Latent air travel preferences: Understanding the role of frequent flyer programs on itinerary choice

Transportation Research Part A 80 (2015) 49–61

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Transportation Research Part A journal homepage: www.elsevier.com/locate/tra

Latent air travel preferences: Understanding the role of frequent flyer programs on itinerary choice Michael Seelhorst a,⇑, Yi Liu b a b

Revenue Analytics, 3100 Cumberland Blvd. Suite 1000, Atlanta, GA 30339, United States Civil and Environmental Engineering, UC Berkeley, Berkeley, CA 94720, United States

a r t i c l e

i n f o

Article history: Received 20 September 2014 Received in revised form 25 April 2015 Accepted 14 July 2015 Available online 8 August 2015 Keywords: Air traveler behavior Stated preference Itinerary choice Latent class models

a b s t r a c t Many studies have used air itinerary choice data to identify preferences and tradeoffs of various flight service attributes, such as travel time, number of connections, and fare. Little has been done, however, to estimate the effect Frequent Flyer Programs (FFPs) have on itinerary choice. The goal of this paper is to quantify the impact of FFP membership on itinerary choice and identify discrete patterns of unobserved preference heterogeneity. For this purpose, we apply two modeling techniques using a set of stated preference data collected on 830 individuals. A Multinomial Logit Model (MNL) is first estimated and Willingness-To-Pay (WTP) values are calculated for the choice of flying an airline with which the individual has FFP membership compared with another airline where the individual has no FFP membership. These WTP estimates vary across different trip purposes and levels of FFP status. Our results indicate that FFP membership plays a strong role in airline choice, particularly for individuals with elite membership. We then capture random heterogeneity through the use of latent class models, using sociodemographic variables as class-membership covariates. The latent class model results indicate three groups of individuals with very different sets of preferences, particularly for FFP membership. The discrete segmentation indicates one class with very low WTP, one class with average WTP, and one class with extremely large WTP values. These results provide evidence that latent class models capture preference heterogeneity much better than the MNL model for air itinerary choice, particularly when considering the effects of FFP membership. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Air travel has changed tremendously in the past decade. Online ticketing sites have replaced travel agents and passengers have access to more information about prices and itineraries than ever before. Airline costs have increased as well, primarily due to the rising costs of fuel (Airlines for America, 2014). Higher costs and more transparency for passengers make it difficult for airlines to attract demand in a profitable way. In the literature of air passenger demand, the focus has been on service attributes, such as flight frequency, on-time performance, and route structure. While these attributes are very important they are often difficult or expensive to change. Recently, increasing attention has been given to another aspect of air travel: Frequent Flyer Programs (FFPs), loyalty programs that are used to distinguish an airline’s product from its competitors. These programs are under direct control of the airline and can contribute greatly to the attractiveness of its product

⇑ Corresponding author. E-mail address: [email protected] (M. Seelhorst). http://dx.doi.org/10.1016/j.tra.2015.07.007 0965-8564/Ó 2015 Elsevier Ltd. All rights reserved.

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over competing airlines (Martin et al., 2011). The focus of this work is to quantify the effects that FFPs have on passenger demand and identify market segments that vary with respect to these effects. It has been claimed that FFPs can distort air transport competition, as the programs have a strong effect on passenger itinerary choice (Chin, 2002; Martin et al., 2011; Toh and Hu, 1988; McCaughey and Behrens, 2011). At the most basic membership level, the flight distance contributes towards future benefits with the airline through the accumulation of miles or points. At higher levels, the benefits are more immediate: free upgrades, complimentary checked bags, and a sense of improved customer service. These benefits likely influence customer itinerary purchasing behavior. A few studies (Adler et al., 2005; Garrow et al., 2007; Proussaloglou and Koppelman, 1999) have looked at the effect of FFP membership on itinerary choice as the part of a larger study of air travel preferences, but this aspect of air travel has received much less attention than other market share determinants, such as fare and on-time performance. The goal of this paper is to quantify the level of FFP attractiveness by calculating Willingness-To-Pay (WTP) values for flying an airline with which the passenger has FFP membership compared to an airline where the passenger has no FFP membership. We will estimate WTP values using discrete choice models on stated preference survey data. A few studies have estimated WTP in a similar way. Hess et al. (2013) estimated WTP values ranging from $20 for standard FFP membership to $120 for elite FFP membership. Hess and Adler (2011) found similar numbers, ranging from $18 for basic FFP membership to $180 for elite FFP membership. Both papers incorporated WTP heterogeneity through the use of interacting socioeconomic dummy variables, such as income, trip purpose, and FFP status, with the service level variables, such as fare, travel time, and airline indicators. This paper advances the research on FFP membership by estimating WTP heterogeneity through the use of a latent class model. We identify WTP heterogeneity using a class-membership model with sociodemographic variables as covariates. This approach is advantageous over explicit segmentation due to the lack of constraints on the characteristics of individuals within each segment. Each class reveals a discrete set of preferences defined primarily by the difference in the preferences observed through the choices of the individuals, rather than differences in individual characteristics. 1.1. Literature review Air travel itinerary choice has been investigated from a variety of perspectives. Airport preferences in multi-airport regions were studied by Harvey (1987), Ishii et al. (2009) and Pels et al. (2003). Adler et al. (2005), Brey and Walker (2011), and Garrow et al. (2007) looked into the preference for desired departure times and arrival times. The choice of air carrier was studied by Hess and Adler (2011) and Proussaloglou and Koppelman (1999). Chin (2002) used stated preference data to estimate a binary choice model for passengers’ choice of flying Singapore Airlines. The model specification used dummy variables for FFP membership in Singapore Airlines’ Krisflyer program. The results indicate that FFP membership is a significant driver in itinerary choice, but the effect is smaller in magnitude than flight schedule. No WTP quantification techniques or advanced specifications were used in this study, however. We use WTP calculations that allow us to quantify the tradeoff of FFP membership with various other flight characteristics, such as travel time and number of connections. Martin et al. (2011) used a stated preference study to identify WTP for various flight characteristics for both FFP and non-FFP members. The results indicate that passengers with FFP membership are generally more willing to pay for certain service attributes, like seat pitch and food quality. Segmentation was made solely based on the FFP membership variable. We are interested in capturing the WTP for flying an airline with which an individual has FFP membership, so we use a different survey structure that allows for this kind of tradeoff between choices for each individual. Adler et al. (2005) and Warburg et al. (2006) captured heterogeneity through the use of mixed logit models. In addition to extensive interactions through sociodemographic dummy variables, a random parameter specification was used to account for the unobserved heterogeneity across passengers. While useful at addressing preference differences across each passenger, the hypothesis of a continuous WTP distribution might not be the best representation of the true behavior. Latent class models enable us to identify discrete WTP heterogeneity, rather than assuming a continuous distribution. Greene and Hensher (2002) explored the differences between latent class models and random parameter specifications using mixed logit models. They highlighted advantages of both models, including the semiparametric nature of the latent class model, which can prevent the researcher from making ‘‘strong or unwarranted distributional assumptions about individual heterogeneity’’. While both model types are subject to assumptions from the researcher (specifically the form of the distributions for the mixed logit models and the number of classes and the class-membership model for latent class models), for this application we find discrete heterogeneity to give more intuitive results. 2. Data The data used in this analysis comes from the RSG Air Passenger Survey which was fielded in 2012. The survey sample includes a total of 830 people across the United States. Each person faced a series of stated preference experiments that included two air travel itinerary alternatives. These experimental itineraries were pivoted off a reported trip the respondent recently completed. The itinerary attributes were varied according to a D-optimal design and include the various service levels such as travel time, connections, airline, aircraft type, arrival time and on-time performance. The D-optimality

