Vacation length choice: A dynamic mixed multinomial logit model

Tourism Management 41 (2014) 158e167

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Vacation length choice: A dynamic mixed multinomial logit model Anna B. Grigolon*, Aloys W.J. Borgers 1, Astrid D.A.M. Kemperman 2, Harry J.P. Timmermans 3 Department of the Built Environment, Unit USS e Urban Science and Systems, The Urban Planning Group, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

h i g h l i g h t s
Panel data used to develop a dynamic mixed logit model for vacation length of stay.
Individual heterogeneity and state dependency are accounted in the model.
Independent variables include lifecycle stages, month and lagged variables.
Long holidays are most strongly affected by trips made in previous years.
Differences between lifecycle reflect flexibility/constraints typical of each group.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 16 May 2012 Accepted 6 September 2013

This paper uses panel data to develop and estimate a dynamic model of choice of the length of stay of a vacation, controlling for unobserved heterogeneity and state dependency. Length of stay options vary from short (1e3 nights), medium (4e9 nights) to long vacations (10 nights or more) and the decision not to go on vacation in a particular year. Independent variables include family lifecycle stage, income, month and lags of the dependent variable. Results indicate that long holidays are most strongly affected by trips made previously in the same year than medium and short vacations. In contrast, there is an increased need for a vacation when any medium or long trips were not yet made in the current year. Monthspecific variables confirm that respondents have preferences for making leisure trips during the main holidays and warm seasons. The observed differences given the various lifecycle stages reflect imposed constraints given age and/or household composition that are typical of each particular group. Ó 2013 Elsevier Ltd. All rights reserved.

Keywords: Vacation length Dynamic mixed multinomial logit model Panel data State dependency

1. Introduction The increasing interest in vacation travel reflects the fact that the share of leisure, recreation and tourism trips is rapidly increasing in many countries and is expected to further increase due to processes such as increasing wealth, ageing populations, and changing lifestyles. In the Netherlands, our case study, it makes up almost 40% of the total number of trips (KIM, 2010). Further research into the various facets of vacation travel thus seems timely and warranted.

* Corresponding author. Tel.: þ31 40 247 2581; fax: þ31 40 243 8488. E-mail addresses: [email protected], [email protected] (A.B. Grigolon), [email protected] (A.W.J. Borgers), [email protected] (A.D.A.M. Kemperman), [email protected] (H.J.P. Timmermans). 1 Tel.: þ31 40 247 4625; fax: þ31 40 243 8488. 2 Tel.: þ31 40 247 3291; fax: þ31 40 243 8488. 3 Tel.: þ31 40 247 2274; fax: þ31 40 243 8488. 0261-5177/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tourman.2013.09.002

When planning a vacation, tourists need to decide upon various aspects of their trip, including destination, transport mode, accommodation, length of stay and so on. These vacation portfolio variables are known to be strongly interrelated (e.g. Dellaert, Ettema, & Lindh, 1998). In tourism research, the better understanding of each of these variables in the decision making process has been the motivation of many studies. For instance, many authors explored the determinants of the choice of destination (e.g. Crompton, 1992; Huybers, 2005; Nicolau & Más, 2006; Um & Crompton, 1990). Others investigated the choice of accommodation (Yavas & Babakus, 2005), airport and airline (Hess, Adler, & Polak, 2007) or vacation type (LaMondia, Bhat, & Hensher, 2008). Compared to these choice facets, the temporal aspect of the holiday, i.e. length of stay, has been less intensively investigated. However, this topic is highly relevant for tourism management as, for example, longer durations may imply more social, economic and environmental impacts (Barros & Machado, 2010), whereas shorter durations may represent greater administration costs for

