Cruise passengers’ expenditure in the Messina port: a mixture regression approach

. In this study, we assess the determinants of cruise ship passengers and crew members expenditure disembarking in the port of Messina (Sicily, Italy), by applying both linear and concomitant mixture regression models. It is shown that duration of visit, nationality, occupation previous visit to Messina and satisfaction an eff ect on expenditures and that there are three diff erent profi le in expenditure are statistically signifi cant. Th is study enables one to obtain the necessary information to implement more adequate tourism policies in a fastest growing sector in the travel market. characteristics and experience in two ports of call in Uruguay, they use a multivariate market segmentation analysis. Th e study identifi es distinct segments by country of residence, occupation, locations visited in Uruguay, satisfaction and previous visits to the country.


INTRODUCTION
Cruise tourism is one of the faster growing sectors of global tourism, with been the fastest growing segment in the travel sector around the world. In 2014, a record 6.39 million Europeans took a cruise, 30,000 more than in 2013. Th is marks a 0.5% growth of Europe's source market compared to the previous year.
While the year-on-year growth rate has considerably slowed down compared to previous years, it is remarkable that more Europeans than ever chose a cruise holidays in 2014 in spite of the continuing challenging economic conditions. Th e average annual growth in the last fi ve years has been positive at 4.9%. Th is confi rms that cruising remains an excellent holiday choice for millions of passengers in Europe and beyond, providing great value for money.
Italy remains Europe's third largest source market, despite a 3.1% decrease, with 842,000 passengers. Th e factors behind the reduction in the industry's growth rate include a decrease in capacity in the Mediterranean and the continuing economic diffi culties throughout much of the European Union. Despite the decline in the Mediterranean cruises, the Italian market is dominated the Mediterranean cruises is the best choice for Italian market (79% of passengers in 2014) and the average annual passenger growth trend since the crisis began in Italy is 3.9%.
Th e elements that express the importance of the cruise sector are represented primarily by showy and persistent processes of expansion for over two decades characterize the cruise market, with demand fl ows that, in the last decade, have maintained growth rates such by doubling the total number of cruise worldwide.
Our study is based on a survey performed in Messina, the 3rd largest in Sicily (after Palermo and Catania) the 13th largest city in Italy (with a population of more than 240,000 inhabitants) and the 10th port in Italy for handled passengers in 2014. Th e city's main resources are its seaports (commercial and military shipyards), cruise tourism, commerce, and agriculture (wine production and cultivating citrus).
Th e aims of this study ware to provide a starting point for a correct planning and management of tourism development, describe the profi le of average tourist and estimate the diff erent determinants of tourist spending according to the importance that each one has in global spending. In this paper most attention was focused on measuring visitor spending because it is, together with the number of visitors, a critical factor in terms of magnitude of the economic impacts. For this purpose we will use both classical linear regression model and mixture regression model according to which it is possible to hypothesize that the statistical distribution of the average expenditure carried by tourists, empirically observed on a sample is the mixture of their distributions of two or more distinct groups among them but mixed in proportions unknowns.
Th e paper is organized as follows: in the next section we present a review of literature, in the section 3 the survey methodology and a descriptive statistics of the main characteristics of cruise passengers and crew arriving to Messina. In Section 4 we briefl y provide a description of the methodologies and in section 5 we present the empirical results. Some fi nal remarks will conclude the paper.