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criterion is one of the most commonly used maximization criteria for experimental choice methods. The D-optimal design seeks to maximize the determinant of the information matrix for the design (Kanninen, 2002). Each person was asked to make a total of eight choices. An example of the two itineraries as displayed to the respondent is shown below in Fig. 1. A list of the attributes used in the surveys, along with the levels for each, is shown below in Table 1. Background information for each passenger was gathered in the survey, including income, trip purpose, and membership in airline FFPs. The median individual income in the sample is $75,000/year, with a roughly symmetric distribution on either side of the median. 324 out of the 830 individuals (39%) indicated a business trip, rather than vacation or visiting family and friends. 661 individuals (79%) were at least a basic member of one FFP, while 176 (21%) were elite FFP members of at least one airline. On average, the individuals with FFP membership of any kind have membership with three different airlines. Southwest has the largest portion of FFP membership in our sample, with 383 members (46%), while Delta was second with 357 members (43%). 3. Multinomial logit model 3.1. Model specification We use a random utility model with a linear-in-parameters utility function to model the choices from respondents. We assume the respondents choose an itinerary that maximizes their utility. The utility that person n attains from alternative j is represented by the following:

U nj ¼ x0nj b þ nj

ð1Þ

where x0nj is a vector of explanatory variables and b is a vector of coefficients to be estimated. We assume that ij is distributed iid extreme value, resulting in the familiar Mulinomial Logit (MNL) model. The MNL model has the following closed-form expression for the probability of choosing alternative i: 0

exni b Pni ¼ PJ x0 b nj j¼1 e

ð2Þ

Fig. 1. Survey itinerary choice example.

Table 1 Survey attributes and levels. Variable name

Levels

Airline Aircraft type Departure time Number of connections Total travel time Flight arrival time On-time performance (%) Fare (%)

Most preferred airline as listed by respondent, 2nd most preferred, 3rd most preferred, and least preferred Prop, regional jet, narrow body, wide body Based on calculated travel time and arrival time 0, 1, or 2 Calculated time based on origin, destination, and number of connections multiplied by a factor of 0.9, 1, 1.1, or 1.2 Relative to preferred arrival time as listed by respondent: 1 h earlier, same time, 1 h later, and 2 h later 90, 80, 70, and 60 40, 20, +20, or +40 of original fare

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Service level variables for a particular alternative include travel time, number of connections, fare, aircraft type, on-time performance, and the difference between scheduled arrival time and preferred arrival time. We enter travel time and fare in the utility function nonlinearly. Specifically, we use the natural log of both travel time and fare to capture travel time and fare sensitivities that are a function of the travel time and fare, respectively. For example, consider the marginal utility of fare when a natural log transformation is used:

@U @ðbFare ln FareÞ 1 ¼ ¼ b @Fare @Fare Fare Fare

ð3Þ

The natural log transformation causes the marginal utility for fare to decrease as fare increases. This specification changes the interpretation of the marginal utility for fare to be a constant percentage of the fare rather than a constant magnitude for all fares. This might not sound like a reasonable assumption, but it can be argued that the sensitivity to air fare works on a proportional basis, where a constant fare difference has less of an impact relative to a larger base fare than a smaller base fare. For this reason, along with the drastically improved model fit, we keep the log transformations for both air fare and travel time. The marginal utility for travel time is calculated in the same manner as fare. We include dummy variables for seven airlines (Delta, American, Southwest, Jet Blue, US Airways, United, and Continental), with the other airlines set to zero as a base category. The airlines with dummy variables are the airlines with which we have FFP membership information for each respondent. A total of 25 airlines are included in the survey, but we are primarily interested in accounting for airline-specific effects only for those airlines where we have FFP information, thus we set the remaining 18 airlines to zero as a base category. Since the choice situations are constructed based on a recently completed trip for each person, we include a dummy variable that indicates whether the alternative has the same airline as the original itinerary. This variable will capture any inertia effects separate from airline-specific preferences that are present in the choice experiment. We also include variables that capture the type of aircraft, the on-time performance of the flight, and the difference between the respondent’s stated preferred arrival time and the actual arrival time of the flight. Heterogeneity with respect to fare sensitivity is captured by multiplying a trip purpose dummy variable (business or leisure) with the fare variable. FFP membership enters our model as an interaction between a user-specific FFP membership dummy variable for each airline (one variable for basic membership and one variable for elite membership) and an alternative-specific airline dummy variable. Our FFP membership variable is alternative-specific, having a value equal to one if the respondent has FFP membership with the airline for a given alternative and zero otherwise. The full list of explanatory variables used in the model is shown below in Table 2. 3.2. Estimation results Estimation results from the MNL model are shown in Table 3. The coefficient estimates for log(travel time), number of connections, and log(fare) are all negative and highly significant, which is consistent with our expectations. In general, respondents prefer lower fares, shorter flights, and fewer connections. The FFP Membership variables (both basic and elite) are both positive and highly significant, indicating that the respondents have a preference for flying with an airline with which they have FFP membership compared to a non-FFP airline. The elite FFP variable has a larger magnitude than the basic FFP variable, indicating a higher preference when the passenger is an elite member of an airline’s FFP. Elite FFP membership provides more benefits than basic membership, some of which include more upgrade opportunities, mileage bonuses, checked bags, faster security lines, and improved customer service. It is no surprise that respondents exhibit a stronger preference for airlines with which they have elite FFP membership compared with one with which they have basic FFP membership. We should mention here the possibility of endogeneity for our FFP membership variables. FFP membership for a particular airline might indicate the presence of an unobserved pattern of selecting that airline or the presence of unobserved

