Semiparametric APC analysis of destination choice patterns: Using generalized additive models to quantify the impact of age,period,and cohort on travel distances

Abstract

This study investigates how age, period, and birth cohorts are related to altering travel distances. We analyze a repeated cross-sectional survey of German pleasure travels for the period 1971–2018 using a holistic age–period–cohort (APC) analysis framework. Changes in travel distances are attributed to the life cycle (age effect), macro-level developments (period effect), and generational membership (cohort effect). We introduce ridgeline matrices and partial APC plots as innovative visualization techniques facilitating the intuitive interpretation of complex temporal structures. Generalized additive models are used to circumvent the identification problem by fitting a bivariate tensor product spline between age and period. The results indicate that participation in short-haul trips is mainly associated with age, while participation in long-distance travel predominantly changed over the period. Generational membership shows less association with destination choice concerning travel distance. The presented APC approach is promising to address further questions of interest in tourism research.

Keywords

APC analysis cohort analysis destination choice generalized additive models ridgeline matrices travel distance

Introduction

Overcoming geographic distances is, by definition, one of the constitutive elements of tourism as people need to temporarily travel to places outside their everyday environment to be defined as tourists (Cooper and Hall, 2016). Alterations of tourist flow can be attributed to time-related factors, including developments across the life cycle, over time periods or between successive generations (Oppermann, 1995). Technological developments in transportation (Castro et al., 2020), economic conditions of the source market (Sun and Lin, 2019) and the greater availability of information through modern communication technology (Yang et al., 2018) have facilitated long-distance travel over time. Apart from these external influences, destination choice, and hence travel distance, depends on sociodemographic and psychological characteristics of the traveler (Wong et al., 2016). Travel behavior changes over the course of someone’s life cycle due to changing personal circumstances and increasing age (Bernini and Cracolici, 2015) and between generations (Lohmann and Danielsson, 2001). Furthermore, travel-related factors such as time availability also affect destination choice (McKercher and Mak, 2019).

Thorough analyses of such temporal patterns particularly rely on quantifying and comprehensively communicating the developments over age, period, and cohort. The separation of these factors is performed with statistical age–period–cohort (APC) analysis methods. Therein, each temporal dimension describes characteristic developments regarding the individual traveler or external circumstances of holiday trips. Following Yang and Land (2008), age effects represent the ageing process of an individual, period effects refer to external events and environmental changes, and cohort effects relate to specific groups of individuals who experience the same events in a specific span of time. APC analyses require long-term panel or repeated cross-sectional data (Yang and Land, 2013). Due to the sparse availability of adequate data and the complexity of existing methods, only few studies in tourism research have examined alterations in travel behavior based on all three temporal dimensions so far (e.g. Oppermann, 1995). In this work, we introduce an established APC approach into tourism research by analyzing the temporal development of travel distances of German tourists, investigating the research question:

How are age, period, and cohort related to altering travel distances?

The key challenge in APC analyses is to separate these temporal effects by overcoming the identification problem that each component is a linear combination of the others (Clayton and Schifflers, 1987), for example, age = period − cohort. In other words, the three components can never be fully separated and interpretation requires a thorough understanding of their interrelations. Statistical models based on linear effect structures only yield a unique solution if further assumptions about these interrelations are made. The quality of the solution highly depends on the adequacy of the substantial assumptions and the underlying data.

Novel to tourism research and based on a repeated cross-sectional German survey which covers travel information from almost 50 years, our study highlights the potential of holistic APC modeling to generate a more comprehensive understanding of the factors that drive changes in travel behavior. We provide three major contributions. First, we introduce a state-of-the-art approach for APC analysis into the field of tourism research. It is based on a generalized additive modeling framework, where cohorts are represented as an interaction between age and period. The approach is applicable for panel and repeated cross-sectional data as well as individual and aggregated data. Secondly, we introduce ridgeline matrices and partial APC plots as novel graphical tools for analyzing APC structures to facilitate the communication of complex temporal patterns. The former build on the visualization concept of Lexis diagrams (Carstensen, 2007). Finally, we contribute new insights about the key factors that trigger destination choice by analyzing the associations of age, period, and cohort with altering travel distances using a comprehensive statistical approach which has not yet been applied in tourism science. The latter comprises both the pure analysis of APC structures and the inclusion of further variables potentially associated with altering travel distances. In terms of practical implications, understanding the spatiotemporal movements of tourists and their influencing factors can support practitioners and policy-makers in the planning and management of destinations, including future travel behavior predictions.

Literature review

Geographic distance and destination choice

Tourism literature emphasizes the importance of geographic distance in destination choices (Lee et al., 2012; Yang et al., 2018). Adopted from Tobler’s (1970) first law of geography, the negative impact of distance between origin and destination on destination choice can be explained by distance decay theory: tourism demand declines with increasing geographic distance (McKercher et al., 2008). This spatial decline of outbound tourism demand is associated with rising physical, temporal, and monetary costs (Taylor and Knudson, 1973).

Advances in transportation and communication technologies coupled with reduced travel time and costs have facilitated long-haul travel in the last decades (McKercher and Mak, 2019). These developments lead to the assumption that the negative impact of distance (i.e. the friction effect of distance) on tourism demand diminished over time (Yang et al., 2018), indicating a strong period effect. Even so, studies investigating temporal changes of international tourism flows show that geographic distance still has a substantial impact on demand patterns, supporting the robustness of distance decay theory (Lee et al., 2012; McKercher and Mak, 2019).

How far one is willing to travel depends on sociodemographic and psychographic traits of the traveler such as age, household size, or income (Eugenio-Martin and Campos-Soria, 2011), tripographic characteristics such as trip duration (Guillet et al., 2011), and socioeconomic factors of the place of residence (Sun and Lin, 2019; Wong et al., 2016). The distribution of traveled distances can be visualized by demand curves. Their shape varies depending on the respective source market, type of tourist, and type of travel (McKercher and Mak, 2019; Wong et al., 2017), indicating the influence of such factors on destination choices.