LITERATURE REVIEW
A review of literature reveals a large number of empirical studies aimed at measuring the demand for tourism, both in terms of number of tourists and their expenditures. Some authors have modeled expenditures levels as function of socio-demographic, trip-related and psychographic variables, plus budget constraints. Recently, Hung et al (2012) and Marcussen, (2011) have used of Ordinary Lest Squares OLS estimation, in order to consider only the average response of tourist expenditure to changes in its determinants while possible diff erences among consumer segments are overlooked. More recently, quantile regression was adopted in tourism study by Chen and Chang (2012) on the infl uence of travel agents in Taiwan, and by Marrocu et al (2015) on the eff ect of the main determinants of tourist expenditure to non -resident tourists in Sardinia. Abbruzzo et al (2014) have introduced the use of graphical models for assessing the determinants of individual tourist spending in Uruguay, emphasizing with these models have the advantage of synthesizing and visualizing the relationships occurring within large sets of random variables, through an easy interpret output. While in literature there are numerous studies of tourist expenditure, the research of the cruise tourism expenditure has become more popular since the beginning of this decade. Kester (2003) asserts that main obstacle for the analysis of economic impacts is the absence of data describing the economic behavior of the tourist. Th e sudden growth in demand for cruising points to numerous impacts arising from its accelerated development. Many authors address the impacts of cruise tourism development in diff erent ways, e.g. Carwright and Baird (1999) mention the social, technological, economic, political and environmental impacts. Brida and Zapata (2010) elaborate on economic, political, socio-cultural and environmental impacts. Gargano et al (2012) estimated the ECSI (European Customer Satisfaction Index) model parameters using a PLS (Partial Least Square) approach in order to identify the types of cruise passenger who visit Messina, and determine the main social and environmental variables that infl uence their levels of satisfaction. Th ey showed that most of the tourists visiting Messina have relatively high levels of satisfaction, but the satisfaction level was infl uenced by perceived value which seems to be a dimension of strategic importance as a mediator of the eff ects on the perception of quality satisfaction.
At the same time, economic impacts are the main topic of numerous research work for example Dwyer and Forsyth (1998) developed a framework for assessing the economic impact of cruise tourism for nation and its sub regions. Four types of travel expenditures must be calculated to measure the economic contribution of cruise industry: (1) passenger-related expenditure; (2) crew-related expenditure; (3) vessel-related expenditure; and (4) support expenditure. Henthorne (2000) in a study of factors determining expenditure of cruise passengers looks at how much money was actually spent by cruisers while in port as well as the infl uences on these expenditures. Th e results reveal that vendors who are perceived as friendly, helpful, and knowledgeable fare better than those who come across as manipulative and aggressive and that older consumers can be expected to spend more in port than their younger counterparts. It suggests that cruise lines select particular ports providing their customers with positive in port experiences and are willing to change itineraries and drop specifi c port of call if an inordinate number if customers experiences dissatisfaction. Brida and Risso (2010) estimated a cross-sectional regression model in order to analyze the diff erent variables infl uencing cruising expenditure levels in Costa Rica. Th ey showed that heavy spenders are distinguishable from the other segments in terms of income levels, hours spent out of the ship, nationality, age and their spending pattern. Brida et al (2012) estimated two cross-sectional regression models for the cruise expenditures, showing that the group size the visitors travel with and the mobility the visitors have within the country are the most important variables to explain individual expenditure behaviour. Th ey provided a better understanding of the cruise industry, considering the expenditure of cruise ship passengers disembarking in the ports of call of Montevideo and Punta del Este as a key variable in the economic analysis of the cost and benefi ts. Brida et al. (2014) provide a better understanding of cruise travel from passengers' characteristics and experience in two ports of call in Uruguay, they use a multivariate market segmentation analysis. Th e study identifi es distinct segments by country of residence, occupation, locations visited in Uruguay, satisfaction and previous visits to the country.