Table 2 Explanatory variables for multinomial logit model.

a

Variable name

Description

log(Travel time) Connections log(Fare) Business FFP (basic) FFP (elite) Aircraft type On-time performance Preferred versus scheduled arrival time Airline Original airline

Natural log of total flight time (h) Categorical (0a, 1, or 2) Natural log of air fare, in dollars ($) Dummy variable, 1 if trip purpose is business Dummy variable, 1 if individual has basic FFP membership for airline in the given alternative Dummy variable, 1 if individual has elite FFP membership for airline in the given alternative Categorical (Widebody, Narrowbody, Regional Jet, Propa) Categorical (60%a, 70%, 80%, 90%) Categorical (1 h early, Samea, 1 h late, 2 h late) Dummy variables for each airline Dummy variable, 1 if airline in the alternative is the same as one in original itinerary

Bolded categories set as base.

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M. Seelhorst, Y. Liu / Transportation Research Part A 80 (2015) 49–61 Table 3 Multinomial Logit Estimation Results. Variable

Estimate

ASC (Option 1) log(Total travel time (hr))a No connection (base) 1 Connection 2 Connections log(Fare ($))a log(Fare ($))  businessb FFP membership (basic) FFP membership (elite) Widebody Narrowbody Regional jet Prop(Base) 60% on-time (base) 70% on-time 80% on-time 90% on-time Arr. time 1 hour early Arr. time = preferred time (base) Arr. time 1 hour late Arr. time 2 hours late Delta American Southwest JetBlue US airways United Continental Original airline Log likelihood Rho-squared Adjusted rho-squared

0.168 1.497 0.000 0.671 1.276 2.901 0.717 0.405 0.669 1.174 0.947 0.653 0.000 0.000 0.369 0.480 0.618 0.143 0.000 0.028 0.039 0.034 0.083 0.267 0.064 0.056 0.126 0.103 0.321 3400.84 0.301 0.296

SE ⁄⁄ ⁄⁄

⁄⁄ ⁄⁄ ⁄⁄ ⁄⁄ ⁄⁄ ⁄⁄ ⁄⁄ ⁄⁄ ⁄⁄

⁄⁄ ⁄⁄ ⁄⁄ ⁄⁄

⁄⁄

⁄⁄

0.030 0.196 – 0.083 0.108 0.101 0.144 0.070 0.119 0.119 0.095 0.096 – – 0.061 0.061 0.062 0.059 – 0.061 0.059 0.087 0.092 0.087 0.095 0.100 0.093 0.119 0.056

⁄

Significant at 5% level. a Prior to settling on this specification, we estimated a model with fare and travel time entering linearly. We do not show the results here, but simply emphasize that the specification using the natural log of travel time and fare yield significant improvements to model fit (LL: 3400 versus 3785). Thus, we have strong evidence that sensitivity to fare and travel time is non-linear. Although there are many ways of capturing non-linear preferences, the natural log specification lends itself to an easy interpretation. The marginal utility of fare and travel time is a constant percentage value of fare and travel time, respectively (see Eq. (3)). b The fare variable with no business interaction corresponds to those respondents with non-business trips. The positive sign for the fare-business interaction variable suggests that business passengers have lower price sensitivity than non-business passengers. ⁄⁄ Significant at 1% level.

attributes for that airline that the individual finds beneficial. We cannot separate these possible unobserved factors from FFP membership itself, however. If these unobserved factors are present, we would expect the estimated FFP coefficients in our model to have an upward bias. We would also expect the bias to be stronger for the case of elite membership relative to basic membership. The possibility of endogeneity does not change the interpretation of the results, however. We must simply keep in mind the possible upward bias on all of the FFP membership coefficient estimates. Train and Winston (2007) found a similar issue with respect to brand loyalty in a study on vehicle choice. The authors could not rule out the possibility of the brand loyalty variables being correlated with unobserved factors influencing demand. Similarly, we acknowledge the possibility of endogeneity and continue with the interpretation of the results. The aircraft type variables are all positive and significant, with the largest coefficients corresponding to the largest aircraft type (widebody). The smaller the aircraft type, the less preferred it is by the respondents. The on-time performance variables are all significant and positive, with the higher on-time performance categories having larger coefficients. This indicates that flights with higher on-time performance are preferred to those with lower on-time performance. For the preferred arrival time variables, the category for arriving 1 h earlier than the preferred arrival time is negative and significant and both of the late arrival variables are not significant. These variables are defined as the difference between the arrival time of the flight and the stated preferred arrival time by the respondent in the survey. These results indicate that respondents do not prefer an early arrival and are indifferent between an on-time or late arrival, relative to their stated preferred arrival time. While this might seem counterintuitive, we must remember that we are not measuring the effect of departure times in our model. Earlier arrival times are associated with earlier (often early in the morning) departure times. It is possible that these variables are capturing a disutility towards earlier departure times, rather than a preference for late arrival times.