Distance decay studies usually take advantage of available macro data on tourist flows. They use aggregated international tourist arrival or departure data to examine the association between travel distance and international travel patterns (McKercher and Mak, 2019; McKercher et al., 2008; Sun and Lin, 2019). The data sources limit these studies to the analysis of period effects (i.e. the influence of societal and economic factors on temporal changes). For example, Sun and Lin (2019) found that economic welfare and transport capacity are key factors for longer travel distances. The influence of sociodemographic or travel-related characteristics on tourist flows is often neglected in such studies (Yang et al., 2018). Identifying the key factors for changing destination choices considering both external and internal factors remains a challenge in tourism research. It requires both long-term data on individual level and complex statistical approaches such as APC analysis.

Age–period–cohort analysis

Association of age, period, and cohort with travel behavior

Travel behavior is changing over time due to various reasons. To explain temporal developments, research suggests considering three dimensions: age, period, and cohort (e.g. Oppermann, 1995). The effect of an individual’s age on the propensity to travel or the type of holiday experience is generally explained by life cycle theory (Bernini and Cracolici, 2015). According to this concept, age-related shifts in travel behavior are mainly associated with the varying life stages an individual or family passes (Chen and Shoemaker, 2014), ranging from childhood, young adulthood, newly married couple, parenting, empty nest to retirement. Most notably, the different stages are characterized by the change of marital status as well as altering income levels over the life cycle (Bowen and Clarke, 2009). This indicates that age serves as a proxy for these and other personal changes such as physical health (Scheiner and Holz-Rau, 2013). Studies indicate a nonlinear age effect on tourism demand including a small mid-30s to 40s dip in the overall decreasing curve (Collins and Tisdell, 2002). In terms of distance traveled, Oppermann (1995) found a bimodal pattern showing that the propensity for long-distance travel has its maximum among young people in their 20s and a second peak around age 50 (i.e. when children have moved out). The overall negative correlation of age with long-haul travel is associated with a gradual decline in health and mobility (You and O’leary, 2000). However, due to social change and modern life cycles, modifications and extensions of the traditional family life cycle need to be considered. For example, while single-parent families are less likely to choose long-distance destinations, this is not the case for couples of the same age without children (Collins and Tisdell, 2002).

Alterations in travel behavior are also caused by external factors of the macro environment simultaneously affecting people of all ages (Pennington-Gray and Spreng, 2002). These period effects comprise various factors including single events such as terror attacks, which have short- and long-term impacts on travel behavior (Karl et al., 2017), pandemic crises (Romagosa, 2020), as well as long-term trends such as economic developments in the source market (Wong et al., 2016), technological advances in transportation (Castro et al., 2020), and mobile technology (Cohen et al., 2014) or climate change (Gössling et al., 2012). While modern developments in transportation permanently encourage long-distance travel, events such as economic downturns can deter people from traveling overseas (Sun and Lin, 2019). New climate change protection policies and changes in consumers’ perception of air travel (e.g. flight shame) may reduce travel distance in the future (Becken and Carmignani, 2020). Potential long-term changes are also expected due to the COVID-19 pandemic which leads to a revival of short-distance travel (Romagosa, 2020). The impact of such external factors on (future) travel behavior is assessed in tourism demand modeling. Methodological approaches in this field comprise predictive methods purely based on historic tourist data (i.e. time series studies) or based on known causal relationships between demand and explanatory variables (i.e. econometric studies) (Song and Li, 2008). More recent advances in tourism demand modeling include artificial intelligence-based models, where different data sources can be combined to estimate models that are mainly focused on deriving sound predictions (Song et al., 2019).

Besides age and period effects, researchers indicate that travel behavior is also shaped by generational membership (McKercher et al., 2020). According to generational theory, members of a birth cohort share collective values and experiences through epochal events (Pendergast, 2010), reflected in similar consumer behavior patterns (Glover and Prideaux, 2009). Reviewing consumer behavior research in tourism, Cohen et al. (2014) identified generational membership as one of the core influential factors of tourism behavior. The specific beliefs and attitudes of each generation remain consistent over the ageing and life cycle process (Schewe and Noble, 2000). Targeted cohort analyses were applied in various tourism research settings, investigating generational differences regarding travel motivation and preferences (Chen and Shoemaker, 2014; Huang and Lu, 2017; Pennington-Gray et al., 2003), tourism expenditure (Bernini and Cracolici, 2015), online travel information search (Beldona, 2005), tourism experiences sought (Lehto et al., 2008), activity participation (You and O’leary, 2000), and destination choice (Huang and Lu, 2017; Li et al., 2013). Regarding destination selection, studies found that younger generations are more inclined to travel abroad to visit off-the-beaten path destinations (Li et al., 2013). This can be related to the effect of generation-specific socialization experiences on travel behavior (Oppermann, 1995).

Evidently, changes in travel behavior are triggered simultaneously and interactively by the effects of age, period, and cohort. In tourism research, the above stated cohort analyses aim to separate these effects with the main goal of identifying generation-specific consumption patterns. These insights are used for market segmentation (Schewe and Noble, 2000) and as a tool for tourism forecasting (Pennington-Gray et al., 2002). However, due to the sparse availability of long-term data on tourist behavior, studies investigating the temporal variations of travel behavior with a comprehensive (APC) approach are rare (Bernini and Cracolici, 2015). Instead, cohort analyses in tourism are often based on single cross-sectional surveys (e.g. Huang and Lu, 2017) or include only a few time points (e.g. Beldona, 2005). Such data settings exacerbate a reliable separation of age and cohort effects in these studies. Although research confirmed an association between these factors and destination choice (e.g. Bernini and Cracolici, 2015; Oppermann, 1995), to our knowledge no empirical studies have yet analyzed travel distance alterations based on all three temporal dimensions.

Statistical APC approaches

Examining to which extent observed developments can be attributed to each temporal component requires a joint analysis framework. APC analyses have primarily originated in epidemiological science to analyze mortality rates for specific population groups defined by age, period, and cohort (Kupper et al., 1985). The last decades showed an increasing use of APC methods across various research fields (Yang and Land, 2013), also due to the availability of more sophisticated statistical approaches. Descriptive analysis is usually performed with Lexis diagrams (Figure 1), that is, a two-dimensional table or graph depicting age groups and periods in horizontal and vertical direction, respectively (Carstensen, 2007). Accordingly, unique cohorts are displayed along the diagonals.