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some tourism companies (Martinez-Garcia & Raya, 2008). It is expected that length of stay choice may be dependent on i) the months of the year, as travellers have time constraints, such as for example, limited amount of leave days and school holidays, ii) socio-demographic characteristics, both at the personal and the household level, and iii) choices made in the past. Our study therefore seeks to explore the influence of these factors on the choice of vacation length of stay. To articulate the contribution of this study to the state-of-theart, this introduction section is followed by a summary of previous methods and models applied in studies of vacation length of stay, the role of socio-demographic characteristics and effects of the months of the year. The section ends with a discussion on how the present study aims to contribute to the literature and the structure of the remainder of the paper. 2. Literature review 2.1. Previous studies of vacation length of stay Several studies have involved mainly descriptive analysis of differences in length of stay given tourist’s socio-demographic and/ or trip-related characteristics. For instance, Seaton and Palmer (1997) found that respondents pertaining from social classes D (working class: semi- and unskilled workers) and E (those at subsistence levels: state pensioners, widowers, students etc) tend to spend more days at their holiday destinations. Sung, Morrison, Hong, and O’Leary (2001) found that American domestic travellers with the purpose of visiting friends or relatives had the longest length of stay comparing to other trip purposes. Other studies have adopted more complex modelling approaches. Two main modelling streams can be identified in the literature: duration models (Barros, Butler, & Correia, 2010; Barros & Machado, 2010; Gokovali, Bahar, & Kozak, 2007; Gomes de Menezes, Moniz, & Cabral, 2008; Martinez-Garcia & Raya, 2008) and discrete-choice models (such as tobit (Fleischer & Pizam, 2002; Mak & Moncur, 1979), ordered logit (Yang, Wong, & Zhang, 2011), binomial logit (Alegre & Pou, 2006), latent class (Alegre, Mateo, & Pou, 2011) or nested logit model (Nicolau & Más, 2009)). Even though the cited studies have demonstrated the importance of length of stay in the overall vacation decision-making process, to the best of our knowledge, there is no modelling of length of stay choice accounting for the influence of past choices on actual choices. This inter-temporal dependence, or dynamics, can be ideally captured by means of a panel survey, in which a sample of respondents is followed over a longer period of time. Many authors have suggested the effectiveness of panels in detecting changes in behaviour over time (e.g. Chatterjee, 2011; Kitamura, Yamamoto, & Fujii, 2003), as past choices can affect the probability of selecting a given product/ destination again at a later occasion. The study of a dynamic process on the choice of vacation length of stay not only analyses the effect of previous vacations on a future vacation, but also allows one to explore substitution patterns between short, medium and long-sized vacations. Moreover, repeated observations collected from panel members allows one to control for possible unobserved factors that might contribute to the phenomenon that is being studied (Heckman, 1981; Kitamura, 1990). The modelling of panel data raises new specification issues. However, if heterogeneity in choices is not accounted explicitly, it may lead to model parameters that are inconsistent and/or meaningless (Washington, Karlaftis, & Mannering, 2003). 2.2. The role of socio-demographics characteristics Length of stay choice also seems strongly influenced by sociodemographic characteristics of respondents. For instance, Nicolau

159

and Más (2009) analyzed the effects of income, age, household size and size of the city of residence on length of stay choice and confirmed that (i) tourists with higher incomes prefer taking less holidays with higher quality than the inverse, (ii) younger groups are more likely to take holidays, (iii) larger households have a smaller propensity to go on holiday and (iv) respondents living in larger cities tend to stay more days away from home during holidays. Alegre and Pou (2006) included age, labour status and nationality and found significant parameters only for age. They concluded that younger groups (under 30s) tend to stay less than 1 week on holidays, in contrast with the group over 60 years-old, which usually spend more than 1 week on holidays. Other studies have examined the role of lifecycle, a concept that has played a central role in tourism and travel research since the 1970’s (Cosenza & Davis, 1981). Many authors found that individual’s preferences for travel and consequently travel behaviour changes in response to different lifecycle stages, which is a variable composed by age and household composition. For instance, Oppermann (1995; 1998) focused on destination choice across the lifecycle and found that younger generations gained different experiences when compared to previous generations and tend to make different tourist decisions in later life stages. Collins and Tisdell (2002) suggested that there are differences in travel demand according to both gender and lifecycles. Similarly, Gibson and Yiannakis (2002) indicated that tourist preferences may well be a function of psychological needs that are linked to a particular life stage. Cosenza and Davis (1981) and Fodness (1992) also found that differences across groups in the family lifecycle are reflected in information search and final vacation decisions. Differences were also found in tourist behaviour in relation to the type of vacation taken and expenditures over the stages of the family lifecycle (Lawson, 1991). Davison and Ryley (2009) found that key life stages, like having children and entering retirement, influence air travel behaviour. Finally, Grigolon, Kemperman, and Timmermans (2012) concluded that discount airlines are influencing student’s vacation decisions. Thus, all these studies suggest that lifecycle is an important variable influencing many facets of vacation decisions, including the choice of length of stay. It should therefore be included in any valid model of length of stay. 2.3. Seasonality effects As discussed, the vast majority of studies on vacation decisions have focused on single vacation trips. We contend however that vacation decisions are also influenced by several temporal considerations. One of these is seasonality, a facet of tourism that reflects intra-year fluctuations in the arrival to destinations (Lim & McAleer, 2001). In vacation travel, seasonality can be categorized as natural or institutional. Natural seasonality is usually associated with climate and seasons of the year, whereas institutional seasonality relies on religious, cultural, industrial or social holidays (Hartman, 1986). Most authors analysed seasonality effects in tourist flows by including month-specific variables in their models. For instance, Lim and McAleer (2001) estimated the monthly seasonal patterns of tourist from Hong Kong, Malaysia and Singapore arriving in Australia. Likewise, Koc and Altinay (2007) analysed seasonal monthly variations per tourist spending in Turkey. Similarly, GilAlana (2005) modelled international monthly arrivals to the United States, whereas Martinez-Garcia and Raya (2008) included variables for high and low seasons in their model of length of stay for low-cost tourism to Spain. In general, they found that tourists tend to travel during high seasons and main holidays.