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The airline dummy variables are used to capture respondents’ preferences for specific airlines, independent of FFP membership. Note that only one of the airlines, Southwest Airlines, has a significant estimate at the 1% or 5% level. This suggests that Southwest is more attractive to respondents than all of the other airlines, beyond any differences in flight characteristics or FFP membership of the respondent. Another interpretation of these estimates is the lack of any particular preference order among the six remaining airlines, which include five legacy carriers (Delta, American, United, US Airways, and Continental) and JetBlue. Other than differences between FFP programs, there is no strong preference for any one of these airlines among our sample. These airlines could be effectively treated like commodities, with FFP membership and flight characteristics being the primary distinguishing factors between brands. The coefficient for the original airline chosen in the respondent’s reference trip is positive and highly significant. This is an indication that an inertia effect exists where respondents tend to prefer their original airline, even after controlling for flight characteristics, FFP membership, and specific airline effects. 3.3. Willingness-to-pay estimates Willingness-to-Pay (WTP) is estimated for both travel time (Value-of-Time, or VOT) and FFP membership, using the MNL model results. As shown in Eq. (3), fare sensitivity is a function of the fare itself. As a result, the WTP estimates vary with fare. In Table 4, we thus present WTP estimates for four representative air fares, ranging from $100 to $700. In the same way, travel time sensitivity is also a function of travel time. WTP for travel time is calculated for two representative trip times, 4 h and 6 h. The WTP estimates are calculated separately for non-business and business trips. For each type of trip, we also estimate the average WTP value by calculating the WTP for each choice situation and aggregating over all choice situations and respondents in the dataset. We did this by using the fare and travel time for each alternative that was chosen by the respondent in the calculation of WTP and averaging the results for all non-business respondents and business respondents separately. Our average WTP estimates for travel time, $36/hr for non-business travelers and $54/hr for business travelers, appear to be slightly low compared to previous research (Adler et al., 2005; Garrow et al., 2007; Warburg et al., 2006). When we estimate a model specification without a natural log transformation for fare, we get slightly larger estimates, $40 for non-business and $70 for business trips. These estimates more closely match the results found in the literature. However, our results suggest these WTP estimates could be inflated, since using a nonlinear price sensitivity specification resulted in a much better model fit (Log-Likelihood: 3400 versus 3785). Non-business travelers are willing to pay about 13% more to fly with an airline that they have basic FFP membership with, and 23% more if they have elite status. Business travelers are willing to pay about 18% to 30% more, for individuals with basic and elite FFP membership, respectively. These WTP estimates are roughly similar in magnitude to the results from literature. Proussaloglou and Koppelman (1999) have shown WTP estimates for airlines with which the respondent has FFP membership ranging from $7 to $72, depending on trip purpose and FFP level. Hess and Adler (2011) found WTP estimates differentiated based on the level of FFP membership and trip purpose, with values over $100 for elite membership business travelers. Our model is able to generate WTP estimates for travelers based on trip purpose, FFP membership level and fare level. This model is a good first step towards identifying market segments that differ in both price sensitivity and preferences for airlines where the individual has FFP status. However, we anticipate that there exists preference heterogeneity beyond that which is found using socioeconomic interactions. In the next section, we will employ latent class models to account for unobserved heterogeneity that is not captured by our MNL model. 4. Latent class model In this section, we use latent class models to identify discrete market segments such that each class has a different set of coefficients, and thus preferences, for the same set of explanatory variables. Specifically, we are interested in determining Table 4 Multinomial logit model, willingness-to-pay estimates. Fare ($)

Time ($/hr) (4-h trip)

Time ($/hr) (6-h trip)

FFP basic

FFP elite

Non-business $100 $300 $500 $700 Average

$12 $38 $64 $90 All trip lengths: $36 per hour

$9 $25 $43 $60

$13 $41 $68 $96 $45

$23 $69 $115 $161 $74

Business $100 $300 $500 $700

$17 $51 $86 $120

$11 $34 $57 $80

$18 $55 $92 $130

$30 $92 $153 $214

Average

All trip lengths: $54 per hour

$68

$113

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different patterns of WTP that vary across groups of individuals in the population. In the previous section, we captured WTP heterogeneity through interacting trip purpose with fare. That segmentation was highly significant, but overly simplistic and restrictive. In this section, we estimate three sets of unobserved, or latent, classes of coefficients without making any assumptions as to the individuals corresponding to each class. The benefit of this method is that we are not restrictive in our assignment of individuals to certain classes based on our choice of variable interactions, as we were in the previous model. We let the choices made by the individuals determine the segmentation for us. Latent class models will allow us to explore a much richer level of heterogeneity with respect to WTP values than an MNL model with variable interactions. The framework for latent class models is not able to deterministically place respondents into one class or another solely based on their sociodemographic characteristics, however. Instead, each respondent is assigned probabilities for each class based on a class-membership model that includes sociodemographic information. The sociodemographic variables act as indicators of class-membership, rather than deterministic predictors. Specifically, we will use income, trip purpose, gender, age, and average flight frequency to determine the class-membership probabilities for each respondent. For us to acquire the same level of granularity in an MNL model we would have to use the full combination of interactions for all five sociodemographic variables with fare. Such a fine segmentation would likely lead to identification issues and make interpretation difficult if not impossible. Using a class-membership model allows us to see which sociodemographic variables are significant drivers of WTP heterogeneity without the issues associated with multiple variable interactions. The model form of the class-membership model is logit, so the class-membership probabilities will be calculated using the same formula as to determine the choice probabilities in a logit model (Eq. 2). 4.1. Model specification Latent class models are comprised of two components: the class-membership model and the class-specific model. The class-membership model assigns a probability of class membership to each person in a similar way that an MNL model assigns a probability for each alternative in a single choice. The class membership probability is shown below:

