A context-specific causal model for estimating the effect of extended length of overnight stay on traveller's total expenditure

Journal Title Here , YEAR, , 1–19 DOI added during production Published: Date added during production Paper A context-sp ecific causal mo del fo r estimating the effect of extended length of overnight sta y on traveller’s total exp enditure Lauri V alk onen 1,2, ∗ and Juha Ka rvanen 2 1 HAMK T ech, H¨ ame University of Applied Sciences, V ankanl¨ ahde 9, 13100, H¨ ameenlinna, Finland 2 Department of Mathematics and Statistics, Universit y of Jyv¨ askyl¨ a, P .O. Bo x 35, 40014, Jyv¨ askyl¨ a, Finland ∗ Corresponding author. lauri.valk onen@hamk.fi Abstract T ourism significantly affects the economies of many countries. Understanding the causal relationship b et ween the length of overnight sta y and traveller’s exp enditure is crucial fo r stak eholders to characterize sp ending p rofiles and to design mark eting strategies. Causal mechanisms differ b etw een personal and wo rk-related travel b ecause the decision-making p ro cesses have different drivers and constraints. We apply context-sp ecific indep endence relations to mo del causal mechanisms in contexts specified by trip purp ose and identify the causal effect of the length of sta y on exp enditure. Using the international visito r survey data on foreign travellers to Finland, we fit a hierarchical Ba yesian model to estimate the p osterior distribution of the counterfactual exp enditure due to extending the length of stay by one night. We also p erform a Bay esian sensitivity analysis of the estimated causal effect with resp ect to omitted va riable bias. Keyw ords Bay esian mo del, Causal Inference, Context-sp ecific Independence, Exp enditure, T ourism 1. Intro duction T ourism comp rises a major share of the global economy b etw een countries, covering a wide variet y of different industries from transp ortation to accommo dation and catering services, as well as event management. In 2024, tourism represented appro ximately 10 % of the gross domestic p ro duct (GDP) wo rldwide (Statista, 2025). Among the va rious facto rs that influence economic impact and tourist behaviour, the length of sta y is an essential determinant of the total exp enditure of a traveller. Extending the length of sta y ma y contribute to an increase in overall exp enditure by allowing travellers to consider additional consumable services and exp eriences. How ever, the relationship b etw een the length of stay and the total exp enditure may not b e linea r. Fo r example, during a longer stay , a traveller may prefer cheap er alternatives for accommo dation and activities. Identifying the numb er overnight sta ys at which an additional night leads to the highest increase in the total exp enditure enables stakeholders, such as businesses and destination management organizations, to tailor their efforts within the tourism ma rket. In addition to the economic p oint of view, the relationship b etw een the length of stay and sustainabilit y objectives has gained increasing attention. Generally , promoting a longer length of sta y over multiple sho rter trips can help to decrease transp ort emissions (e.g. G¨ ossling et al. (2016)), but also p otentially mitigate overcro wding in the destinations (e.g. Oklevik et al. (2021)). The asso ciations betw een the length of stay and traveller exp enditure has b een extensively studied (Brida and Scuderi, 2013). F or example, Fieger et al. (2021) rep orted a non-linea r relationship b etw een total exp enditure and the length of sta y , with total expenditure exhibiting a steep er grow for shorter-duration trips and then decelerating © The Author(s) YEAR. Cop yright and licence statements to be up dated by the publisher during production. 2 Journal Title Here, YEAR, Volume XX, Issue x fo r longer stays. Furthermo re, a saturation effect in the tourist exp enditure has b een suggested with the exp enditure diminishing after a certain length of stay (e.g., Wang et al., 2018). The need fo r understanding causality in the context of travelling has b een already recognized (Mazanec, 2007; Brathwaite and Walk er, 2018). T raditional metho ds for assessing causal questions in tourism typically rely on exp erimental framew orks, for which Viglia and Dolnica r (2020) use the categorization betw een lab orato ry exp eriments, field exp eriments, natural and quasi experiments, and discrete choice exp eriments, each having their o wn pros and cons. The p revious exp eriment types a re commonly emplo yed in business-related questions, such as purchase intentions, consumption of services and supplies, as w ell as destination choice. How ever, insp ecting the effect of the length of stay p oses challenges for exp erimental research due to the limited control of the intervention va riable. It is not possible to intervene directly on travellers’ choice regarding the length of stay . Causal inference based on observational data (Pea rl, 2009) is wa rranted given that a significant proportion of data generated within the tourism sector stems from passive observations. The purp ose of the trip is a context that strongly impacts other choices the traveller makes related to the trip. Fo r example, a traveller attending a conference will select the destination based on the lo cation of the event. This makes the destination dictated by the w ork requirements and thus removes the causal pathwa y from p ersonal p references to the choice of the destination. On the other hand, individuals travelling for p ersonal purp oses usually make the decision ab out destination based on their p ersonal preferences, which implies a causal path b etw een these variables in t his context. In this pap er, we aim to estimate the effect of extended length of stay on traveller’s total exp enditure using causal inference (Pea rl, 2009). The ultimate estimand of interest is the average counterfactual increase in total exp enditures if a traveller had stay ed one night longer than they actually did. W e use a lab elled directed acyclic graph (LDA G) (Pensa r et al., 2015) to form a context-sp ecific causal mo del (Tikk a et al., 2019) that allows us to take into account the difference b etw een wo rk-related trips and p ersonal trips when identifying and estimating causal effects. Context-sp ecific indep endence (CSI) relations (Boutilier et al., 1996) extend do-calculus (Pea rl, 1995) and can enable the identification of causal effects that would otherwise remain unidentifiable (Tikka et al., 2019; Mokhtarian et al., 