Each of them may have a significant effect on the length of stay. Unfortunately, most of those questions are not included in our survey questionnaire mainly due to the consideration of interviewees' cooperation. 7. Conclusion One of the most important decisions made by tourists before or while visiting a given destination concerns their length of stay. In fact, length of stay most likely conditions overall tourists' expenditure and stress imposed on local resources; just to name a few of the implications of varying lengths of stays. However, and as Alegre and Pou (2006) document, despite the rich literature on tourism demand, very few studies have resorted to econometric models in order to shed light on the determinants of length of stay. This paper estimated an econometric parametric survival analysis model to learn the determinants of length of stay, in a novel way in the tourism demand literature. The results suggest that survival analysis may be a fertile ground to analyze tourism demand if time dimension is of the essence, as is obviously the case with length of stay studies. An interesting avenue for future research may lie on tourism demand modeling strategies where time is explicitly modeled, with structural models of consumer demand theory leading to reduced form survival analysis regression exercises, as the ones found in this paper. The results in this paper are statistically significant and economically important. Quite interestingly, a number of covariates, pertaining to detailed individual socio-demographic profiles and actual trip experiences of the representative tourists interviewed, were considered in the regressions in order to control for heterogeneous individual behavior. Concomitantly, the richness of the information embedded in the covariates used allows the design of effective marketing policies, in the sense that the regression results allow one to estimate, for a given synthesized, policy relevant individual or target group, not only mean or median expected stays, but also the probability that stays exceed a given threshold. Hence, policymakers and private operators may benefit from such tools that disclose individual socio-demographic profiles and trip attributes that promote longer stays and act or advertise accordingly. Among the several results found, it can be argued that being a repeat visitor and having a far travel distance are important criteria to identify tourists who are likely to experience longer stays. Thus, future research should characterize such groups and their economic and activity involvement. Level of tourist income and age also play highly statistically significant roles in determining length of stay. This result is very important as the Dalian government, in its quest to promote high quality tourism to attract more higher income tourists to come, is expanding and upgrading airport, and railway station and encouraging the construction of more five-star hotels, and therefore, the government must assess the socioeconomic implications of such proposals. Apparently, such policy is successful in terms of promoting longer stays. A higher degree of education is associated with shorter expected stays. It would be interesting to investigate if this result follows from the idea that better educated tourists face more stringent time constraints or is purely due to differences in preferences across education levels.
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References Alegre, J., & Pou, L. (2006). The length of stay in the demand for tourism. Tourism Management, 27, 1343–1355. António, G., & José, C. (2009). Determinants of length of stay — A parametric survival analysis (pp. 85–104). Bargeman, B., & Poel, V. (2006). The role of routines in the decision making process of Dutch vacationers. Tourism Management, 27, 707–720. Barros, C. P., Correia, A., & Crouch, G. (2008). Determinants of the length of stay in Latin American tourism destinations. Tourism Analysis, 13(4), 329–340. Barros, C. P., & Machado, L. P. (2010). The length of stay in tourism. Annals of Tourism Research, 37(3), 692e706. Carlos, P. B., & Richard, B. (2010). The length of stay of golf tourism: A survival analysis. Tourism Management, 31, 13–21. Crouch, G. (1994). A meta-analysis of tourism demand. Annals of Tourism Research, 22, 103–118. Crouch, G., & Louviére, L. (2000). A review of choice modeling research in tourism, hospitality, and leisure. Tourism Analysis, 5, 97–104. Dalian Statistics Yearbook. (2009). Dalian Statistics Yearbook. (2010). Davies, B., & Mangan, J. (1992). Family expenditure on hotels and holidays. Annals of Tourism Research, 19, 691–699. Fleischer, A., & Pizam, A. (2002). Tourism constraints among Israeli seniors. Annals of Tourism Research, 29, 106–123. Gokovali, U., Bahar, O., & Kozak, M. (2007). Determinants of length of stay: A practical use of survival analysis. Tourism Economics, 14(1), 205–222. Hosmer, D., & Lemeshow, S. (1999). Applied survival analysis. New York: Wiley. Huygens, Christiaan (1669). Annual review of psychology, Vol. 52. (pp. 305–335). Kieffer, N. (1988). Economic duration and hazard functions. Journal of Economic Literature, 26, 646–667. Kozak, M. (2001). Repeaters' behavior at two distinct destinations. Annals of Tourism Research, 28, 785–808. Legoherel, P. (1998). Toward a market segmentation of the tourism trade: Expenditure levels and consumer behavior instability. Journal of Travel and Tourism Marketing, 7, 19–39. Lehto, X., O'Leary, J., & Morrison, A. (2004). The effect of prior experience on vacation behavior. Annals of Tourism Research, 31, 801–818.
Lim, C. (1997). An econometric classification and review of international tourism demand models. Tourism Economics, 3, 69–81. Machado, L. P. (2010). Does destination image influence the length of stay in a tourism destination? Tourism Economics, 16, 443–456. Manning, R. (2001). Visitor experience and resource protection: A framework for managing the carrying capacity of national parks. Journal of Park and Recreation Administration, 19(1), 93–108. Martinez-Garcia, E., & Raya, J. M. (2008). Length of stay for low cost tourism. Tourism Management, 29, 1064–1075. Menezes, A. G., Moniz, A., & Vieira, J. C. (2008). The determinants of length of stay of tourists in the Azores. Tourism Economics, 14, 205–222. Mok, C., & Iverson, T. (2000). Expenditure-based segmentation: Taiwanese tourists to Guam. Tourism Management, 21, 299–305. Oppermann, M. (1997). First-time and repeat visitors to New Zealand. Tourism Management, 18, 177–181. Prato, T. (2009). Fuzzy adaptive management of social and ecological carrying capacities for protected areas. Journal of Environmental Management, 90, 2551–2557. Saarinen, J. (2006). Traditions of sustainability in tourism studies. Annals of Tourism Research, 33, 1121–1140. Saveriades, A. (2000). Establishing the social tourism carrying capacity for the tourist resorts of the east coast of the Republic of Cyprus. Tourism Management, 21, 147–156 (2000). Seaton, A., & Palmer, C. (1997). Understanding VFR tourism behavior: The first five years of the United Kingdom tourism survey. Tourism Management, 18, 345–355. Sung, H., Morrison, A., Hong, G., & O'Leary, J. (2001). The effects of household and trip characteristics on trip types: A consumer behavioral approach for segmenting the US domestic leisure travel market. Journal of Hospitality & Tourism, 25, 46–68. Tassiopoulos, D., & Haydam, N. (2008). Golf tourists in South Africa: A demand-side study of a niche market in sports tourism. Tourism Management, 29, 870–882. Thrane, C. (2011). Analyzing tourists' length of stay at destinations with survival models: A constructive critique based on a case study. Tourism Management, 33(2012), 126–132. Wang, E. D., Yang, Y., Little, B. B., & Li, Z. Z. (2010). Crop insurance premium design based on survival analysis model. International Conference on Agricultural Risk and Food Security 2010. Elsevier ScienceDirect, Available online at www.sciencedirect.com Zhou, D. Q., & Grumbine, R. E. (2011, May). National parks in China: Experiments with protecting nature and human livelihoods in Yunnan province, People's Republic of China (PRC). Biological Conservation, 144(5), 1314–1321.