Figure 1.

Sketch of a Lexis diagram. Period and age are displayed on the x-axis and y-axis, respectively. Cohorts are represented as diagonals.

The most popular version of an APC model for repeated cross-sectional data is defined as a multiplicative three-factor regression model (see, e.g. Holford, 1983). More generally, it is a generalized linear model (GLM, Nelder and Wedderburn, 1972) of the form

g (μ_{apc}) = β_{0} + β_{a} \times {age}_{a} + β_{p} \times {period}_{p} + β_{c} \times {cohort}_{c}

where µ_apc denotes the expected value of an exponential family response for age group $a = 1, \dots, A$ , period $p = 1, \dots, P$ , and cohort $c = 1, \dots, C$ , $g (\cdot)$ denotes the link function, $β_{0}$ denotes the intercept, and $β_{j}$ $(j \in \{a, p, c\})$ denotes the linear coefficients. The parameterization of this classical APC model is based on cross-sectional data aggregated over age groups, periods, and cohorts. However, the structure is easily adaptable to individual data (e.g. Fannon et al., 2018). Panel data can be analyzed by introducing random effects into the model (Diggle et al., 2002).

Given its linear predictor and the linear dependency of age, period, and cohort, model (1) cannot be estimated without setting constraints on the effect structures. Numerous strategies have been developed to overcome the identification problem. While early methods often used strict linear constraints such as the equality of two of the three effects (e.g. Fienberg and Mason, 1979), modern approaches rely on less restrictive assumptions. For instance, Bayesian hierarchical models restrict first- and second-order differences of the effects (e.g. Schmid and Held, 2007); the intrinsic estimator applies a form of principal components regression (Fu, 2000). Clayton and Schifflers (1987) give a detailed consideration to the identification problem and common issues in estimation and interpretation. A thorough overview of existing methodology is given by Yang and Land (2013).

A model class which has gained popularity in APC analysis since the late 1990s (e.g. Carstensen, 2007; Heuer, 1997) is spline-based regression. This approach overcomes the identification problem by estimating potentially nonlinear age, period, and cohort effects. Building on this approach, Clements et al. (2005) propose an APC model using a bivariate spline function depending on age and period in a generalized additive regression model (GAM). The resulting two-dimensional interaction surface implicitly contains information about cohorts on the diagonals. Given data on aggregated level, the model structure is given by

g (μ_{a j c}) = β_{0} + f_{a p} ({age}_{a}, {period}_{p})

where $f (\cdot, \cdot)$ is a nonlinear interaction surface represented by a two-dimensional spline basis. As a direct extension of GLMs, generalized additive regression is a robust and flexible approach for modeling nonlinear effect structures (Wood, 2017). GAMs are applicable to all exponential family responses and to research settings with additional explanatory variables. Penalized splines (e.g. Eilers and Marx, 1996) enable the estimation of nonlinear relationships in the data but avoid overfitting by imposing a penalty on the effect’s roughness. The application of GAMs is facilitated by sophisticated and freely available software (e.g. Wood, 2017).

Data and methods

Database

The data used in this study were collected in the Reiseanalyse, an annual cross-sectional survey on pleasure travel among approximately 7500 German residents (FUR, 2020b). Survey data are available from 1971 to 2018 and comprise around 227,000 holiday trips. Travelers from former East Germany have been included since 1990. The target population comprises (West) German citizens until 2009, and all German-speaking residents thereafter. Data are representative respective to federal state, city size, age, sex, household size and income, education level and citizenship (FUR, 2020a). We focus on five generations following the classification of Herhoffer and Meurer (2018). A description of these generations and their observed data is given in Table 1.

Table 1.

Overview of the generations in the data and the respective periods and age groups in which they were observed.

Generation	Birth years	Relative frequency (%)	Observed periods	Observed ages
Generations born before 1939	1874–1938	25.0	1971–2018	33–99
Silent Generation	1939–1946	13.8	1971–2018	25–79
Baby Boomer	1947–1966	37.5	1971–2018	14–71
Generation X	1967–1982	17.7	1981–2018	14–51
Generation Y	1983–1994	5.2	1997–2018	14–35
Generation Z	1995–2010	0.8	2009–2018	14–23

Note: Generations before 1939 are not of special interest and are summarized.

We analyze travel distances of the main holiday trips, each one defined as the personally most important trip within a year, lasting at least 5 days. This comprises both domestic and outbound travel. Direct distances were calculated in kilometers between the region of origin (i.e. the centroid of the federal state) and the destination. For the latter, we typically use the centroid of the stated country. Information on farther destinations was often not available explicitly but only as part of its greater region (e.g. “Southeast Asia”). To distinguish short-, medium-, and long-haul travel, distances were analyzed in five categories similar to Frick et al. (2014). Distance categories and exemplary destination countries are displayed in Table 2 and Figure 2. Since travel distances are approximated from the respective federal state of origin, some European countries are not assigned to a consistent group.

Table 2.

Overview of the travel distance categorization used in the analyses.

Travel distance	Exemplary destinations	Relative frequency
<500 km	Germany and neighboring countries	1971: 57.9%
<500 km	Germany and neighboring countries	2018: 31.9%
500–1000 km	Neighboring and close European countries	1971: 24.5%
500–1000 km	Neighboring and close European countries	2018: 18.7%
1000–2000 km	European countries (e.g. Spain, Portugal, Malta, and Finland)	1971: 15.3%
1000–2000 km		2018: 28.4%
2000–6000 km	North Africa, Middle East, Russia, and Mongolia	1971: 1.5%
2000–6000 km	North Africa, Middle East, Russia, and Mongolia	2018: 11.5%
>6000 km	America, Africa (excluding North Africa), Asia, and Australia	1971: 0.8%
>6000 km		2018: 9.5%

Figure 2.

Travel distance categorization for travelers from Bavaria, Germany. Germany is framed in gray.