Pðsjxn Þ

ð4Þ

where xn is a set of characteristics for individual n and latent class s, with the number of classes defined by the researcher. We will use income, trip purpose, gender, age, and average flight frequency as our individual characteristics. The class-membership model provides the probability of a given individual to be a member of each class. The class-specific model estimates the set of preferences for each class. The set of preferences defined in this model vary across each class. Conditional on class membership, the choice probability for the class-specific model is shown below:

Pðijyn ; sÞ

ð5Þ

which represents the probability of choosing alternative i given explanatory variables yn and class-membership, s. The choice probabilities of each model must be estimated simultaneously, using a latent class choice model:

Pðijxn ; yn Þ ¼

S X Pðijyn ; sÞPðsjxn Þ

ð6Þ

s¼1

Both the class-membership model and the class-specific model can take on many forms. For this study we use the MNL form for both models. Any or all of the explanatory variables can be estimated as class-specific, or can be constrained to be the same across all classes. Our focus in this study is to capture preference heterogeneity across classes for certain variables only, specifically fare and FFP membership. The large number of variables (and resulting degrees of freedom) created by using class-specific estimates for all explanatory variables is not justified from the standpoint of succinctness, behavioral interpretation, or improved model fit (using BIC as our criterion). Preliminary model estimations were performed using class-specific effects for all of the explanatory variables. Many of the estimates indicated preferences that were not statistically different across classes, and the model fit was much worse than a model with some of the variables’ coefficients constrained across all classes. As such, we will constrain the coefficients for the following variables to be equal across classes in the estimation: on-time performance, preferred versus scheduled arrival time, airline fixed effects, and the airline chosen in the original itinerary. The coefficient estimates for these variables are interpreted as being the same for each person in the sample, regardless of class membership. The explanatory variables for each model are shown below in Table 5. Class membership probabilities will be a function of income, trip purpose, gender, age, and the typical travel patterns of the respondent, represented by the average number of flights taken per year. For each class, we will estimate a set of parameters for the explanatory variables in the class-specific model category, including a class-specific constant (CSC). Our final specification includes three classes. We tested three different specifications, each with a different number of classes, ranging from two to four. We evaluated each model based on three goodness-of-fit measures: log-likelihood, Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC). We chose the specification with three classes because it resulted in the lowest BIC value and also had results that were intuitive and easily interpretable. The summary of model fits for each class is shown below in Table 6.

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Table 5 Latent class model variables.

a

Variable

Description

Class-membership model variables Income Business Male Age Flight frequency

Continuous, annual income ($10,000s per year) Dummy variable, equal to 1 if trip purpose is business Dummy variable, equal to 1 if respondent is male Continuous, age of respondent (10s of years) Continuous, average number of trips made per year (10s trips per year)

Class-specific model variables log(Travel time) Connections log(Fare) FFP (Basic) FFP (Elite) Aircraft Type

Natural log of total flight time (hours) Categorical (0a, 1, or 2) Natural log of air fare, in dollars ($) Dummy variable, 1 if individual has basic FFP membership for given alternative Dummy variable, 1 if individual has elite FFP membership for given alternative Categorical (Widebody, Narrowbody, Regional Jet, Propa)

Coefficients fixed across classes On-time Performance Preferred versus Scheduled Arrival Time Airline Original Airline

Categorical (60%a, 70%, 80%, 90%) Categorical (1 h early, Samea, 1 h late, 2 h late) Dummy variables for each airline Dummy variable, 1 if airline in the alternative is the same as one in original itinerary

Bolded categories set as base.

Table 6 Latent class model fit summary. Model specification

Number of parameters

Log-likelihood

AIC

BIC

2 Classes 3 Classes 4 Classes

26 42 58

3253.3 3143.5 3111.4

6558.5 6370.9 6338.9

6736.8 6658.9 6736.6

4.2. Estimation results The estimation results from the class membership model are shown below in Table 7. The coefficient signs are interpreted relative to Class 1, since it is set to zero as a base. First, consider the income variables. High income individuals are less likely to be in Class 3 than Class 1 or Class 2, since the coefficient for Class 3 is negative and significant while the coefficient for Class 2 is not significant. Now consider the business variables. An individual traveling for business is less likely to be in Class 3 than Class 1 or Class 2, similar to the high income traveler. By a similar interpretation, males are more likely to be in Class 2 than Class 1 or Class 3, older individuals are less likely to be in Class 3 than Class 1 or Class 2, and individuals with high trip frequency are more likely to be in Class 2 than Class 1 or Class 3. We can get an idea for the most likely class for certain types of individuals from the sign and significance of the coefficient estimates. For example, older, male, wealthy business travelers who travel frequently are much more likely to be in Class 2 than Class 1 or Class 3. To be more explicit with the relative likelihood of class membership for specific individuals, we can calculate the probability of class membership for various combinations of the variables shown above using the class-membership probability function, which follows a closed form since we are using the MNL model as our structure: 0

exn bs Pðsjxn Þ ¼ PS x0n bp p¼1 e

ð7Þ

where bs is the set of coefficient estimates for a particular class, s. Rather than just use the point estimates of the coefficients in the class membership probability calculations, we simulate the sampling distribution of each estimate with one thousand draws, calculate class membership probabilities for each draw, and average the results. The probabilities of class membership for three hypothetical individuals are shown below in Table 8. The probabilities in Table 8 are read as the probability of a particular class membership, given the socioeconomic characteristics listed for each person. Given the trends in the class membership results in Table 7, we chose three sets of class-membership variables that result in high probabilities for each of the three classes. For instance, Person A was selected as a low-income, young, female leisure traveler to have a high probability of being in Class 3. Person B was selected as a high-income, old, female, business traveler with low flight frequency to have a high probability of being in Class 1. And person C was selected as a high-income, young, male business traveler with high flight frequency to have a high probability of being in Class 2. The highest class membership probability for our three sample persons was 0.74 for Class 2 for person C. Also, the average class-membership probabilities across all individuals in our sample were 0.39 for Class 1, 0.25 for Class 2, and 0.36 for Class 3.