2022). Our study seems to be the first to apply CSI-relations in ca usal analysis of real data. W e use the context-sp ecific causal mo del to identify the counterfactual effect of the extended length of stay on the traveller’s total exp enditure based on the survey data of foreign travellers visited in Finland. We fit a hierarchical Ba yesian mo del to estimate the p osterio r distribution of this quantity . W e also propose a Bay esian approach for sensitivit y analysis for estimating the omitted va riable bias regarding traveller’s annual income which has not been measured. We adopt ideas from Cinelli and Hazlett (2020) and calculate the bias in the causal effect estimates based on the prio r understanding on the relationships b etw een the income and length of stay and b et ween the income and total total exp enditure in b oth contexts. The structure of the pap er is the follo wing. In Section 2, we outline the framewo rk of the context-sp ecific causal mo dels. Section 3 describ es the data set used in the analysis and the mo del for the data-generating process. In Section 4 we leverage CSI-relations to derive a formula fo r the causal effect of extended length of sta y . Subsequently , in Section 5, we fit a Bay esian model to estimate he total exp enditure in the counterfactual case where the length of stay is extended b y one night. Follo wing this, in Section 6 w e present the sensitivit y analysis to investigate the robustness of estimates to unobserved income. Finally , in Section 7 we discuss the strengths and limitations of the p rop osed app roach and the data used. 2. Intro duction to context-sp ecific causal mo dels W e start with a demonstration of the use of CSI-relations in the causal effect identification p roblem. Consider causal graphs presented in Figure 1, containing observed variables X , Y , Z , M , and an unobserved variable U . In the left causal graph the causal effect P ( Y | do( X )) is non-identifiable b ecause the unobserved confounder U affects X but also Y through Z which is a child of X . The situation changes in the right causal graph where CSI-relations a re tak en into account. Let us then assume that we have context-specific information ab out the causal relationship b et ween X , Z , and U , which is presented by the LDA G in the right panel of Figure 1. In the LDA G the dashed edges describ e the causal directions that vanish in the specific context indicated by the context lab el. By applying the Do-search identification algo rithm (Tikka et al., 2021, 2019), we obtain the identifying functional Journal Title Here, YEAR, Volume XX, Issue x 3 M U X Z Y M U X Z Y M = 1 M = 1 M = 0 Figure 1 DA G (left) and LDA G (right) fo r illustrating the same data generating process, where additional context sp ecific information resulting from no de M makes the query P ( Y | do( X )) to b e identifiable. In the graph nodes indicate the observed (circles) and unobserved variables (squares) and the edges represent the causal directions. Dashed edges with notation indicate the vanishing causal directions in the sp ecific context. A circle node with an inner circle p oints out to the variable to b e intervened. P ( Y | do( X )) = X Z,M p ( Y | X , Z, M )  1 ( M = 1) p ( Z | X , M = 1) p ( M = 1) + 1 ( M = 0) p ( Z | M = 0) p ( M = 0)  , (1) where the indicator function 1 tells in which context M , we are calculating the conditional distribution of Z in Equation (1) . Equation (1) can b e simplified if we consider one context at a time. In context M = 1 , one can marginalize out Z , which serves as a mediator b et ween X and Y , and thus should not b e conditioned on. In context M = 0 conditioning on Z is needed to blo ck the backdoor path X ← U → Z → Y . Thus, an alternative presentation fo r equation (1) can b e expressed as P ( Y | do( X )) = p ( Y | X, M = 1) p ( M = 1) + X Z p ( Y | X , Z, M = 0) p ( Z | M = 0) p ( M = 0) , (2) In the case of LDA G in Figure 1, the result of equation (2) could be obtained also by applying an identification algo rithm separately to contexts M = 0 and M = 1 and combining then the identifying functionals. How ever, in general, the identifiability in all contexts is neither necessary no r sufficient condition for the overall identifiability (Tikk a et al., 2019, Theo rem 6). 3. Data and assumptions 3.1. Survey data W e use op en data from Visit Finland’s International visitor survey (“Rajahaastattelut” in Finnish) which consists of interviews of international travellers depa rting from Finland (Avoindata.fi, 2025). Visit Finland, a unit of Business Finland, is a public organization which builds the brand of Finland as an international destination and helps Finnish companies to develop their travel business internationally (Visit Finland, 2025a). Statistics Finland, Norstat Finland 4 Journal Title Here, YEAR, Volume XX, Issue x Oy , and Visitory Oy are resp onsible for the data collection procedure including survey planning, interviews, data p ro cessing, and data publishing (Visit Finland, 2025b; Oksa and Nurmi, 2024). The survey including sampling plan, questionnaire, and the data processing is described in Oksa and Nurmi (2024). The op en data set and detailed do cumentation of the variables and the survey process are available at https://www.avoindata.fi/data/en_GB/ dataset/visit- finland- matkailijamittari (Avoindata.fi, 2025). The data used in our study covers observations from March 2023 to June 2025 and it has b een collected on a monthly basis with interviews conducted at va rious b o rder crossing p oints in Finland. We next describ e the data processing and the p ost-processed data. The descriptive statistics fo r the p ost-p ro cessed data sets are provided in T ables 3, 4, 5, and 6 in the App endix A. F oreign travellers are defined to b e those who a re not residing in Finland (Visit Finland, 2025b). In the survey , the interviewer records the traveller’s resp onses using a tablet device (Visit Finland, 2025b). According to Oksa and Nurmi (2024), an interviewee can rep o rt the exp enditure in the chosen currency and for t he chosen group of p ersons. The question was formulated as follows: “How much money did you sp end in Finland? Currency , fo r the whole part y just mentioned. If you do not know, leave the field blank. If there w ere no exp enses, enter 0.” The reported total exp enditure is transformed into euros and then normalized to represent one person’s exp enditure p er one trip (Oksa and Nurmi, 2024). In addition to exp enditure, background variables age, gender, and country of residence