Methods

Our methodological framework consists of descriptive and model-based analysis of APC structures. For descriptive visualization, we introduce ridgeline matrices as a novel technique. These are a two-dimensional extension of ridgeline plots (Wilke, 2018), an established tool to display densities against a secondary grouping variable. In accordance with Lexis diagrams, we display age groups along the horizontal axis and periods along the vertical axis, so that diagonals represent specific cohorts. The resulting plot layout enables a direct comparison of distributions over several age groups, periods, and cohorts. For our individual-level data setting, we exploit the survey structure by calculating travel distances based on the weighted observations, leading to representative results for German travelers within each group. Following Clements et al. (2005), our modeling approach builds on model (2), addressing the identification problem by implicitly regarding the cohort effect as a statistical interaction between age and period, represented by the diagonal of the estimated nonlinear surface. We apply semiparametric additive logistic regression to model the individual travel distance categories as binary outcomes. In accordance with Fannon et al. (2018), we use the following model structure for our repeated cross-sectional data setting with observations on individual level

log (\frac{π_{i}}{1 - π_{i}}) = β_{0} + f_{ap} ({age}_{i}, {period}_{i}), i = 1, \dots, n

with $π_{i}$ the probability to travel in the respective distance category, $β_{0}$ the intercept, $f (\cdot, \cdot)$ a two-dimensional nonlinear function, and n the number of individuals. In the remainders of this work, we call model (3) the pure APC model. All quantitative interpretations and visualizations of effects in this study are based on odds ratios (OR = $\frac{π_{i}}{1 - π_{i}}$ ).

We represent the two-dimensional function $f (\cdot, \cdot)$ by a tensor product basis, defined as the Kronecker product of two one-dimensional marginal spline bases over age and period (Wood, 2017). More specifically, each marginal basis function of age is multiplied with each marginal basis function of period to obtain the two-dimensional spline basis. We use penalized B-splines (Eilers and Marx, 1996) to define marginal spline bases, each of them made up of 10 basis functions and the penalization of second-order differences. The estimated tensor product surface is visualized by a heatmap, giving a compact overview of the interrelations of age, period, and cohort. To facilitate the comprehension of effect structures, we use a lower resolution of the heatmap by computing mean effects over APC groups of 5 years. Uncertainty is displayed using 95% pointwise confidence intervals (Marra and Wood, 2012). As an additional graphical tool, individual marginal effects for age, period, and cohort f_a(age), f_p(period), and f_c(cohort) offer a more accessible visualization of temporal developments by focusing on a specific dimension only. This also facilitates effect strength comparisons within and between different models. The mean marginal effects are extracted from the tensor product estimate

\begin{array}{l} f_{a} ({age}_{a}) = \frac{1}{P} \sum_{p = 1}^{P} f_{a p} ({period}_{p} | {age}_{a}) \\ f_{p} ({period}_{p}) = \frac{1}{A} \sum_{a = 1}^{A} f_{a p} ({age}_{a} | {period}_{p}) \\ f_{c} ({cohort}_{c}) = \frac{1}{A \times P} \sum_{a = 1}^{A} \sum_{p = 1}^{P} f_{a p} ({age}_{a}, {period}_{p} | {cohort}_{c}) \end{array}

To visualize the interplay of APC effects, we propose partial APC plots as an extension of marginal effect plots with specific focus on the interrelation of two selected temporal factors. In our experience, this substantially facilitates communication of the model complexity to practitioners. In addition to one marginal effect of interest, partial APC plots display appropriate slices of the tensor product where, for example, the nonlinear variation over cohorts is shown for one specific age group only.

The pure APC model aims at a descriptive interpretation of the estimated temporal structures. Causal conclusions should not be drawn as age, period, and cohort each represent underlying internal and external factors that are not directly incorporated in the model. To estimate the attribution of observed temporal developments to such factors, we integrate additional covariates into the model structure

log (\frac{π_{i}}{1 - π_{i}}) = β_{0} + f_{a p} ({age}_{i}, {period}_{i}) + η_{i}

where $η_{i}$ denotes a linear predictor containing further (non)linear effects. While we primarily focus on the pure APC model in this study, we also estimate an extended covariate model by evaluating a selected set of sociodemographic and travel-related variables on individual level to exemplarily demonstrate the application of APC models in tourism research. Effects obtained through this covariate model have to be interpreted with caution since we do not account for all factors potentially associated with travel behavior.

Based on both models, we apply additive logistic regression for all five distance categories, similar to a multinomial modeling approach. Model performance is evaluated by area under the curve (AUC) values (Japkowicz and Shah, 2011), calculated on a hold-out test set comprising 20% of the data when re-estimating each model on the remaining training set. AUC values vary between 0.55 and 0.67 for the pure APC models and 0.58 to 0.83 for the models including covariates with best model performances for the highest (“>6000 km”: 0.66 pure model, 0.83 covariate model) and lowest (“<500 km”: 0.63, 0.72) distance categories.

The changes in the underlying population in 1990 and 2010 were accounted for by sensitivity analyses. For this purpose, all models were re-calculated based only on the population of Western German travelers and German citizens, respectively. No substantial deviations from the presented results were found. Results of these analyses are listed in the Online Appendix C.

All statistical analyses were performed with the open source software R (R Core Team, 2019). Models are estimated with the function gam from the package mgcv (Wood, 2017), and all visualizations are based on the package ggplot2 (Wickham, 2016). Code for the statistical analysis is freely available in an open source GitHub repository (Weigert et al., 2020).

Results

Descriptive analysis

Over the last 50 years, Germans travel considerably longer distances for their main holiday. As illustrated in Figure 3, trips of less than 500 km have decreased, while the share of trips with a distance of 2000 km and more has steadily increased. Since 2000, the distribution of trips across all distance categories is stable with one-third of trips being conducted within 500 km.

Figure 3.

Relative frequency of travel distance of main holiday trips between 1971 and 2018. Some abrupt developments are caused by minor changes in the survey design.

The demand curve for pleasure trips in the most recent year 2018 (Figure 4) follows the European tourism demand pattern observed by McKercher and Mak (2019). Proceeding from the majority of holidays spent in rather close destinations, demand declines with increasing distance. The popularity of package holiday destinations in the Mediterranean regions is reflected by a secondary peak around 1800 km distance.