DATA AND STRUCTURE OF THE QUESTIONNAIRE
Our study is based on a survey performed in Messina's city, where cruise tourism is becoming increasingly important, as a result, cruise passengers' expenditures are increasingly contributing to the local economy. 1995 to 2014 the number of cruise passengers in the City increased by 1085.95% (from 26.959 passengers in 1995 to 319750 in 2014). We interviewed cruise passengers and crows members in the cruise terminal port Messina at the end of their tour when they are returning to their cruise from march 1 to October 30 2014. We have chosen to interview tourists and crew members at the end of their tour once all the Messina city expenses had been incurred allows us to obtain a more reliable measure of tourist expenditures and to avoid its estimation (Marrocu et al. 2015, Craggs & Schofi eld, 2009).
Structured self-administered questionnaires were preferred, as they have higher response rate and the interference of the researcher is minimized (Oppenheim, 1992). Th e questionnaire, designed for this study, was reproduced in 5 languages (Italian, English, French, German, Spanish) and was composed of three sections for a 35 items total. Th e fi rst section collects socio-demographic information on the interviewees, the second section aims to measure overall expenditure. Travel expenditure includes the total consumption of goods and services made in the city divided into seven expenditure categories: food and beverage, handicraft, clothes, personal services (hairdresser, beautician), public transport, pharmaceutical, other (telephone and internet, watch and jewellery and museum tickets). Th e third part aims to obtain information about motivations, satisfaction for the city and its services and the intention to return to Messina or recommend it to other tourists. In terms of the response format, the 5-point Likert scale was used (''1'' Strongly Disagree-''5'' Strongly Agree), as it has been consistently documented (e.g. Andereck & Nyaupane, 2011;Vargas-Sanchez et al., 2009).
We used a two-step stratifi ed sampling approach to select our sampling. At fi rst, cruise ships were selected randomly from a list of boats expected to stop at the Messina port through systematic sampling. In the second stage, interviewees from travel groups were chosen to ensure equiprobability, in this layer we stratifi ed by type of visitors and we assigned a share of to 85% cruise ship passengers and 15% to crew members. We collected a total of 5.500 valid questionnaires. Table 1 reports the socio-demography profi le of all respondents (cruise passengers and crew members). Overall, the majority of survey respondents were male (52.78%); were aged 46 or older, have at least secondary education level (85.01%) and visit Messina for the fi rst time (78%). Among the cruise passengers, 72.21 percent were travelling as family, 55.22% were more aged 55 or older (48.52%), 49.01% percent were retired, 45.55 % were on holidays from work and 1.59% were not currently working, 3.85% were students. Over 78% of passengers were from Europe countries, and of these 29% were from Italy, 12% from USA and Canada, only 8.5% from other countries. Crew members were predominantly from Asia (70%) followed by 22% from Europe and 8% from other countries; they, were more likely to be younger than 35 (85%) and they are rooms and kitchens personnel (56.45%) and engine room personnel (33.91%) especially.  Table 2 reports average and percentage of cruise passengers and crew members expenditure. Th e 95% of visitors spend at least 1 euro; in particular, cruise passengers approximately expend 88.62 euro on average and crew members expend 75.71 euro on average. Th ey spend mainly for food and beverage (26.35 euro and 23.50 euro respectively) and clothes (28.62 euro and 25.32 respectively), but should not be underestimated expenses for personal services (10.25 and 8.95 euro respectively). Our results underestimated the expenditure incurred by cruise passengers and crew members described in a previous research of Penco (L. Penco, 2013). Th e mean scores and standard deviation of tourists' (cruise passengers and crew members) satisfactions on each of the 7 attributes were reported in table 3. Th e mean score is medium-high for overall rating of Messina city, in particular the very high score is observed in food and beverage and in the medium range for shop, kindness of local people and historical and cultural heritage, and low scores are observed for public transport and general organization.
A comparison of tourists satisfaction levels and cruise member satisfaction levels using t test for independent samples indicated that there are not a statistically diff erences signifi cant (all p-value > 0.05).