have b een measured. Due to the low numb er of observations in the gender variable categories ’Other’ and ’Don’t want to say’, we merged them with the ’Female’ category to create a binary gender va riable. The purpose of the trip has seven classes which are divided into tw o contexts: ”V acation, leisure, or recreation” and ”Some other purp ose” are categorized as p ersonal trips, and ”Studying”, ”Meeting or wo rk trip in the service of a non-Finnish employ er”, ”Conference or congress or fair”, ”Wo rk p erformed in Finland for a Finnish employ er”, and ”Some other w ork-related reason” a re catego rized as w ork-related trips. In the original data study trips were categorized as p ersonal trips but we catego rize them as w ork-related trips category b ecause we assume that the decision-making mechanism for study trips shares the essential fea tures with wo rk-related trips. The length of stay (nights) is the variable whose causal effect on exp enditure will b e analysed. In T able 1, the distribution of overnight sta ys is presented for the both contexts. The majorit y of trips have the duration of four nights or less but p ersonal trips have a spike also at seven nights. T able 1. Distribution of the length of stays for p ersonal and w ork-related trips. Number of overnight stays Personal trips (freq.) % W ork-related trips (freq.) % 1 895 11.8 531 15.7 2 1225 16.2 752 22.3 3 1325 17.5 557 16.5 4 944 12.4 450 13.3 5 604 8.0 273 8.1 6 469 6.2 168 5.0 7 1265 16.7 150 4.4 8 212 2.8 85 2.5 9 176 2.3 78 2.3 10 113 1.5 66 2.0 11 91 1.2 70 2.1 12 70 0.9 41 1.2 13 57 0.8 29 0.9 14 85 1.1 85 2.5 15 54 0.7 41 1.2 Other trip-related factors have also b een measured, such as the main destinations, and the time of the trip. As the Finland’s tourism is significantly concentrated to Helsinki and Lapland, we use the majo r regions of main destination in Finland indicating the main destination of the tourists. The majo r regions are Helsinki metrop olitan a rea, Coast and a rchip elago, Lakeland, and Lapland. In addition, Helsinki is separated from Helsinki metrop olitan area as an o wn region in our dataset, making the final classification of the variable to consider five regions. Fo r the time of the trip, we use the quarter of departure from Finland to represent the traveller’s visiting p eriod in Finland. Journal Title Here, YEAR, Volume XX, Issue x 5 The travellers interviewed were also asked to rep ort up to three secondary destinations and the length of stay at these. Given the substantial proportion of missing observations in the rep o rted secondary destinations, we adopt the assumption that missing responses indicate the absence of secondary visits. Furthermo re, due to low frequency of visits to secondary destinations, this information was summarized as t he total sum of overnight stays in the secondary destinations. The travellers were ask ed ab out the main accommo dation and the travel group. Due to relatively low numb er of observations in some categories of the accommodation variable, we keep the three catego ries with the highest numb er of observations and combine the rest of the categories into a single category lab elled ’Other’. This procedure w as applied separately to the data sets of b oth contexts. In addition, dichotomous questions have b een used fo r different exp eriences and activities, such as nature or cultural exp eriences, sp ecifically indicating whether a traveller had participated in such an exp erience or activity . In these, the travellers interviewed were allow ed to rep ort three activities at a maximum. In addition, the first reservation made in months since the trip occurred was used in the analysis. Sp ecific questions were also ask ed ab out transp ortation, considering whether there were trips longer than 50 kilometres within Finland, and the mean of transport when leaving Finland. As a part of data, Statistics Finland provides sampling weights that a re needed, for instance, to estimate the total national income from foreign travellers. Statistics Finland has also imputed some of the variables in the data set. The imputed variables include six sub-exp enditures (e.g. total exp enditures fo r accommo dation, restaurants, fuels, etc.), that is, the costs that form the total exp enditure as w ell as the length of stay and the purp ose of the trip. Acco rding to Oksa and Nurmi (2024), missing data were imputed using the nearest neighb our method. From the original data dimension ( n =17 297) the numb er of imputed values for the length of stay and the purp ose of the trip consider only 52 and 40 observations resp ectively . How ever, the share p er sub-exp enditure variables missingness va ries from 12% to 38% . Not all missing values in data a re imputed by Statistics Finland. In the original data, the explanatory va riables containing lots of missing values, such as information ab out package trips and the numb er of children pa rticipating in the trip have b een excluded from the data. Empty values or unknown values rep orted in the main destination va riable are treated as missing data. Accommo dation services constitute a major comp onent of travellers’ expenses with a possible exception of travellers who meet their friends and relatives. Thus, we fo cus on p ersonal and w ork-related trips excluding the trips made fo r meeting friends or relatives. W e restrict to travellers whose length of stay is b etw een 1 to 15 nights and whose expenditure is greater than zero. Studying the effect of length of stay for travellers with zero exp enditure o r large numb er of overnight stays w ould b e atypical b ehaviour from mainstream and out of our scop e. Although daily travellers w ould b e a relevant segment to include in the study , their characteristics in the decision-making process w ould differ significantly from the overnight stay visitors, e.g. excluding the decision related to accommo dation. The p ro cessed data sets contain 7585 observations in p ersonal trip context data and 3376 observations in the w ork-related trip context data. In the final data sets used in fitting the mo dels in Section 5, rows containing missing values a re excluded, which reduces the numb er of observations from 7585 to 6894 in the context of personal trips and from 3376 to 3267 in the context of wo rk-related trips. As describ ed by Oksa and Nurmi (2024), the survey has some limitations related to the data collection process. Road border crossing points were excluded, which reduces the number of Swedish and Norw egian travellers in the data. The costs