Figure 4.

Distribution of travel distances of German travelers in 2018. Travel distance values 0 mark travels inside the traveler’s federal state. Higher density values encode higher frequency.

The two-dimensional ridgeline matrix (Figure 5) represents an extension of the demand curve and gives a first impression of the extent to which travel distances simultaneously change over age, period, and cohort. Density functions of distances are displayed on a log10 scale to focus on changes in lower distance categories. The figure reveals increasing travel distances since the 1970s as the highest peak of the densities moves towards the right for all age groups. An association between age and travel distances is visible as travel distance is consistently highest for 20- and 30-year-olds. Only minor differences are visible comparing different generations.

Figure 5.

Ridgeline matrix depicting the development of travel distances for different age, period, and cohort groups. Cohorts born between 1950 and 1959 and between 1970 and 1979 as representatives of Baby Boomers and Generation X are exemplarily highlighted brown and green, respectively. Higher densities encode higher frequency. Distances are displayed on a log10 scale.

APC models

Pure APC model

Our attribution of the observed developments to the three temporal dimensions is based on separate logistic regression models purely conditioning on age, period, and cohort. The main model results are visualized by a heatmap of the estimated tensor product surface allowing the comparison of areas with a higher chance to travel in the examined distance category and areas with a respective lower chance. The according heatmap for distance category “>6000 km” is displayed in the left panel of Figure 6. Overall, younger age groups, recent periods, and younger cohorts are all attributed the highest chance to travel long distance. Substantial uncertainty is only present for age groups 90 or higher since very few such travelers were observed. The uncertainty of the effect estimates is similar for all distance category models (see the Online Appendix A).

Figure 6.

Heatmaps of the estimated tensor product surface (left panel) and the respective lower (center) and upper (right) 95% CI boundary for distance category “>6000 km”. Effects are averaged over 5-year blocks. Exponentiated values smaller than 0.1 are trimmed to 0.1. CI: confidence interval.

Figure 7 shows the respective marginal effects for the temporal domains. The displayed ORs have a multiplicative interpretation, dependent on the currently focused distance category: for example, the age effect for distance category “<500 km” shows that the chance to make one’s holiday trip within 500 km is about twice as high for persons aged 62 (estimated OR $\approx 0.98$ ) compared to persons aged 30 (OR $\approx 0.49$ ) since the effects show a difference in chance of around +100% ( $= \frac{0.98}{0.49} - 1$ ).

Figure 7.

Estimated marginal odds ratios of age, period, and cohort for each distance category on a log2 scale. The dashed vertical lines in the cohort plot mark the boundaries between the generations defined in “Database” section.

Age

The age effects show pronounced differences between short- and long-haul travel. The tendency for short-haul trips within 500 km increases with age (age 23: OR $\approx 0.39$ ) and reaches its peak at age 88 (OR $\approx 2.94$ ). Teenagers also are more likely to travel to closer destinations. Reversed and partly bimodal age effects are obtained for travel distances over 1000 km with the highest chances around age 25 (“>6000 km”: OR $\approx 2.01$ ) and 50 (“>6000 km”: OR $\approx 1.50$ ). The dip between 35 years and 45 years becomes more pronounced with increasing distances and is most visible in the distance category “>6000 km” (age 41: OR $\approx 1.30$ ). From the mid-50s onwards, the chance for long-distance holidays decreases continuously.

The results are in accordance with life cycle theory (e.g. Collins and Tisdell, 2002; Oppermann, 1995). The increase in choosing longer distance travel between the ages of 14 and 30 might be explained by increasing travel experience. Teenagers most commonly are in the early stages of their travel careers (independent from their parents) and prefer more familiar, low-risk destinations closer to home. In contrast, self-sufficient young people in their 20s seem to become more adventurous and therefore are more likely to choose distant destinations (Karl, 2018). The changing marital status between mid-30 and mid-40 associated with parenting reduces preference for long-haul trips as families with dependent children prefer easily accessible and safe destinations (Collins and Tisdell, 2002; Karl, 2018). With the transition to the empty nest stage, the demand for distant destinations is growing again due to the reduction of travel constraints (Bernini and Cracolici, 2015). The decline in travel distance with age can be explained by decreasing physical health, limited mobility, and reduced disposable income of the elderly (You and O’leary, 2000).

Period

Regarding the period effect, long-distance travels have strongly increased over the last decades. Particularly, the effect structures of short- and long-distance travels reversed around the year 1992, suggesting that Germans were inclined to visit rather close destinations beforehand, while the tendency to choose distant destinations has been increasing ever since. The strongest period effect is observed for destinations within “2000–6000 km” (1971: OR $\approx 0.14$ ; 2018: OR $\approx 2.35$ ) as well as “>6000 km” (1971: OR $\approx 0.25$ ; 2018: OR $\approx 1.75$ ). Since 2000, the effects are comparably stable.

The growth in travel distance over time can be mainly explained by technological developments in transportation which have led to distant destinations being faster and more cheaply accessible, especially for low-income populations (Castro et al., 2020). Additionally, the regular confrontation with information about foreign destinations increased with the advent of digital media (Beldona, 2005; Kim et al., 2015) leading to a decrease in perceived distance (Yang et al., 2018). According to positive correlations between the economic situation of the source market and outbound travel participation (Sun and Lin, 2019; Wong et al., 2016), it can be assumed that the growing economy of Germany is reflected in the period effect. The increase in travel within 2000–6000 km distance can be attributed to the growing popularity of specific destinations, such as Turkey or Egypt. The emerging saturation since 2000 can be linked to declining population dynamics and flattening economic growth rates (Frick et al., 2014).

Cohort

The cohort effect shows a clear association between generational affiliation and distance traveled. Overall, younger generations show a greater chance for overseas travels and lower tendencies for short-haul trips than older generations. For instance, members of Generation Y (mean OR $\approx 5.69$ ) have more than twice the chance to travel within 2000–6000 km compared to Baby Boomers (mean OR $\approx 2.59$ ), while travels to destinations within 500 km are about 47% more likely for Baby Boomers (OR $\approx 0.53$ ) than for Generation Y (mean OR $\approx 0.36$ ). In parts, the cohort effect reflects the observed age differences since, for example, our data on the youngest cohorts only comprise teenagers. Further detail is given in the discussion of Figure 8.