THE EMPIRICAL MODEL
In this paper we assess the eff ect of the determinants of visitor expenditures by applying both linear model and concomitant fi nite mixture model. A general linear model can be written in matrix notation as: is a column vector of observations, ε = (ε 1 , ε 2 ,…, ε n )′ the error column vector, we assume that ε , 0 ( 2  N ), β = (β 0 , β 1 , β 2 ,…, β p )′ is the column vector of parameters, and X, called design matrix, is the j×p matrix of independent variables (with a column of 1 in the fi rst column for the intercept).
Th e log of the distribution was performed in order to alleviate the potential heteroskedasticity and to normalize a distribution. Th e explicative variables included are related to the distinct sets, in particular: socio-demographic characteristics (age, gender, education level, residence, occupation status), trip characteristic (length of visit (in hours) and season of visit (low season or high season, use of public transports) and psychographic characteristics (previous holiday in Messina and recommendation Messina to friends and relatives).
Successively, according the idea that not all tourists have the same opportunity and desire to spend money in a specifi c place, we have applied a fi nite mixture model that provides a natural representation of heterogeneity in a fi nite number latent class (McLachlan e Peel, 2000) and in order to exploit the covariates, we fi t a concomitant variable mixture model (Dayton and Macready, 1988). Finite mixture models are a popular technique for modeling unobserved heterogeneity or to approximate general distribution functions in a semi-parametric way. Th is models suggest that the statistical distribution of the average expenditure carried by tourists, empirically observed on a sample is the mixture of their distributions of two or more distinct groups among them but mixed in proportions unknowns (Kamakura e Russell 1989;Wedel e Desarbo, 2000). With this approach it is possible to identify homogeneous subsets of tourists on the basis of the estimated relationship between a dependent variable and a set of explanatory variables (sociodemographic characteristics, trip characteristics and psychographic characteristics).
Th e mixture is assumed to consist of K components where each component follows a parametric distribution. Each component has a weight assigned which indicates the a priori probability for an observa-tion to come from this component and the mixture distribution is given by the weighted sum over the k components. If the weights depend on further variables, these are referred to as concomitant variables. In a concomitant variable mixture model the component probabilities of the fi nite mixture vary across subjects according to a vector of covariates (usually including a constant for the intercept). Th e mixture model is given by: where: Th e parameters of the mixture model are usually estimated by maximum likelihood using the Expectation-Maximization (EM) algorithm (Dempster et al, 1977, McLachlan andPeel, 2000). Th e EM algorithm has the advantage of providing a general framework for estimating diff erent kinds mixture models as often only the M-step has to be modifi ed if diff erent component specifi c models are used. In addition, already available tools for weighted maximum likelihood estimation can be applied.
Fit indices such as the log-likelihood (logLik), the Integrated Complete Likelihood (ICL; Biernacki et al. 2000), the Bayesian Information Criterion (BIC) and the Consistent Akaike Information Criterion (CAIC; the lowest score being the best solution of the appropriate number of segments) are used to determine the number of groups. Th ey are of the form twice the negative loglikelihood plus number of parameters times k where k = 2 for the AIC and k equals the logarithm of the number of observations for the BIC. Th e ICL is the same as the BIC except that the complete likelihood (where the missing class memberships are replaced by the assignments induced by the maximum a-posteriori probabilities) instead of the likelihood is used.

Linear regression model
Preliminary, according to literature, a regression model in which the depend variable was total visitors' expenditure and the covariates were all the other considered variables was estimated in order to verify the possible relationship between expenditure and characteristic and satisfaction of visitors. Table 4 presents the results of the estimation of general linear model to total expenditure of visitors (passengers and crew members). We considered all visitors together because there are not diff erences between two typology for expenditure and for general satisfaction. Each estimated eff ect must be considered as the expected response to a change in a given determinant of visitor expenditures in Messina. It is important recalling that as most covariates are binary variables and the coeffi cients must be interpreted as the diff erential eff ect with respect to that associated with the reference case. Th e R 2 value (0.719) shows high explanatory power of our model. Our results confi rm previous evidence on socio-economic characteristics, gender and education level are not found to signifi cantly infl uence holiday expenditure (Marrocu et al 2015, Wang et al 2006, and as for age, we fi nd a small positive eff ect; in particular it possible to show that older visitors spend more than younger ones. Focusing on the occupation status, we fi nd that unemployed and the students spend less than employed tourists. Unemployed visitors tend to spend 8% less on average, while students spend 10% less with respect to employed tourist. On the contrary, retired people tend to spend more than people still employed. Foreign tourists, in particular tourists from USA and Canada, have a signifi cantly higher level of expenditure with respect to Italian tourists. Focusing on trip characteristic our fi ndings show that the visitor who pass more hours in the city spend more money, and that tourists taking their holidays during the high season period (mainly July and August) tend to expend less. A possible explanation is that in this months in the shops there are the summer sale or that during the high season period tourists tend to compensate the travel expenditure (in July and August cruise prices increase) with the expenditures for shopping.
Observing the results on the psychographic characteristics, it's possible to show that visitors with previous holiday in Messina spend 5% more than to fi rst time ones. Th is result, in line with some previous evidence (Rosenbaum andSpears, 2005, Marrocu et al 2015), may be due to the fact that returning tourists are likely to have spent satisfactory holidays in the past and therefore are more inclined to spend more money.
Finally focusing the attention on satisfaction levels, we fi nd that more satisfi ed visitors tend to spend more respect to unsatisfi ed ones, supporting the idea that higher satisfaction levels result in signifi cant increases of expenditure.