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Table 1 Sample characteristics. Variables

Classes

N ¼ 838 (%)

Gender

Female Male 0e17 18e34 35e54 55e64 >65 Alone Household with children 0 to 5 years-old (Full nest I) Household with children 6 to 17 years-old (Full nest II) Household all members 18þ (Full nest III) Couples Young single Young couple Household with children 0 to 5 years-old (Full nest I) Household with children 6 to 17 years-old (Full nest II) Household all members 18þ (Full nest III) Middle-aged single Middle-aged couple Mature single Mature couple Low (<28.500) Medium (28.501e68.000) High (>68.001) Not working 40 h/week or more Between 20 and 39 h/week Less than 19 h/week Not applicable (0e15 years) Low Medium High Not applicable

47.4 52.6 9.2 6.1 34.0 23.1 27.7 17.2 13.7

Age

Household composition

Lifecycle stages

Year income

Working hours/week

Education

17.8 7.7 43.6 1.6 2.2 9.9 15.3

Fig. 1. Total number of vacations trips per month.

model results are presented. In the last section, the paper is concluded with a summary of results and some policy implications of the study.

8.5 6.1 12.6 5.5 38.2 37.7 43.9 18.5 57.1 12.9 23.2 6.8 12.9 37.7 33.1 16.3 12.9

3. Current research and paper structure Based on the results of this literature review, the present paper aims to contribute to the literature by addressing some specific limitations of previous studies. Particularly, we estimate a dynamic mixed multinomial panel data model accounting for state dependency and unobserved factors that may influence the choice of length of stay for vacation trips. Length of stay options vary from short (1e3 nights), medium (4e9 nights) and long vacations (10 nights or more) and the decision not to go on vacation in a particular month in a specific year. Independent variables include lagged variables related to the number of holidays of each length of stay category that were made previously in the same year, in the last year and two years ago. In addition to these temporal effects that allow us to examine both variety seeking and substitution effects, the effects of sociodemographic factors will be investigated by including traveller’s lifecycle stage characteristics. Following previous research, seasonality will be analyzed by means of month-specific variables. Interaction effects between the dependent and independent variables will be included in the model as combinations of attributes can give an extra positive or negative effect to an alternative’s utility, reflecting non-linear relationships between explanatory variables and choice probabilities. The paper is organized as follows. Next section describes the data source and sample characteristics, followed by some descriptive analysis of the data. Subsequently, the model specification and

4. Data and sample The analysis reported in this article is based on the CVO database (Continu Vakantie Onderzoek, in Dutch), which contains information about annual vacation behaviour of Dutch people. More specifically, panelists are invited to report for four quarters their sociodemographics characteristics and holiday-related variables. This data is collected by NBTC-NIPO Research, a joint venture between the Netherlands Bureaus for Tourism and Congresses (NBTC) and TNS NIPO (part of the TNS Group, focusing on market research), specialized in research in the fields of holidays, business travel and leisure. Each year, approximately 6.500 respondents participate in the CVO panel. However, a selection of 838 respondents participated in the panel between the years 2002 and 2009. They make up the sample for our analyses. The respondents were selected by means of an ID number that was present in all databases. The availability of panel data within tourism research is rare, especially when considering that this sample contains information about the same respondents over a time period of 7 years. In total, they made 16.433 trips over those seven years. The dataset contains numerous socio-demographic and trip-related variables organized in several categories. In the present study only some variables were selected and the data was reclassified in order to simplify the analysis of the groups. The selected socio-demographic variables include personal and household characteristics, and are shown in Table 1. The year 2009 was taken as a reference. Results indicate that in both samples males are slightly overrepresented. The annual income of the majority of the households is not higher than 68.000 Euros and most respondents are not working (young people and retired are included). Regarding household composition, most people indicated to live only with a spouse. Age and household composition were used to create the lifecycle variable. Age was originally in the CVO data a continuous variable, and household composition had many different categorical levels. In order to simplify the classification, age and household composition were categorized in 5 classes. From these, 9 lifecycle categories were created based on the literature (Fodness, 1992; Huntsinger & Rouphail, 2012; Lawson, 1991; Wells & Gubar, 1966). In the present study, the young group is composed by respondents aged between 18 and 34 years-old. In the case of families with younger (between 0 and 5 years-old) and older children

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161

options include 4 alternatives: (1) short, (2) medium and (3) long vacations and (4) the decision not to go on holidays in a specific month, which was considered as the reference level. In order to explore the determinants of length of stay choices, we included the following independent variables in the model: month-specific variables, lagged variables accounting for previous choices, respondent’s lifecycle stage, and income level. The present model formulation follows the traditional mixedlogit model, where the utility Ujimt that an individual i associated with alternative j on choice occasion mt (mth month of year t) may be described as:

Fig. 2. Total number of vacations trips per lifecycle group.