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M. Seelhorst, Y. Liu / Transportation Research Part A 80 (2015) 49–61 Table 7 Class membership model results.

⁄ ⁄⁄

Variable

Estimate

SE

Class-specific constant (Class2) Class-specific constant (Class3) Income ($10,000s/year) (Class2) Income ($10,000s/year) (Class3) Business (Class2) Business (Class3) Male (Class2) Male (Class3) Age (10s) (Class2) Age (10s) (Class3) Flight Frequency (10s trips/yr) (Class2) Flight Frequency (10s trips/yr) (Class3)

0.545 1.083 0.041 0.069 0.023 0.473 0.764 0.412 0.102 0.167 0.603 0.238

0.468 0.386 0.023 0.019 0.258 0.228 0.266 0.227 0.097 0.079 0.177 0.165

⁄⁄

⁄⁄

⁄ ⁄⁄

⁄ ⁄⁄

Significant at 5% level. Significant at 1% level.

Table 8 Class membership probabilities. Sample individual

Average

A

B

C

Class-membership variable Income ($10,000s) Business Male Age (10s) Flight Frequency (10s trips/yr)

2 0 0 2 0.5

15 1 0 6 0.5

15 1 1 2 6

8.93 0.39 0.41 4.21 0.77

Class-membership probabilities Class 1 Class 2 Class 3

0.27 0.17 0.56

0.60 0.21 0.18

0.08 0.74 0.18

0.39 0.25 0.36

The three sample sets of class-membership variables are indicative of the range of the variables observed in the sample. The range of each variable across the three sample individuals represents at least 90% of all individuals in our sample. We can think of the sample individuals as being individuals within our sample that are most likely to be in a particular class based on the class-membership variables. These results indicate that the class-membership probabilities for any individual will be at most around 0.75, even with an ideal set of sociodemographic characteristics for any particular class. This points to a significant amount of heterogeneity with respect to class-membership that is not captured directly in the model. Rather, the sociodemographic characteristics are used as indicators of class membership, but are certainly not deterministic. These class-membership probabilities further support our inferences based on the class-membership estimates in Table 7. Now we present the results from the class-specific models. The fixed coefficient estimates are shown below in Table 9. These estimation results do not vary across classes and are interpreted in a similar fashion as the MNL results in Table 3. We see a similar trend as the MNL model results for on-time performance, with utility increasing as the average on-time performance increases. For the preferred arrival time, arriving early is less desired than the other options, which is also consistent with the MNL results. The results indicate there is no difference between arriving late and arriving on-time, however. The airline preferences match the MNL results almost exactly. Southwest Airlines is the only airline with a positive and significant sign. The original airline flown by the respondent still has a very strong effect on the choice, indicating that respondents are more likely to choose an itinerary with their original airline than another itinerary with a different airline. Now we discuss the different preferences found in each latent class. The class-specific estimates for each class are shown below in Table 10. We first compare the estimates across classes and then take a close look at each class separately. The travel time variable is significant in all three classes, with Class 2 having the smallest magnitude coefficicent. The number of connections is only significant in Class 1 and Class 3, with Class 1 having a larger effect. Thus, Class 2 is the class least sensitive to travel time and number of connections, while Class 1 is the most sensitive. The fare coefficient is significant in all three classes, with Class 3 having the largest magnitude and Class 2 having the lowest magnitude. The FFP membership variables are significant in Class 2 and Class 3, but not in Class 1. Lastly, the aircraft type variables are only significant for Class 1. Our results identify three distinct sets of air traveler preferences. Class 1 individuals have a strong aversion for long flights with many connections, average price sensitivity, a strong preference for large aircraft, and almost no sensitivity to FFP membership. This class makes up 39% of our sample, which is much larger than the percentage of individuals without any FFP membership (20%), so we can conclude that we do find evidence that some individuals who have FFP membership with at least one airline tend to place little focus on FFP membership when choosing itineraries, instead placing a higher

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M. Seelhorst, Y. Liu / Transportation Research Part A 80 (2015) 49–61 Table 9 Fixed coefficient estimates.

⁄ ⁄⁄

Variable

Estimate

60% On-time (base) 70% On-time 80% On-time 90% On-time Arr. time 1 h early Arr. time = preferred time (base) Arr. time 1 h late Arr. time 2 h late Delta American Southwest JetBlue US airways United Continental Original airline

0.000 0.458 0.679 0.827 0.162 0.000 0.056 0.137 0.066 0.033 0.307 0.125 0.111 0.102 0.012 0.490

SE – 0.078 0.081 0.076 0.076 – 0.077 0.075 0.109 0.115 0.112 0.119 0.123 0.116 0.150 0.072

⁄⁄ ⁄⁄ ⁄⁄ ⁄

⁄⁄

⁄⁄

Significant at 5% level. Significant at 1% level.

Table 10 Class-specific model results. Variable

ASC (Option 1) log(Total travel time (hr)) No connection (base) 1 Connection 2 Connections log(Fare ($)) FFP membership (basic) FFP membership (elite) Widebody Narrowbody Regional jet Prop(Base) ⁄ ⁄⁄

Class 1

Class 2

Est.

SE

Est.

0.08 3.31 0.00 1.54 3.07 3.21 0.27 0.57 4.32 4.01 3.64 0.00

0.07 0.66 – 0.25 0.40 0.32 0.16 0.35 0.56 0.56 0.59 –

0.35 1.59 0.00 0.05 0.11 0.44 0.98 0.97 0.01 0.09 -0.27 0.00

⁄⁄

⁄⁄ ⁄⁄ ⁄⁄

⁄⁄ ⁄⁄ ⁄⁄

Class 3

⁄⁄ ⁄⁄

⁄⁄ ⁄⁄ ⁄⁄

SE

Est.