covered by emplo yer seem to b e rep o rted inconsistently and the real exp enditures of wo rk related trips a re likely to b e higher than those in the data. 3.2. Causal mo del fo r traveller’s total exp enditure Next, we discuss the causal mechanisms related to the variables in the b order survey data and present the assumed causal mo del as an LDA G. In T able 2, we have listed the symb ols for the variables used when constructing the causal graph. Our context variable M is the purp ose of the trip considering ’p ersonal trips’ ( M = 0 ) and ’w ork-related trips’ ( M = 1 ). These t wo contexts allow us to expand the description of the data-generating process, leading to distinct indep endence structures b et ween variables in the causal graph. In p ersonal trips, a diverse a rray of motives to travel can b e assumed, rendering it ambiguous as to which factors drive the trip planning process. On the other hand, in the case of wo rk-related trips, the wo rk assignments guide the planning. 6 Journal Title Here, YEAR, Volume XX, Issue x T able 2. V ariables and their definitions. V ariable Definition D • Age group, gender, and the country of residence M • Purp ose of the trip (p ersonal or wo rk-related) X • Length of stay (in numb er of overnight stays) C • Main destination (Major region of main destination in Finland) S • Quarter of departure from Finland Z Other decisions assumed to b e made b efore the trip • Means of transp o rt for departure from Finland • Main type of accommo dation • How many months prio r to the trip was the first reservation made • T ravel group • Overnight stays in other destinations in Finland W Other decisions assumed to b e made b efo re o r during the trip • (Did or exp erienced) nature exp eriences in Finland • (Did or exp erienced) physical or sp ort activities outdo ors in Finland • (Did or exp erienced) wellbeing and relaxation activities in Finland • (Did or exp erienced) cultural exp eriences in Finland • (Did or exp erienced) a city break in Finland • (Did or exp erienced) participation in a cultural or sp ort event in Finland • (Did or exp erienced) shopping in Finland • (Did or exp erienced) touring or road trip in Finland • T ravelled more than 50 kilometres (30 miles) in Finland Y • T otal exp enditure The ke y variables in the data related to trip planning are denoted as follo ws: Va riable X is the trip length in numb er of nights. Va riables C and S indicate the main destination (majo r region of main destination) and the season the trip was made (departure time), resp ectively . Z represents additional characteristics of the trip that are assumed to have b een determined b efo re the trip, that is, months the first reservation was made prio r to the trip, the mean of transp o rt from Finland, the main t yp e of accommo dation, overnight stays in secondary destinations and the travel group. Additional factors that are assumed to have been decided b efore or during the trip are included in va riable W , that is, different exp eriences or activities done and trips over 50 kilometres in Finland. Va riables D (age, gender, country of residence), Z and W are clustered va riables and a re assumed to represent transit clusters (Tikka et al., 2023). In the context of personal trips M = 0 , there exists a broad degree of flexibility in the trip planning, and we assume a common unobserved confounder U 1 b et w een all the factors related to the decisions X , C , S , Z , and W describ ed ab ove. This U 1 could represent, fo r instance, different types of consumer preferences o r lifestyles, advertising, o r recommendations from other travellers. Additional unmeasured confounder U 2 b et w een key facto rs X , C , and S could include other unmeasured confounders, such as constraints related to timing and scheduling. In the context of wo rk-related trips M = 1 , we assume that the requirements of wo rk or studies are essentially guiding the cho ose b etw een prima ry factors, that is, the destination and timing (season and length of stay). This means that the unobserved U 1 (e.g. consumer preferences) is no longer affecting on the choice of X , C , S . How ever, the effect of U 1 is p resent b et ween Z and W , reflecting the influence of U 1 on the consumption of services and activities. Besides the aforementioned traveller’s constraints in personal trip contexts, the unmeasured confounder U 2 b et w een key factors X , C , and S could here include e.g. additional information ab out the requirements and features of the wo rk or studies. The key factors X , C , and S together further affect the rest of the decisions related to the trip, that is, Z and W . T o combine the information from b oth of the contexts together into LDA G presented in Figure 2, we first describ e the rest of the assumed causal relations b etw een data variables. In the LDA G, D is assumed to affect directly the purp ose of the trip M , cha racteristics X , C , S , Z , and W , and the total exp enditure Y . The purpose of the trip M (the context variable) is a confounder b et ween total exp enditure Y and all the factors concerning the decisions. Journal Title Here, YEAR, Volume XX, Issue x 7 In addition, all of these variables directly affect to the total expenditure Y . By using LDA G, the differences in the causal mechanisms due the contexts are easy to present and thus the whole data generating process is describ ed in one graph instead of multiple DA Gs. D U 1 M Y X C S U 2 Z W M = 0 M = 0 M = 0 M = 0 M = 0 M = 0 M = 1 M = 1 M = 1 Figure 2 LDA G representing traveller’s total exp enditure process: The circle nodes represent the observed variables in the data. The lab els in the arrows, describ e the causal paths that vanish when context is either p ersonal trip ( M = 0 ), or wo rk-related trip ( M = 1 ). The rectangle no des U 1 and U 2 indicate unobserved confounders. The data lacks some key background variables of travellers considering traveller’s financial resources, such as income. In Figure 3, we present an augmented LDA G incorporating traveller’s income in the process. It is plausible to assume, that traveller’s income influences b oth the length of stay and total exp enditure, thus preventing the identification and intro ducing bias in the estimates if not accounted for. T o address this issue, we implement a sensitivit y analysis in Section 6. 8 Journal Title Here, YEAR, Volume XX, Issue x D U 1 M Y X C S U 2 Z W M = 0 M = 0 M = 0 M = 0 M = 0 M = 0 M = 1 M = 1 M = 1 I Figure 3 An augmented LDA G, where traveller’s income I intro duces new causal links including a confounding pathwa y b etw een the length of stay X and traveller’s total exp enditure Y . 