(between 6 and 17 years-old), labelled as Full nest I and II, we believe that the vacation choices are rather affected by the age of the children present in the household than by the age of the parents. The Full nest III group contains household members aged over 18 years-old. We did not differentiate between retired or still in the labour force mature couples or mature singles. We are not considering middle-aged or mature couples as empty nesters because we do not have the information whether they had children or not. The shares between the lifecycle groups indicate that almost 40% of the respondents of the sample were mature couples. Young single and young couples represent less than 4% of the respondents. Before discussing the approach and results of the estimated model it is interesting to descriptively analyze the observed data. Fig. 1 shows the total number of vacations taken from 2004 to 2009. Short holidays were almost equally spread throughout the whole year, with a slight peak in May and June. Medium holidays have their higher peak in May. Long holidays are mostly taken in the summer holidays, which is in July. In the winter period (November to January) the number of holidays is relatively low with medium holidays being the most popular. In sum, medium vacations were the most chosen (49.8%), followed by long (33.5%) and short vacations (16.8%). The present model also includes respondent’s lifecycle stage characteristics as independent variables. The frequency distribution of number of vacation trips taken between 2004 and 2009 illustrated in Fig. 2 shows that mature couples took more vacation trips compared to all other groups. The young groups, in contrast, made less vacation trips. Even though the present model was formulated to capture observed heterogeneity given lifecycle groups, each lifecycle group may still show unobserved heterogeneity not captured by the current model. 5. Model specification and estimation The model applied in the present study is based on the mixedlogit model, which is one of the most powerful discrete choice models that is currently available (McFadden & Train, 2000). One of the many advantages of this model formulation is the possibility to capture unobserved heterogeneity, as it allows parameters associated with each variable to vary randomly across individuals and across alternatives (Bliemer & Rose, 2010; Revelt & Train, 1998). Thus, it is an efficient tool when the data contains repeated choices by the same respondents. Inter-temporal dynamics can be achieved with the addition of state dependency to the mixed logit formulation, by including historical information (lagged variables) of the dependent variable. In the present study, a dynamic mixed multinomial logit model for panel data (dynamic-MMNL) that accounts for heterogeneity in individual preferences and state dependence was estimated, using length of stay choice as the dependent variable. Length of stay

* Uijmt ¼ aij þ bjk Xikt þ qjn Iint þ

11 X

m¼1

ðm1Þ djm Mm þ gj0 jt Nijt

þ gj’ jt1 Nijt1 þ gj’ jt2 Nijt2 þ εijmt The first term (aij) is an alternative-specific constant associated with individual i and length of stay alternative j (j ¼ 1, 2, 3). For the reference level of not going on vacation (j ¼ 4), the utility is equal to zero. The constant was entered in the model as a non-random parameter. * The component bjk Xikt represents the effects of k lifecycle * groups (k ¼ lifecycle categories). bjk is a vector of individualspecific random parameters. Xikt ¼ 1 if individual i belongs to lifecycle group k in year t, 0 otherwise. The value of each random * parameter bjk is drawn from a Normal distribution with a particular mean and standard deviation. A Normal distribution is assumed as we expect preferences to deviate from the mean in both directions equally, that most deviations will be around the mean, and that extreme deviations occur less frequently. This means that for the lifecycle groups not only mean coefficients were estimated, but also the standard deviations (see Table 2). This approach allows the estimation of the distributions for each of these lifecycle groups (except for young singles, which were considered as the reference level), providing a rich array of preference information. Income effect is added by the component qjnIint, where the coefficient qjn is a non-random coefficient representing n income levels (n ¼ low, medium). The highest income level was considered as the reference level. Iint ¼ 1 if individual i belongs to income group n in year t, 0 otherwise. The fourth component captures the effect of month, where djm is a non-random coefficient representing 11 months (December was considered the reference level). Only the effect of a particular month is accounted for in that particular month, meaning that Mm ¼ 1 when m ¼ m and Mm ¼ 0, otherwise. The following three components represent state dependency and the effect of the history of past travel choices (past behaviour). The index j’ illustrates that the alternatives were estimated relatively to each other. Specifically, the coefficient gj0 jt measures the effect of the number of short (j’ ¼ 1), medium (j’ ¼ 2) or long (j’ ¼ 3) vacation trips made previously in the current year (t ¼ 0), last year ðm1Þ denotes that (t ¼ 1) or the year before (t ¼ 2). In addition, Nijt for a given month m, the number of vacations made previously in the current year are summed up from January to the month m-1. For the previous years, Nijt just amounts the number of holidays (per type) made in that year. Most dynamics models include only the effect of the previous period (wave/week/month/year), to account for state dependency (e.g. Chatterjee, 2011). However, in the vacation context, we believe that vacation decisions, especially those involving longer durations and expenditures, can be influenced by choices made up to 2 years ago. Therefore, although our dataset contains vacation information from years 2002e2009, in the present analysis we use the first 2 years of the dataset only to calculate the lagged variables, as Fig. 3 illustrates.