0.06 0.42 – 0.18 0.26 0.17 0.18 0.26 0.25 0.19 0.21 –

0.19 3.30 0.00 0.75 1.23 9.92 0.44 1.29 0.03 0.24 0.04 0.00

SE ⁄ ⁄⁄

⁄⁄ ⁄⁄ ⁄⁄ ⁄ ⁄⁄

0.09 0.65 – 0.24 0.32 1.00 0.19 0.44 0.39 0.33 0.32 –

Significant at 5% level. Significant at 1% level.

emphasis on typical flight attributes such as travel time, number of connections, and fare. Higher income, older, female business travelers that do not travel often are the individuals with the highest probability of being in Class 1, based on the results from the class-membership model. Class 2 individuals have a strong preference for flying with their FFP airline, low price and travel time sensitivity, and virtually no sensitivity to aircraft type or number of connections. This group of travelers consists of highly loyal frequent flyers, for both basic and elite members, who prefer their FFP airline over other airlines without much regard to other flight attributes. This behavior might be indicative of additional factors not captured in the model, such as limited choice of airline or brand loyalty for some individuals. Those individuals that are hub captive with a particular carrier or those who are required to fly certain carriers for their jobs might not consider all airlines in the same way as other individuals. This class is the smallest of the three, at 25% of our sample. Higher income, younger, male business travelers with many annual trips are the individuals with the highest probability of being in Class 2. Class 3 individuals have the highest price sensitivity of all classes, average sensitivity to number of connections and travel time, and strong preference for their FFP airline, particularly for the elite members. The elite membership FFP coefficient is the highest for all three classes, while the basic membership FFP coefficient is smaller than that of Class 2. While this class is fairly sensitive to the traditional flight attributes, particularly fare, this class exhibits a strong preference for FFP airlines as well. This class represents 36% of our sample. Lower income, female, younger, non-business travelers with few annual trips are the individuals with the highest probability of being in Class 3. 4.3. Willingness-to-pay estimates In Table 11, we present the WTP estimates for each class from the latent class model results. The WTP estimates were calculated using the point estimates from Table 10. The left side of Table 11 shows the Value-of-Time (VOT) calculations

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M. Seelhorst, Y. Liu / Transportation Research Part A 80 (2015) 49–61 Table 11 Latent class model, willingness-to-pay estimates. VOT ($/hr) Fare ($)

4-h trip

Class

1

WTP for FFP Airline ($) 6-h trip 2 $89 $268 $448 $627

3

$100 $300 $500 $700

$25 $77 $128 $180

$8 $24 $41 $58

Average

All trip lengths: $106/hr

1 $17 $51 $85 $120

Basic 2 $59 $179 $298 $418

3 $5 $16 $27 $38

1 a

$8 $25 $42 $59 $217

Elite 2

3

1

2

3

$220 $661 $1104 $1544

$4 $13 $22 $31

$17 $53 $88 $123

$219 $658 $1096 $1535

$13 $39 $65 $91

$238

a

Both FFP variables for Class 1 were not significant at a 5% level. These WTP values were calculated using the point estimates without considering standard errors, so the WTP estimates themselves are also not significantly different from zero.

for a four hour and six hour reference trip time, while the right side shows the WTP values for both basic FFP membership and elite FFP membership. The WTP values for each class are shown side-by-side for easier comparison. There is large variation in the VOT estimates across classes. Class 3 has the lowest VOT, ranging from 5% of the fare cost for a 6-h trip to 8% of the fare cost for a 4-h trip. In contrast, Class 2 has extremely large VOT estimates, ranging from 59% of the fare for a six hour flight to 89% of the fare of a four hour flight. The individuals in Class 2 would be willing to pay a premium of over 50% for a reduction in travel time of one hour on a six hour flight. The FFP estimates show even more dramatic differences across classes. The WTP estimates for Class 3 are lower than those for Class 2 and Class 1. Class 1, however, does not have significant estimates for the FFP variables, so these estimates are considered to be not significantly different from zero. The WTP estimates for Class 3 range from 4% of the fare for basic FFP membership to 13% of the fare for elite FFP membership. These are somewhat lower than the WTP estimates for non-business passengers shown in Table 10. The WTP estimates for Class 2 are much larger, however. Class 2 individuals will pay a 220% premium to fly with their FFP airline, for both basic and elite members. These individuals appear to have no regard for price when considering FFP membership and airline choice. These results are qualitatively very different than those obtained from the MNL model. The MNL model results indicate distinct WTP values for business and leisure travelers for both basic and elite FFP membership. The WTP values are larger for elite membership and for business travelers. All individuals in our sample would be given a moderate, non-zero value of WTP using this method. The latent class models, however, indicate that there exist three very different classes of individuals within the population. First, we have Class 1, which does not have any significant preference for FFP membership, but has a reasonably large VOT. Second, we have Class 2, which has such low price sensitivity that we see very large WTP estimates for both time and airlines with which the individuals have FFP membership. Finally, we have Class 3, which has a significant preference for airlines with which the individuals have FFP membership, but are price sensitive enough to not produce large WTP values. These classes of estimates are very interesting, if for no other reason than they could not have easily been estimated with traditional model structures that capture random heterogeneity, such as the mixed logit model. While the mixed logit model is a very flexible model, it is not the best choice if discrete heterogeneity of preferences is of interest. Furthermore, these results indicate that segments of the population with WTP values near zero (Class 1) or with price coefficients near zero (Class 2) can distort the estimates when using a MNL specification, even with systematic heterogeneity.