4. Identification of causal effects and counterfactuals In this section, we first consider the identification of causal effects in the LDA Gs presented in Figures 2 and 3. Then w e study the counterfactual situation where travellers would have stay ed one night longer than they in reality did. W e are interested in the p ost-interventional distribution P ( Y | do( X )) that describ es the causal effect of length of sta y ( X ) on the total exp enditure ( Y ). Without CSI-relations the graph of Figure 2 reduces to a regular DA G, where the context-specific edges are alwa ys present. In this case, the query P ( Y | do( X )) is not identifiable. With CSI-relations, P ( Y | do( X )) is identifiable from the observational distribution P ( Y , X, C , S, Z, W , D, M ) and the Do-sea rch algorithm (Tikka et al., 2019, 2021) returns an identifying functional P ( Y | do( X )) = X M, S 0  1 ( M = 0) p ( M ) p ( S 0 | M ) p ( Y | X , M , S 0 )  +  1 ( M = 1) p ( Y | X, M , S 0 ) p ( W | X, M , S 2 ) p ( Z | X , M , S 1 ) p ( M , S 1 )  , (3) where S 0 = { C, S, Z, W, D } and S 1 = { C, S, D } , and S 2 = { C, S, Z, D } . The causal effects conditioned on the context P ( Y | do( X ) , M ) are identified as follows P ( Y | do( X ) , M = 0) = p ( M = 0) P S 0 p ( S 0 | M = 0) p ( Y | X, M = 0 , S 0 ) P Y h p ( M = 0) P S 0 p ( S 0 | M = 0) p ( Y | X, M = 0 , S 0 ) i (4) Journal Title Here, YEAR, Volume XX, Issue x 9 P ( Y | do( X ) , M = 1) = P S 1 p ( Y | X, M = 1 , S 1 ) p ( M = 1 , S 1 ) P Y h P S 1 p ( Y | X, M = 1 , S 1 ) p ( M = 1 , S 1 ) i . (5) In the ab ove, the identifiability of P ( Y | do( X ) , M ) could also be reached b y p resenting the CSI-relations sepa rately with DA Gs for b oth contexts. From a conceptual standp oint, P ( Y | do( X ) , M ) means intervening directly the traveller’s length of stay , i.e. setting the overnight stay as X = x . The main question of interest is finding the traveller’s total exp enditure if he/she had stay ed one night longer than originally planned. The estimand of interest is then a counterfactual difference which can b e defined separately fo r b oth contexts as ∆ x → x +1 ( x, m ) := E( Y x +1 | X = x, M = m ) − E( Y x | X = x, M = m ) , (6) where E( Y x | X = x, M = m ) is the exp ected total exp enditure for travellers who stay ed x nights and E( Y x +1 | X = x, M = m ) is the counterfactual total exp enditure for the same travellers if they had stay ed one night longer. The identifiabilit y of counterfactuals can evaluated by applying the algorithm b y Shpitser and Pea rl (2007) implemented in the R package cfid (Tikka, 2023). The following formulas can b e derived from the identifying functionals: E( Y x | X = x, M = 0) = P ( S 0 | X = x, M = 0)E( Y | X = x, S 0 , M = 0) P ( X = x | M = 0) , (7a) E( Y x | X = x, M = 1) = P ( S 1 | X = x, M = 1)E( Y | X = x, S 1 , M = 1) P ( X = x | M = 1) , (7b) E( Y x +1 | X = x, M = 0) = P ( S 0 | X = x, M = 0)E( Y | X = x + 1 , S 0 , M = 0) P ( X = x | M = 0) , (7c) E( Y x +1 | X = x, M = 1) = P ( S 1 | X = x, M = 1)E( Y | X = x + 1 , S 1 , M = 1) P ( X = x | M = 1) , (7d) where again S 0 = { C, S, Z, W, D } and S 1 = { C, S, D } . Note that in equations (7c) and (7d) , the distributions of S 0 and S 1 a re conditional on X = x but the distribution of Y is conditional on X = x + 1 . The counterfactual E( Y x +1 | Y = y , X = x, M = m ) , where the condition for Y x +1 contains also the actual exp enses y would b e interesting as well. How ever, this counterfactual is not identifiable. 5. Estimating the effect of extending the length of sta y W e estimate the effect of extending the length of sta y on total exp enditure, i.e., the counterfactual difference ∆ x → x +1 ( x, m ) in Equation (6) , in b oth contexts m = { 0 , 1 } . T o mo del b oth exp ected total exp enditure and counterfactual total exp enditure in Equation (6) , we need a mo del for the exp ected value E( Y | X , M ) for both contexts. The equations in (7a) - (7d) tell that we sp ecifically need to mo del the conditional exp ectations E( Y | X , S 0 , M = 0) and E( Y | X, S 1 , M = 1) . As we have restricted the total exp enditure to consider only p ositive values, we fit gamma distribution mo dels. W e apply logarithmic link functions and allow the intercepts to vary by inco rp o rating random effects for the country of residence ( L ) of a traveller. We assume the effect of increasing the length of sta y on the expenditure to be non-decreasing, and therefore monotonic effects for the length of stay (B ¨ urkner and Cha rp entier, 2020) are estimated. Let the sup erscripts define the context related to the variables and pa rameters, that is, zero fo r context M = 0 and one for context M = 1 . The mo dels fo r the the total exp enditure Y of a traveller i with country of residence L [ i ] can b e expressed as 10 Journal Title Here, YEAR, Volume XX, Issue x log(E( Y i | X i = x, S 0 , M i = 0)) = α (0) + β (0) M (0) [ i ] + γ (0) S ∗ 0 i + u (0) L [ i ] + a (0) mo( x, ζ (0) ) , (8) log(E( Y i | X i = x, S 0 , M i = 1)) = α (1) + β (1) M (1) [ i ] + γ (1) S ∗ 1 i + u (1) L [ i ] + a (1) mo( x, ζ (1) ) , (9) where α is a constant, β is the parameters regarding the different purp oses of travel in each context, and γ refers to parameters related to other covariates in the specific context. Pa rameter a defines the direction and the magnitude of the monotonic effect and mo function is the monotonic transform with simplex parameters ζ (B ¨ urkner and Cha rp entier, 2020). Random intercept u L [ i ] mo del the effect of the i th traveller’s country of residence L . In the fo rmulas, va riables M (0) and M (1) no w include the sub-categories of the purp ose of the travel in the corresponding contexts, presented in Section 3. Note also, that sets S ∗ 0 i and S ∗ 1 i include the variables from sets S 0 and S 1 co rresp ondingly , excluding the country of residence already presented in random effect u L [ i ] j . In sets S ∗ 0 i and S ∗ 1 i , categorical va riables are p resented by binary indicators for each class. The mo del is implemented in the R environment (R Core T eam, 2023) by using the brms package (B¨ urkner, 2017) for Bay esian regression mo delling. Weakly informative prio rs are used in the mo delling. We cho ose N (0 , 0 . 