Concomitant mixture model
Th e concomitant variable fi nite mixture model (1) is fi tted to a response variable y i defi ned as the logarithm of total expenditure of visitors during the visit at Messina. In this study, the logarithm of total expenditure of visitors during the visit at Messina by concomitant variable fi nite mixture model (1) is modeled in order to individualize the possible factors infl uencing expenditure in visitors (cruise passengers and crew members) with diff erent satisfaction levels (concomitant variables). Th is choice is due the awareness that higher satisfaction levels result in signifi cant increases of expenditure and, which in turn, may depend on diff erent covariates, within each subgroup. Th e mixture regression models represent the methodologically adequate solution, because it allows us to study if the visitors expenditure depends on various factors in visitors with diff erent satisfaction levels (concomitant variables).
In this paper, conditionally on the latent class, we assume that y i follows a Gaussian distribution with mean ( )  Th e following step is to identify regressors by using the BIC again from the our three component finite mixture model identifi ed above. Diff erent Gaussian mixture models with three components are fi tted: a model with all covariates ignoring the group (level of satisfaction), a model with all covariates considering the group (level of satisfaction) as concomitant variables, diff erent models with only few covariates and the groups as concomitant.
Th e BIC value is used for models comparison and we preferred the model with BIC smaller. Th e fi nal model is a concomitant Gaussian mixture model including the constant and fi ve covariates: nationality (in this model we considered the nationality as binary variable where 0 is Italian and 1 is non Italian), length of visit, season, previous holiday in Messina, recommendation to Messina. Table 6 shows the parameter estimates, the standard error, z value and p-values. It is important emphasize that the three components are very well separated and that the fi rst subpopulation is composed mainly by visitors with high levels of general satisfaction, the second subgroup is mainly constituted by visitors with medium-high levels, fi nally the third component is formed by visitors with low satisfaction levels.

CONCLUSIONS
In this paper we proposed to estimate expenditure distribution by general linear model and by concomitant Gaussian mixture model.
Our analysis was based on sample 5.500 of cruise ship passengers and crew members face to face interviews conducted in spring -summer 2014. Th e case study was Messina, a Mediterranean port of call in the island of Sicily (Italy). Empirically a general linear model has been run to investigate what socio-demographic, trip-related and psychographic characteristics may have potential eff ect (infl uence) on cruise tourists expenditure in Messina. Successively, a concomitant Gaussian mixture model was used for the analysis of heterogeneous populations, such as visitors and tourists, in order to explain part of heterogeneity with known explanatory variables. In this contest the applications of standard statistical models, such as linear regression, model the population average, which is the mean response of all individuals, without considering the existence of possible subpopulations.
A descriptive framework it is possible note that the 95% of visitors interviewed has spent at least 1 euro, and an economic benefi t that should not be overlooked is the value of return visitation and word of mouth recommendations. Th e survey data indicated that the 78% of visitors has the high likelihood of recommending Messina visited to family and friends.
According previous evidence our results confi rmed the role played by foreign nationality on cruise visitors expenditure; occupational status (students and unemployed spend less to retired and employed), duration and period of visit (the visitors who pass more hours in Messina and visit the city in high season period spend more money). Moreover the visitors with previous holiday in Messina spend more than fi rst time ones; and the cruise ship visitors more satisfi ed spend more respect to unsatisfi ed ones. Finally, our concomitant Gaussian mixture model showed indeed that the three components of our model are well separated, so that we can affi rm that the total expenditure is signifi cantly diff erent according to diff erent satisfaction levels. In particular our model showed that the expenditure is infl uenced by diff erent factors in the subgroups of cruise ship visitors. In the fi rst subpopulation, that is composed mainly by visitors with high levels of general satisfaction, the nationality, the length of visit and recommendation Messina have a significant infl uence on total expenditure; the second subgroup, composed mostly by visitors with medium-high levels, only nationality and previous holiday in Messina are statistically signifi cant, fi nally the third component, composed by visitors with low satisfaction levels; length of visit, season period and previous holiday in Messina have signifi cant infl uence on total expenditure in Messina.
In conclusion, this research suggests several characteristics of the cruise ship experience that should be considered when examining this visitor market. Th e our survey uncovered a array of perceptions around the behavior and economic impacts of diff erent visitor types and the factors that infl uence the economic benefi ts these visitors generate. Th ese results should have some obvious implications for those developing travel services directed at specifi c activity groups and for businesses engaging with, and hosting, cruise ships in any port.

ANNOTATION
Th is article was conceived and prepared by both authors, however Romana Gargano is the author of paragraphs 2, 3, 4 and 5, Filippo Grasso wrote paragraphs 1 and 6.