162

Table 2 Model results. MNL (without state dependency)

MMNL (with state dependency)

Medium vacation

Long vacation

Short vacation

Medium vacation

Long vacation

Short vacation

Medium vacation

Long vacation

2.939***

2.395***

3.894***

3.286***

2.702***

4.434***

3.573***

2.949***

4.782***

0

0

0

0

0

0

0

0

0

.415 .211 .320 .013 .078

.165 .066 .401*** .034 .298**

.255 .059 .029 .005 .075

.574(.949) .523(1.08)*** .563**(.954)*** 1.16***(1.39)*** 1.47***(1.63)***

.016(.394) .081(.489)*** .415**(.620)*** .229(.918)*** .883(1.37)***

.082(.757) .005(.573)*** .062(.602)*** .304(.848) .664**(1.31)

.441(.566) .556**(.683)*** .567**(.687)*** .992***(.935)*** 1.034***(.98)***

.028(.007) .126(.160) .385***(.312)*** .253(.423)*** .783***(.818)

.363(.316) .240(.183) .159(.079) .082(.222) .172***(.778)***

.026

.058

.709**(1.09)***

.313*(.718)***

.302(1.13)***

.671**(.635)***

.301**(.305)***

.051***(.709)***

.588** .166

.437*** .080

.124 .279

1.09***(1.28)*** 1.05***(1.27)***

.928***(1.34)*** .291*(.851)***

.671**(1.81)*** .131(1.104)***

1.10***(1.07)*** .980***(.835)***

.803***(.771)*** .333**(.463)***

.251***(.497)*** .061***(.732)***

0

0

0

0

0

0

0

0

.387*** .455*** .280*** .758*** 1.190*** .804*** .751*** .888*** .720*** .589*** .259***

.277* .221 .186 1.074*** 1.937*** 1.871*** 2.680*** 2.180*** 1.624*** .349** .497***

.959*** .299* .014 .039 .569*** .759*** .052 .123 .373*** .021 .405**

.493*** .545*** .185* .821*** 1.343*** .872*** .971*** 1.033*** .828*** .724*** .352***

.337* .371* .397** 1.448*** 2.341*** 2.285*** 3.315*** 2.716*** 2.105 .632*** .135

1.061*** .365** .126 .117 .514*** .675*** .091 .178 .449*** .011 .397**

1.145*** .052 .391*** .266*** .878*** .491*** .661*** .839*** .734*** .671*** .363***

1.125*** 1.025*** 1.027*** .124 1.242*** 1.364*** 2.591*** 2.294*** 1.884*** .545*** .167

0

0

0

0

0

0

0

0

.584*** .213***

.544*** .142***

.579*** .148

.564*** .135

.607** .152

.504*** .128

.341*** .086

.421*** .091

Non-random parameters: Months (dm) (Base level: 0 December) January .546*** February .185 March .213* April .242** May .601*** June .740*** July .080 August .276** September .539*** October .122 November .085 Income (qn) (Base level: 0 High income) Low .882*** Medium .315*** Lagged variables (gtj0 j ) Short, current e year Medium, e current year Long, current e year Short, e previous year

.115

e

e

e

e

e

.185***

.025

.105**

e

e

e

e

e

.005

.240***

.209***

e

e

e

e

e

.325***

.492***

1.541***

e

e

e

e

e

.193***

.084***

.054*

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Constants (aji) (young singles, high income, December) Random parameters: * Lifecycle stages (bk ) (Base level: Young single) Young couple Full nest I Full nest II Full nest III Middle aged single Middle aged couple Mature single Mature couple

MMNL (without state dependency)

Short vacation

Medium, previous year Long, previous year Short, 2 years ago Medium, 2 years ago Long, 2 years ago

e

e

e

e

e

e

.175***

.264***

.220***

e

e

e

e

e

e

.209***

.205***

.703***

e

e

e

e

e

e

.150***

.047**

.026

e

e

e

e

e

e

.065**

.185***

.118***

e

e

e

e

e

e

.039

.192***

.517***

Goodness of fit statistics: LL(0) LL(estimated model) Number of parameters McFadden’s Rho-square (c2) LL ratio test:

83643.45 33135.36 90 .603

83643.45 32256.93 117 .614

Comparison MNL  dynamic-MMNL

Comparison MNL  MMNL

Comparison MMNL  dynamic-MMNL

51 8688.32 68.67

24 6931.46 36.42

27 1756.86 40.11

Note 1: ***,**,*: Significant at 1%, 5% and 10%. Note 2: Standard deviations of random parameters are showed between parentheses.