5 2 ) p riors for regression co efficients, and Dir ichl et (2) prio rs for the concentration parameters (simplex). Fo r intercept term of the mean parameter, N (0 , 2 2 ) prio r is used, and t (3 , 0 , 1) prio r for the standard deviation, with 3 degrees of freedom, 0 location and 1 scale pa rameter. Otherwise, the default p riors from the brms package are used. W e use 2000 iterations with 1000 wa rm-up perio d, and run 4 chains. The exp ected values of the p osterior predictive distribution were scaled with the sampling weights p rovided by Statistics Finland. F or estimating the effect of extending the length of stay , we calculate the counterfactual difference in Equation (6) fo r all posterior samples b = 1 , ..., B , where θ b stands fo r all mo del parameters fo r sample b . The exp ected counterfactual difference of increasing the length of stay on the total exp enditure by one night is estimated b y the mean b ∆ x → x +1 ( x, m ) = 1 B B X b =1 ∆ x → x +1 ( x, m ; θ b ) , (10) where b represents the p osterior sample and B the total numb er of p osterio r samples. 95% credible interval (CI) is obtained from the 2.5th and 97.5th quantiles of ∆ x → x +1 ( x, m ; θ b ) . Figure 4 p resents the exp ected counterfactual difference resulting from increasing the length of stay on total exp enditure by one night. Corresponding numerical estimates and their 95 % credible intervals are presented in T able 7 in the App endix B. F or p ersonal trips, the increase in total exp enditure within one to seven overnight stays va ries appro ximately b et w een 90 to 160 euros. Fo r overnight stays longer than seven nights, the increase in exp enditure decreases nea r to 50 euros, with spik e at thirteen nights. How ever, the credible intervals fo r the longer length of stays are wide. Fo r w ork-related trips the highest increase in exp enditure is observed at t wo overnigth stays (appro ximately 174 euros). After sho rt length of sta ys, the inrease va ries from 60 to 150 euros alb eit with substantial uncertainty . 6. Sensitivit y analysis fo r omitted va riable bias Next, w e consider the confounding effect of traveller’s income which was not ask ed in the survey . W e assume that demographics D affect income I , which in turn affects travel-related cha racteristics X , C , S , Z , W , and also the purp ose of the trip M and the total exp enditure Y . As it was mentioned in Section 4, adding the income in the graph in Figure3 makes the causal effect of interest unidentifiable due to the intro duction of additional confounding pathw ays b et ween X and Y . Journal Title Here, YEAR, Volume XX, Issue x 11 0 50 100 150 200 250 300 350 400 1 (+1) 2 (+1) 3 (+1) 4 (+1) 5 (+1) 6 (+1) 7 (+1) 8 (+1) 9 (+1) 10 (+1) 11 (+1) 12 (+1) 13 (+1) 14 (+1) Original length of stay (increase) Euros (increase) P ersonal Work−related Figure 4 Counterfactual difference of increasing the length of stay by one night for p ersonal trips and wo rk-related trips. Lab els on the x-axis indicate the original length of stay and the increment applied (in parenthesis). T o implement a sensitivity analysis of omitted variable bias concerning income, we adapt concepts presented b y Cinelli and Hazlett (2020) fo r Ba y esian analysis. We assume a linear relationship b et ween income ( I ) and total exp enditure ( Y ), as well as b et ween income ( I ) and the length of stay ( X ). Based on this assumption, we sp ecify p rior distributions for the correlations b et ween I and Y , and b etw een I and X . W e assume that in the context of p ersonal trips, I and X have a weak p ositive correlation with mo derate uncertaint y . Although it is plausible that travellers with higher incomes can afford longer trips, it is unclear whether longer stays would b e preferred over sho rt visits. Fo r I and Y , a mo derate co rrelation is assumed, b ecause travellers t ypically finance their trip expenses by themselves. Also in the context of wo rk-related trips, I and X are assumed to have a weak p ositive co rrelation with mo derate uncertaint y . This is due to the constraints imp osed by wo rk-related obligations which restrict the length of stay even if the traveller could affo rd a longer stay . The correlation b etw een I and Y is mo derate but weak er than in the context of p ersonal trips. Employ ers subsidize travel costs but an important p osition at wo rk ma y imply b oth high income and high travel costs. Even if emplo yers covered the costs, it is unclear whether travellers differentiate costs unambiguously when rep orting them in the survey . The correlations are simulated from their prio rs for each p osterior sample of the fitted mo del b y using an app ropriate normal distributions in combination with the Inverse Fisher z -transformation. Fo r p ersonal trips, this leads to prio r distribution N (0 . 1 , 0 . 15 2 ) for the co rrelation b etw een I and X , and N (0 . 45 , 0 . 1 2 ) for the co rrelation b et w een I and Y . Fo r wo rk-related trips, we obtain prio r distribution N (0 . 05 , 0 . 15 2 ) for the correlation b etw een I and X , and N (0 . 2 , 0 . 1 2 ) fo r the correl ation b et ween I and Y . W e calculate the bias of the causal effect by applying the following formula (Cinelli and Hazlett, 2020): d bias = sign ( co rr ( Y ⊥S ,X , I ⊥S ,X ) corr ( X ⊥S , I ⊥S )) v u u t R 2 Y ∼ I | X, S R 2 X ∼ I |S 1 − R 2 X ∼ I |S sd ( Y ⊥S ,X ) sd ( X ⊥S ) . (11) 12 Journal Title Here, YEAR, Volume XX, Issue x In Equation (11) the partial co efficients of determinations R 2 Y ∼ I | X, S and R 2 X ∼ I |S can b e computed from the co rrelations co rr ( Y ⊥S ,X , I ⊥S ,X ) and corr ( X ⊥S , I ⊥ S ) generated ab ove, which also defines the sign of the bias. The standa rd deviation sd ( Y ⊥S ,X ) can b e calculated from the residuals of the mo dels (8) and (9) . T o estimate the standa rd deviations sd ( X ⊥S ) , w e fit gamma mo dels with loga rithmic link functions for the length of stay in b oth contexts using the same covariate sets in than in the total exp enditure mo dels, that is, S 0 fo r the p ersonal trip context mo del, and S 1 fo r the wo rk-related trip context mo del (excluding the length of sta y X which is now the resp onse variable). The mo dels a re fitted with prio r distributions N (0 , 2 2 ) for the regression co efficients, otherwise the default prio rs are used. 0 1 2 3 4 5 −0.4 −0.2 0.0 0.2 0.4 0.6 Correlation Density P ersonal: corr ( I , X ) P ersonal: corr ( I , Y ) Work−related: corr ( I , X ) Work−related: corr ( I , Y ) Figure 5 Prio r distributions fo r correlations betw een income (I) and length of sta y (X), and betw een income and total exp enditure (Y) in both p ersonal trip and wo rk-related trip context. Figure 6 sho ws the bias of the counterfactual difference ∆ x → x +1 