5. Conclusions In this paper, we investigate the effects of FFP membership on itinerary choice through the use of a multinomial logit model and a latent class model. In the multinomial logit model, we capture FFP membership through an interaction term between a dummy variable for the FFP membership of the individual and a dummy variable for the airline of the itinerary. The interaction term is equal to one if the respondent has FFP membership with the airline listed in the itinerary. We distinguish between basic and elite FFP membership with two different variables. The only means of preference heterogeneity is captured with respect to trip purpose and price through an interaction term with a dummy variable representing a business trip and by using the log of air fare as the price variable. We also use airline dummy variables to capture preferences for particular airlines, including a separate dummy variable for the airline chosen by the respondent on an earlier itinerary. We include other effects related to the choice of flight itinerary, including aircraft type, on-time performance, and preferred arrival time. Results from the MNL model indicate that FFP membership, particularly elite membership, is a strong driver of itinerary choice. Using the coefficients for fare and FFP membership we calculate WTP values for choosing an airline with which the traveler has FFP membership. Four different WTP values are calculated due to the specification having separate variables for basic and elite FFP membership and fare entering by itself and as an interaction with trip purpose. The fare variable is entered in the model as the log of fare, which implies that the WTP values are a constant percentage of air fare for a given trip purpose and FFP membership. We calculate WTP estimates ranging from 13% of the fare for non-business travelers with

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basic FFP membership to 30% of air fare for business travelers with elite FFP membership. Aggregated over all individuals in our sample, the average WTP value for non-business travelers with basic FFP membership is $45 and for business travelers with elite FFP membership is $113. Our average values of time are $36/hr for non-business travelers and $54/hr for business travelers. Compared to the values of time, the FFP WTP estimates are quite large. We see strong evidence that FFP membership is a major driver of itinerary choice. We also find that most airlines, with the exception of Southwest, do not exhibit strong effects on itinerary choice beyond the preference for airlines where the respondent has FFP membership. This indicates that without considering FFP effects, airlines are effectively treated like commodities, where a greater emphasis is placed on flight attributes such as price, number of connections, and on-time performance when determining itinerary choice. We also estimate a latent class model to investigate heterogeneity with respect to FFP membership and other flight characteristics. We use sociodemographic variables, such as income, trip purpose, gender, age, and average flight frequency, to determine the class membership for each individual. Our final model specification uses three classes, each with its own set of coefficient estimates for travel time, number of connections, fare, FFP membership, and aircraft type. Since our primary focus is on the effects of FFP membership and to limit the number of estimated variables in our model, we constrain the coefficients for on-time performance, preferred arrival time, and airline fixed effects to remain constant across all classes. From our results we identify three very different sets of preferences and WTP values corresponding to each class. To recall, higher income, older, female business travelers that do not travel often are the individuals with the highest probability of being in Class 1. Higher income, younger, male business travelers with many annual trips are the individuals with the highest probability of being in Class 2. Lower income, female, younger, non-business travelers with few annual trips are the individuals with the highest probability of being in Class 3. Class 1, which represents 39% of our sample, exhibits average sensitivity to travel time, fare, and connections, but has no preference for airlines with which the individual has FFP membership. Class 2 has very low sensitivity to travel time, fare, and connections, and strong preference for airlines with which the individual has FFP membership, for both basic and elite membership levels. Class 3 has the highest price sensitivity of all the classes as well as moderate sensitivity to travel time and connections, but exhibits a strong preference for flying with the FFP airline of the individual, particularly for elite FFP memberships. From these three classes we estimate WTP values for both travel time and for airlines with which the individual has FFP membership. The WTP estimates are not significant for Class 1, extremely large for Class 2, and low compared to the MNL estimates for Class 3. The original estimates from the MNL model suggest moderate WTP estimates that are larger for elite versus basic FFP membership and for business versus leisure travelers. Our latent class model estimates suggest three classes of individuals, where two classes are at opposite ends of the WTP spectrum (not significant for Class 1 and very high for Class 2) and one class has moderate WTP values (Class 3). A latent class model is sufficient to capture the differences in choice behavior observed in this analysis. If a researcher relies solely on MNL or random heterogeneity modeling such as mixed logit, then she might not be able to capture the true underlying heterogeneity, which could be discrete in nature. Systematic heterogeneity is useful for easy segmentation, but can drastically skew the underlying heterogeneity unless latent classes are considered. Latent class models thus provide a good framework for properly identifying heterogeneity with respect to itinerary choice preferences, particularly the effects of FFP membership. Acknowledgements The authors would like to thank Kenneth Train for providing access to his Matlab code that is used as a base for our model estimation and Joan Walker for her comments and discussions. We would also like to thank the following researchers at RSG, Inc. for allowing us to use their survey data as well as providing feedback and suggestions: Jeff Dumont, Jeff Keller, Dan Weinstein, and Tom Adler. References Adler, T., Falzarano, C.S., Spitz, G., 2005. Modeling service trade-offs in air itinerary choices. Transport. Res. Rec.: J. Transport. Res. Board 1915, 20–26. Airlines for America, 2014. Annual crude oil and jet fuel prices. Web. 5 February 2014. Brey, R., Walker, J., 2011. Latent temporal preferences: an application to airline travel. Transport. Res. A 45, 880–895. Chin, A.T.H., 2002. Impact of frequent Flyer programs on the demand for air travel. J. Air Transport. 7, 53–86. Garrow, L.A., Jones, S.P., Parker, R.A., 2007. How much airline customers are willing to pay: an analysis of price sensitivity in online distribution channels. J. Revenue Pricing Manage. 5, 271–290. Greene, W.H., Hensher, D.A., 2002. A latent class model for discrete choice analysis: contrasts with mixed logit. Institute of Transport Studies Working Paper ITSWP-02-08, University of Sydney, April. Harvey, G., 1987. Airport choice in a multiple airport region. Transport. Res. A 21, 439–449. Hess, S., Adler, T., 2011. An analysis of trends in air travel behavior using four related SP datasets collected between 2000 and 2005. J. Air Transport Manage. 17, 244–248. Hess, S., Ryley, T., Davison, L., Adler, T., 2013. Improving the quality of demand forecasts cross nested logit: a stated choice case study of airport, airline and access mode choice. Transportmetrica 9 (4), 358–384. Ishii, J., Jun, S., Dender, K.V., 2009. Air travel choices in multi-airport markets. J. Urban Econ. 65, 216–227. Kanninen, B., 2002. Optimal design for multinomial choice experiments. J. Market. Res. 39 (2), 214–227. Martin, J.C., Roman, C., Espino, R., 2011. Evaluating frequent flyer programs from the air passengers perspective. J. 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