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Degrees of freedom Dif c2 function Critical c2 (95% sig)

83643.45 36601.09 66 .562

163

164

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Fig. 3. Lagged variables of vacation length of stay.

Finally, εijmt is an unobserved random term assumed to be independent from the other components, and that represents the effect of omitted variables that are not individual-specific but time (month and year) specific. Maximum simulated likelihood procedure is used to estimate the proposed MMNL model. The standard approach to simulation estimation is to use random draws from the specified distribution. For a good performance, very large numbers of draws are required. Train (2003) and Bhat (2001) suggest using a Halton sequence of draws instead of a large number of random draws. These sequences allow drawing from a distribution random numbers which are more uniformly spread over the unit interval. Five hundred Halton sequences were used to estimate the parameters of the present model, using the Econometric software NLOGIT version 4.0 (Greene, 2007). 6. Model results A dynamic-MMNL model was estimated using respondents’ preferences for length of stay choice for their vacation trip. For each length of stay option, the effects of lifecycle stages, income levels, month-specific variables and the lagged variables accounting for the number of previous vacations made in the past were analysed. The indicator variables representing all variables and its levels were dummy coded. The lifecycle stages variables were entered in the model as random parameters. The remaining variables were entered in the model as non-random parameters. Estimation results, showed on the bottom of Table 3, indicate that the dynamic-MMNL model improves the model fit over the MMNL and MNL models. It resulted in a McFadden’s Rho-square value of .614, while .603 for the MMNL model and .562 for the MNL model. Besides, the dynamic-MMNL model provides a higher number of statistically significant parameters. It is interesting though to analyse that the estimated coefficients are very similar, especially when comparing the MMNL and the dynamic-MMNL model.

To test whether the addition of state dependency in the panel data model improves the prediction of future vacation choices, the dynamic-MMNL model was compared to two other models: (i) a multinomial mixed logit model panel (MMNL) without state dependency (without the lagged variables) and (ii) a multinomial logit model (MNL), which does not take state dependency or respondents’ heterogeneity into account. The LL ratio-test (Theil, 1971) was used to check whether the log likelihood of the estimated models provide a statistical improvement over the log likelihood of the base model (LL[0]) (i.e. statistically closer to zero). If so, the model may be thought of as being statistically significant overall (e.g. Hensher, Rose, & Greene, 2005). This test can also be used more generally to compare the goodness-of-fit of hierarchically related models, where the degrees of freedom are equal to the difference in the number of estimated coefficients. If the c2 value exceeds the critical chi-square value, then the specified model performs significantly better than the comparison model. If on the other hand, the c2 is less than the critical chi-square value, it is not possible to conclude that the specified model is better than the base model. For the present analysis, the LL ratio tests comparing the MNL and the MMNL with the dynamic-MMNL model are reported on Table 3. It shows that the dynamic-MMNL is statistically different than the other two models. Based on these results, it may be concluded that individual heterogeneity in responses exist, and that the inclusion of information about past vacation choices provides better model results. Thus, we will only discuss the estimated coefficients for the dynamic-MMNL model in the remainder of this article. The estimated coefficients are shown in Table 3. The t-statistics of each part-worth utility, represented by the stars, indicate any significant differences against the base alternative (no trip) and the base group (young singles). In the case of the random parameters, i.e., parameters for lifecycle groups, the standard deviation is indicated between parentheses. The parameters for the constants represent choice behaviour of young singles, with high income and travelling in December. All remaining parameters represent deviations from this reference. Regarding the effects of the lifecycle stages in the choice of vacation length, coefficients for short trips are negative for all lifecycle groups, meaning that these groups tend to make less short trips than the base level group, which was dummy-coded and is represented by the young singles. The same holds for medium trips, except for the young couples, with a positive but non-significant coefficient. Finally, the young couples and families (full nest I, II and III) tend to make more long vacation trips than the young single

Table 3 Calculation of average probabilities for two case scenarios. Attribute Constant Lifecycle Income Month Number short (current year) Number medium (current year) Number long (current year) Number short (1 year ago) Number medium (1 year ago) Number long (1 year ago) Number short (2 years ago) Number medium (2 years ago) Number long (2 years ago)

Case 1 Full nest I Medium July 1 1 0 3 2 1 2 1 1

Average Probabilities Case 1 Average Probabilities Case 2 Note: standard deviations showed between brackets.