across all posterior samples θ l ( l = 1 , 2 , ..., 4 000 ) in b oth contexts. The estimated average bias of the total exp enditure is appro ximately 11 euros with 95% quantile interval [-20.00, 45.94] for the p osterio r distribution for personal trips. Fo r wo rk-related trips, the estimated average bias is app roximately 1.9 euros with 95% quantile interval [-9.91, 15.03] for the p osterior distribution. Given the prio r b elief, omitting income tends to underestimate the bias related to the estimated effect of length of stay in p ersonal trips, although this effect is uncertain with substantial p robability mass b elow zero. F or wo rk-related trips, the bias is near zero with high uncertainty . The effect of extending the length of stay on total exp enditure in p ersonal trips has tendency to b e underestimated if omitting income variable, although the uncertainty related to this is quite large as the pr obability mass has also lots of mass under zero. The effect of bias on the estimates are presented in Figure 7. The numerical estimates in the omitted variable case are collected in table 8 in the App endix B. Journal Title Here, YEAR, Volume XX, Issue x 13 0.000 0.025 0.050 0.075 0.100 −50 −25 0 25 50 75 Bias (euros) Density P ersonal Work−related Figure 6 Posterio r distributions of omitted va riable biases related to missing income variable fo r p ersonal trips (left) and wo rk-related trips (right). 7. Discussion W e implemented a context-sp ecific causal mo del for estimating the counterfactual difference of extending the length of sta y on the traveler’s total exp enditure. T o the b est of our knowledge, the study p resented is the first one to apply context-sp ecific causal inference approach with real data. LD AGs with CSI-relations enable handling the whole mo deling scheme coherently in one causal graph instead of multiple graphs separated by contexts. The approach is theoretically app ealing b ecause identifiability in all context- sp ecific DA Gs is neither necessary nor sufficient condition for the identification in LDA G (Tikka et al., 2019). The limitations of our analysis are related to data collection, handling of missing data and validity of causal assumptions. The survey design do es not include all border crossing p oints. Recall bias, misundersto o d questions due to a lack of a common language, and variabilit y in the rep o rting of the costs paid by the employ er a re also p otential sources of bias in the data collection. Our analysis fo cused on short-term p ersonal and wo rk related travel excluding trips where the main purp ose was meeting friends and relatives. Mo deling of the excluded groups as an additional context would b e p ossible but the main financial interest lies in travelers who use accommo dation services. The missing exp enditures have b een imputed by Statistics Finland using single imputation. This means that the rep orted p osterior intervals are to o narro w b ecause they do not reflect the uncertainty due to missing data. The missing data mechanism could b e mo deled as a pa rt of the LDA G and included in the identification. Multiple imputation or Bay esian mo deling of missing data would be theoretically more justifiable approaches than single imputation, but on the other hand, the imputed data provided by Statistics Finland is used to produce national statistics on international travelers. 14 Journal Title Here, YEAR, Volume XX, Issue x 0 50 100 150 200 250 300 350 400 1 (+1) 2 (+1) 3 (+1) 4 (+1) 5 (+1) 6 (+1) 7 (+1) 8 (+1) 9 (+1) 10 (+1) 11 (+1) 12 (+1) 13 (+1) 14 (+1) Original length of stay (increase) Euros (increase) Personal Personal (O VB included) Work−related Work−related (O VB included) Figure 7 Counterfactual difference of increasing the length of stay by one night on the total exp enditure. Mo dels for personal trips and wo rk-related trips excluding and including omitted variable bias related to income are presented. Labels in the x-axis indicates the original length of stay and the increment (in parenthesis). Unobserved confounding is a main concern in causal inference with observational data. We addressed this concern through sensitivity analysis examining the impact of missing income data on our results. We devised a Ba yesian app roach to estimate p osterior distributions of the counterfactual exp enditure when the co rrelations b etw een income and the length sta y and income and total exp enditure follow ed informative p rior distributions. While there remain opp ortunities to further refine the sensitivity analysis with additional covariates, our approach gives the basic understanding on the extend of omitted variable bias. The obtained results pinp oint the overnight stays that generate the highest additional exp enditure from an extended visit. This knowledge could b e used by destination management organizations to design mark eting effo rts, such as sp ecial offers for extended stay . Conflicts of interest The authors declare that they have no comp eting interests. F unding L.V. was supp orted b y the Foundation for Economic Education. This w ork w as supported by the Research Council of Finland under grant numb er 368935 and ”Enhancing data oriented management of H¨ ameenlinna city tourism and travelling” project co-funded by the Europ ean Union and City of H¨ ameenlinna. Data availabilit y The data is available at https://avoindata.suomi.fi/data/en_GB/dataset/visit- finland- matkailijamittari and the co des are available at https://github.com/lpkvalkonen/cscm Autho r contributions statement The study was designed by b oth authors. Data analysis was p erformed by L.V., and the manuscript was written by L.V., and J.K.. Both authors reviewed, read and approved the final manuscript. Journal Title Here, YEAR, Volume XX, Issue x 15 Ackno wledgments The a utho rs thank Ella Oksa for the aid in data description and Olli Kosk ela for the comments on the manuscript. 