The cohort effect is in line with other research showing that younger generations travel to more distant (Oppermann, 1995) and international destinations (Pennington-Gray et al., 2002). The higher probability of long-distance travel among young cohorts can be attributed to the socialization processes, also shaped by advances in transport and communication technologies in formative years (Oppermann, 1995), increasing the potential to gain greater travel experiences in childhood. This is closely linked to younger cohorts showing higher tendencies to be novelty seekers that prefer nonmainstream destinations (Li et al., 2013).

Comparison of effects

While substantially varying travel distances are observed over all temporal dimensions, the marginal association structures show differences in their effect strengths. As given in Table 3, the chance for short-haul trips, especially those under 500 km, is mainly associated with age differences. Long-distance travel predominantly varies over the period. Particularly within destinations in 2000–6000 km distance, a noteworthy period effect is shown, underlining the findings of the marginal effects. Differences between generations born from 1939 onwards are less pronounced regarding travel distances. Overall, the effect strengths underpin the developments visualized in the ridgeline matrix (Figure 5).

Table 3.

Overview of marginal effects of the pure APC model (see Figure 7).

Model	Effect	Value with maximum OR	Value with minimum OR	Maximum OR	Minimum OR	Ratio
<500 km	Age	88	23	2.94	0.39	7.5
	Period	1971	2018	2.13	0.66	3.2
	Cohort	1939	1989	0.77	0.36	2.1
500–1000 km	Age	14	99	1.49	0.59	2.5
	Period	1983	2018	1.14	0.85	1.3
	Cohort	2004	1989	1.30	0.97	1.3
1000–2000 km	Age	22	86	2.27	0.39	5.8
	Period	2018	1971	1.51	0.46	3.3
	Cohort	1994	2004	2.50	1.35	1.9
2000–6000 km	Age	25	99	2.54	0.14	18.1
	Period	2009	1971	3.01	0.14	21.5
	Cohort	2004	1939	6.54	1.97	3.3
>6000 km	Age	27	99	2.10	0.32	6.6
	Period	2018	1971	1.75	0.25	7.0
	Cohort	1979	2004	2.64	1.11	2.4

Note: APC: age–period–cohort; OR: odds ratio. For each model and effect, the following information is listed, from left to right. Variable value where the OR reaches its maximum/minimum; maximum/minimum of the OR; ratio between the respective maximum OR and minimum OR. The maximum ratios per model are highlighted in bold. According to the generations defined in “Database” section, cohort effects are considered for birth years from 1939 onwards only.

The observed tendencies may imply that choosing short-haul destinations depends on personal characteristics and age-related travel constraints such as physical or family restrictions (You and O’leary, 2000). Contrarily, long-distance travel might be more constrained by macro-level factors such as developments in transport technology attributed to reduced costs for long-haul travel or economic growth in the source market leading to an increase in disposable income which can be used for more expensive long-distance travel (Sun and Lin, 2019). In Germany, the positive economic development in the time period investigated in this study has made long-term travels considerably more accessible. Moreover, technological advances in transportation (Castro et al., 2020) have considerably reduced flight costs for German travelers in the past five decades. The access to a wider range of information sources through modern communication technologies further reduces perceived (cultural) distances to previously inaccessible destinations (Yang et al., 2018), which might also explain the strong increase in long-distance travel over time. In comparison with age and period, generational membership seems to be less important for alterations in travel distances. This broadens previous insights of cohort studies that focused on generational differences without accounting for all three temporal dimensions (e.g. Bernini and Cracolici, 2015).

Interrelations of age, period, and cohort

Figure 8 shows an exemplary partial APC plot that highlights the interrelations between the temporal dimensions. In addition to the marginal cohort effect, it includes one line for each partial cohort effect, that is, for the estimated differences between cohorts when just focusing on travelers with a specific age (left panel) or travels in a specific period (right panel). The displayed effects originate from the model for long-distance travels “>6000 km”.

Figure 8.

Partial APC plot of estimated odds ratios for the cohort effect dependent on age group (left panel) and period (right) for the model “>6000 km.” The mean marginal effect is marked as bold blue line. APC: age–period–cohort.

The figure displays different kinds of information: First, it shows which cohort entails observations in which age group or period, as already listed in Table 1. For instance, the age-dependent plot highlights that the youngest cohorts solely comprise observations of teenagers. Secondly, it is easily deducible how substantial this partial observation structure affects the marginal cohort effect. The drop in the marginal effect for the youngest cohorts can be fully traced back to the observed age groups, since teenagers travel distinctively lower distances than travelers in their 20s or 30s. Thirdly, the partial cohort effects separately display the cohort differences in each age group and period. For example, 14-year-olds show less variation over the observed cohorts than 20-year-olds. Overall, very young (light gray lines) and very old (dark gray lines) people show more consistent travel distances than middle-aged, generally less constrained travelers. Regarding the cohort differences for a given period, more consistent travel distances are observed in the older periods (light gray) compared to the most current periods (dark gray). The partial age and period effects and the effects on other distance categories are given in the Online Appendix B.

Covariate model

Travel behavior is shaped by several internal and external factors (Moutinho, 1987). To showcase the integration of additional factors associated with travel behavior, particularly destination choice, we extend the pure APC model for distance category “>6000 km” by the following internal covariates: (i) inflation-adjusted household net income (as a nonlinear effect)—the integration of this covariate is motivated by the income elasticity of tourism demand which assumes an overall positive correlation, especially for outbound travel participation (Eugenio-Martin and Campos-Soria, 2011); (ii) household size—this reflects the marital, financial, and social situation of an individual and the related travel constraints (Alegre and Pou, 2004). It is well-established that the larger the household, the less likely it is to travel abroad (Guillet et al., 2011); (iii) trip duration is included because of its positive association to travel distances since higher costs owing to longer distances are compensated by longer trip lengths (Jackman et al., 2020). External, macro-level factors like the economic climate in the source market and technological developments are not explicitly accounted for. As outlined, these are jointly reflected by the period effect.