Case 2

Short

Medium

Long

Full nest I Medium July 0 0 0 2 1 0 1 0 0

3.573 .556 (.683) .128 .091 .185 .005 .325 .193 .175 .209 .150 .065 .039

2.494 .126 (.160) .086 .661 .025 .240 .492 .084 .264 .205 .047 .185 .192

4.782 .240 (.187) .091 2.591 .105 .209 1.541 .054 .220 .703 .026 .118 .517

3.4% 2.3%

14.0% 9.9%

40.8% 13.8%

No vacation 0 0 0 0 0 0 0 0 0 0 0 0 0 41.9% 74.0%

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group, but the effects are insignificant. The other groups appear to prefer long holidays less; their estimates are significantly negative. It should be noted that the high standard deviations imply that even within the lifecycle groups, preferences are quite heterogeneous. Month-specific significant coefficients for short trips indicate higher preferences for June, May and September and lower preferences for January, February and November. Medium vacations are preferred from April to October, but the highest coefficient is in May, when Dutch schools have their spring vacation. Preferences for medium holidays are low for January, March and November. Long vacations are mostly taken in July, August and September, but June, May and October are also highly chosen months for longer breaks. The least chosen months in general are in the winter, as indicated by negative (or close to zero) coefficients from November to March. These results confirm respondent’s preferences observed in the descriptive analysis of the data, shown previously in Fig. 3. In the case of income, model results show that utility linearly increases with increasing income, which is an expected finding. The estimated coefficients show significant effects for almost all length of stay lagged variables, which capture the effects of the number of previous vacations trips on the choice of a future vacation. Short holidays made in the past have a positive influence on the choice of a future short holiday. It means that there is a tendency for making short trips when other short trips were previously arranged. The influence of previous short vacations in the choice of a future medium or long trip is less substantial, expressed by coefficients that are positive, but relatively close to zero. Medium length vacations taken in the current year do not affect the choice of a short holiday, but have a negative influence on the choice of a medium or long vacation. Similarly although much stronger is the effect of a long holiday already taken in the current year. Coefficients decrease as length of stay grows higher, meaning that the probability that another vacation will be arranged if a long vacation was already taken in the current year is lower, especially for long vacations. In contrast, coefficients are positive and significant for vacations taken in previous years, indicating that there is an increased need for a future trip when a vacation was not yet arranged in the current year. On top of that, short, medium, and long holidays made in previous years especially affect the probability of making a corresponding holiday. This may be considered as an indication of habitual behaviour. 7. Scenarios The dynamic-MMNL model can be used to simulate scenarios based on the estimated utilities for each attribute level. The total utility of a particular length of stay choice can be calculated by summing the part-worth utilities of each attribute level according to the utility function presented in Section 5. The overall utility of a particular set of attributes can be compared with another, to estimate the preference for each length of stay option given changes in lifecycle, income, month and/or length of stay lagged variables. Because the dynamic-MMNL model includes both random and non-random parameters, the choice probabilities could be calculated by applying Monte Carlo simulation. It was done by drawing a random number from the normal distributions of each random parameter and calculating the choice probability. For the nonrandom parameters, only the means were considered. Simulation was conducted by taking ten thousand random draws and averaging the probabilities calculated per draw according to the MMNL formula. Table 3 illustrates an example for a respondent pertaining from the group Full Nest I, middle level income and travelling in July. In

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the first case, the probability of choosing a short, medium, long or no vacation is respectively 3.4%, 14%, 40.8% and 41.9%. In the second case, fewer previous holidays of each kind were made. Therefore, the probabilities of making short, medium or long holidays are smaller (2.3%, 9.9% and 13.8%) than compared to the previous case, whereas the probability of not making a holiday is higher (74%), which is expected because in the second case as fewer trips were made previously, the propensity to travel is smaller than in the first case. 8. Conclusion and discussion In the present study we developed a dynamic mixed multinomial logit model (dynamic-MMNL) for vacation length of stay choice. The dynamic model accounts for both state dependence and heterogeneity in respondent’s preferences. The panel data includes information about vacation trips made by 838 Dutch respondents, from years 2002e2009. Length of stay options include short (1e3 nights), medium (4e9 nights) and long (10 nights or more) vacations, and the decision not to go on vacation in a particular month in a specific year, used as the reference level in the model specification. The effects of seasonality and lifecycle stage characteristics in the choice of vacation length of stay were explored. The relevance of the approach was also exemplified with the application of case scenarios. Results demonstrated that the proposed model formulation is valuable to analyse tourist’s choices over time as it allows parameters associated with each variable to vary randomly across individuals. The high McFadden Rho-square value and most estimated coefficients being significant confirm the successful application of the dynamic mixed multinomial logit model. Besides the robust formulation of the mixed-logit model (McFadden & Train, 2000), the inclusion of dynamic aspects, by means of lags of the dependent variable was the most important contribution to the existent literature on vacation length of stay choice (e.g. Alegre et al., 2011; Alegre & Pou, 2006; Nicolau & Más, 2009). Length of stay choice was associated with three different aspects: seasonality, lifecycle stage characteristics and the influence of past choices. Seasonality effects were accounted with the inclusion of month-specific variables. Results indicate that Dutch vacationers have preferences for taking their vacation during the main holidays periods and warm seasons. Martinez-Garcia and Raya (2008) included a binary variable capturing seasonality (high versus low seasons) and confirmed that travelling in high seasons further increase the amount of days spend on holidays. Complementarily, Nicolau and Más (2009) found that larger number of days available for holidays, which are usually associated with main holidays, increases the duration of stay. The observed differences given the various lifecycle stages reflect imposed constraints given age and/or household composition that are typical of each particular group. For instance, Alegre and Pou (2006), Martinez-Garcia and Raya (2008) and Nicolau and Más (2009) found that the mature group have preferences for longer trips. Our findings also suggest that young tourists tend to take more short breaks in comparison to mature tourist, which may be due to the total costs involved. None of the previous studies considered lifecycle stage as an exogenous variable, the closest association can be found with respect to household size, explored by Nicolau and Más (2009). They found that larger household size reduces the propensity to go on holidays. However, they did not explore the role of household composition. We believe that the vacation choices are rather affected by the age of the children present in the household than by the age of the parents. Therefore, our results suggested that a household with small children involves a much more extensive