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URL https://doi.org/10.1177/0047287517700315 . A. Data tables T able 3. P ersonal trips data ( n =7585): Summary statistics of continuous variables. Va riable Mean Median SD Min Max Missing Observations Expenditure (Euros) 879.04 680.00 784.68 0.24 17613.16 0 Length of stay (overnight stays) 4.58 4.00 2.95 1.00 15.00 0 First reservation (months before the trip) 3.73 2.00 4.10 0.00 40.00 393 Overnight sta ys in the secondary destinations 0.52 0.00 1.27 0.00 12.00 152 T able 4. W ork-related trips data ( n =3376): Summa ry statistics of continuous va riables. Va riable Mean Median SD Min Max Missing Observations Expenditure (Euros) 652.07 487.07 645.56 0.58 10798.64 0 Length of stay (overnight stays) 4.27 3.00 3.35 1.00 15.00 0 First reservation (months before the trip) 1.61 1.00 3.68 0.00 40.00 266 Overnight sta ys in the secondary destinations 0.28 0.00 0.92 0.00 14.00 44 Journal Title Here, YEAR, Volume XX, Issue x 17 T able 5. P ersonal trips data ( n =7585): Frequencies and proportions of categorical variables. Va riable Categories Frequencies Proportions (%) Missing observations Main destination Helsinki 3294 44 111 Helsinki metropolitan a rea 117 2 Coast and archipelago 644 9 Lakeland 520 7 Lapland 2899 39 Quarter 1 2208 29 0 2 1806 24 3 1753 23 4 1818 24 Gender Male 3725 50 141 Other than male 3719 50 Age group 15-24 y ears 705 9 0 25-44 y ears 3619 48 45-64 y ears 2516 33 Minimum 65 years 745 10 Purpose of the trip Vacation, leisure, or recreation 7272 96 0 Some other purp ose? 313 4 Mode of transportation Ferry 2818 37 0 Airplane 4767 63 T ravel group I travel alone 1257 17 109 I travel with my spouse/significant other 2547 34 I travel with my family , relatives or friends 3489 47 Other 183 2 Accommodation Hotel o r hostel 4689 62 16 Rental cottage or apa rtment (rented privately or from an intermediary , e g Airbnb or booking com) 1669 22 With friends or relatives (incl couchsurfing) 524 7 Other 687 9 Experienced nature No 2954 39 30 Y es 4601 61 Experienced sports No 4941 65 30 Y es 2614 35 Experienced wellbeing No 5164 68 30 Y es 2391 32 Experienced culture No 4518 60 30 Y es 3037 40 Experienced city life No 5153 68 30 Y es 2402 32 Experienced events No 7163 95 30 Y es 392 5 Experienced shopping No 5526 73 30 Y es 2029 27 Experienced road trip No 6321 84 30 Y es 1234 16 Over 50km trips Y es 4126 55 124 No 3335 45 18 Journal Title Here, YEAR, Volume XX, Issue x T able 6. W ork-related trips data ( n =3376): F requencies and proportions of catego rical variables. Va riable Categories Frequencies Proportions (%) Missing observations Main destination Helsinki 1742 52 48 Helsinki metropolitan a rea 324 10 Coast and archipelago 647 19 Lakeland 524 16 Lapland 91 3 Quarter 1 762 23 0 2 1323 39 3 618 18 4 673 20 Gender Male 2384 72 71 Other than male 921 28 Age group 15-24 y ears 188 6 0 25-44 y ears 1686 50 45-64 y ears 1408 42 Minimum 65 years 94 3 Purpose of the trip Study 128 4 0 Meeting o r wo rk trip in the service of a non-Finnish employ er 969 29 Conference o r congress or fair 688 20 Wo rk performed in Finland for a Finnish employer 919 27 Some other work-related reason 672 20 Mode of transportation Ferry 1271 38 0 Airplane 2105 62 T ravel group I travel alone 2236 68 64 I travel with my spouse/significant other 176 5 I travel with my family , relatives or friends 235 7 Other 665 20 Accommodation Hotel o r hostel 1991 59 5 Rental cottage or apa rtment (rented privately or from an intermediary , e g Airbnb or booking com) 404 12 Housing p rovided by an employ er 586 17 Other 390 12 Experienced nature No 2589 77 9 Y es 778 23 Experienced sports No 2824 84 9 Y es 543 16 Experienced wellbeing No 2734 81 9 Y es 633 19 Experienced culture No 2725 81 9 Y es 642 19 Experienced city life No 2524 75 9 Y es 843 25 Experienced events No 3202 95 9 Y es 165 5 Experienced shopping No 2560 76 9 Y es 807 24 Experienced road trip No 3039 90 9 Y es 328 10 Over 50km trips Y es 1644 50 68 No 1664 50 Journal Title Here, YEAR, Volume XX, Issue x 19 B. Estimates T able 7. Context group, average causal effects (A CE, in euros) of the extended length of stay on the total expenditure, and the corresponding 95 % credible intervals (CI). Context group Length of stay (increase) ACE Lo wer 95 % CI Upp er 95 % CI Personal 1 (+1) 142.23 123.22 161.23 Personal 2 (+1) 109.12 85.48 133.45 Personal 3 (+1) 159.37 122.28 196.94 Personal 4 (+1) 110.78 58.69 164.16 Personal 5 (+1) 89.96 29.05 156.47 Personal 6 (+1) 139.94 72.76 207.76 Personal 7 (+1) 100.00 24.61 190.42 Personal 8 (+1) 71.75 12.38 159.24 Personal 9 (+1) 71.50 12.16 161.30 Personal 10 (+1) 54.28 6.74 135.40 Personal 11 (+1) 65.50 9.39 159.40 Personal 12 (+1) 58.90 7.83 156.59 Personal 13 (+1) 130.12 28.63 270.65 Personal 14 (+1) 89.17 12.22 237.56 Wo rk-related 1 (+1) 142.52 107.98 179.08 Wo rk-related 2 (+1) 174.40 126.81 224.74 Wo rk-related 3 (+1) 125.53 63.40 189.01 Wo rk-related 4 (+1) 63.06 13.19 130.35 Wo rk-related 5 (+1) 78.64 14.23 164.41 Wo rk-related 6 (+1) 101.25 22.49 207.23 Wo rk-related 7 (+1) 84.50 14.31 195.47 Wo rk-related 8 (+1) 115.81 19.93 247.86 Wo rk-related 9 (+1) 92.23 14.02 219.90 Wo rk-related 10 (+1) 101.47 14.55 246.48 Wo rk-related 11 (+1) 115.02 16.18 270.78 Wo rk-related 12 (+1) 112.24 15.20 271.19 Wo rk-related 13 (+1) 95.56 12.02 254.27 Wo rk-related 14 (+1) 146.78 20.24 383.92 20 Journal Title Here, YEAR, Volume XX, Issue x T able 8. Context group, average causal effects (A CE, in euros) of the extended length of stay on the total expenditure, and the corresponding 95 % credible intervals (CI) in the case of omitted variable bias (OVB). Context group Length of stay (increase) ACE Lo wer 95 % CI Upper 95 % CI Personal (OVB included) 1 (+1) 153.47 117.02 192.66 Personal (OVB included) 2 (+1) 120.36 78.98 161.18 Personal (OVB included) 3 (+1) 170.61 120.99 221.88 Personal (OVB included) 4 (+1) 122.02 59.18 185.88 Personal (OVB included) 5 (+1) 101.21 32.16 172.89 Personal (OVB included) 6 (+1) 151.18 76.44 228.88 Personal (OVB included) 7 (+1) 111.24 25.18 209.50 Personal (OVB included) 8 (+1) 82.99 13.02 175.95 Personal (OVB included) 9 (+1) 82.74 13.34 177.27 Personal (OVB included) 10 (+1) 65.52 6.41 150.71 Personal (OVB included) 11 (+1) 76.74 8.90 174.06 Personal (OVB included) 12 (+1) 70.14 5.33 170.28 Personal (OVB included) 13 (+1) 141.36 33.90 284.08 Personal (OVB included) 14 (+1) 100.41 12.69 249.64 Wo rk-related (OVB included) 1 (+1) 144.16 107.07 183.48 Wo rk-related (OVB included) 2 (+1) 176.04 126.69 226.98 Wo rk-related (OVB included) 3 (+1) 127.17 62.31 191.91 Wo rk-related (OVB included) 4 (+1) 64.70 12.62 131.90 Wo rk-related (OVB included) 5 (+1) 80.28 14.90 166.57 Wo rk-related (OVB included) 6 (+1) 102.90 22.35 209.70 Wo rk-related (OVB included) 7 (+1) 86.15 14.95 196.97 Wo rk-related (OVB included) 8 (+1) 117.45 21.59 250.94 Wo rk-related (OVB included) 9 (+1) 93.87 14.19 221.06 Wo rk-related (OVB included) 10 (+1) 103.11 14.93 250.33 Wo rk-related (OVB included) 11 (+1) 116.66 16.80 274.41 Wo rk-related (OVB included) 12 (+1) 113.88 15.91 273.17 Wo rk-related (OVB included) 13 (+1) 97.20 11.92 257.98 Wo rk-related (OVB included) 14 (+1) 148.43 21.20 387.59