Overall, Figure 9 illustrates substantial associations between the chance to travel farther than 6000 km and all included covariates. While trip duration shows a very strong positive association, the chance for long-distance travel decreases continuously with increasing household size. More specifically, someone from a two-person household has on average a 293% ( $\approx \frac{0.48}{0.12} - 1$ ) higher chance to travel farther than 6000 km than a member of a ≥5-person household. Regarding the positive income effect, the chance for long-distance travel increases almost linearly within income levels of 1000–5000 € before flattening for high-income values (1000 €: OR $\approx 0.40$ ; 8000 €: OR $\approx 4.63$ ).

Figure 9.

Estimated odds ratios of the variables household income, household size (reference category: one-person household) and trip duration (reference category: trips of 5 days) in the model for the distance category “>6000 km” on a log2 scale. Uncertainty is displayed by 95% confidence intervals.

The inclusion of additional covariates alters the strengths of the estimated age, period, and cohort effects compared to the pure APC model (Figure 10). Accounting for household size attenuates the age-related dip around 40. This can be related to the impact of travel constraints caused by specific personal circumstances of this age group. The variations in the period and cohort effect are mainly triggered by conditioning on the trip duration. More specifically, assuming trips of equal length, the chance for holiday trips over 6000 km increases more steeply both over time and across generations underlining the higher affordability and easier accessibility of long-haul trips in recent years and for younger cohorts.

Figure 10.

Estimated odds ratios of the full model for distance category “>6000 km versus <6000 km” including covariates (covariate model) compared to the APC effects in the model without covariates (pure APC model) on a log2 scale. The dashed vertical lines in the cohort plot mark the boundaries of the analyzed generations. APC: age–period–cohort.

Conclusion

Comprehension of changing destination choice patterns requires a thorough understanding of all temporal interrelations and their respective drivers. APC analysis is an established tool for the investigation of such time-related changes, separating cohort effects from age and period (Yang and Land, 2013). Nevertheless, this method and its possibilities for the examination of behavioral changes in tourism science are not yet fully exploited. The purpose of this study was threefold: (1) establish a flexible, state-of-the-art statistical modeling approach for APC analysis in tourism science, (2) introduce ridgeline matrices and partial APC plots as novel graphical tools for visualizing complex APC structures in a comprehensive way, and (3) generate new insights into temporal developments of travel behavior by applying the comprehensive APC approach, based on a rich secondary data set.

From a methodological perspective, our contributions focus on refining and showcasing a widely applicable and well accessible APC approach. We build our modeling framework on semiparametric GAMs to overcome the identification problem without using restrictive assumptions on the temporal effects. The approach can be formulated for aggregated and individual data settings (i.e. travel information for groups of travelers or for individual travelers) as well as repeated cross-sectional or panel data, making it adaptable to a variety of research settings. The GAM framework is highly flexible and offers robust and efficient concepts for estimation and inference, accompanied by sophisticated and freely available software. Since APC analyses rely on a thorough understanding of the temporal interrelations, we offer innovative visualizations to facilitate their comprehension. Ridgeline matrices present an easily accessible tool for displaying three-dimensional temporal changes. On a model-based level, partial APC plots are a novel way to visualize bivariate interrelations of the individual effects. Their application is vital in APC analyses since birth cohorts are most commonly not observed across all available age groups and periods. In such settings, partial APC plots can help understand to which extent the estimated association structures are due to the specific data structure.

From a tourism perspective, the holistic APC framework contributes to new insights about temporal changes of destination choice. It offers a more comprehensive alternative to previously applied approaches in tourism research. In combination with our long-term data set comprising travel behavior on individual level, it allows a deeper understanding of the temporal structures. Our study confirms that alterations in travel behavior occur in accordance with life cycle theory (age), macro-level developments in economy and society (period), and generational theory (cohort). Moreover, we produced new insights on the main temporal drivers that alter destination choices. In contrast to cohort studies focusing on generational differences (e.g. Huang and Lu, 2017), our findings especially suggest that cohort differences seem less pronounced when all three temporal dimensions are considered. Contrary to common approaches in studies on changes in travel behavior (e.g. Bernini and Cracolici, 2015), our simultaneous analysis of developments over age, period, and cohort does not neglect any specific interrelations in the temporal structures. Since destination choice is determined by various internal and external factors (Wong et al., 2017), another benefit of our framework is the possibility to incorporate additional explanatory variables. For example, our approach allows to investigate to what extent the observed developments can be attributed to specific characteristics of the travel decision process. If data are modeled on individual level, this most notably comprises the simultaneous incorporation of explaining variables on individual (e.g. income of the traveler) and macro level (e.g. general economic indices). Especially for studies observing individual travelers, accounting for further variables offers great potential for future tourism research by identifying the influences and interactions of socioeconomic and travel-related factors (e.g. travel motivation or transportation mode). Often it is the interplay between such internal and external factors, related to the tourist and the destination, that shapes travel decision-making (Karl, 2018) and consequently tourism demand. For instance, the individual motivation to travel and the price level at and transport costs to a destination commonly influence tourists’ destination choices (Nicolau and Más, 2006). Finally, both the academic sector and the industry can make use of these newly generated insights. Understanding which and how different factors cause changes in travel behavior (e.g. domestic and outbound tourist flows) may lead to better predictions of future tourism demand, supporting touristic stakeholders in tourism planning and management.