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vacation planning, which may be linked to taking vacations during main holidays, which in general involves longer durations of stay. None of the consulted literature explored the effect of previous length of stay choices in future plans. Our results suggest that long vacations are the most strongly affected by trips made previously in the same year compared to medium or short vacations, which is an expected finding as long vacations are usually associated with greater distances and therefore, higher costs. In contrast, we found that there is an increased need for a vacation (short, medium or long) when any medium or long trips were not yet arranged in the current year. In addition, coefficients indicated that short, medium, and long holidays made previously more strongly affect the probability of making a corresponding holiday, which is an indicative of habitual behaviour in the sense that the effect of a particular vacation length made in the past affects travellers’ choice of a future vacation with the same vacation length. Habitual behaviour in Dutch people’s vacation decision making was also found by Bargeman and van der Poel (2006). The findings indicate that especially the month-specific variable strongly influences the choice of a vacation. The study of the determinants of length of stay choice is important for both tourism marketers and policy makers. Shorter vacation periods may imply visiting only major touristic points, whereas longer durations allow tourists to better explore the city, generating more social, economic and environmental impacts (Barros & Machado, 2010). In relation to destination marketing, Alegre and Pou (2006) confirm that length of stay is a relevant facet of the vacation as it determines the revenue for tourism. This implies that in general longer lengths of stay are at first sight responsible for higher profits (i.e. regarding to tourist accommodations), but shorter lengths of stay allow an increased number of tourists to visit a destination and make a larger contribution to tourism revenues, especially in the higher seasons. From the point of view of urban planners it is also relevant to know the total number of visitors as a function of the number of days spent at the destination. For instance, shorter stays imply higher demand for public transport, as there are more people arriving at airports, bus or train stations, implying higher efforts to manage the accessibility to hotels and other touristic areas. It should be noted that vacation length of stay is very likely to be affected by other variables such as destination type and distance, available transport modes, etc. These variables were not considered in this study because it would add in model complexity and number of parameters, and the present model was already quite complex. Future research should include these and other variables that might influence the vacation length of stay. Acknowledgement The study was conducted as part of the project “The value of recreation: Now, and in a completely different future”, which is part of the DBR (Duurzame Bereikbaarheid van de Randstad e Sustainable Accessibility of the Randstad) programme. It was financially supported by the Netherlands Organization for Scientific Research (NWO). References Alegre, J., Mateo, S., & Pou, L. (2011). A latent class approach to tourist’s length of stay. Tourism Management, 32(3), 555e563. Alegre, J., & Pou, L. (2006). The length of stay in the demand for tourism. Tourism Management, 27(6), 1343e1355. Bargeman, B., & van der Poel, H. (2006). The role of routines in the vacation decision-making process of Dutch vacationers. Tourism Management, 27(4), 707e720.

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Dr. Anna Grigolon is a researcher at the Eindhoven University of Technology since 2009. Her research is focused on modelling dynamics aspects of recreation behaviour and agenda formation, with a lifecycle perspective. She has research interests in modelling choice behaviour and spatial decisions support systems

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MSc. Aloys Borgers is an associate professor of urban planning at the Eindhoven University of Technology, the Netherlands. His research interest is in modelling behaviour of (groups of) individuals in urban contexts in order to support spatial decision-making. Specific application domains include transportation, retailing, housing, and recreation and tourism.

Dr. Astrid Kemperman is an assistant professor of urban planning at the Eindhoven University of Technology, the Netherlands. Her research focuses on the impacts of urban environments on individuals’ leisure choices and tourist route and activity choice behaviour. She has a specific interest in modelling dynamic aspects of tourist choice and shopping behaviour.

Harry Timmermans is chaired professor of urban planning and director of European Institute of Retailing and Services Studies (EIRASS) at the Eindhoven University of Technology. He holds research interests in modelling spatial choice behaviour and spatial decision support systems in a variety of application context, including retailing, tourism, recreation, transportation and housing.