Using repeated cross-sectional data from an established long-term survey has its advantages (valid and representative sample, cost-efficiency) but is not without limitations. A critical aspect which had to be considered in the analysis were changes of the underlying population in 1990 after German reunification, and in 2010 from German citizens to the German-speaking population. However, our comparative sensitivity analyses show that these modifications have no substantial impact on the overall results. Regarding our main findings, transferability is limited to source markets like Western European countries, with conditions similar to the German market (economic situation, transportation system and freedom of travel). Future studies should apply our proposed approach to other source markets to investigate how APC structures change when different macroeconomic and sociocultural conditions are considered. Finally, as generally is the case in observational studies, findings should be interpreted with caution regarding causal relationships. The overall APC effects can be differentiated reasonably well. Causal conclusions, however, should not be drawn as all observed temporal interdependencies can be traced back to specific socioeconomic factors, societal changes, or shared socialization processes that affect each individual tourist. Accordingly, a clear distinction between these underlying factors is not possible without explicitly accounting for them as further covariates in the model. To make accurate predictions of tourism demand, future research needs to focus on integrating relevant factors from tourism demand modeling (e.g. economic development and technological advancement) and the travel decision-making literature (see review by Smallman and Moore, 2010) into the outlined analyses of individual travel data. Among others, this includes the impact of economic changes in the source market, technological advancement leading to reduced transport costs or political events (e.g. German reunification and establishment of the Schengen area) on destination choices regarding short- or long-haul destinations.

Due to the identification problem, separating the effects of age, period, and cohort remains the crucial challenge in APC analysis. Generally speaking, the GAM framework is an adequate basis for estimating mean APC structures in widespread research settings. Since perfect separation of the three temporal effects is not possible, future research should specifically focus on tools to make association structures more accessible. Especially model-related visualization techniques such as partial APC plots are promising to be further refined for this purpose. Ridgeline matrices are extendable by further building on additional concepts of ridgeline plots (Wilke, 2018) to display the distribution of each matrix cell conditional on, for example, socioeconomic groups. While we designed both novel visualization techniques specifically for the application on cross-sectional data, their adaptation to panel data remains to be evaluated. Regarding our application, alternative statistical approaches to model travel distances should be taken into consideration. In the regression context, this comprises modeling the raw distances as a response as well as the evaluation of more complex techniques like functional data analysis (Bauer et al., 2018) to compare the demand curves between different groups.

In conclusion, the outlined modeling approach proved its worth in the application on travel distances and contributed to deeper knowledge in destination choice. Combining the flexibility of semiparametric regression with modern visualization tools offers great potential for future studies analyzing temporal changes in diverse fields of (tourism) research.

Supplemental material

Supplemental Material, sj-pdf-1-teu-10.1177_1354816620987198 - Semiparametric APC analysis of destination choice patterns: Using generalized additive models to quantify the impact of age, period, and cohort on travel distances

Supplemental Material, sj-pdf-1-teu-10.1177_1354816620987198 for Semiparametric APC analysis of destination choice patterns: Using generalized additive models to quantify the impact of age, period, and cohort on travel distances by Maximilian Weigert, Alexander Bauer, Johanna Gernert, Marion Karl, Asmik Nalmpatian, Helmut Küchenhoff and Jürgen Schmude in Tourism Economics

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Supplemental Material, sj-tex-2-teu-10.1177_1354816620987198 for Semiparametric APC analysis of destination choice patterns: Using generalized additive models to quantify the impact of age, period, and cohort on travel distances by Maximilian Weigert, Alexander Bauer, Johanna Gernert, Marion Karl, Asmik Nalmpatian, Helmut Küchenhoff and Jürgen Schmude in Tourism Economics

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Supplemental Material, sj-pdf-3-teu-10.1177_1354816620987198 for Semiparametric APC analysis of destination choice patterns: Using generalized additive models to quantify the impact of age, period, and cohort on travel distances by Maximilian Weigert, Alexander Bauer, Johanna Gernert, Marion Karl, Asmik Nalmpatian, Helmut Küchenhoff and Jürgen Schmude in Tourism Economics

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Supplemental Material, sj-tex-4-teu-10.1177_1354816620987198 for Semiparametric APC analysis of destination choice patterns: Using generalized additive models to quantify the impact of age, period, and cohort on travel distances by Maximilian Weigert, Alexander Bauer, Johanna Gernert, Marion Karl, Asmik Nalmpatian, Helmut Küchenhoff and Jürgen Schmude in Tourism Economics

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Supplemental Material, sj-bib-5-teu-10.1177_1354816620987198 for Semiparametric APC analysis of destination choice patterns: Using generalized additive models to quantify the impact of age, period, and cohort on travel distances by Maximilian Weigert, Alexander Bauer, Johanna Gernert, Marion Karl, Asmik Nalmpatian, Helmut Küchenhoff and Jürgen Schmude in Tourism Economics

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Supplemental Material, sj-tex-6-teu-10.1177_1354816620987198 for Semiparametric APC analysis of destination choice patterns: Using generalized additive models to quantify the impact of age, period, and cohort on travel distances by Maximilian Weigert, Alexander Bauer, Johanna Gernert, Marion Karl, Asmik Nalmpatian, Helmut Küchenhoff and Jürgen Schmude in Tourism Economics

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Supplemental Material, sj-bst-7-teu-10.1177_1354816620987198 for Semiparametric APC analysis of destination choice patterns: Using generalized additive models to quantify the impact of age, period, and cohort on travel distances by Maximilian Weigert, Alexander Bauer, Johanna Gernert, Marion Karl, Asmik Nalmpatian, Helmut Küchenhoff and Jürgen Schmude in Tourism Economics

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Supplemental Material, sj-cls-8-teu-10.1177_1354816620987198 for Semiparametric APC analysis of destination choice patterns: Using generalized additive models to quantify the impact of age, period, and cohort on travel distances by Maximilian Weigert, Alexander Bauer, Johanna Gernert, Marion Karl, Asmik Nalmpatian, Helmut Küchenhoff and Jürgen Schmude in Tourism Economics

Footnotes

Acknowledgments

The authors would like to thank Forschungsgemeinschaft Urlaub und Reisen e.V. for providing the underlying data and help regarding questions of any type to the data set. They also thank the anonymous reviewer whose insightful comments were highly appreciated and helped making the article more accessible.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work has been funded by the German Research Foundation (DFG) under Grant Nos KU 1359/4-1, SCHM 850/22-1, and KA 4976/2-1 and by the German Federal Ministry of Education and Research (BMBF) under Grant No. 01IS18036A. The authors of this work take full responsibility for its content.

ORCID iD

Maximilian Weigert

Marion Karl

Supplemental material

Supplemental material for this article is available online.

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